Solution of an Economic Dispatch Problem Through Particle Swarm Optimization: A Detailed Survey - Part I
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paper_title: A new honey bee mating optimization algorithm for non-smooth economic dispatch

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The non-storage characteristics of electricity and the increasing fuel costs worldwide call for the need to operate the systems more economically. Economic dispatch (ED) is one of the most important optimization problems in power systems. ED has the objective of dividing the power demand among the online generators economically while satisfying various constraints. The importance of economic dispatch is to get maximum usable power using minimum resources. To solve the static ED problem, honey bee mating algorithm (HBMO) can be used. The basic disadvantage of the original HBMO algorithm is the fact that it may miss the optimum and provide a near optimum solution in a limited runtime period. In order to avoid this shortcoming, we propose a new method that improves the mating process of HBMO and also, combines the improved HBMO with a Chaotic Local Search (CLS) called Chaotic Improved Honey Bee Mating Optimization (CIHBMO). The proposed algorithm is used to solve ED problems taking into account the nonlinear generator characteristics such as prohibited operation zones, multi-fuel and valve-point loading effects. The CIHBMO algorithm is tested on three test systems and compared with other methods in the literature. Results have shown that the proposed method is efficient and fast for ED problems with non-smooth and non-continuous fuel cost functions. Moreover, the optimal power dispatch obtained by the algorithm is superior to previous reported results.
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paper_title: Firefly Algorithm technique for solving Economic Dispatch problem

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This paper presents the implementation of Firefly Algorithm (FA) in solving the Economic Dispatch (ED) problem by minimizing the fuel cost and considering the generator limits and transmission losses. ED is one of the most challenging problems of power system since it is difficult to determine the optimum generation scheduling to meet the particular load demand with the minimum fuel cost and transmission loss. Until now, there are a lot of researches that have been done to seek for closest optimum result in determining the power generation of each generator especially in large scale power system. FA is a meta-heuristic algorithm which is inspired by the flashing behavior of fireflies. The primary purpose of firefly's flash is to act as a signal system to attract other fireflies. In this paper, 26-bus system is utilized to show the effectiveness of the FA in solving the ED problem. Comparison with Continuous Genetic Algorithm (CGA) and conventional method are also given.
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paper_title: A Simulated Annealing-Based Goal-Attainment Method for Economic Emission Load Dispatch with Nonsmooth Fuel Cost and Emission Level Functions

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A novel multiobjective optimization method for economic emission load dispatch (EELD) with nonsmooth fuel cost and emission level functions in power system operation andscheduling phases is presented. In this paper, the problem treats economy, emission, and transmission line security as competing objectives. The load constraints and operating constraints are taken into account. Assuming that the decision maker (DM) has goals for each of the objective functions, the multiobjective problem is converted into a single-objective optimization by the goal-attainment method, which is then handled by the simulated annealing (SA) technique. The solution methodology can offer a global or near-global noninferior (best compromising) solution in a sense close to the DM's requirements. Results for a sample test system have been presented to demonstrate the applicability and validity of the proposed method.
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paper_title: Multiple tabu search algorithm for economic dispatch problem considering valve-point effects

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This paper presents a multiple tabu search (MTS) algorithm to solve the economic dispatch (ED) problem by taking valve-point effects into consideration. The practical ED problem with valve-point effects is represented as a non-smooth optimization problem with equality and inequality constraints that make the problem of finding the global or near global optimum difficult. The proposed MTS algorithm is the sequential execution of individual tabu search (TS) algorithm simultaneously by only one personal microcomputer. The MTS algorithm introduces additional techniques for improvement of search process, such as initialization, adaptive searches, multiple searches, replacing and restarting process. To show its effectiveness, the MTS is applied to test two studied systems consisting of 13 and 40 power generating units with valve-point effects. The optimized results by MTS are compared with those of conventional approaches, such as simulated annealing (SA), genetic algorithm (GA), TS algorithm and particle swarm optimization (PSO). Studied results confirm that the proposed MTS approach is capable of obtaining higher quality solution efficiently and lowest computational time.
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paper_title: A new hybrid technique for solution of economic load dispatch problems based on Biogeography Based Optimization

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This paper presents a hybrid technique combining Evolutionary Strategy(ES) with Biogeography Based Optimization (BBO/ES) algorithm to solve economic load dispatch problems of thermal plants considering equality and inequality constraints, transmission losses and valve point loading. Biogeography is a recently developed heuristic algorithm which has shown impressive performance on many well known benchmarks. In order to improve BBO, distinctive features from ES are incorporated in BBO modification. This algorithm searches for the global optimum mainly through two steps: migration and mutation. The effectiveness of the proposed algorithm has been verified on two different test systems, both small and large involving varying degree of complexity. A comparison of simulation results reveals that the proposed algorithm is better than those listed in the comparison table in terms of the quality of the solution. This method seems to be promising alternative approach for solving the ELD problems in practical power systems.
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paper_title: Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch

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A novel stochastic optimisation approach to solve constrained economic load dispatch problem using hybrid bacterial foraging (BF) technique is presented. in order to explore the search space for finding the local minima of the current location, the simplex algorithm called nelder-mead is used along with BF algorithm. the proposed methodology easily takes care of solving non-convex economic dispatch problems along with different constraints such as transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones. simulations were performed over various standard test systems with different number of generating units and comparisons are performed with other existing relevant approaches. the findings affirmed the robustness and proficiency of proposed methodology over other existing techniques.
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paper_title: A clonal algorithm to solve economic load dispatch

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This paper presents a novel optimization approach to constrained economic load dispatch (ELD) problem using artificial immune system (AIS). The approach utilizes the clonal selection principle and evolutionary approach wherein cloning of antibodies is performed followed by hypermutation. The proposed methodology easily takes care of transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones and also accounts for non-smoothness of cost function arising due to the use of multiple fuels. Simulations were performed over various systems with different number of generating units and comparisons are performed with other prevalent approaches. The findings affirmed the robustness, fast convergence and proficiency of proposed methodology over other existing techniques.
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paper_title: A MIXED INTEGER QUADRATIC PROGRAMMING FORMULATION FOR THE ECONOMIC DISPATCH OF GENERATORS WITH PROHIBITED OPERATING ZONES

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In this paper, an optimisation-based approach is proposed using a mixed integer quadratic programming model for the economic dispatch of electrical power generators with prohibited zones of operation. The main advantage of the proposed approach is its capability to solve case studies from the literature to global optimality quickly and without any targeting of solution procedures.
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paper_title: Evolutionary programming techniques for economic load dispatch

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Evolutionary programming has emerged as a useful optimization tool for handling nonlinear programming problems. Various modifications to the basic method have been proposed with a view to enhance speed and robustness and these have been applied successfully on some benchmark mathematical problems. But few applications have been reported on real-world problems such as economic load dispatch (ELD). The performance of evolutionary programs on ELD problems is examined and presented in this paper in two parts. In Part I, modifications to the basic technique are proposed, where adaptation is based on scaled cost. In Part II, evolutionary programs are developed with adaptation based on an empirical learning rate. Absolute, as well as relative, performance of the algorithms are investigated on ELD problems of different size and complexity having nonconvex cost curves where conventional gradient-based methods are inapplicable.
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paper_title: A homogeneous linear programming algorithm for the security constrained economic dispatch problem

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This paper presents a study of the simplified homogeneous and self-dual (SHSD) linear programming (LP) interior point algorithm applied to the security constrained economic dispatch (SCED) problem. Unlike other interior point SCED applications that consider only the N security problem, this paper considers both (N-1) and (N-2) network security conditions. An important feature of the optimizing interior point LP algorithm is that it can detect infeasibility of the SCED problem reliably. This feature is particularly important in SCED applications since line overloading following a contingency often results in an infeasible schedule. The proposed method is demonstrated on the IEEE 24 bus test system and a practical 175 bus network. A comparison is carried out with the predictor-corrector interior point algorithm for the SCED problem presented previously (see ibid., vol. 12, no.2, p.803-10, 1997).
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paper_title: Dynamic Economic Dispatch with Valve-Point Effect Using Maclaurin Series Based Lagrangian Method

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Dynamic Economic Dispatch (DED) plays a vital role in power generation, operation and control. It is a complicated, non-linear constrained problem. In this paper, Maclaurin series based Lagrangian method (MSL) is used to solve the DED problem for generating units with valve-point effect, considering the ramp rate limits. Using Maclaurin series, the sine term used to model the valve-point effect is expanded and solved with Lagrangian method. The feasibility of the proposed method is validated for static economic dispatch problem for forty unit system and DED problem for five unit test system for 24 hour time interval. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving static and dynamic economic dispatch problems with non-smooth cost functions.
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paper_title: Economic dispatch using hybrid grey wolf optimizer

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This paper presents the application of one of the latest swarm intelligence algorithms, the grey wolf optimizer, for solving economic dispatch problems that are nonlinear, non-convex and discontinuous in nature, with numerous equality and inequality constraints. Grey wolf optimizer is a new metaheuristic algorithm that is loosely based on the behavior of the grey wolves. The optimizer has been hybridized to include crossover and mutation for better performance. Four economic dispatch problems (6, 15, 40, and 80 generators), with prohibited operating zones, valve point loading effect and ramp rate limit constraints have been solved, with and without transmission losses. The losses are calculated using B-coefficients. The results obtained are compared with those reported using other methods in the literature. The comparisons show that the hybrid grey wolf optimizer used in this paper either matches or outperforms the other methods.
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paper_title: Application of Krill Herd and Water Cycle Algorithms on Dynamic Economic Load Dispatch Problem

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Dynamic economic dispatch (DED) is a complicated nonlinear constrained optimization problem and one of the most important problems in operation of power systems. In this paper two novel optimization algorithms have been proposed to be applied on DED problem. The first method, Krill herd (KHA) is a novel meta heuristic algorithm for solving optimization problems which is based on the simulation of the herding of the krill swarms as a biological and environmental inspired method and is applied on DED problem with two configurations named KHA1 and KHA2. The second algorithm is based on how the streams and rivers flow downhill toward the sea and change back in nature, named Water Cycle (WCA) method. Two common case studies considering various constraints have been used to show the effectiveness of these methods. The results and convergence characteristics show that the proposed methods are capable of giving high quality results which are better than many other previously applied algorithms.
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paper_title: Solution of economic load dispatch using hybrid chemical reaction optimization approach

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Hybrid chemical reaction optimization (CRO) algorithm applied to ELD is proposed.To improve solution quality hybridization of DE and CRO is made.Effectiveness is checked by applying it in six different test systems.The performance of HCRO-DE is compared with other optimization techniques.Robustness of the proposed method is checked through statistical analysis. In this paper, a new and efficient optimization technique based on hybridization of chemical reaction optimization (CRO) with differential evolution (DE) is developed and demonstrated to solve the ELD problem with thermal cost function having valve point loading effect together with and without multiple fuel options and with and without considering prohibited operating zone and ramp rate constraint. When valve-point effects, multi-fuel operations and the constraints of prohibited operating zone and ramp rate are taken into account, ELD problem become more complex than conventional ELD problem. To show the priority of the proposed algorithm, it is implemented on six different test systems for solving ELD problems. Comparative studies are carried out to examine the effectiveness of the proposed HCRO-DE approach with conventional DE, CRO and the other algorithms reported in the literature. The simulation results show that the proposed HCRO-DE method is capable of obtaining better quality solutions than DE, CRO and the other well popular optimization techniques.
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paper_title: Short-term scheduling of thermal power systems using hybrid gradient based modified teaching–learning optimizer with black hole algorithm

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Abstract Nowadays, a challengeable subject facing the electric power system operator is how to manage optimally the power generating units over a scheduling horizon of one day considering all of the practical equality, inequality and dynamic constraints. These constraints are comprised of load plus transmission losses balance, valve-point effects, prohibited operating zones, multi-fuel options, line flow constraints, operating reserve and minimum on/off time. In this regard, the proposed framework first presents a practical formulation for the short-term thermal generation scheduling (STGS). It has high-dimensional, high-constraints, non-convex, non-smooth and non-linear nature and needs an efficient algorithm to be solved. Then, a new optimization approach, known as gradient-based modified teaching–learning-based optimization combined with black hole (MTLBO–BH) algorithm, has been proposed to seek the optimum operational cost. Despite the superior characteristics of the MTLBO and BH algorithms, both of them suffer from the problem of entrapping in local optima. Consequently, the powerful combination of MTLBO and BH and a novel self-adaptive wavelet mutation operator for the organization of the new robust algorithm are proposed in this work. Although the MTLBO–BH algorithm has many properties, some problems still remain to be solved pleasantly. One of these problems is the produced further robust solution that the classical gradient-based technique can overcome it. Finally, performance of the suggested technique is tested on different thermal power systems.
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paper_title: Enhanced cross-entropy method for dynamic economic dispatch with valve-point effects

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This paper proposes an enhanced cross-entropy (ECE) method to solve dynamic economic dispatch (DED) problem with valve-point effects. The cross-entropy (CE) method, originated from an adaptive variance minimization algorithm for estimating probabilities of rare events, is a generic approach to combinatorial and multi-extremal optimization. Exploration capability of CE algorithm is enhanced in this paper by using chaotic sequence and the resultant ECE is applied to DED with valve-point effects. The performance of the proposed ECE method is rigorously tested for optimality, convergence, robustness and computational efficiency on a 10-unit test system. Additional test cases with different load patterns and increased number of generators are also solved by ECE. Numerical results show that the proposed ECE approach finds high-quality solutions reliably with faster convergence. It outperforms CE and all the previous approaches.
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paper_title: BIG BANG-BIG CRUNCH OPTIMIZATION ALGORITHM FOR ECONOMIC DISPATCH WITH VALVE-POINT EFFECT

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The Big Bang–Big Crunch (BB–BC) optimization algorithm is a new optimization method that relies on the Big Bang and Big Crunch theory, one of the theories of the evolution of the universe. In this paper, a Big Bang–Big Crunch algorithm is presented for solving optimal power flow (OPF) problems with valve-point effects. The proposed algorithm has been tested with the IEEE 30-bus system with different fuel cost characteristics, quadratic cost curve model, and quadratic cost curve with valve-point effects model. Numerical results demonstrate the efficiency of the BB–BC algorithm compared to other heuristic algorithms.
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paper_title: Economic load dispatch using population-variance harmony search algorithm

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This paper presents a novel stochastic optimization approach to solve the constrained economic load dispatch (ELD) problem using the harmonic search algorithm (HS). HS is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work analyses the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. The proposed methodology easily takes care of solving non-convex ELD problems along with different constraints like transmission losses, ramp rate limits of the generators and prohibited operating zones. Simulations were performed over various standard test systems with different number of generating units and a comparative study is carried out with other existing relevant approaches. The findings affirmed the robustness and proficiency of the proposed methodology over other existing techniques.
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paper_title: Combined economic and emission dispatch solution using Flower Pollination Algorithm

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Abstract Economic Load Dispatch (ELD) is the process of allocating the required load between the available generation units such that the cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. The dual-objective Combined Economic Emission Dispatch (CEED) problem is considering the environmental impacts that accumulated from emission of gaseous pollutants of fossil-fueled power plants. In this paper, an implementation of Flower Pollination Algorithm (FPA) to solve ELD and CEED problems in power systems is discussed. A comparison of the simulated results using the proposed FPA is carried out to confirm its effectiveness against other swarm intelligent algorithms for six various power systems. The superiority of the proposed FPA compared with other algorithms is demonstrated even for large scale power system considering valve point loading effect.
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paper_title: Dynamic economic dispatch using artificial immune system for units with valve-point effect

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Dynamic economic dispatch (DED) is an important dynamic problem in power system operation and control. The objective of the problem is to schedule power generation for the online units over a time horizon, satisfying the unit and ramp-rate constraints. In this paper, clonal selection based artificial immune system (AIS) algorithm is used to solve the dynamic economic dispatch problem for generating units with valve-point effect. The feasibility of the proposed method is validated with ten and five unit test systems for a period of 24 h. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the robustness and proficiency of the proposed methodology over other existing techniques in terms of solution quality and computational efficiency.
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paper_title: Large scale economic dispatch of power systems using oppositional invasive weed optimization

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Application of invasive weed optimization to economic dispatch problems.The oppositional based learning is implemented in IWO algorithm.The merits of proposed methodology are high accuracy and less execution time.The results of OIWO algorithm show its superiority to other tested techniques. This paper presents an evolutionary hybrid algorithm of invasive weed optimization (IWO) merged with oppositional based learning to solve the large scale economic load dispatch (ELD) problems. The oppositional invasive weed optimization (OIWO) is based on the colonizing behavior of weed plants and empowered by quasi opposite numbers. The proposed OIWO methodology has been developed to minimize the total generation cost by satisfying several constraints such as generation limits, load demand, valve point loading effect, multi-fuel options and transmission losses. The proposed algorithm is tested and validated using five different test systems. The most important merit of the proposed methodology is high accuracy and good convergence characteristics and robustness to solve ELD problems. The simulation results of the proposed OIWO algorithm show its applicability and superiority when compared with the results of other tested algorithms such as oppositional real coded chemical reaction, shuffled differential evolution, biogeography based optimization, improved coordinated aggregation based PSO, quantum-inspired particle swarm optimization, hybrid quantum mechanics inspired particle swarm optimization, modified shuffled frog leaping algorithm with genetic algorithm, simulated annealing based optimization and estimation of distribution and differential evolution algorithm.
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paper_title: A modified Shuffled Frog Leaping algorithm for nonconvex Economic Dispatch problem

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This paper presents a new approach to Economic Dispatch (ED) problems with nonconvex cost functions using Shuffled Frog Leaping (SFL) algorithm. The practical ED problems have nonconvex cost functions with equality and inequality constraints that makes the problem of finding the global optimum difficult using any optimization approaches. In this paper, the standard SFL is improved to deal with the equality and inequality constraints in the ED problem. To validate the results obtained by proposed SFL, a modified SFL is adopted from the literature and applied for comparison. Also, the results obtained by the SFL algorithms are compared with other approaches reported in the literature. The results show that the proposed SFL produces better solutions for two study systems due to extra diversification provided by the algorithm.
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paper_title: Economic load dispatch using krill herd algorithm

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Abstract Economic load dispatch (ELD) is an important topic in the operation of power plants which can help to build up effective generating management plans. The practical ELD problem has non-smooth cost function with nonlinear constraints which make it difficult to be effectively solved. This paper presents, a new and efficient krill herd algorithm (KHA) to solve both convex and non-convex ELD problems of thermal power units considering valve point loading, multiple fuel operation, transmission losses and constraints such as ramp rate limits and prohibited operating zones. To enhance the overall performance and effectiveness of the proposed algorithm, the crossover and mutation operation of differential evolution (DE) are integrated with the proposed method. The different versions of KHA are successfully applied to small, medium, and large-scale power systems for solving six different ELD problems. The simulation results obtained by the proposed algorithms are compared with the results obtained using other recently develop methods available in the literature. From numerical results, it is found that the proposed KHA with crossover and mutation operators approach is able to provide better solution than other reported techniques in terms of fuel cost. Furthermore, this algorithm is better in terms of robustness than most of the existing algorithms used in this study.
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paper_title: Solution of firefly algorithm for the economic themal power dispatch with emission constraint in various generation plants

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Economic load dispatch (ELD) is an important optimization task in power system. It is the process of allocating generation among the committed units such that the constraints imposed are satisfied and the energy requirements are minimized. There are three criteria in solving the economic load dispatch problem. They are minimizing the total generator operating cost, total emission cost and scheduling the generator units. In this paper Firefly Algorithm(FA) solution to economic dispatch problem is very useful when addressing heavily constrained optimization problem in terms of solution accuracy. Results obtained from this technique clearly demonstrate that the algorithm is more efficient in terms of number of evolution to reach the global optimum point. The result also shows that the solution method is practical and valid for real time applications In this paper the Firefly Algorithm(FA) solves economic load dispatch (ELD) power system problem of three generator system, six generator system with emission constraints and twelve generator system with introduced population-based technique - is utilized to solve the DED problem. A general formulation of this algorithm is presented together with an analytical mathematical modeling to solve this problem by a single equivalent objective function. The results are compared with those obtained by alternative techniques proposed by the literature in order to show that it is capable of yielding good optimal solutions with proper selection of control parameters. The validity and quality of the solution obtained Firefly Algorithm(FA) based economic load dispatch method are checked and compared with Artificial colony algorithm(ABC), Particle Swarm Optimization Algorithm (PSO), simulated Annealing Algorithm(SA).
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paper_title: Bid-based dynamic economic dispatch with an efficient interior point algorithm

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Abstract An efficient interior point algorithm for solving the bid-based dynamic economic dispatch (BBDED) problem is proposed in this paper. This algorithm is an extension of interior point quadratic programming (IPQP), and is called the predictor–corrector interior point quadratic programming (PCIPQP) algorithm. In a competitive electricity market, the dynamic economic dispatch has evolved to become bid-based framework to maximize the profits and achieve the resource scheduling. To generate a physically feasible dispatch and market spot prices, we form BBDED problem of dealing with various constraints such as ramp rates, transmission line capacity and emission constraints. In this paper, BBDED allows both supply-side and demand-side bids in the spot market, which includes multi-player, multi-period and a large number of constraints. Compared with the pure IPQP algorithm, PCIPQP is more attractive in performance, robustness, and the property of convergence. Many numerical tests reconfirmed the advantages of the predictor–corrector method.
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paper_title: MULTIOBJECTIVE ENVIRONMENTAL AND ECONOMIC DISPATCH USING IMPERIALIST COMPETITIVE ALGORITHM

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In this research a multi-objective Imperialist Competitive Algorithm (MOICA) is applied for Environmental and Economic Power Dispatch (EED) problem. Due to the environmental concerns that arise from the emissions produced via fossil-fueled electric power plants, the classical economic dispatch, which operates electric power systems so as to minimize only the total fuel cost, can no longer be considered alone. Hence, by environmental dispatch, emissions can be reduced by dispatch of power generation to minimize emissions. Also, power generated, system loads, fuel cost and emission coefficients are subjected to inaccuracies and uncertainties in real-world situations. The proposed technique has been carried out on the IEEE 30-bus and 118-bus test system. The results demonstrate the capability of the proposed MOICA approach to solve of multi-objective EED problem. The comparison reported results with MODE and other techniques reveals the superiority of the proposed MOICA approach and confirms its potential for solving other power systems multi-objective optimization problems.
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paper_title: Application of linear programming redispatch technique to dynamic generation allocation

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Consideration is given to dispatch problems that involve the allocation of system generation optimally among generating units while tracking a load curve and observing the power rate limits of the units, system spinning reserve requirements, and other security constraints. Two methods are used in the solution of the problem. The first method is a quadratic programming technique combined with a linear programming redispatch technique. The latter utilizes a linear programming formulation of the dynamic dispatch problem about the base case static economic dispatch solution. The second method is based on the Dantzig-Wolfe decomposition technique. Tests and computer results of four systems of different combinations of units and intervals are given to show the advantages of the techniques proposed. >
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paper_title: A hybrid Hopfield neural network-quadratic programming approach for dynamic economic dispatch problem

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This paper introduces a solution of the dynamic economic dispatch (DED) problem using a hybrid approach of Hopfield neural network (HNN) and quadratic programming (QP). The hybrid algorithm is based on using enhanced HNN; to solve the static part of the problem; and the QP algorithm for solving the dynamic part of the DED. This technique guarantees the global optimality of the solution due to its look-ahead capability. The new algorithm is applied and tested to an example from the literature and the solution is then compared with that obtained by some other techniques to prove the superiority and effectiveness of the proposed algorithm.
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paper_title: Genetic algorithm solution to the economic dispatch problem

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Two genetic algorithm (GA) solutions to the economic dispatch problem are presented. An advantage of the GA solutions is that they do not impose any convexity restrictions on the generator cost functions. Another advantage is that GAs can be very effectively coded to work on parallel machines. Test results with systems of up to 72 generating units with nonconvex cost functions show that both GAs outperform the dynamic programming solution to the economic dispatch problem. Furthermore, the execution time of the second GA solution increases almost linearly with the number of generators.
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paper_title: Dynamic adaptive bacterial foraging algorithm for optimum economic dispatch with valve-point effects and wind power

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This study presents a dynamically adapted bacterial foraging algorithm (BFA) to solve the economic dispatch (ED) problem considering valve-point effects and power losses. In addition, wind power is included in the problem formulation. Renewable sources and wind energy in particular have recently been getting more interest because of various environmental and economical considerations. The original BFA is a recently developed evolutionary optimisation technique inspired by the foraging behaviour of the Escherichia coli bacteria. The basic BFA has been successfully implemented to solve small optimisation problems; however, it shows poor convergence characteristics for larger constrained problems. To deal with the complexity and high-dimensioned search space of the ED problem, essential modifications are introduced to enhance the performance of the algorithm. The basic chemotactic step is adjusted to have a dynamic non-linear behaviour in order to improve balancing the global and local search. The stopping criterion of the original BFA is also modified to be adaptive depending on the solution improvement instead of the preset maximum number of iterations. The proposed algorithm is validated using several test systems. The results are compared with those obtained by other algorithms previously applied to solve the problem considering valve-point effects and power losses in addition to wind power.
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paper_title: Dynamic Economic Dispatch of Generation

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A set of procedures and algorithms are developed for dynamic economic dispatch of generation units. When coupled with a short-term load predictor, "look- ahead" capability is provided by the dynamic economic dispatch that coordinates predicted load changes with the rate-of- response capability of generation units. Dynamic economic dispatch also enables valve-point loading of generation units. Two examples are provided which demonstrate that our approach overcomes the severe limits on the number of units that could be dynamically dispatched in past approAches.
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paper_title: Economic Dispatch Problem using Bat Algorithm

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A BAT algorithm to solve the economic dispatch problem is presented in this paper. The modern power system has become very complex in nature with consumption of the electric power which is in rise progression and this tendency increases with the industrialization and the growth of the population. Moreover, one loss of alimentation can cause the interruption of the various production processes, and in front of consumers who become increasingly demanding by wanting more energy and better quality, the companies of production of electrical energy must thus ensure the regular provisioning of this request, and without interruption, but these requirements compromise the cost of generation. Application of BAT algorithm in this paper is based on mathematical modeling to solve economic dispatch problems by a single equivalent objective function. The algorithm is tested on 6-unit system. BAT algorithm is easy to implement and better than other algorithms in terms of accuracy and efficiency.
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paper_title: Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm

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This paper presents a novel stochastic optimisation approach to determining the feasible optimal solution of the economic dispatch (ED) problem considering various generator constraints. Many practical constraints of generators, such as ramp rate limits, prohibited operating zones and the valve point effect, are considered. These constraints make the ED problem a non-smooth/non-convex minimisation problem with constraints. The proposed optimisation algorithm is called self-tuning hybrid differential evolution (self-tuning HDE). The self-tuning HDE utilises the concept of the 1/5 success rule of evolution strategies (ESs) in the original HDE to accelerate the search for the global optimum. Three test power systems, including 3-, 13- and 40-unit power systems, are applied to compare the performance of the proposed algorithm with genetic algorithms, the differential evolution algorithm and the HDE algorithm. Numerical results indicate that the entire performance of the proposed self-tuning HDE algorithm outperforms the other three algorithms.
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paper_title: Economic load dispatch with valve-point loading effect by using Differential Evolution Immunized Ant Colony optimization technique

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Economic load dispatch is conducted by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.
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paper_title: Economic emission load dispatch with line flow constraints using a classical technique

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An attempt is made to explore the feasibility of developing an approach to solve the power system economic emission load dispatch (EELD) problem with line flow constraints using a classical technique based on co-ordination equations. The inability of the classical technique to handle the line flow constraints so far is circumvented innovatively by expressing the line flows in terms of active power generations through distribution factors. These distribution factors are elegantly developed from existing load flow information using a perturbation technique. The proposed model based on the classical technique for EELD is tested on IEEE 14- and 30-bus test systems and the results are compared with those obtained by quadratic programming, the Hessian method, the Ricochet gradient method and the linear programming method.
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paper_title: Ant colony optimisation for economic dispatch problem with non-smooth cost functions

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This paper presents a novel and efficient optimisation approach based on the ant colony optimisation (ACO) for solving the economic dispatch (ED) problem with non-smooth cost functions. In order to improve the performance of ACO algorithm, three additional techniques, i.e. priority list, variable reduction, and zoom feature are presented. To show its efficiency and effectiveness, the proposed ACO is applied to two types of ED problems with non-smooth cost functions. Firstly, the ED problem with valve-point loading effects consists of 13 and 40 generating units. Secondly, the ED problem considering the multiple fuels consists of 10 units. Additionally, the results of the proposed ACO are compared with those of the conventional heuristic approaches. The experimental results show that the proposed ACO approach is comparatively capable of obtaining higher quality solution and faster computational time.
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paper_title: Nonlinear Programming Solutions for Load-Flow, Minimum-Loss, and Economic Dispatching Problems

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A unified approach to load-flow, minimum-loss, and economic dispatching problems is presented. A load-flow solution is shown to coincide with the minimum of a function of the power system equations. An unconstrained minimization method, developed by Fletcher-Powell, is used to solve the load-flow problem. The method always finds a solution or indicates the nonexistence of a solution. Its performance is highly independent of the reference- slack bus position and requires no acceleration factors. Several constrained minimization techniques that solve the minimum-loss and economic dispatching problems are investigated. These include the Fiacco-McCormick, Lootsma, and Zangwill methods. The technique finally recommended is shown to be an extension of the method used to solve the load-flow problem. The approved IEEE test systems, and other systems whose response to conventional methods was known, have been solved.
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paper_title: A practical approach to real time economic dispatch considering unit's prohibited operating zones

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This paper develops an efficient and practical approach for determining the feasible optimal solution of the economic dispatch problem when some of the online units have prohibited operating zones. When a unit has prohibited operating zones, its operating region will be broken into isolated sub-regions, which results in multiple decision spaces for the economic dispatch problem. For each of the decision spaces, it can be either feasible or unfeasible with respect to the system demand. The feasible optimal solution for the dispatch problem can only reside in one of the feasible, spaces, and can be found by performing the conventional /spl lambda/-/spl delta/ iterative search based on the equal-incremental-cost criterion in each of the feasible spaces. However, for a system with a large number of decision spaces, such an exhaustive search method would not be acceptable in real time operation due to its high computational time requirement. In this paper, a novel approach is proposed. It defines a small and advantageous set of decision spaces, uses an efficient algorithm to determine the most advantageous space and then utilizes the conventional /spl lambda/-/spl delta/ iterative method to find the feasible optimal dispatch solution. >
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paper_title: Refined genetic algorithm-economic dispatch example

paper_content:

A genetic-based algorithm is used to solve a power system economic dispatch (ED) problem. The algorithm utilizes payoff information of perspective solutions to evaluate optimality. Thus, the constraints of classical LaGrangian techniques on unit curves are eliminated. Using an economic dispatch problem as a basis for comparison, several different techniques which enhance program efficiency and accuracy, such as mutation prediction, elitism, interval approximation and penalty factors, are explored. Two unique genetic algorithms are also compared. The results are verified for a sample problem using a classical technique. >
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paper_title: Cuckoo Search for Solving Economic Dispatch Load Problem

paper_content:

Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.
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paper_title: Grey Wolf Optimizer for solving economic dispatch problems

paper_content:

This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) which inspired by grey wolves (Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encircling prey, and attacking prey, are implemented. The algorithm is then benchmarked on 20 generating units in economic dispatch, and the results are verified by a comparative study with Biogeography-based optimization (BBO), Lambda Iteration method (LI), Hopfield model based approach (HM), Cuckoo Search (CS), Firefly, Artificial Bee Colony (ABC), Neural Networks training by Artificial Bee Colony (ABCNN), Quadratic Programming (QP) and General Algebraic Modeling System (GAMS). The results show that the GWO algorithm is able to provide very competitive results compared to these well-known meta-heuristics.
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paper_title: Maclaurin series-based lagrangian method for economic dispatch with valve-point effect

paper_content:

Power utilities in general use Lagrangian method to solve economic dispatch (ED) problem for ease of implementation. This is possible only if the cost function of generating units is convex. Owing to valve-point effect exhibited by multi-valve steam turbines, the cost function is non-convex. The Maclaurin series-based Lagrangian method is proposed to solve complicated, non-convex and non-linear ED problems. In this method, the rectified sinusoid function is represented by Maclaurin sine series expansion and is solved using the Lagrangian method. The problem is solved iteratively using lambda iteration method. The proposed methodology is validated using IEEE 30-bus test system. In addition, the effectiveness of the new algorithm is demonstrated with 3, 13 and 40 generator test systems available in the literature. The results obtained substantiate the applicability of the proposed method for solving ED problems with non-smooth cost functions at par with stochastic search techniques generally used.
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paper_title: Simulated annealing approach for solving economic load dispatch problems with valve point loading effects

paper_content:

This paper presents Simulated Annealing (SA) algorithm for optimization inspired by the process of annealing in thermodynamics to solve economic load dispatch (ELD) problems. The proposed approach is found to provide optimal results while working with operating constraints in the ELD and valve point loadings effects. In order to prove the robustness of the algorithm it is investigated on four different standard test cases consisting of 3, 13, 40 generating unit system with valve point effect and a Crete Island system of 18 thermal generating units having convex fuel cost characteristics. The proposed method has been compared with other existing relevant approaches available in literatures. Experimental results support to justify superiority of the approach over other reported techniques in terms of fast convergence, robustness and most significantly its optimal search behavior. Keywords: Thermodynamics, Simulated Annealing, Economic load dispatch, Valve point loadings effects.
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paper_title: New approach to economic load dispatch based on improved evolutionary programming

paper_content:

New insecticidal ( beta -phenyl- beta -substituted-vinyl)cyclopropanecarboxylates in which the beta -substituent may be halogen or lower haloalkyl are described and their preparation and insecticidal utility are exemplified.
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paper_title: Adaptive Hopfield neural networks for economic load dispatch

paper_content:

A large number of iterations and oscillations are those of the major concern in solving the economic load dispatch problem using the Hopfield neural network. This paper develops two different methods, the slope adjustment and bias adjustment methods, in order to speed up the convergence of the Hopfield neural network system. Algorithms of economic load dispatch for piecewise quadratic cost functions using the Hopfield neural network have been developed for the two approaches. The results are compared with those of a numerical approach and the traditional Hopfield neural network approach. To guarantee and for faster convergence, adaptive learning rates are also developed by using energy functions and applied to the slope and bias adjustment methods. The results of the traditional, fixed learning rate and adaptive learning rate methods are compared in economic load dispatch problems.
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paper_title: Environmental Economic Load Dispatch with Quadratic Fuel Cost Function Using Cuckoo Search Algorithm

paper_content:

In this paper, a Cuckoo Search Algorithm (CSA) is proposed for solving environmental economic load dispatch (EELD) problem with quadratic fuel function. Cuckoo Search is a new meta-heuristic algorithm inspired from the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds of other species for solving optimization problems with promising results. However, Cuckoo Search has not been applied to EELD problem so far. Therefore, the paper presents application of CSA to the problem. The effectiveness of the proposed method is tested on several cases of dispatch and loads. The obtained result including fuel cost, emission and computation time from CSA are compared to those from other method reported in the paper. The comparison result has indicated that the proposed CSA is a very efficient method for solving EELD problem.
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paper_title: A New Modified Shuffle Frog Leaping Algorithm for Non-Smooth Economic Dispatch

paper_content:

This paper presents an effective evolutionary method for solve economic dispatch (ED) with units having prohibited operating zones. ED has been widely used in power system operation and planning for determination of electricity prices. ED problem is a non smooth problem when valve point effects of generation units are considered. With addition the valve point effect and prohibited zones in ED problem this problem complicates more and more respect before and is needed to solve with a strong and accuracy algorithm. This paper presents a very robust algorithm (SLFA) to solve ED problem with valve point effect, furthermore in an attempt to reduce processing time and improve the quality of solutions, particularly to avoid being trapped in local optima, this paper present a modified SLFA that called MSLFA algorithm to solve ED problem. The performance of the MSFLA has been tested on two typical systems consisting of 6 and 40 thermal units and compared with conventional approaches such as genetic algorithm (GA), tabu search algorithm (TSA), PSO and others in literatures. The comparison results show that the efficiency of proposed approach can reach higher quality solution and faster computational time than the conventional methods.
---
paper_title: Computer analysis of power systems

paper_content:

This book describes the main computer modelling techniques that constitute the framework of modern power system analysis. After describing the main computational and transmission system developments influencing power system analysis, the book covers load or power flow, AC system faults, and the electromechanical behavior of power systems. Dynamic models of power system plants and their use in multi-machine transient stability analysis are discussed, and chapters also cover the electromagnetic transients program, harmonic flow analysis, and power system security and optimization analysis. Recent advances in interactive power system analysis and developments in computer graphics are also presented.
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paper_title: A zoom feature for a dynamic programming solution to economic dispatch including transmission losses

paper_content:

An iterative dynamic programming method for solving the economic dispatch problems of a system of thermal generating units including transmission line losses is presented along with a clear explanation of modifying generator cost functions during each iteration. A zoom feature is applied during the iterative process in order to converge to the economic dispatch solution with low computer time and storage requirements, Dynamic programming including a short-term load forecast is briefly discussed. A three-generator example is used to illustrate the method. Computer memory and time requirements are presented, along with results for a 15-unit system. >
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paper_title: A Distributed Auction-Based Algorithm for the Nonconvex Economic Dispatch Problem

paper_content:

This paper presents a distributed algorithm based on auction techniques and consensus protocols to solve the nonconvex economic dispatch problem. The optimization problem of the nonconvex economic dispatch includes several constraints such as valve-point loading effect, multiple fuel option, and prohibited operating zones. Each generating unit locally evaluates quantities used as bids in the auction mechanism. These units send their bids to their neighbors in a communication graph that supports the power system and which provides the required information flow. A consensus procedure is used to share the bids among the network agents and resolves the auction. As a result, the power distribution of generating units is updated and the generation cost is minimized. The effectiveness of this approach is demonstrated by simulations on standard test systems.
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paper_title: Application of flower pollination algorithm to multi-objective environmental/economic dispatch

paper_content:

AbstractEnvironmental/economic dispatch is a fundamental issue in power system operations as it deals with the scheduling of the generating output among available units for simultaneous minimization of fuel cost and emission output, two objectives that collide. Furthermore the violation of specific constraints must be avoided. In this paper, environmental/economic dispatch is solved applying a new meta-heuristic optimization method, namely flower pollination algorithm. The proposed method is inspired by the pollination process of flowering plants with Levy flight to imitate the movement of insect pollinators. The multi-objective environmental/economic dispatch problem can be described by polynomial objective functions and converted into single-objective using weighted sum method that produces non-dominated solutions. The most satisfactory solution is chosen according to a decision maker that is based on fuzzy set theory. Effectiveness of the proposed approach is examined on two test systems. The first sys...
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paper_title: Solution of economic dispatch problem using Gravitational Search Algorithm

paper_content:

An efficient and optimum economic operation of electric power generation systems has always played an important role in the operation of the electric power industry. Low fuel cost and reliable operation of power systems is desired the available electricity generation resources to supply the load demand on the power system. Economic dispatch problem is one of the nonlinear optimization problems of electrical power systems. This study presents a new heuristic approach to solve the well-known power system economic dispatch problem using Gravitational Search Algorithm (GSA). In order to test the effectiveness of proposed approach it was applied to different test systems. To show that effectiveness of proposed algorithm the results obtained are compared to those reported in the literature. The simulation results demonstrate that this proposed approach is a very useful and efficient approach to solve economic dispatch problem.
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paper_title: Differential evolution for economic load dispatch problems

paper_content:

In this work, differential evolution (DE) algorithm was studied for solving economic load dispatch (ELD) problems in power systems. DE has proven to be effective in solving many real world constrained optimization problems in different domains. ELD problems are complex and nonlinear in nature with equality and inequality constraints and here special measures were taken to satisfy those. Five ELD problems of different characteristics were used to investigate the effectiveness of the proposal. Comparing with the other existing techniques, the current proposal was found better than, or at least comparable to, them considering the quality of the solution obtained.
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paper_title: Non convex economic load dispatch problem by Efficient Biogeography Based Optimization algorithm

paper_content:

In this paper a new Efficient Biogeography Based Optimization (EBBO) algorithm is discussed and it is applied to solve the non convex Economic Load Dispatch (ELD) problem for the minimization of fuel cost. This EBBO uses the concept of Particle Swarm Optimization (PSO), mutation of Differential Evolution (DE) and migration of Biogeography Based Optimization (BBO). The conventional PSO is improved by using the mutation operators of DE and migration of BBO. Thus, the EBBO method gives a global optimal solution to the ELD problem and it also improves the computational time in comparison to other optimization methods. The combined methodology is applied to test the performance of the test system consisting of 40 thermal units. Fuel cost function takes into account the valve-point loading effects. The simulation result shows that this method has the capability to generate the best solution with better convergence speed.
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paper_title: An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems

paper_content:

Abstract Solving the non-convex economic load dispatch (ELD) problem with evolutionary algorithms has gained increasing research in recent years. In this paper, a differential harmony search (DHS) algorithm is proposed by combining the mechanisms of both differential evolution and harmony search. In the DHS, the pitch adjustment operation is cooperated with the different mutation operation to enhance the exploitation ability of harmony search, and both the memory consideration and the pitch adjustment are used to enhance the exploration ability of evolution search. In addition, a repair procedure and three simple selection rules are proposed for constraint handling. Numerical simulations are carried out based on different kinds of testing problems with various constraints including valve point effects, multi-fuels, ramp rate limit and prohibited operation zones. Simulation results and comparisons with the some existing algorithms demonstrate the effectiveness, efficiency and robustness of the proposed DHS algorithm. Finally, the effect of parameter setting on the DHS is investigated as well.
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paper_title: Optimal generation expansion planning via the Cross-Entropy method

paper_content:

The Generation Expansion Planning (GEP) problem is a highly constrained, large-scale, mixed integer nonlinear programming problem. The objective of the GEP problem is to evaluate the least cost investment plan for addition of power generating units over a planning period subject to demand, availability, and security constraints. In this paper, a GEP model is presented and the Cross-Entropy (CE) optimization method is developed to solve the problem. The CE method is an effective algorithm for solving large combinatorial optimization problems. The main advantage of the CE method over other metaheuristic techniques is that it does not require decomposition of the problem into a master problem and operation subproblems, greatly reducing the computational complexity. This method also provides a fast and reliable convergence to the optimal solution.
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paper_title: Constrained dynamic economic dispatch solution using particle swarm optimization

paper_content:

This paper proposes using the particle swarm optimization (PSO) to solve the constrained dynamic economic dispatch (DED) problem in power system operation. The constrained DED must not only satisfy the system load demand and the spinning reserve capacity, but some practical operation constraints of generators, such as ramp rate limits and prohibited operating zone, are also considered in practical generator operation. The feasibility of the proposed PSO method is demonstrated for two power systems, and it is compared with the other stochastic methods in terms of solution quality and computation efficiency. The experimental results showed that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in constrained DED problems.
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paper_title: Optimal reactive dispatch through interior point methods

paper_content:

An implementation of an interior point method to the optimal reactive dispatch problem is described. The interior point method used is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications. >
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paper_title: Reserve constrained economic dispatch with prohibited operating zones

paper_content:

A method is described for solving the reserve constrained economic dispatch problem when some of the online generating units have prohibited operating zone(s). For a unit with prohibited zone(s), the zone(s) divide the operating region between the minimum generation limit (Pmin) and the maximum generation limit (Pmax) into disjoint convex subregions. These disjoint subregions form a nonconvex decisions space and the associated economic dispatch problem is thus a nonconvex optimization problem. As a result, the conventional Lagrangian relaxation (LR) approach (e.g. the lambda - delta iterative approach) cannot be applied directly. The method proposed decomposes the nonconvex decision space into a small number of subsets such that each of the associated dispatch problems is either infeasible or one that can be directly solved via the conventional LR approach. Based on the decomposition, the optimal solution is the least costly one among all the feasible solutions of the associated dispatch problems. Examples are also given to illustrate the proposed method. >
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paper_title: $\theta$-Multiobjective Teaching–Learning-Based Optimization for Dynamic Economic Emission Dispatch

paper_content:

This paper presents a -multiobjective-teaching-learning-based optimization algorithm to solve the dynamic economic emission dispatch problem. Teaching-learning-based-optimization (TLBO) algorithm works on the effect of a teacher on learners. This paper proposes several modifications on the basic TLBO. In the suggested method, the optimization process is done based on the phase angles, instead of the design variables themselves whereby the nonlinear characteristics of the problem are considered more efficiently. To avoid entrapping into local optima, a new learning method is proposed. Moreover, several metaheuristic techniques are applied to make a satisfactory multiobjective optimization method. A new approach is employed to select the population; thereby uniformly distributed Pareto-optimal front as well as the extreme points of the tradeoff surface can be achieved. Furthermore, a niching mechanism is applied to direct the individuals to seek the lesser explored regions. A fuzzy clustering approach is utilized to handle the size of the repository and obtain profitable solutions from the decision maker's point of view. To involve the decision maker's favor through the search process perfectly, a min-max approach is developed to select the best candidate solutions for the next generation. The applicability of the method is validated on three test systems, including 5-unit, 10-unit, and 120-unit test systems.
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paper_title: Power Generation, Operation, and Control

paper_content:

Topics considered include characteristics of power generation units, transmission losses, generation with limited energy supply, control of generation, and power system security. This book is a graduate-level text in electric power engineering as regards to planning, operating, and controlling large scale power generation and transmission systems. Material used was generated in the post-1966 period. Many (if not most) of the chapter problems require a digital computer. A background in steady-state power circuit analysis is required.
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paper_title: Gravitational search algorithm: A novel optimization approach for economic load dispatch

paper_content:

The application of Gravitational Search Algorithm a heuristic optimization approach for solution of economic load dispatch is presented here. GSA optimization approach is inspired by Newtonian gravity and law of motion. The efficacy and robustness of the GSA approach is analyzed on four different standard test cases. Comparison of computational results is made with the recent available methods. The computational results confirm superiority, faster convergence and adeptness of the algorithm.
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paper_title: Solution of Economic Emission Load Dispatch problems of power systems by Real Coded Chemical Reaction algorithm

paper_content:

Abstract This paper presents a Real Coded Chemical Reaction algorithm (RCCRO) approach to solve the Economic Emission Load Dispatch (EELD) problem of thermal generators of power systems. Emission substance like NOX, power demand equality constraint and operating limit constraint are considered here. EELD problem has been originated as a multi-objective problem by considering both economy and emission simultaneously. Chemical Reaction Optimization (CRO) mimics the interactions of molecules in a chemical reaction to reach a low energy stable state. Basically, the CRO is designed to work in the discrete domain optimization problems. A real coded version of it, known as Real-Coded Chemical Reaction Optimization (RCCRO) is applied here to solve multi-objective EELD problems, in order to show the advantages of proposed algorithm to solve complex continuous optimization problems. Different test systems having 10, 13 and 40 generators, addressing valve-point loading and NOX emission have been considered. The solutions obtained are quite encouraging and superior to different existing optimization techniques.
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paper_title: Security-constrained economic dispatch using dual quadratic programming

paper_content:

Abstract This paper presents a procedure for efficiently handling real power transmission constraints on branch flows and inter-area exchanges to supplement the classic economic dispatch (ED) formulation. A sequential quadratic programming (SQP) method is employed to solve the resulting non-linear programming problem. Each quadratic subproblem is approached by a dual programming technique — a dual feasible starting point is obtained by relaxing transmission limits; constraint violations are then enforced using the dual quadratic algorithm by Goldfarb and Idnani. The Hessian matrix of the Lagrangian function is approximated by a diagonal matrix thus keeping the objective function of each quadratic subproblem separable. Two versions of the proposed procedure exploit different assumptions in the evaluation of the sensitivities of the slack bus balance equation and of transmission constraints. For comparison purposes, the exact model of the security-constrained economic dispatch (SCED) is solved using a standard SQP algorithm taken from the NAG library. Tests on a CIGRE sample network and on actual medium and large-scale systems show that feasible and nearly optimal solutions of the SCED problem can be obtained. The proposed method presents limited computation times and a sufficiently good accuracy; it can be profitably employed whenever computation speed and algorithmic robustness are important issues as in real time operation to update the trajectories of thermal generations, as well as in system planning and hydro-thermal co-ordination studies.
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paper_title: A review of recent advances in economic dispatch

paper_content:

A survey is presented of papers and reports that address various aspects of economic dispatch. The time period considered is 1977-88. Four related areas of economic dispatch are identified and papers published in the general areas of economic dispatch are classified into these. These areas are: optimal power flow, economic dispatch in relation to AGC, dynamic dispatch, and economic dispatch with nonconventional generation sources. >
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paper_title: Dynamic economic dispatch using artificial bee colony algorithm for units with valve‐point effect

paper_content:

Dynamic economic dispatch (DED) is an important dynamic problem in power system operation and control. The objective of the problem is to schedule power generation for the online units over a time horizon, satisfying the unit and ramp rate constraints. In this paper, artificial bee colony (ABC) algorithm is used to solve the dynamic economic dispatch problem for generating units with valve-point effect. The feasibility of the proposed method is validated with ten- and five-unit-test systems for a period of 24 hours. In addition, the effects of control parameters on the performance of ABC algorithm for DED problem are studied. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving DED problems with non-smooth cost functions in terms of solution quality and computation efficiency. Copyright © 2010 John Wiley & Sons, Ltd.
---
paper_title: Power Generation, Operation, and Control

paper_content:

Topics considered include characteristics of power generation units, transmission losses, generation with limited energy supply, control of generation, and power system security. This book is a graduate-level text in electric power engineering as regards to planning, operating, and controlling large scale power generation and transmission systems. Material used was generated in the post-1966 period. Many (if not most) of the chapter problems require a digital computer. A background in steady-state power circuit analysis is required.
---
paper_title: Present Practices in the Economic Operation of Power Systems

paper_content:

This paper presents present practices within the utility industry in the economic operation of electric power systems. It is intended primarily as a reference for those new in this area of endeavor. It also discusses certain shortcomings of present practices and areas requiring further development.
---
paper_title: Computer analysis of power systems

paper_content:

This book describes the main computer modelling techniques that constitute the framework of modern power system analysis. After describing the main computational and transmission system developments influencing power system analysis, the book covers load or power flow, AC system faults, and the electromechanical behavior of power systems. Dynamic models of power system plants and their use in multi-machine transient stability analysis are discussed, and chapters also cover the electromagnetic transients program, harmonic flow analysis, and power system security and optimization analysis. Recent advances in interactive power system analysis and developments in computer graphics are also presented.
---
paper_title: Multiobjective evolutionary algorithms for electric power dispatch problem

paper_content:

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.
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paper_title: Bid-based dynamic economic dispatch with an efficient interior point algorithm

paper_content:

Abstract An efficient interior point algorithm for solving the bid-based dynamic economic dispatch (BBDED) problem is proposed in this paper. This algorithm is an extension of interior point quadratic programming (IPQP), and is called the predictor–corrector interior point quadratic programming (PCIPQP) algorithm. In a competitive electricity market, the dynamic economic dispatch has evolved to become bid-based framework to maximize the profits and achieve the resource scheduling. To generate a physically feasible dispatch and market spot prices, we form BBDED problem of dealing with various constraints such as ramp rates, transmission line capacity and emission constraints. In this paper, BBDED allows both supply-side and demand-side bids in the spot market, which includes multi-player, multi-period and a large number of constraints. Compared with the pure IPQP algorithm, PCIPQP is more attractive in performance, robustness, and the property of convergence. Many numerical tests reconfirmed the advantages of the predictor–corrector method.
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paper_title: Optimal reactive dispatch through interior point methods

paper_content:

An implementation of an interior point method to the optimal reactive dispatch problem is described. The interior point method used is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications. >
---
paper_title: Present Practices in the Economic Operation of Power Systems

paper_content:

This paper presents present practices within the utility industry in the economic operation of electric power systems. It is intended primarily as a reference for those new in this area of endeavor. It also discusses certain shortcomings of present practices and areas requiring further development.
---
paper_title: Economic dispatch of generators with prohibited operating zones: a genetic algorithm approach

paper_content:

The work explores the use of a genetic algorithm for the solution of an economic dispatch problem in power systems where some of the units have prohibited operating zones. Genetic algorithms have a capability to provide global optimal solutions in problem domains where a complete traversion of the whole search space is computationally infeasible. Two different implementations of the genetic algorithm for the solution of this dispatch problem are presented: a standard genetic algorithm, and a deterministic crowding genetic algorithm model. The results demonstrate that the genetic algorithm can be applied successfully in the solution of problems represented with nonconvex functions.
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paper_title: EFFICIENT EVOLUTIONARY STRATEGY OPTIMISATION PROCEDURE TO SOLVE THE NONCONVEX ECONOMIC DISPATCH PROBLEM WITH GENERATOR CONSTRAINTS

paper_content:

A simple and efficient algorithm based on evolutionary strategies is proposed for the solution of the economic dispatch (ED) problem with noncontinuous and nonsmooth/nonconvex cost functions and with generator constraints being considered. The proposed method solves both, the ED problem with nonconvex/nonsmooth cost functions due to valve-point loading and the ED problem that takes into account nonlinear generator characteristics such as ramp-rate limits and prohibited operating zones in the power system operation. The effectiveness of the algorithm is demonstrated using six different test systems and the performance is compared with other relevant methods reported in the literature. In all cases, the proposed algorithm either matches or outperforms the behaviour reported for the existing algorithms. This level of performance is obtained despite the simplicity of the approach.
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paper_title: Reserve constrained economic dispatch with prohibited operating zones

paper_content:

A method is described for solving the reserve constrained economic dispatch problem when some of the online generating units have prohibited operating zone(s). For a unit with prohibited zone(s), the zone(s) divide the operating region between the minimum generation limit (Pmin) and the maximum generation limit (Pmax) into disjoint convex subregions. These disjoint subregions form a nonconvex decisions space and the associated economic dispatch problem is thus a nonconvex optimization problem. As a result, the conventional Lagrangian relaxation (LR) approach (e.g. the lambda - delta iterative approach) cannot be applied directly. The method proposed decomposes the nonconvex decision space into a small number of subsets such that each of the associated dispatch problems is either infeasible or one that can be directly solved via the conventional LR approach. Based on the decomposition, the optimal solution is the least costly one among all the feasible solutions of the associated dispatch problems. Examples are also given to illustrate the proposed method. >
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paper_title: A MIXED INTEGER QUADRATIC PROGRAMMING FORMULATION FOR THE ECONOMIC DISPATCH OF GENERATORS WITH PROHIBITED OPERATING ZONES

paper_content:

In this paper, an optimisation-based approach is proposed using a mixed integer quadratic programming model for the economic dispatch of electrical power generators with prohibited zones of operation. The main advantage of the proposed approach is its capability to solve case studies from the literature to global optimality quickly and without any targeting of solution procedures.
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paper_title: Real-time economic dispatch with line flow and emission constraints using quadratic programming

paper_content:

The presence of multiple constraints due to network line flow limits and emission allowances in the economic dispatch of modern power systems makes the conventional Lambda-Delta iterative approach no longer effective. This paper proposes a practical strategy based on quadratic programming (QP) techniques to solve the real-time economic dispatch problem. It formulates the problem with a quadratic objective function based on the unit's cost curves in quadratic or piecewise-quadratic forms. The operation constraints are modeled as linear equality/inequality equations, resulting in a typical QP problem. Goal programming techniques are also incorporated in the formulation which guarantees the best available solution even under infeasible conditions. In addition, the proposed strategy formulates the problem in the second phase dispatch in real-time by including a set of emergency control variables to provide effective control strategies for properly relieving constraint violations if they exist. The effectiveness of the proposed strategy is demonstrated by an example power dispatch problem.
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paper_title: Dynamic Economic Dispatch of Generation

paper_content:

A set of procedures and algorithms are developed for dynamic economic dispatch of generation units. When coupled with a short-term load predictor, "look- ahead" capability is provided by the dynamic economic dispatch that coordinates predicted load changes with the rate-of- response capability of generation units. Dynamic economic dispatch also enables valve-point loading of generation units. Two examples are provided which demonstrate that our approach overcomes the severe limits on the number of units that could be dynamically dispatched in past approAches.
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paper_title: Particle swarm optimization

paper_content:

A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described.
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paper_title: Tracking and optimizing dynamic systems with particle swarms

paper_content:

Using particle swarms to track and optimize dynamic systems is described. Issues related to tracking and optimizing dynamic systems are briefly reviewed. Three kinds of dynamic systems are defined for the purposes of this paper. One of them is chosen for preliminary analysis using the particle swarm on the parabolic benchmark function. Successful tracking of a 10-dimensional parabolic function with a severity of up to 1.0 is demonstrated. A number of issues related to tracking and optimizing dynamic systems with particle swarms are identified. Directions for future research and applications are suggested.
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paper_title: Particle swarm optimization for various types of economic dispatch problems

paper_content:

This paper describes a successful adaptation of the particle swarm optimisation (PSO) algorithm to solve various types of economic dispatch (ED) problems in power systems such as, multi-area ED with tie line limits, ED with multiple fuel options, combined environmental economic dispatch, and the ED of generators with prohibited operating zones. Numerical examples typical to each type are solved on Matlab 6.5 platform, using both the PSO method and the classical evolutionary programming (CEP) approach. The results obtained show that the proposed PSO based ED algorithm can provide comparable dispatch solutions with reduced computation time for all types of ED problems.
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paper_title: Development of an Educational Simulator for Particle Swarm Optimization and Economic Dispatch Applications

paper_content:

This paper presents a windows-based educational simulator with user-friendly graphical user interface (GUI) for the education and training of particle swarm optimization (PSO) technique for mathematical optimization problems and economic dispatch (ED) applications. The main objective for developing the simulator is to provide information with the electrical engineering undergraduate students that the up-to-date artificial intelligent (AI) techniques including PSO are actively used in power system optimization problems. The simulator can be used as a lecturing tool to stimulate an interest in the power system engineering of the undergraduate students. The students can be more familiar with the optimization problems including power system ED problem through the iterative uses of the simulator. Also, they can increase understandings on PSO mechanism by the homework on the optimal design of several control parameters such as inertia weight, acceleration coefficients, and the number of population, etc. In the developed simulator, instructors and students can select the optimization functions and set the parameters that have an influence on PSO performance. The simulator is applied not only to mathematical optimization functions but also to economic dispatch (ED) problems with non-smooth cost functions, which is designed so that users can solve other mathematical functions through simple additional MATLAB coding.
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paper_title: Economic load dispatch of different bus systems using particle swarm optimization

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In this paper, particle swarm optimization (PSO) which is one of the evolutionary computing techniques is applied successfully to solve the problem of economic load dispatch (ELD). The objective function considered here is minimization of fuel cost of generators for three different bus systems. The results obtained from PSO have better convergence as compared to the conventional technique of using lambda iteration model. Further the paper explains the vulnerability of different parameters on fuel cost and transmission losses.
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paper_title: Economic Load Dispatch Using PSO And TLBO

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This paper presents the application of Bio-inspired algorithms like Particle Swarm Optimization (PSO) and Teaching-learning Based Optimization (TLBO) for solution of economic load dispatch (ELD) problem. The algorithms are used to find the optimum solution with lowest fuel cost for four different network consisting of three, six, fifteen, and twenty generating units respectively for different load demand. Results obtained using PSO and TLBO are compared with the results obtained using lambda iteration method. The study has been done neglecting line losses as well as considering the line losses for different load demand. Both the algorithms are presented and described in this paper. The optimization has been done considering total fuel cost as the fitness function. The simulation results for all the cases are analyzed and presented in this paper.
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paper_title: Implementation of different optimization techniques to solve ELD problem

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Optimization is a mathematical technique that concerns the finding of maxima or minima of functions in some feasible region. There is no business or industry which is not involved in solving optimization problems. A variety of optimization techniques compete for the best solution. Economic load dispatch (ELD) problem is a common task in the operational planning of a power system, to schedule the connected generating units of plant outputs so as to fulfill demands at minimum operating cost while satisfying all operational constraints. In this paper different optimization technique like simulated annealing, genetic algorithm, pattern search, fmincon, minimax optimization, hybrid genetic algorithm & particle swarm optimization have been successfully applied on IEEE-30 bus (6 machines) system to solve the ELD problem for the standard demand of 283.40 MW. All above algorithms have been compared for ten trial runs. The best, worst, average fitness and their standard deviation for all the algorithms have been determined. The results show that PSO techniques give the optimum operating cost.
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paper_title: Economic Load Dispatch Using Particle Swarm Optimization

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Economic load dispatch is a non linear optimization problem which is of great importance in power systems. While analytical methods suffer from slow convergence and curse of dimensionality particle swarm optimization can be an efficient alternative to solve large scale non linear optimization problems. This paper presents an overview of basic PSO to provide a comprehensive survey on the problem of economic load dispatch as an optimization problem. The study is carried out for three unit test system and then for six unit generating system for without loss and with loss cases.
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paper_title: A modified particle swarm optimizer applied to the solution of the economic dispatch problem

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In this paper, a modified approach, based on the particle swarm optimizer (PSO) is presented and explained in detail. As a case study, this PSO technique is applied to the solution of the economic dispatch (ED) problem of thermal generating units. A piecewise quadratic function is used to represent the fuel cost of each generating unit. The B-coefficient method is used to model the transmission losses. A modification to the standard PSO algorithm is proposed to allow dealing with the power balance equality constraint. Unlike the traditional methods, this modification does not depend on penalizing the infeasible solutions using a pre-defined penalty function. The application of the proposed method to several case studies shows that it is applicable to large networks with multigenerating units including transmission losses with very promising results.
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paper_title: Particle swarm optimization to solving the economic dispatch considering the generator constraints

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This paper proposes a particle swarm optimization (PSO) method for solving the economic dispatch (ED) problem in power systems. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and nonsmooth cost functions are considered using the proposed method in practical generator operation. The feasibility of the proposed method is demonstrated for three different systems, and it is compared with the GA method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
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paper_title: Economic load dispatch using improved particle swarm optimization algorithms

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The main objective of Economic Load Dispatch (ELD) problem is to schedule the connected generating units of plant outputs so as to fulfill load demands at minimum operating cost while satisfying all operational constraints. Recently particle swarm optimization algorithms inspired by collective behavior of swarm has been applied successfully to solve ELD problem. It is a population based stochastic optimization process driven by the simulation of a social psychological metaphor. In this paper three improved PSO algorithms- IPSO-A, IPSO-B and IPSO-C have been developed and implemented to solve ELD for IEEE 5, 14 and 30 bus systems. Conventional PSO (CPSO) using inertia weight and constriction factor individually as well as simultaneously have been also implemented to solve ELD problem. PSO algorithms have been compared for twenty trial runs. The best, worst, average fitness and their standard deviation for all the algorithms have been determined. The results show that proposed improved PSO techniques gives the optimum operating cost with consistent results in terms of diversity of results.
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paper_title: Swarm intelligence solution to large scale thermal power plant Load Dispatch

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Economic Load Dispatch is one of the major functions of modern Energy Management System (EMS), which determines the optimal real power settings of generating units with an objective of minimizing the total fuel cost. All industrial practice, the fuel cost of generators can be treated as a quadratic function of real power generation. In fact, valve point loading effect in thermal power plants calls discontinuity. The classical optimization methods require continuous differentiable objective functions; therefore they fail to provide global minima. The evolutionary computation methods can handle non-differential and non-convex objective functions and give global or near global optimum solutions. Evolutionary techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP) are applied to economic dispatch problem. Similar to evolutionary computation, social behaviour artificial intelligence called swarm intelligence is applied in many fields. Use of swarm intelligence not only avoids coding and monotonous decoding as prevalent transformations of GA and also results in less burden on parameter settings, population size and number of iterations. In this paper, swarm intelligence is applied to solve large scale economic load dispatch problem with valve point loading. Particle Swarm Optimization (PSO) algorithm is tested on a 13 and 40 unit test system. Results obtained show that PSO algorithm has a great potential in handling large size complex optimization problems and capable to produce results in very less time.
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paper_title: Particle swarm optimization (PSO) technique in economic power dispatch problems

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Economic power dispatch problem plays an important role in the operation of the power systems. It is a method of determine the most efficient, low cost and reliable operation of a power system by dispatching the available electricity generation resources to supply the load on the system. The primary objective of economic dispatch is to minimize the total cost of generation while maintaining the operational constraints of the available generation resources. In this paper, a particle swarm optimization algorithms (PSO) with one of the accelerating coefficients being constant are proposed to solve the economic power dispatch problem. Particle swarm optimization (PSO) is algorithms modeled on swarm intelligence that finds a solution to an optimization problem in a search space, or model and predict social behavior in the presence of objectives. In this study, the proposed technique was tested using the standards IEEE 26-BUS RTS and the results revealed that the proposed technique has the merit in achieving optimal solution for addressing the problems.
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paper_title: Comparison of Intelligent Techniques to Solve Economic Load Dispatch Problem with Line Flow Constraints

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A comparative analysis using different intelligent techniques has been carried out for the Economic Load Dispatch (ELD) problem considering line flow constraints for the regulated power system to ensure a practical, economical and secure generation schedule. The objective of this paper is to minimize the total production cost of the thermal power generation. Economic Load Dispatch (ELD) has been applied to obtain optimal fuel cost. Optimal Power Flow has been carried out to obtain ELD solutions with minimum operating cost satisfying both unit and network constraints. In this paper, various intelligent techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), Particle Swarm Optimization (PSO), and Differential Evolution (DE) have been applied to obtain ELD solutions. The proposed algorithm has been tested on two sample systems viz IEEE 30 bus system and a 15 unit system. The results obtained by the various intelligent techniques are compared. The solutions obtained are quite encouraging and useful in the economic environment. The algorithm and simulation are carried out using Matlab software.
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paper_title: Implementing Particle Swarm Optimization to Solve Economic Load Dispatch Problem

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Economic Load Dispatch (ELD) is one of an important optimization tasks which provides an economic condition for a power systems. In this paper, Particle Swarm Optimization (PSO) as an effective and reliable evolutionary based approach has been proposed to solve the constraint economic load dispatch problem. The proposed method is able to determine, the output power generation for all of the power generation units, so that the total constraint cost function is minimized. In this paper, a piecewise quadratic function is used to show the fuel cost equation of each generation units, and the B-coefficient matrix is used to represent transmission losses. The feasibility of the proposed method to show the performance of this method to solve and manage a constraint problems is demonstrated in 4 power system test cases, consisting 3,6,15, and 40 generation units with neglected losses in two of the last cases. The obtained PSO results are compared with Genetic Algorithm (GA) and Quadratic Programming (QP) base approaches. These results prove that the proposed method is capable of getting higher quality solution including mathematical simplicity, fast convergence, and robustness to solve hard optimization problems
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paper_title: A new approach for real power optimization of generation with nonsmooth cost function using particle swarm optimization

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This paper describes a successful adaptation of particle swarm optimization (PSO) algorithm to solve the economic dispatch (ED) problem with valve point effects in power system. In this paper, PSO method is used to describe the equality and inequality constraints in the Economic Dispatch problems. The proposed algorithm has been tested on 3 unit system with quadratic cost functions. Numerical example are solved on Matlab 7 platform using PSO method. Numerical results shows that the proposed PSO based ED algorithm can provide comparable dispatch solutions with reduced cost.
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paper_title: A proposed particle swarm optimization technique for solving non-linear economic dispatch problem

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This paper proposes a particle swarm optimization (PSO) method for solving the economic dispatch (ED) problem in power systems. Many nonlinear characteristics of the generator are considered for practical generator operation, such as ramp rates, prohibited operating zones, and non-smooth cost functions. The feasibility of the proposed method is demonstrated for two different systems, and is Compared with both Genetic Algorithm (GA) method and another PSO method in terms of the cost optimization and computation time where an improvement in both terms is achieved.
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paper_title: Particle Swarm Based Optimal Estimation of Block Incremental Cost Curve

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Competitive electricity market (EM) requires the bid from the electricity supply companies in the required formats which are defined in the market regulations. Block (stair-case) bid and linear bid are two most commonly used bid format for both market and research purposes. In most of the EM, the generating companies (so called energy suppliers) are required to bid their power outputs in blocks with the associated price of each block. For a unit having with multiple fuel and valve point loading effect, the generating company must divide the output power of the unit into the blocks so that it can be bid into the electricity market with and/or without gaming. This paper addresses the estimation of optimal block incremental cost from the instantaneous incremental heat rate curve of a generating unit using particle swarm optimization approach. During each block, the total cost is the same to the cost obtained with the instantaneous incremental cost curve. The formulation is simple and can be used for any generating unit with minimum error at block edges. The effectiveness of the proposed method is illustrated with the case studies.
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paper_title: An enhanced time effective particle swarm intelligence for the practical economic load dispatch

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Economic load dispatch is an important problem to be considered in the generation side where the power demand plays the vital role for the economic operation of thermal power plants. The Economic dispatch problem is formulated by a smooth differentiable or piecewise quadratic objective function, which is the same approach used by classical optimization methods. Even though, due to the valve-point effects, the real input output characteristics becomes a higher order nonlinear and discontinuous one which results in a non-convex, non-smooth fuel cost function. Even the most popular PSO technique also presents decade to have a more optimized value in certain applications. Power system is one such application where the naturally inspired algorithms are giving better results than the conventional methods like lambda iteration method , gradient method etc. In this paper, particle swarm optimization which solves economic and practical economic load dispatch problem (with valve point effect) with better optimized results in a little fraction of seconds is explained. In this case, 3 generator system, 13 generator system and 20 generator systems are considered and the optimal values of power of each generator which gives optimal cost was found by this time effective particle swarm intelligence is proposed in this paper.
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paper_title: Implementation of particle swarm optimization for dynamic economic load dispatch problem

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The economic operation of the generating systems has always occupied an important position in the electric power industry. It is one of the complex problems of the power system. The aim of the dynamic economic load dispatch problem is to find the optimal combination of generators in order to minimize the operating costs of the system. The load demand must be appropriately shared among the various generating units of the system. This work is done by using the particle swarm optimization (PSO) algorithm. PSO is applied to search for the optimal schedule of all the generator units that can supply the required load demand at minimum fuel cost while satisfying all system constraints such as Generator constraints, Ramp rate limits, Transmission losses and valve point effect. The PSO method was developed through the simulation of a simplified social system. The simulations were performed over various test systems with 5 generation units. So by using PSO we have done the dynamic economic load dispatch thereby reducing the operating costs of the system.
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paper_title: Constrained dynamic economic dispatch solution using particle swarm optimization

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This paper proposes using the particle swarm optimization (PSO) to solve the constrained dynamic economic dispatch (DED) problem in power system operation. The constrained DED must not only satisfy the system load demand and the spinning reserve capacity, but some practical operation constraints of generators, such as ramp rate limits and prohibited operating zone, are also considered in practical generator operation. The feasibility of the proposed PSO method is demonstrated for two power systems, and it is compared with the other stochastic methods in terms of solution quality and computation efficiency. The experimental results showed that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in constrained DED problems.
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paper_title: Particle swarm optimization algorithm for the solution of nonconvex economic dispatch problem with valve point effect

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In this study, particle swarm optimization (PSO) algorithm has been used for the solution of the economic dispatch problem with valve point effect. In these kind of problems, fuel cost curve increases as sinusoidal oscillations. In the solution of the problem B loss matrix has been used for the calculation of the transmission line losses. Total fuel cost rate has been minimized under electrical constraints. PSO algorithm has been applied to three different test systems one with 6 buses 3 generators, the other with 14 buses 5 generators (IEEE) and the last one with 30 buses 6 generators (IEEE). The obtained optimum solution values have been compared with optimum solution values obtained by the application of different methods in literature and the results of them have been discussed.
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paper_title: Economic Load Dispatch Optimization of Six Interconnected Generating Units Using Particle Swarm Optimization

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This paper describe about the optimization of economic loading dispatch (ELD) problem. Economic loading dispatch is one of the important optimization tasks which provide economic condition for a power system. The ELD problems have non-smooth objective function with equality and inequality constraints. This paper presents particle swarm optimization (PSO) method for solving the economic dispatch(ED) problem in power system. The particle swarm optimization is an efficient and reliable evolutionary computational technique, which is used to solve economic load dispatch with line power flows. This paper describes, a new PSO framework used to deal with the equality and inequality constraints in ELD problem. The proposed PSO can always provide satisfying results within a realistic computation time. The PSO is applied with non-smooth cost function. The six thermal units, 26 buses and 46 transmission lines system is used in this paper. The proposed PSO method results are compared with the genetic algorithm (GA) and conventional method to show the effectiveness of PSO method to solve the ELD problems in power system. Keywords- Economic load dispatch, generating unit, genetic algorithm, power system, loss minimization, particle swarm optimization.
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paper_title: Dynamic Economic Dispatch with Valve-Point Effect Using Maclaurin Series Based Lagrangian Method

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Dynamic Economic Dispatch (DED) plays a vital role in power generation, operation and control. It is a complicated, non-linear constrained problem. In this paper, Maclaurin series based Lagrangian method (MSL) is used to solve the DED problem for generating units with valve-point effect, considering the ramp rate limits. Using Maclaurin series, the sine term used to model the valve-point effect is expanded and solved with Lagrangian method. The feasibility of the proposed method is validated for static economic dispatch problem for forty unit system and DED problem for five unit test system for 24 hour time interval. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the applicability of the proposed method for solving static and dynamic economic dispatch problems with non-smooth cost functions.
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paper_title: Comparing inertia weights and constriction factors in particle swarm optimization

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The performance of particle swarm optimization using an inertia weight is compared with performance using a constriction factor. Five benchmark functions are used for the comparison. It is concluded that the best approach is to use the constriction factor while limiting the maximum velocity Vmax to the dynamic range of the variable Xmax on each dimension. This approach provides performance on the benchmark functions superior to any other published results known by the authors.
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paper_title: Constriction Coefficient Particle Swarm Optimization for Economic Load Dispatch with valve point loading effects

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This paper presents an efficient method to Economic Load Dispatch (ELD) problem using a Particle Swarm Optimization (PSO) technique. The practical ELD problems have nonsmooth cost functions with equality and inequality constraints. It is difficult to find the optimum solution using mathematical approaches. In this paper Constriction Coefficient PSO(CPSO) is used to solve ELD problem with valve point loading effects. The results of this method are compared with Standard PSO (SPSO) and inertia based PSO (IPSO) method. The results of the proposed method are illustrated with 3 and 6 generator unit systems.
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paper_title: A Comparative Study on Particle Swarm Optimization for Optimal Steady-State Performance of Power Systems

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In this paper, three new particle swarm optimization (PSO) algorithms are compared with the state of the art PSO algorithms for the optimal steady-state performance of power systems, namely, the reactive power and voltage control. Two of the three introduced, the enhanced GPAC PSO and LPAC PSO, are based on the global and local-neighborhood variant PSOs, respectively. They are hybridized with the constriction factor approach together with a new operator, reflecting the physical force of passive congregation observed in swarms. The third one is based on a new concept of coordinated aggregation (CA) and simulates how the achievements of particles can be distributed in the swarm affecting its manipulation. Specifically, each particle in the swarm is attracted only by particles with better achievements than its own, with the exception of the particle with the best achievement, which moves randomly as a "crazy" agent. The obtained results by the enhanced general passive congregation (GPAC), local passive congregation (LPAC), and CA on the IEEE 30-bus and IEEE 118-bus systems are compared with an interior point (IP)-based OPF algorithm, a conventional PSO algorithm, and an evolutionary algorithm (EA), demonstrating the excellent performance of the proposed PSO algorithms
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paper_title: Economic load dispatch considering valve-point effects using time varying constriction factor based particle swarm optimization

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This paper proposes a new optimization algorithm suitable to solve economic load dispatch problem of power system considering valve-point loading effects. The new optimization algorithm is a time varying constriction factor based particle swarm optimization (VCF_PSO). In the proposed algorithm, the two acceleration coefficients of particle swarm optimization are varied in order to obtain a varying constriction as the iteration proceeds which lead to give a fast and efficient algorithm. To test the effectiveness and the robustness of the proposed algorithm, economic load dispatch problems with valve-point effects of two IEEE test systems of 3-unit and 13-unit has been solved and the results obtained have been compared with some other methods present in the literature.
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paper_title: Particle Swarm Optimisation for Economic Dispatch with Cubic Fuel Cost Function

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This paper presents an efficient and reliable particle swarm optimisation (PSO) algorithm for solving the economic dispatch (ED) problems with smooth cost functions as well as cubic fuel cost functions. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. For such cases, the PSO is applied to the ED problems with real power of generator in a system as state variables. However when the incremental cost of each unit is assumed to be equal, the complexity involved in this may be reduced by using the Incremental cost as state variables. To show its efficiency and effectiveness, the proposed PSO is applied to test one with smooth cost functions and then with cubic fuel cost function. The proposed PSO algorithm has been tested on 3 generator systems with smooth cost functions and 3 generator systems, 5 generator systems and 26 generator systems with cubic fuel cost function. The results are compared with Genetic algorithm (GA) and shown better results and computation efficiency than Genetic algorithm.
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paper_title: Improved particle swarm optimization combined with chaos

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Abstract As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality.
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paper_title: A new hybrid technique for solution of economic load dispatch problems based on Biogeography Based Optimization

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This paper presents a hybrid technique combining Evolutionary Strategy(ES) with Biogeography Based Optimization (BBO/ES) algorithm to solve economic load dispatch problems of thermal plants considering equality and inequality constraints, transmission losses and valve point loading. Biogeography is a recently developed heuristic algorithm which has shown impressive performance on many well known benchmarks. In order to improve BBO, distinctive features from ES are incorporated in BBO modification. This algorithm searches for the global optimum mainly through two steps: migration and mutation. The effectiveness of the proposed algorithm has been verified on two different test systems, both small and large involving varying degree of complexity. A comparison of simulation results reveals that the proposed algorithm is better than those listed in the comparison table in terms of the quality of the solution. This method seems to be promising alternative approach for solving the ELD problems in practical power systems.
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paper_title: A particle swarm optimization for economic dispatch with nonsmooth cost functions

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This work presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. A constraint treatment mechanism is devised in such a way that the dynamic process inherent in the conventional PSO is preserved. Moreover, a dynamic search-space reduction strategy is devised to accelerate the optimization process. To show its efficiency and effectiveness, the proposed MPSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost functions considering valve-point effects and multi-fuel problems. The results of the MPSO are compared with the results of conventional numerical methods, Tabu search method, evolutionary programming approaches, genetic algorithm, and modified Hopfield neural network approaches.
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paper_title: An efficient Particle Swarm Optimization for Economic Dispatch with valve-point effect

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This paper presents a new efficient approach to Economic Dispatch (ED) problems with smooth and non smooth cost functions using a Particle Swarm Optimization (PSO) technique. The practical ED problems have non-smooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. In this paper, an efficient PSO technique is employed so that faster convergence is obtained for the same results published in IEEE Proceedings so far. To show its efficiency and effectiveness, the proposed PSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost Functions considering valve-point loading effects. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
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paper_title: Economic Load Dispatch Problem using Particle Swarm Optimization with Inertial Weight and Constriction Factor

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The Economic Load dispatch (ELD) problem plays a significant role in the functioning of power systems. It is used in determining the optimal cost for satisfying the demand with available electric generation resources. The ELD problem of thermal units results in significant saving for electrical utilities. The formation of ELD has been discussed and solution is obtained by Particle swarm optimization (PSO). The algorithms based on various PSO variants such as inclusion of inertia weight (named as I-PSO); constriction factor (C-PSO) and constriction factor-inertia weight (CI-PSO) have been developed and have been tested on systems comprising four and six units. The results obtained with the proposed PSO techniques are matched with the existing results, which thereby show the correctness and effectiveness of the developed algorithm.
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paper_title: Hierarchical economic load dispatch based on chaotic-particle swarm optimization

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The economic load dispatch (ELD) optimization is an important approach to decrease the power consumption. In this paper, a network-plant hierarchical economic load dispatch mode is proposed based on the conventional load dispatch mode. The concept of plant coal consumption is proposed, as well as the method to obtain it. The model to achieve the least coal consumption in the full network depending on the plant coal consumption characteristic is also proposed. And it is theoretically proved that the optimization result of hierarchical ELD is consistent with that of conventional ELD. The chaotic particle swarm optimization (CPSO) algorithm is used to solve the optimal dispatch problem, adopting the adaptive inertia weight to accelerate the convergence speed. The hybrid optimization algorithm is improved from particle swarm optimization (PSO) algorithm by chaotic searching in the neighborhood to avoid getting into the local optimum, with the algorithm steps listed in the paper. A numerical example is done and analyzed, verifying the validity of the hierarchical optimization mode and CPSO.
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paper_title: A NOVEL PARTICLE SWARM OPTIMIZATION ALGORITHM SOLUTION OF ECONOMIC DISPATCH WITH VALVE POINT LOADING

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It is widely recognized that a proper schedule of available generating units may save utilities millions of dollars per year in production costs. A novel particle swarm optimization (PSO) combined with the direct search method (DSM) is developed in this paper for the solution of economic dispatch (ED) problem with valve-point effect. A new inertia weight mechanism is incorporated into PSO to enhance its search capacity that leads to a higher probability of obtaining the global optimal solution. The main attractive feature of the proposed inertia weight mechanism is to monitor the weights of particles, which were linearly decreased in general applications, and to further provide a well-balanced mechanism between the global and local exploration abilities. The DSM algorithm is used as a fine tuning to determine the eventual global optimal solution with a reduced computing time. The validity, robustness, and effectiveness of the proposed approach is verified through numerical experiments for extended economic dispatch application.
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paper_title: An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems

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This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using an improved particle swarm optimization (IPSO). Although the particle swarm optimization (PSO) approaches have several advantages suitable to heavily constrained nonconvex optimization problems, they still can have the drawbacks such as local optimal trapping due to premature convergence (i.e., exploration problem), insufficient capability to find nearby extreme points (i.e., exploitation problem), and lack of efficient mechanism to treat the constraints (i.e., constraint handling problem). This paper proposes an improved PSO framework employing chaotic sequences combined with the conventional linearly decreasing inertia weights and adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. In addition, an effective constraint handling framework is employed for considering equality and inequality constraints. The proposed IPSO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones with ramp rate limits as well as transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. Also, the results are compared with those of the state-of-the-art methods.
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paper_title: Genetic algorithm solution to the economic dispatch problem

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Two genetic algorithm (GA) solutions to the economic dispatch problem are presented. An advantage of the GA solutions is that they do not impose any convexity restrictions on the generator cost functions. Another advantage is that GAs can be very effectively coded to work on parallel machines. Test results with systems of up to 72 generating units with nonconvex cost functions show that both GAs outperform the dynamic programming solution to the economic dispatch problem. Furthermore, the execution time of the second GA solution increases almost linearly with the number of generators.
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paper_title: Reserve constrained dynamic dispatch of units with valve-point effects

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This paper addresses a hybrid solution methodology integrating particle swarm optimization (PSO) algorithm with the sequential quadratic programming (SQP) method for the reserve constrained dynamic economic dispatch problem (RCDEDP) of generating units considering the valve-point effects. The cost function of the generating units exhibits the nonconvex characteristics, as the valve-point effects are modeled and imposed as rectified sinusoid components. The hybrid method incorporates the PSO algorithm as the main optimizer and SQP as the local optimizer to fine-tune the solution region whenever the PSO algorithm discovers a better solution region in the progress of its run. Thus, the SQP guides PSO for better performance in the complex solution space. To validate the feasibility of the proposed method, a ten-unit system is taken and studied under three different load patterns. The effectiveness and computation performance of the proposed method for the RCDEDP of units with valve-point effects is shown in general.
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paper_title: Adaptive particle swarm optimization approach for static and dynamic economic load dispatch

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Abstract This paper presents a novel heuristic optimization approach to constrained economic load dispatch (ELD) problems using the adaptive–variable population – PSO technique. The proposed methodology easily takes care of different constraints like transmission losses, dynamic operation constraints (ramp rate limits) and prohibited operating zones and also accounts for non-smoothness of cost functions arising due to the use of multiple fuels. Simulations were performed over various systems with different numbers of generating units, and comparisons are performed with other existing relevant approaches. The findings affirmed the robustness, fast convergence and proficiency of the proposed methodology over other existing techniques.
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paper_title: A novel hybrid particle swarm optimisation method applied to economic dispatch

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Economic load dispatch is complex and non-linear problem, it is difficult to solve the problem using traditional optimisation method. PSO has been successfully applied to a wide range of applications, in solving continuous non-linear optimisation problems. This paper presents a novel hybrid PSO algorithm with dynamic inertial weight and chaotic search to solve the problem. The improved hybrid PSO enhanced the global search ability of the algorithm and improved its convergence speed. The hybrid PSO algorithm was successfully validated for two test systems. Numerical simulation results show that the modified hybrid PSO algorithm outperformed standard PSO algorithm and genetic algorithm on the same problem and can save considerable cost of economic load dispatch.
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paper_title: Particle swarm optimization with Exponentially Varying Inertia Weight Factor for solving Multi-Area Economic Dispatch problem

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This paper aimed at exploring the performance of Particle Swarm Optimisation with Exponentially Varying Inertia Weight Factor (PSO-EVIWF) for solving Multi-Area Economic Dispatch (MAED) problem with tie line constraints considering valve-point loading in each area. The effectiveness of the proposed algorithm has been verified on 4 interconnected areas with 16 generators standard test system. The paper presents the search capability and convergence behavior of the proposed method. Simulation results show that the PSO-EVIWF achieved quality solutions and smooth convergence characteristics and it is an alternative method for solving MAED problem.
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paper_title: Particle swarm optimization with smart inertia factor for solving non-convex economic load dispatch problems

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SUMMARY ::: ::: This paper proposes a new approach to solve the non-convex economic dispatch problem using particle swarm optimization with smart inertia factor (PSO-SIF) algorithm in which, inertia coefficients are controlled with respect to cost function in each population. Hence, each population has unique inertia coefficient and as a result unique velocity in convergent direction for the best group solution. The new algorithm has been implemented on four test systems in different dimensions (6, 15, 20 and 40 units) with convex and non-convex cost functions. The numerical results have been compared with the results of a few PSO variants and some recently published results. The results prove the robustness and effectiveness of the proposed method and show that it could be used as a reliable tool for solving optimization problems. Copyright © 2013 John Wiley & Sons, Ltd.
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paper_title: Particle swarm optimization with crazy particles for nonconvex economic dispatch

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The paper presents an effective evolutionary method for economic power dispatch. The idea is to allocate power demand to the on-line power generators in such a manner that the cost of operation is minimized. Conventional methods assume quadratic or piecewise quadratic cost curves of power generators but modern generating units have non-linearities which make this assumption inaccurate. Evolutionary optimization methods such as genetic algorithms (GA) and particle swarm optimization (PSO) are free from convexity assumptions and succeed in achieving near global solutions due to their excellent parallel search capability. But these methods usually tend to converge prematurely to a local minimum solution, particularly when the search space is irregular. To tackle this problem ''crazy particles'' are introduced and their velocities are randomized to maintain momentum in the search and avoid saturation. The performance of the PSO with crazy particles has been tested on two model test systems, compared with GA and classical PSO and found to be superior.
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paper_title: Application of Swarm-Based Optimization Algorithms for Solving Dynamic Economic Load Dispatch Problem

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Dynamic economic load dispatch is one of the most important roles of power generation’s operation and control. It determines the optimal controls of production of generator units with predicted load demand over a certain period of time. Economic dispatch at minimum production cost is one of the most important subjects in the power network’s operation, which is a complicated nonlinear constrained optimization problem. Since dynamic economic load dispatch was introduced, several intelligent methods have been used to solve this problem. In this paper, an Improved Particle Swarm Optimizer (IPSO) and Water Cycle optimizer (WCO), as swarm-based optimization algorithms, have been proposed to solve dynamic economic load dispatch problem and their results compare with each other. These algorithms are applied to a dynamic economic dispatch problem for 6-unit power systems with a 24-h load demand at each one hour time intervals. The goal of the research is categorized in two parts; first of all, introduction of application of new heuristic method for solving economic load dispatch problem and second, comparison between two swarm-based algorithms. Obtained results show that WCO is very fast and also reach to better results and minimum.
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paper_title: Improved particle swarm optimization approach for nonconvex static and dynamic economic power dispatch

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The cost of power generation in fossil fuel plants is very high and economic dispatch helps in saving a significant amount of revenue. For practical generators the economic dispatch problem gets translated into a complex non-convex, multimodal optimization problem which can not be solved by traditional gradient based optimization methods. The complexity further increases due to the multiple constraints that need to be satisfied. This paper proposes an improved particle swarm optimization approach (IPSO) for solving nonconvex static and dynamic economic dispatch. The classical PSO (CPSO) approach suffers from the problem of premature convergence, particularly for complex multimodal functions. The idea behind IPSO is i) to enhance the search capability of the CPSO by reinitializing the velocity vector whenever saturation sets in and ii) to use a parameter automation strategy to strike a proper balance between local and global search. The performance of IPSO has been tested on five standard test cases. The results are compared with previously published literature and are found to be comparable/or superior.
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paper_title: Chaotic Adaptive Particle Swarm Optimisation using logistics and Gauss map for solving cubic cost economic dispatch problem

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This paper proposes Chaotic Adaptive Particle Swarm Optimisation (CAPSO) algorithm to solve Cubic Cost Economic Dispatch (CCED) problem. A Chaotic Local Search operator (CLS) is introduced in the proposed algorithm to avoid premature convergence. The basic strategy of the proposed algorithm is combining PSO with Adaptive Inertia Weight Factor (AIWF) and CLS, in which PSO with AIWF is applied to perform global exploration and CLS is used to perform exploitation to find the optimal solution. Logistics and Gauss map technique is used in performing CLS and the results are compared. The applicability and high feasibility of the proposed method is validated on a standard 5-generator test system. The simulation results confirm that this algorithm is capable of giving higher quality solutions with fast convergence characteristics.
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paper_title: Chaotic particle swarm optimization for economic dispatch considering the generator constraints

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Abstract Chaotic particle swarm optimization (CPSO) methods are optimization approaches based on the proposed particle swarm optimization (PSO) with adaptive inertia weight factor (AIWF) and chaotic local search (CLS). In this paper, two CPSO methods based on the logistic equation and the Tent equation are presented to solve economic dispatch (ED) problems with generator constraints and applied in two power system cases. Compared with the traditional PSO method, the convergence iterative numbers of the CPSO methods are reduced, and the solutions generation costs decrease around 5 $/h in the six unit system and 24 $/h in the 15 unit system. The simulation results show that the CPSO methods have good convergence property. The generation costs of the CPSO methods are lower than those of the traditional particle swarm optimization algorithm, and hence, CPSO methods can result in great economic effect. For economic dispatch problems, the CPSO methods are more feasible and more effective alternative approaches than the traditional particle swarm optimization algorithm.
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paper_title: A novel weight-improved particle swarm optimization algorithm for optimal power flow and economic load dispatch problems

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The optimization problems of optimal power flow (OPF) and the economic load dispatch (ELD) with valve-point effects in power systems are recently solved by some types of artificial intelligent (AI) algorithms. In this paper, based on improving the function of weight parameters, we present a novel weight-improved particle swarm optimization (WIPSO) method for computing two above problems. To evaluate the accuracy, convergence speed and applicability of the proposed method, we first compare the OPF results of proposed method to those of traditional particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), ant colony optimization (ACO) methods on the standard IEEE 30-bus system. We second compare our results of ELD problem to those of classical evolutionary programming (CEP), improved fast evolutionary programming (IFEP), and various improved particle swarm optimization methods on the IEEE 13-unit and 40-unit systems. The tested results indicate that the proposed method is more efficient than the others in terms of total fuel costs, total losses and computational times. Thus it can be applied to large power systems.
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paper_title: Constrained dynamic economic dispatch solution using particle swarm optimization

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This paper proposes using the particle swarm optimization (PSO) to solve the constrained dynamic economic dispatch (DED) problem in power system operation. The constrained DED must not only satisfy the system load demand and the spinning reserve capacity, but some practical operation constraints of generators, such as ramp rate limits and prohibited operating zone, are also considered in practical generator operation. The feasibility of the proposed PSO method is demonstrated for two power systems, and it is compared with the other stochastic methods in terms of solution quality and computation efficiency. The experimental results showed that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in constrained DED problems.
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paper_title: A Simulated Annealing-Based Goal-Attainment Method for Economic Emission Load Dispatch with Nonsmooth Fuel Cost and Emission Level Functions

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A novel multiobjective optimization method for economic emission load dispatch (EELD) with nonsmooth fuel cost and emission level functions in power system operation andscheduling phases is presented. In this paper, the problem treats economy, emission, and transmission line security as competing objectives. The load constraints and operating constraints are taken into account. Assuming that the decision maker (DM) has goals for each of the objective functions, the multiobjective problem is converted into a single-objective optimization by the goal-attainment method, which is then handled by the simulated annealing (SA) technique. The solution methodology can offer a global or near-global noninferior (best compromising) solution in a sense close to the DM's requirements. Results for a sample test system have been presented to demonstrate the applicability and validity of the proposed method.
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paper_title: A novel crazy swarm optimized economic load dispatch for various types of cost functions

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Economic load dispatch (ELD) is the scheduling of generators to minimize the total operating cost depending on equality and inequality constraints. The transmission line loss also is to be kept as minimum as possible. So, the problem is of multi-objective optimization. The authors have studied the comparative effectiveness of GA, Improved fast EP (IFEP) and various particle swarm optimizations (PSO) reported in the literature and a novel particle swarm algorithm namely CRAZYPSO for such multi-objective optimization in two test cases. The first test case deals with some well-known Benchmark functions and then the second case deals with a general power system having 40 thermal generating units with non-monotonically increasing cost functions with valve point loadings and other constraints. The generators are interconnected through lossy transmission lines. The proposed method out performs and provides true global optimal solutions as compared to other existing techniques for economic load dispatch.
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paper_title: Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem

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Abstract This paper presents an advanced parallelized particle swarm optimization algorithm with modified stochastic acceleration factors (PSO-MSAF) to solve large scale economic dispatch (ED) problems with prohibited operating zones, ramp-rate limits and transmission losses. In this parallel algorithm, the range within which the random cognitive and social learning parameters are to be chosen is bounded. Different values for these boundaries are tried simultaneously using multiple workers in a parallel computing environment with a manger scheduling the tasks to the workers. The results produced by these workers are subsequently compared and the best result is given as the final optimal solution. This algorithm prevents premature convergence and achieves better speed up, especially for large scale ED problems, mitigating the burden of multimodality and heavy computation. To improve the performance of the proposed algorithm, penalty parameter-less constraint handling scheme is employed to handle power balance, prohibited operating zones and ramp-rate limits. The dispatch results obtained by this algorithm satisfy Karush–Kuhn–Tucker (KKT) conditions, conforming optimality. The KKT-based error metric termination criterion is implemented for successful termination of the proposed algorithm. The proposed architecture effectively controls the local search ability thereby leading to better convergence towards the true optimal solution.
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paper_title: Solving nonconvex economic load dispatch problem using particle swarm optimization with time varying acceleration coefficients

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This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve-point effects, multi-fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3-machines 6-bus, IEEE 5-machines 14-bus, IEEE 6-machines 30-bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve-point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity, 2015
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paper_title: Variable Acceleration Coefficient-based Particle Swarm Optimization for Non-Convex Economic load dispatch problem

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This paper presents Variable Acceleration Coefficient-based Particle Swarm Optimization (VACPSO) method to solve the economic load dispatch for minimizing fuel cost while considering prohibited operating zones and valve point effect. The proposed VACPSO is a modified version of the conventional Particle Swarm Optimization (PSO). Three modifications are suggested in the proposed VACPSO. First, the cognitive behavior of particle is influenced by best and worst experience. Second, three acceleration coefficients, instead of two as in the conventional PSO, are suggested. Third, the acceleration coefficients are made variable rather than assigning them merely a fixed value. These suggested modifications facilitate better exploration of the search space with less computational burden. The proposed method is tested on two standard generating systems available in the literature. The application results and comparison with other recent approaches show that the proposed approach provides good quality solution with less computational time.
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paper_title: Iteration particle swarm optimization procedure for economic load dispatch with generator constraints

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In this paper, iteration particle swarm optimization (IPSO) has been applied to determine the feasible optimal solution of the economic load dispatch (ELD) problem considering various generator constraints. Many realistic constraints, such as ramp rate limits, generation limitation, prohibited operating zone, transmission loss and nonlinear cost functions are all considered for practical operation. The performance of the classical particle swarm optimization (CPSO) greatly depends on its parameters, and it often suffers the problem of being trapped in local optima. A new index named, Iteration Best, is incorporated in CPSO to enrich the searching behavior, solution quality and to avoid being trapped into local optimum. Two test power systems, including 6 and 15 unit generating, are applied to compare the performance of the proposed algorithm with PSO, chaotic PSO, hybrid GAPSO, self organizing hierarchical PSO (SOH_PSO) methods. The numerical results affirmed the robustness and proficiency of proposed approach over other existing methods.
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paper_title: Modified iteration particle swarm optimization procedure for economic dispatch solving with non-smooth and non-convex fuel cost function

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This paper proposes a novel technique named modified iteration particle swarm optimization for finding possible optimal solution in the economic load dispatch problem considering non-convex and non-smooth fuel cost function. Many constrains such as ramp rate limits, transmission losses and prohibited operating zones are considered. The valve point effects with nonlinear cost function in non-convex economic dispatch are also considered. Classical particle swarm optimization (CPSO) highly depends on its parameters and often suffers from being involved in local optima. The proposed approach incorporates two new index named “first iteration best” and “second iteration best” in CPSO. It results that searching behavior is enhanced and solution quality is promoted. To ensure the efficiency of the proposed approach, it is applied for four test system including 3, 6, 13 and 15 units. From the simulation results, the capabilities and effectiveness of the proposed approach compared with existing methods is confirmed.
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paper_title: Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch

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The economic dispatch has the objective of generation allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. Conventional optimization methods assume generator cost curves to be continuous and monotonically increasing, but modern generators have a variety of nonlinearities in their cost curves making this assumption inaccurate, and the resulting approximate dispatches cause a lot of revenue loss. Evolutionary methods like particle swarm optimization perform better for such problems as no convexity assumptions are imposed, but these methods converge to sub-optimum solutions prematurely, particularly for multimodal problems. To handle the problem of premature convergence, this paper proposes to apply a novel self-organizing hierarchical particle swarm optimization (SOH_PSO) for the nonconvex economic dispatch (NCED). The performance further improves when time-varying acceleration coefficients are included. The results show that the proposed approach outperforms previous methods for NCED.
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paper_title: A hybrid particle swarm optimisation with social weight for non-convex economic dispatch problem

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This paper presents a hybrid particle swarm optimisation with social weight HSWPSO to solve the economic dispatch ED problem in power system. Due to equality constraints and non-convex characteristics in ED problem, HSWPSO employs social weight factor, extremum disturbance operator and correction operator to overcome difficulties. The social weight factor is used to improve the global and local search ability of the swarm. The extremum disturbance operator helps trapped particles escape from the local optima. The correction operator ensures the position of particle satisfy the power balance equation. HSWPSO algorithm is applied to two kinds of ED problems, namely ED with valve-point effects and ED with multiple fuels. Experiment results show the effectiveness and feasibility of HSWPSO.
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paper_title: Automatic generation control application with craziness based particle swarm optimization in a thermal power system

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In this study, a novel gain scheduling Proportional-plus-Integral (PI) control strategy is suggested for automatic generation control (AGC) of the two area thermal power system with governor dead-band nonlinearity. In this strategy, the control is evaluated as an optimization problem, and two different cost functions with tuned weight coefficients are derived in order to increase the performance of convergence to the global optima. One of the cost functions is derived through the frequency deviations of the control areas and tie-line power changes. On the other hand, the other one includes the rate of changes which can be variable depends on the time in these deviations. These weight coefficients of the cost functions are also optimized as the controller gains have been done. The craziness based particle swarm optimization (CRAZYPSO) algorithm is preferred to optimize the parameters, because of convergence superiority. At the end of the study, the performance of the control system is compared with the performance which is obtained with classical integral of the squared error (ISE) and the integral of time weighted squared error (ITSE) cost functions through transient response analysis method. The results show that the obtained optimal PI-controller improves the dynamic performance of the power system as expected as mentioned in literature.
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paper_title: Optimization of economic load dispatch of higher order general cost polynomials and its sensitivity using modified particle swarm optimization

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Abstract This paper presents a modified particle swarm optimization (MPSO) for constrained economic load dispatch (ELD) problem. Real cost functions are more complex than conventional second order cost functions when multi-fuel operations, valve-point effects, accurate curve fitting, etc., are considering in deregulated changing market. The proposed modified particle swarm optimization (PSO) consists of problem dependent variable number of promising values (in velocity vector), unit vector and error–iteration dependent step length. It reliably and accurately tracks a continuously changing solution of the complex cost function and no extra concentration/effort is needed for the complex higher order cost polynomials in ELD. Constraint management is incorporated in the modified PSO. The modified PSO has balance between local and global searching abilities, and an appropriate fitness function helps to converge it quickly. To avoid the method to be frozen, stagnated/idle particles are reset. Sensitivity of the higher order cost polynomials is also analyzed visually to realize the importance of the higher order cost polynomials for the optimization of ELD. Finally, benchmark data sets and methods are used to show the effectiveness of the proposed method.
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paper_title: Dynamic adaptive bacterial foraging algorithm for optimum economic dispatch with valve-point effects and wind power

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This study presents a dynamically adapted bacterial foraging algorithm (BFA) to solve the economic dispatch (ED) problem considering valve-point effects and power losses. In addition, wind power is included in the problem formulation. Renewable sources and wind energy in particular have recently been getting more interest because of various environmental and economical considerations. The original BFA is a recently developed evolutionary optimisation technique inspired by the foraging behaviour of the Escherichia coli bacteria. The basic BFA has been successfully implemented to solve small optimisation problems; however, it shows poor convergence characteristics for larger constrained problems. To deal with the complexity and high-dimensioned search space of the ED problem, essential modifications are introduced to enhance the performance of the algorithm. The basic chemotactic step is adjusted to have a dynamic non-linear behaviour in order to improve balancing the global and local search. The stopping criterion of the original BFA is also modified to be adaptive depending on the solution improvement instead of the preset maximum number of iterations. The proposed algorithm is validated using several test systems. The results are compared with those obtained by other algorithms previously applied to solve the problem considering valve-point effects and power losses in addition to wind power.
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paper_title: A particle swarm optimization-based method for multiobjective design optimizations

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A particle swarm optimization (PSO) based algorithm for finding the Pareto solutions of multiobjective design problems is proposed. To enhance the global searching ability of the available PSOs, a novel formula for updating the particles' velocity and position, as well as the introduction of craziness, are reported. To handle a multiobjective design problem using the improved PSO, a new fitness assignment mechanism is proposed. Moreover, two repositories, together with the age variables for their members, are introduced for storing and selecting the previous best positions of the particle as well as that of its companions. Besides, the use of age variables to enhance the diversity of the solutions is also described. The proposed method is tested on two numerical examples with promising results.
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paper_title: Economic Dispatch Problem using Bat Algorithm

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A BAT algorithm to solve the economic dispatch problem is presented in this paper. The modern power system has become very complex in nature with consumption of the electric power which is in rise progression and this tendency increases with the industrialization and the growth of the population. Moreover, one loss of alimentation can cause the interruption of the various production processes, and in front of consumers who become increasingly demanding by wanting more energy and better quality, the companies of production of electrical energy must thus ensure the regular provisioning of this request, and without interruption, but these requirements compromise the cost of generation. Application of BAT algorithm in this paper is based on mathematical modeling to solve economic dispatch problems by a single equivalent objective function. The algorithm is tested on 6-unit system. BAT algorithm is easy to implement and better than other algorithms in terms of accuracy and efficiency.
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paper_title: Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients

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This paper introduces a novel parameter automation strategy for the particle swarm algorithm and two further extensions to improve its performance after a predefined number of generations. Initially, to efficiently control the local search and convergence to the global optimum solution, time-varying acceleration coefficients (TVAC) are introduced in addition to the time-varying inertia weight factor in particle swarm optimization (PSO). From the basis of TVAC, two new strategies are discussed to improve the performance of the PSO. First, the concept of "mutation" is introduced to the particle swarm optimization along with TVAC (MPSO-TVAC), by adding a small perturbation to a randomly selected modulus of the velocity vector of a random particle by predefined probability. Second, we introduce a novel particle swarm concept "self-organizing hierarchical particle swarm optimizer with TVAC (HPSO-TVAC)". Under this method, only the "social" part and the "cognitive" part of the particle swarm strategy are considered to estimate the new velocity of each particle and particles are reinitialized whenever they are stagnated in the search space. In addition, to overcome the difficulties of selecting an appropriate mutation step size for different problems, a time-varying mutation step size was introduced. Further, for most of the benchmarks, mutation probability is found to be insensitive to the performance of MPSO-TVAC method. On the other hand, the effect of reinitialization velocity on the performance of HPSO-TVAC method is also observed. Time-varying reinitialization step size is found to be an efficient parameter optimization strategy for HPSO-TVAC method. The HPSO-TVAC strategy outperformed all the methods considered in this investigation for most of the functions. Furthermore, it has also been observed that both the MPSO and HPSO strategies perform poorly when the acceleration coefficients are fixed at two.
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paper_title: Anti-predatory particle swarm optimization: Solution to nonconvex economic dispatch problems

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This paper proposes a new particle swarm optimization (PSO) strategy namely, anti-predatory particle swarm optimization (APSO) to solve nonconvex economic dispatch problems. In the classical PSO, the movement of a particle (bird) is governed by three behaviors: inertial, cognitive and social. The cognitive and social behaviors are the components of the foraging activity, which help the swarm of birds to locate food. Another activity that is observed in birds is the anti-predatory nature, which helps the swarm to escape from the predators. In this work, the anti-predatory activity is modeled and embedded in the classical PSO to form APSO. This inclusion enhances the exploration capability of the swarm. To validate the proposed APSO model, it is applied to two test systems having nonconvex solution spaces. Satisfactory results are obtained when compared with previous approaches.
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paper_title: Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO

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In this paper an improved coordinated aggregation-based particle swarm optimization (ICA-PSO) algorithm is introduced for solving the optimal economic load dispatch (ELD) problem in power systems. In the ICA-PSO algorithm each particle in the swarm retains a memory of its best position ever encountered, and is attracted only by other particles with better achievements than its own with the exception of the particle with the best achievement, which moves randomly. Moreover, the population size is increased adaptively, the number of search intervals for the particles is selected adaptively and the particles search the decision space with accuracy up to two digit points resulting in the improved convergence of the process. The ICA-PSO algorithm is tested on a number of power systems, including the systems with 6, 13, 15, and 40 generating units, the island power system of Crete in Greece and the Hellenic bulk power system, and is compared with other state-of-the-art heuristic optimization techniques (HOTs), demonstrating improved performance over them.
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paper_title: Economic Load Dispatch of Higher Order Cost Polynomials Using Modified Particle Swarm Optimization

paper_content:

This paper presents a modified particle swarm optimization (MPSO) for economic load dispatch (ELD) problem. Considering multifuel operations, valve-point effects, accurate curve fitting, etc., real cost function is more complex than a conventional second order cost function in the deregulated changing market. Modified PSO consists of problem dependent variable number of promising values (in velocity vector), unit vector, error-iteration dependent step length, etc. It reliably and accurately tracks a continuously changing solution of the complex cost function and no extra concentration/effort is needed for more complex higher order cost polynomial in ELD. Constraint management is incorporated in the modified PSO. The modified PSO has balance between local and global searching abilities, and an appropriate fitness function helps to converge it quickly. To avoid the method to be frozen, stagnated/idle particles are reset. In this paper, sensitivity of higher order cost polynomial is also analyzed visually to realize the importance of higher order cost polynomial in ELD. Finally, benchmark data and methods are used to show the effectiveness of the proposed method.
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paper_title: A New modified particle swarm Optimization (PSO) Technique for Non-Convex Economic Dispatch

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This paper gives a new modified technique for evaluating non-convex economic dispatch (NCED) problem having non-linear, discontinuous cost function. This new particle swarm optimization technique incorporates time varying acceleration coefficients (NPSOTVAC). The highly non-linear cost function due to ramp rate limit, prohibited operating zones and valve point loading effect is considered in the proposed method. The effectiveness of proposed NPSOTVAC algorithm is proved through test on 6 and 15 unit test systems.
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paper_title: Performance analysis of metaheuristic techniques for nonconvex economic dispatch

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Economic load dispatch (ELD) problem is an optimization problem where objective function is highly non linear, non-convex, non differentiable and may have multiple local minima. Therefore classical optimization methods may not convergence or get trapped to any local minima. This paper presents a comparative study of four different heuristic algorithms i.e. classical Particle swarm optimization (CPSO), Particle swarm optimization with Time-varying acceleration coefficients (PSOTVAC), Differential Evolution (DE) and Bacterial Foraging Optimization (BFO) for solving the ELD problem considering various constraints such as ramp rate limits (RRL), prohibited operating zones (POZ) and valve point effects (VPL). A detailed comparison of the various methods is carried out on three test systems having 3-unit, 13-unit and 40-units. Solution quality, convergence behavior, consistency and speed are used as performance metrics.
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paper_title: An Effective Particle Swarm Optimization Algorithm with Social Weight in Solving Economic Dispatch Problem Considering Network Losses

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This paper proposes an effective particle swarm optimization algorithm with social weight (ESWPSO) to solve economic dispatch problem in power system. Many nonlinear characteristics of cost function and operational constraints are all considered for practical operation. The extremum disturbance operator in ESWPSO effectively contributes to finding better solutions by generating random points in promising area. The penalty strategy is adopted to help particles satisfy the dynamic power balance constraints. The effectiveness and feasibility of ESWPSO are demonstrated by two power system cases. Compared with previous literature, the experiment results show ESWPSO can fast find higher quality solutions.
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paper_title: Iteration PSO with time varying acceleration coefficients for solving non-convex economic dispatch problems

paper_content:

This paper presents a novel heuristic algorithm for solving economic dispatch (ED) problems, by employing iteration particle swarm optimization with time varying acceleration coefficients (IPSO-TVAC) method. Due to the effect of valve-points and prohibited operation zones (POZs) in the generating units’ cost functions, ED problem is a non-linear and non-convex optimization problem. The problem even may be more complicated if transmission losses are taken into account. The effectiveness of the proposed method is examined and validated by carrying out extensive tests on three different test systems. Valve-point effects, POZs, ramp-rate constraints and transmission losses are modeled. Numerical results show that the IPSO-TVAC method has a good convergence property. Furthermore, the generation costs of the IPSO-TVAC method are lower than other optimization algorithms reported in recent literature.
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paper_title: Unit commitment with probabilistic reserve: An IPSO approach

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Abstract This paper presents a new algorithm for solution of the nonlinear optimal scheduling problem. This algorithm is named the iteration particle swarm optimization (IPSO). A new index, called iteration best, is incorporated into particle swarm optimization (PSO) to improve the solution quality and computation efficiency. IPSO is applied to solve the unit commitment with probabilistic reserve problem of a power system. The outage cost as well as fuel cost of thermal units was considered in the unit commitment program to evaluate the level of spinning reserve. The optimal scheduling of on line generation units was reached while minimizing the sum of fuel cost and outage cost. A 48 unit power system was used as a numerical example to test the new algorithm. The optimal scheduling of on line generation units could be reached in the testing results while satisfying the requirement of the objective function.
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paper_title: A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems

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This paper proposes a new version of the classical particle swarm optimization (PSO), namely, new PSO (NPSO), to solve nonconvex economic dispatch problems. In the classical PSO, the movement of a particle is governed by three behaviors, namely, inertial, cognitive, and social. The cognitive behavior helps the particle to remember its previously visited best position. This paper proposes a split-up in the cognitive behavior. That is, the particle is made to remember its worst position also. This modification helps to explore the search space very effectively. In order to well exploit the promising solution region, a simple local random search (LRS) procedure is integrated with NPSO. The resultant NPSO-LRS algorithm is very effective in solving the nonconvex economic dispatch problems. To validate the proposed NPSO-LRS method, it is applied to three test systems having nonconvex solution spaces, and better results are obtained when compared with previous approaches
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paper_title: Time-varying acceleration coefficients IPSO for solving dynamic economic dispatch with non-smooth cost function

paper_content:

Abstract The objective of the dynamic economic dispatch (DED) problem is to schedule power generation for the online units for a given time horizon economically, satisfying various operational constraints. Due to the effect of valve-point effects and prohibited operating zones (POZs) in the generating units cost functions, DED problem is a highly non-linear and non-convex optimization problem. The DED problem even may be more complicated if transmission losses and ramp-rate constraints are taken into account. This paper presents a novel and heuristic algorithm to solve DED problem of generating units, by employing time varying acceleration coefficients iteration particle swarm optimization (TVAC-IPSO) method. The effectiveness of the proposed method is examined and validated by carrying out extensive tests on different test systems, i.e. 5-unit and 10-unit test systems. Valve-point effects, POZs and ramp-rate constraints along with transmission losses are considered. To examine the efficiency of the proposed TVAC-IPSO algorithm, comprehensive studies are carried out, which compare convergence properties of the proposed TVAC-IPSO approach with conventional PSO algorithm, in addition to the other recently reported approaches. Numerical results show that the TVAC-IPSO method has good convergence properties and the generation costs resulted from the proposed method are lower than other algorithms reported in recent literature.
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paper_title: A Comparative Study on Particle Swarm Optimization for Optimal Steady-State Performance of Power Systems

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In this paper, three new particle swarm optimization (PSO) algorithms are compared with the state of the art PSO algorithms for the optimal steady-state performance of power systems, namely, the reactive power and voltage control. Two of the three introduced, the enhanced GPAC PSO and LPAC PSO, are based on the global and local-neighborhood variant PSOs, respectively. They are hybridized with the constriction factor approach together with a new operator, reflecting the physical force of passive congregation observed in swarms. The third one is based on a new concept of coordinated aggregation (CA) and simulates how the achievements of particles can be distributed in the swarm affecting its manipulation. Specifically, each particle in the swarm is attracted only by particles with better achievements than its own, with the exception of the particle with the best achievement, which moves randomly as a "crazy" agent. The obtained results by the enhanced general passive congregation (GPAC), local passive congregation (LPAC), and CA on the IEEE 30-bus and IEEE 118-bus systems are compared with an interior point (IP)-based OPF algorithm, a conventional PSO algorithm, and an evolutionary algorithm (EA), demonstrating the excellent performance of the proposed PSO algorithms
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paper_title: Modified Particle Swarm Optimization with Time Varying Acceleration Coefficients for Economic Load Dispatch with Generator Constraints

paper_content:

This paper proposes a Modified Particle Swarm Optimization with Time Varying Acceleration Coefficients (MPSO-TVAC) for solving economic load dispatch (ELD) problem. Due to prohibited operating zones (POZ) and ramp rate limits of the practical generators, the ELD problems become nonlinear and nonconvex optimization problem. Furthermore, the ELD problem may be more complicated if transmission losses are considered. Particle swarm optimization (PSO) is one of the famous heuristic methods for solving nonconvex problems. However, this method may suffer to trap at local minima especially for multimodal problem. To improve the solution quality and robustness of PSO algorithm, a new best neighbour particle called 'rbest' is proposed. The rbest provides extra information for each particle that is randomly selected from other best particles in order to diversify the movement of particle and avoid premature convergence. The effectiveness of MPSO-TVAC algorithm is tested on different power systems with POZ, ramp-rate limits and transmission loss constraints. To validate the performances of the proposed algorithm, comparative studies have been carried out in terms of convergence characteristic, solution quality, computation time and robustness. Simulation results found that the proposed MPSO-TVAC algorithm has good solution quality and more robust than other methods reported in previous work.
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paper_title: A New Improved Particle Swarm Optimization for Solving Nonconvex Economic Dispatch Problems

paper_content:

This paper proposes a new improved particle swarm optimization (NIPSO) for solving nonconvex economic dispatch (ED) problem in power systems including multiple fuel options (MFO) and valve-point loading effects (VPLE). The proposed NIPSO method is based on the self-organizing hierarchical (SOH) particle swarm optimizer with time-varying acceleration coefficients (TVAC). The self-organizing hierarchical can handle the premature convergence of the problem by re-initialization of velocity whenever particles are stagnated in the search space. During the optimization process, the performance of TVAC is applied for properly controlling both local and global explorations with cognitive component and social component of the swarm to obtain the optimum solution accurately and efficiently. The proposed NIPSO algorithm is tested in different types of non-smooth cost functions for solving ED problems and the obtained results are compared to those from many other methods in the literature. The results have revealed that the proposed NIPSO method is effective and feasible in finding higher quality solutions for non-smooth ED problems than many other methods.
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paper_title: Economic load dispatch using a differential particle swarm optimization

paper_content:

In this paper a novel differential particle swarm optimization (DPSO) algorithm is proposed. The proposed algorithm includes an additional term in the velocity equation of the classical particle swarm optimization (PSO) algorithm. The additional term in DPSO is the experience of a particle selected randomly from the swarm for a target particle. The difference of the selected and the target particle is scaled and added to the velocity equation which try the particle to escape from trapping into local minima. The proposed algorithm has been used to solve economic load dispatch (ELD) problem of the IEEE 10 unit system. The results obtained by DPSO have been validated by comparing the results obtained by PSO.
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paper_title: NEW INTELLIGENT PARTICLE SWARM OPTIMIZATION ALGORITHM FOR SOLVING ECONOMIC DISPATCH WITH VALVE-POINT EFFECTS

paper_content:

With increasing fuel prices and restructuring in the power industry, nonconvex economic dispatch (NED) is expected to become crucial because of nonsmooth cost functions. This paper presents an intelligent particle swarm optimization for economic dispatch with valve-point effect. A new index, another particle best (Pbestap), is incorporated into the particle swarm optimization to further improve social behavior. Moreover, a novel diversity-based judgment mechanism for evaluating Pbestap behavior is proposed for maintaining population diversity, which facilitates identification of the near-global region. The direct search algorithm is used to fine-tune and determine the eventual global optimal solution at low computational expense. Numerical experiments demonstrate that the proposed approach offers higher quality solutions than do several existing techniques.
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paper_title: A New Modified Shuffle Frog Leaping Algorithm for Non-Smooth Economic Dispatch

paper_content:

This paper presents an effective evolutionary method for solve economic dispatch (ED) with units having prohibited operating zones. ED has been widely used in power system operation and planning for determination of electricity prices. ED problem is a non smooth problem when valve point effects of generation units are considered. With addition the valve point effect and prohibited zones in ED problem this problem complicates more and more respect before and is needed to solve with a strong and accuracy algorithm. This paper presents a very robust algorithm (SLFA) to solve ED problem with valve point effect, furthermore in an attempt to reduce processing time and improve the quality of solutions, particularly to avoid being trapped in local optima, this paper present a modified SLFA that called MSLFA algorithm to solve ED problem. The performance of the MSFLA has been tested on two typical systems consisting of 6 and 40 thermal units and compared with conventional approaches such as genetic algorithm (GA), tabu search algorithm (TSA), PSO and others in literatures. The comparison results show that the efficiency of proposed approach can reach higher quality solution and faster computational time than the conventional methods.
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paper_title: An Analysis Of Economic Load Dispatch With Prohibited Zone Constraint Using Different Algorithms

paper_content:

Economic load dispatch (ELD) problem plays an important role in power system operation and control today. It is very popular optimization problem in advanced power system. Recently different soft computing techniques are being widely used in many practical applications. Here, fifteen thermal unit system has been considered. This problem has been solved by four types of PSO based optimization problem like particle swarm optimization technique(PSO), particle swarm optimization with constriction factor approach(PSOCFA), particle swarm optimization technique with inertia weight factor approach(PSOIWA) and particle swarm optimization technique with constriction factor and inertia weight factor approach(PSOCFIWA). In this problem, prohibited zone constraint has been considered. In this paper, successful implementation and effectiveness of four types of optimization technique has been shown to solve this problem. The comparative analysis of fuel cost through four optimization techniques has been discussed.
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paper_title: Comparison of PSO variants with traditional solvers for large scale multi-area economic dispatch

paper_content:

Economic load dispatch (ELD) has the objective of generation allocation to the power generators such that the total fuel cost is minimized and all operating constraints are satisfied. Generally ELD is solved without accounting for transmission constraints, however, in deregulated power system environment it is essential to include practical multi-area cases with tie line constraints. A number of traditional methods are used for solving ELD and other power system problems. During the last decade soft computing methods like particle swarm optimization (PSO), have been increasingly proposed for complex optimization problems. This paper proposes some improved PSO technique in which premature convergence is avoided by tuning the PSO parameters for enhanced global and local search. The paper reviews and compares the performance of the proposed PSO variants with traditional solver GAMS for multi-area economic dispatch (MAED) on four standard test systems having different sizes and complexity levels. A large 120-unitpower system is included for validating the results.
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paper_title: Dynamically controlled particle swarm optimization for large-scale nonconvex economic dispatch problems

paper_content:

SUMMARY ::: ::: This paper proposes a dynamically controlled particle swarm optimization method to solve nonconvex economic dispatch problem of large dimensions. It essentially aims to improve the performance of the conventional particle swarm optimization by suggesting improved cognitive and social components of the particle's velocity through preceding and aggregate experience of the swarm, respectively. The control parameters of the governing equation are controlled dynamically by introducing new exponential functions. The overall methodology effectively regulates the velocity of the particles during their whole course of flight and results in substantial improvement. The effectiveness of the proposed method has been investigated on 40 generators and 140 generators test generating systems by considering general operational constraints. The application results show that the proposed method is very promising to solve large-dimensional economic dispatch problems. Copyright © 2014 John Wiley & Sons, Ltd.
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paper_title: Particle swarm optimization of economic dispatch problem: A brief review transfer

paper_content:

Electrical energy production has changed various features of the energy manufacturing. According to this ::: ::: map, lack of energy supplies, improving energy cost, environment matter, require optimal economic dispatch. ::: ::: Economic load dispatch (ED) problem is essentially nonlinear. Since we know that the traditional methods ::: ::: donot have the ability to solve problems like this for reasons such as caught up in the trap of local optimal ::: ::: point or low convergence speed. Therefore, the use of algorithms that are more powerful is inevitable. An ::: ::: efficient algorithm for solving ED problem is particle swarm optimization considering to its fast convergence ::: ::: to global optima and computationally efficiency. PSO based algorithms has achieved a pluperfect ::: ::: identification of the best solution for such kind of EDPs in last decade. In this paper, we try various techniques ::: ::: associated with PSO, fully checked.
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paper_title: STOCHASTIC WEIGHT TRADE-OFF PARTICLE SWARM OPTIMIZATION FOR NONCONVEX ECONOMIC DISPATCH

paper_content:

Abstract This paper proposes a stochastic weight trade-off particle swarm optimization (SWT_PSO) for solving nonconvex economic dispatch. The proposed SWT_PSO preserves the balance between global exploration and local exploitation to improve the algorithm search capabilities. The balance is retained through trading off stochastic weights amongst previous velocity momentum, cognitive and social components together with using dynamic acceleration coefficients trade-off. The mechanisms for increasing diversity of swarm members are also incorporated to avoid premature convergence. In addition, the novel stochastic trade-off momentum control factor is exploited to enhance the capability of refining quality of a candidate solution during the late search process. The proposed SWT_PSO is tested on four economic dispatch test systems. Test results demonstrate that the proposed approach yields better solution quality than the best reported results in the literature for all test systems.
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paper_title: An analysis of economic load dispatch with prohibited zone and ramp-rate limit constraints using different algorithms

paper_content:

The economic load dispatch (ELD) plays an important role in power system operation and control. Different techniques have been used to solve these problems. Recently, the soft computing techniques have widely used in practical applications. This paper shows successful implementation of four evolutionary algorithms, namely particle swarm optimization (PSO), particle swarm optimization with constriction factor approach (PSOCFA), particle swarm optimization with inertia weight factor approach (PSOIWA) and particle swarm optimization with constriction factor and inertia weight factor approach (PSOCFIWA) algorithms are used to economic load dispatch problem. Here prohibited zone and ramp-rate limit constraints are considered to solve this problem. Power output of each generating unit and optimum fuel cost obtained using all four algorithms have been compared.
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paper_title: A particle swarm optimization-based method for multiobjective design optimizations

paper_content:

A particle swarm optimization (PSO) based algorithm for finding the Pareto solutions of multiobjective design problems is proposed. To enhance the global searching ability of the available PSOs, a novel formula for updating the particles' velocity and position, as well as the introduction of craziness, are reported. To handle a multiobjective design problem using the improved PSO, a new fitness assignment mechanism is proposed. Moreover, two repositories, together with the age variables for their members, are introduced for storing and selecting the previous best positions of the particle as well as that of its companions. Besides, the use of age variables to enhance the diversity of the solutions is also described. The proposed method is tested on two numerical examples with promising results.
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paper_title: Economic load dispatch using improved particle swarm optimization algorithms

paper_content:

The main objective of Economic Load Dispatch (ELD) problem is to schedule the connected generating units of plant outputs so as to fulfill load demands at minimum operating cost while satisfying all operational constraints. Recently particle swarm optimization algorithms inspired by collective behavior of swarm has been applied successfully to solve ELD problem. It is a population based stochastic optimization process driven by the simulation of a social psychological metaphor. In this paper three improved PSO algorithms- IPSO-A, IPSO-B and IPSO-C have been developed and implemented to solve ELD for IEEE 5, 14 and 30 bus systems. Conventional PSO (CPSO) using inertia weight and constriction factor individually as well as simultaneously have been also implemented to solve ELD problem. PSO algorithms have been compared for twenty trial runs. The best, worst, average fitness and their standard deviation for all the algorithms have been determined. The results show that proposed improved PSO techniques gives the optimum operating cost with consistent results in terms of diversity of results.
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paper_title: Empirical study of particle swarm optimization for economic load dispatch with valve-point effects

paper_content:

This paper empirically studies the performance of the particle swarm optimization (PSO) technique. A practical test system in power system studies is selected as a testing function. The test system takes into account the valve-point effects. The study aims to tune four main parameters involved in the PSO implementation in a typical economic load dispatch problem. The experimental results illustrate the best values to be chosen for PSO's different parameters. The various ranges of a penalty factor were tested and the paper determines which range of values is best suited in the tested economic dispatch problem.
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paper_title: Nonconvex Economic Dispatch Using Particle Swarm Optimization with Time Varying Operators

paper_content:

This paper presents a particle swarm optimization (PSO) to solve hard combinatorial constrained optimization problems such as nonconvex and discontinuous economic dispatch (ED) problem of large thermal power plants. Several measures have been suggested in the control equation of the classical PSO by modifying its operators for better exploration and exploitation. The inertia operator of the PSO is modulated by introducing a new truncated sinusoidal function. The cognitive and social behaviors are dynamically controlled by suggesting new exponential constriction functions. The overall methodology effectively regulates the velocity of particles during their flight and results in substantial improvement in the classical PSO. The effectiveness of the proposed method has been tested for economic load dispatch of three standard test systems considering various operational constraints like valve-point loading effect, prohibited operating zones (POZs), network power loss, and so forth. The application results show that the proposed PSO method is very promising.
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paper_title: Multi-area Economic Dispatch Using Improved Particle Swarm Optimization

paper_content:

Abstract This paper presents improved PSO (IPSO) to solve Multi Area Economic Dispatch (MAED) problem. The objective of MAED problem is to determine the optimal value of power generation and interchange of power through tie-lines interconnecting areas in such a way that total fuel cost of thermal generating units of all areas is minimized while satisfying operational constraints. The control equation of the proposed PSO is modified by suggesting improved cognitive component of the particle's velocity by suggesting preceding experience. The operating parameters of the control equation are also modified to maintain a better balance between cognitive and social behavior of the swarm. The effectiveness of the proposed method has been tested on four areas, 40 generators test system. The application results show that IPSO is very promising to solve large-dimensional MAED problem.
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paper_title: Economic Dispatch resolution using Adaptive Acceleration Coefficients based PSO considering generator constraints

paper_content:

The Economic Dispatch (ED) is one of the main concerns for the operation of power systems. Several methods have been applied to solve such problem. Unfortunately, the conventional methods are not suitable to deal with this optimization issue because of the practical operating constraints of generators. This paper present an improved Particle Swarm Optimization (PSO) method based on a variation of acceleration coefficients according to iteration number and adaptively with cognitive and social best positions of the swarm. The new approach is founded on Adaptive Acceleration Coefficients (AAC) based PSO and tested on two power systems contain 6 and 15 generating units. The algorithm is compared with other heuristic optimization techniques as demonstrating improved performance and effectiveness over them.
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paper_title: An analysis of economic load dispatch using different algorithms

paper_content:

The economic load dispatch (ELD) plays an important role in power system operation and control. Different techniques have been used to solve these problems. Recently, the soft computing techniques have widely used in practical applications. This paper shows successful implementation of four evolutionary algorithms, namely particle swarm optimization (PSO), particle swarm optimization with constriction factor approach (PSOCFA), particle swarm optimization with inertia weight factor approach (PSOIWA) and particle swarm optimization with constriction factor and inertia weight factor approach (PSOCFIWA) algorithms to economic load dispatch problem. Power output of each generating unit and optimum fuel cost obtained using all four algorithms have been compared.
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paper_title: An analysis of economic load dispatch with ramp-rate limit constraints using different algorithms

paper_content:

The economic load dispatch (ELD) plays an important role in power system operation and control. Different techniques have been used to solve these problems. Recently, the soft computing techniques have widely used in practical applications. This paper shows successful implementation of four evolutionary algorithms, namely particle swarm optimization (PSO), particle swarm optimization with constriction factor approach (PSOCFA), particle swarm optimization with inertia weight factor approach (PSOIWA) and particle swarm optimization with constriction factor and inertia weight factor approach (PSOCFIWA) algorithms. Here ramp-rate limit constraints are considered to solve this problem. Here three cases have been considered. Four algorithms have been applied for each case. Optimum fuel cost is taken from each algorithm is compared for each cases (Case study I, II and III).
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paper_title: Optimal generation expansion planning via the Cross-Entropy method

paper_content:

The Generation Expansion Planning (GEP) problem is a highly constrained, large-scale, mixed integer nonlinear programming problem. The objective of the GEP problem is to evaluate the least cost investment plan for addition of power generating units over a planning period subject to demand, availability, and security constraints. In this paper, a GEP model is presented and the Cross-Entropy (CE) optimization method is developed to solve the problem. The CE method is an effective algorithm for solving large combinatorial optimization problems. The main advantage of the CE method over other metaheuristic techniques is that it does not require decomposition of the problem into a master problem and operation subproblems, greatly reducing the computational complexity. This method also provides a fast and reliable convergence to the optimal solution.
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paper_title: Minimization of fuel cost in solving the power economic dispatch problem including transmission losses by using modified Particle Swarm Optimization

paper_content:

Under normal operating conditions, the generation capacity is more than the total load demand and losses. The objective is to find the real power scheduling of each generator for an interconnected power system under testing condition to minimize the operating cost of the power plant. Hence the generators power are allowed to vary within the given limits to meet the particular load with minimum fuel cost which is called as optimal power flow problem. The objective function of this paper is to minimize the fuel cost of the power system for the various loads under consideration by solving the economic dispatch problem (EDP) of real power generation by using MPSO optimization algorithm. This paper compares the optimization techniques such as Particle Swarm Optimization, Modified Particle Swarm Optimization (MPSO) in a 3-unit generating system to show the effectiveness of the MPSO algorithm. Also by using the optimization technique the power losses of the considered power system were reduced.
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paper_title: Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches

paper_content:

Abstract The objective of the Economic Dispatch Problems (EDPs) of electric power generation is to schedule the committed generating units outputs so as to meet the required load demand at minimum operating cost while satisfying all units and system equality and inequality constraints. Recently, global optimization approaches inspired by swarm intelligence and evolutionary computation approaches have proven to be a potential alternative for the optimization of difficult EDPs. Particle swarm optimization (PSO) is a population-based stochastic algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Inspired by the swarm intelligence and probabilities theories, this work presents the use of combining of PSO, Gaussian probability distribution functions and/or chaotic sequences. In this context, this paper proposes improved PSO approaches for solving EDPs that takes into account nonlinear generator features such as ramp-rate limits and prohibited operating zones in the power system operation. The PSO and its variants are validated for two test systems consisting of 15 and 20 thermal generation units. The proposed combined method outperforms other modern metaheuristic optimization techniques reported in the recent literature in solving for the two constrained EDPs case studies.
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paper_title: A clonal algorithm to solve economic load dispatch

paper_content:

This paper presents a novel optimization approach to constrained economic load dispatch (ELD) problem using artificial immune system (AIS). The approach utilizes the clonal selection principle and evolutionary approach wherein cloning of antibodies is performed followed by hypermutation. The proposed methodology easily takes care of transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones and also accounts for non-smoothness of cost function arising due to the use of multiple fuels. Simulations were performed over various systems with different number of generating units and comparisons are performed with other prevalent approaches. The findings affirmed the robustness, fast convergence and proficiency of proposed methodology over other existing techniques.
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paper_title: Modified particle swarm optimization for nonconvex economic dispatch problems

paper_content:

Abstract This paper presents modified particle swarm optimization to solve economic dispatch problems with non-smooth/non-convex cost functions. Particle swarm optimization performs well for small dimensional and less complicated problems but fails to locate global minima for complex multi-minima functions. This paper proposes Gaussian random variables in velocity term which improves search efficiency and guarantees a high probability of obtaining the global optimum without considerably worsening the speed of convergence and the simplicity of the structure of particle swarm optimization. The efficacy of the proposed method has been demonstrated on four test problems and four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods reported in the literature. It is found that the proposed modified particle swarm optimization based approach is able to provide better solution.
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paper_title: Democratic PSO for truss layout and size optimization with frequency constraints

paper_content:

This paper represents a new algorithm for structural optimization with frequency constraints. The new algorithm is termed Democratic Particle Swarm Optimization. The emphasis is placed upon alleviating the premature convergence phenomenon which is believed to be one of flaws of the original PSO. When considering frequency constraints in a structural optimization problem, the search spaces happen to be highly non-linear and non-convex hyper-surfaces with numerous local optima and naturally the problem of premature convergence is amplified. The proposed algorithm is capable of coping with this problem. Four numerical examples are presented to demonstrate the viability of the algorithm.
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paper_title: Improved Particle Swarm Optimization Based Dynamic Economic Dispatch of Power System

paper_content:

To realize the sustainable development, the manufactories/plants must have efficient management/schedule plan and control methods for systems from the aspects of economy, environment and social community. The optimization algorithms are necessary to obtain the optimal or sub-optimal solutions for the manufactories/plants. As one of the most important systems, the power systems play very important role in world. Most of the generators consume the natural resources such as coal, gas, petrol and nuclear materials, and it is very important that the generators do not waste the natural resources and meet the needs of human beings. Hence it is very important to get an optimal or acceptable sub-optimal dynamical economic dispatch, which determines the optimal generation scheme to meet the predicted load demand over a time horizon satisfying the constraint such as ramp-rate limits of generators between time intervals, for a power system which may involve conventional generators and some other alternate sources (solar, wind) of energy. Since power systems are very complicated and there are many constraints, it is difficult to find the optimal solution(s) based on the classical mathematical methods. In the past several decades, there are many kinds of evolutionary optimization algorithms which have been proposed. As one of the nature-inspired meta-heuristic algorithms, Particle Swarm Optimization (PSO) and its variants have shown its advantages in many applications. In this paper we propose a random dimension velocity updated PSO. Simulations are used to test the proposed PSO based several benchmark functions and then the proposed PSO is applied to the dynamic economic dispatch problems of power system. All the simulation results prove the efficiency of the proposed method.
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paper_title: A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch

paper_content:

Abstract Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the chaotic systems theory, this paper proposed a novel chaotic PSO combined with an implicit filtering (IF) local search method to solve economic dispatch problems. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed PSO introduces chaos mapping using Henon map sequences which increases its convergence rate and resulting precision. The chaotic PSO approach is used to produce good potential solutions, and the IF is used to fine-tune of final solution of PSO. The hybrid methodology is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. Simulation results are promising and show the effectiveness of the proposed approach.
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paper_title: Non-convex Economic Dispatch using Trelea Particle Swarm Optimization

paper_content:

Based in the importance of the Economic Dispatch for operation and planning of power systems, this paper presents the Trelea Particle Swarm Optimization method (Trelea-PSO) applied to this issue. In this paper the ED problem is modeled considering the valve-point effects and multiple fuels, though a non-convex function. Study cases composed of two 10 thermal generators systems are presented to validate the proposed methodology. The results obtained was compared to others presented in literature.
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paper_title: An improved PSO for dynamic load dispatch of generators with valve-point effects

paper_content:

Dynamic load economic dispatch problem (DLED) is important in power systems operation, which is a complicated nonlinear constrained optimization problem. It has nonsmooth and nonconvex characteristics when generator valve-point effects are taken into account. This paper proposes an improved particle swarm optimization (IPSO) to solve DLED with valve-point effects. In the proposed IPSO method, feasibility-based rules and heuristic strategies with priority list based on probability are devised to handle constraints effectively. In contrast to the penalty function method, the constraint-handling method does not require penalty factors or any extra parameters and can guide the population to the feasible region quickly. Especially, equality constraints of DLED can be satisfied precisely. Furthermore, the effects of two crucial parameters on the performance of the IPSO for DLED are also studied. The feasibility and the effectiveness of the proposed method are demonstrated applying it to some examples and the test results are compared with those of other methods reported in the literature. It is shown that the proposed method is capable of yielding higher-quality solutions.
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paper_title: A particle swarm optimization for economic dispatch with nonsmooth cost functions

paper_content:

This work presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. A constraint treatment mechanism is devised in such a way that the dynamic process inherent in the conventional PSO is preserved. Moreover, a dynamic search-space reduction strategy is devised to accelerate the optimization process. To show its efficiency and effectiveness, the proposed MPSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost functions considering valve-point effects and multi-fuel problems. The results of the MPSO are compared with the results of conventional numerical methods, Tabu search method, evolutionary programming approaches, genetic algorithm, and modified Hopfield neural network approaches.
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paper_title: An efficient Particle Swarm Optimization for Economic Dispatch with valve-point effect

paper_content:

This paper presents a new efficient approach to Economic Dispatch (ED) problems with smooth and non smooth cost functions using a Particle Swarm Optimization (PSO) technique. The practical ED problems have non-smooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. In this paper, an efficient PSO technique is employed so that faster convergence is obtained for the same results published in IEEE Proceedings so far. To show its efficiency and effectiveness, the proposed PSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost Functions considering valve-point loading effects. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
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paper_title: BIG BANG-BIG CRUNCH OPTIMIZATION ALGORITHM FOR ECONOMIC DISPATCH WITH VALVE-POINT EFFECT

paper_content:

The Big Bang–Big Crunch (BB–BC) optimization algorithm is a new optimization method that relies on the Big Bang and Big Crunch theory, one of the theories of the evolution of the universe. In this paper, a Big Bang–Big Crunch algorithm is presented for solving optimal power flow (OPF) problems with valve-point effects. The proposed algorithm has been tested with the IEEE 30-bus system with different fuel cost characteristics, quadratic cost curve model, and quadratic cost curve with valve-point effects model. Numerical results demonstrate the efficiency of the BB–BC algorithm compared to other heuristic algorithms.
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paper_title: An Efficient Particle Swarm Optimization (EPSO) for Economic Dispatch Problems With Transmission Losses for Both Smooth and Non-smooth Cost functions

paper_content:

An Efficient Particle Swarm Optimization (EPSO) technique, employed to solve Economic Dispatch (ED) problems including losses in power system is presented in this paper. With practical consideration, ED will have nonsmooth cost functions with equality and inequality constraints that make the problem, a large-scale highly constrained nonlinear optimization problem. The proposed method expands the original PSO to handle a different approach for satisfying those constraints. In this paper, an Efficient Particle Swarm Optimization (EPSO) technique is employed so that faster convergence is obtained for the same results published in IEEE Proceedings. To demonstrate the effectiveness of the proposed method it is being applied to test ED problems, one with smooth and other with non smooth cost functions considering valve-point loading effects. Comparison with other optimization techniques showed the superiority of the proposed EPSO approach and confirmed its potential for solving nonlinear economic load dispatch problems with losses.
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paper_title: Application of an improved Particle Swarm Optimization to economic load dispatch in power plant

paper_content:

In the application of Particle Swarm Optimization (PSO) for the problem of economic load dispatch (ELD) in power plant There are some problems such as premature convergence of PSO, how to deal with constraints of the problem are need to be addressed. An improved PSO with the constraints partially solved combined with penalty function were introduced in this paper, the improved PSO refined in constraints management, swarm initialization method of PSO with respect to the features of ELD in power plant. Based on above improvements, the improved PSO solved the problem of premature convergence in PSO. In the application to a three and a five units power plant respectively, the simulation results shows that the optimization success rate can reach 100% with the improved PSO, which has the advantage of few parameters to adjust, easy to implement, with high computational efficiency and high accuracy.
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paper_title: A New Constraint-Preserving Method for Solving Nonconvex Economic Dispatch with Linear Constraints

paper_content:

This paper proposed the use of a new constraint-preserving method (NCPM) to solve the nonconvex economic dispatch (NED) with linear constraint problems. NCPM always generates feasible solutions every time that reduces the search space (exclude the infeasible domain) to enhance the probability of obtaining the global optimum. Based on the benchmark of the same objective function, NCPM was compared with the other methods upon their search performance. Results show that the proposed algorithm outperforms the existing methods, in both global search capability and computation time.
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paper_title: Chaotic self-adaptive particle swarm optimization algorithm for dynamic economic dispatch problem with valve-point effects

paper_content:

Abstract This paper presents a chaotic self-adaptive particle swarm optimization algorithm (CSAPSO) to solve dynamic economic dispatch problem (DED) with value-point effects. The proposed algorithm takes PSO as the main evolution method. The velocity, a sensitive parameter of PSO, is adjusted dynamically to increase the precision of PSO. To overcome the drawback of premature in PSO, chaotic local search is imported into proposed algorithm. Moreover, a new strategy is proposed to handle the various constraints of DED problem in this paper, the results solved by proposed strategy can satisfy the constraints of DED problem well. Finally, the high feasibility and effectiveness of proposed CSAPSO algorithm is validated by three test systems consisting of 10 and extended 30 generators while compared with the experimental results calculated by the other methods reported in this literature.
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paper_title: Improved chaotic particle swarm optimization algorithm for dynamic economic dispatch problem with valve-point effects

paper_content:

Abstract Dynamic economic dispatch (DED) problem is one of the optimization issues in power system operation. In this paper, an improved chaotic particle swarm optimization (ICPSO) algorithm is proposed to solve DED with value-point effects. In proposed ICPSO, chaotic mutation is embedded to overcome the drawback of premature in PSO. What’s more, enhanced heuristic strategies are proposed to handling the various constraints of DED problem effectively. Comparing with penalty function method, the proposed constraints handling method can guide the population to feasible region without violating any constraints. Moreover, the effects of two crucial parameters on the performance of proposed ICPSO are also studied. Finally, the ICPSO algorithm is validated for two test systems consisting of 10 and extended 30 generators. While compared with other method reported in this literature, the experimental results demonstrated the high feasibility and effectiveness of proposed algorithm.
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paper_title: Economic load dispatch with environmental emission using MRPSO

paper_content:

The economic load dispatch (ELD) is the online process for allocating the generation among the available generating unit to fulfill the load demand in such a way to minimize the total generation cost and satisfying the equality and inequality constraints. In literature many papers have used the particle swarm optimization to solve the economic load dispatch problem with emission constraint which is a population based optimization technique inspired by sociological behavior of bird flocking, It can solve ELD problem to a wide range but it lacks global search ability in the last stage of iterations. So it is difficult to get the global optimal solution for the ELD problem by using PSO. At the time of generation of large power, fossil fuel burns at power plants which produces many toxic gases and pollute the environment. The main objective of this paper is to minimize the total generation cost of thermal units as well as to minimize the pollutant emission emitted by toxic gases. This paper, a novel PSO with a moderate random search strategy called as moderate-random particle swarm optimization (MRPSO) is used for solving ELD problem with emission as constraints. MRPSO enhances the ability of particles to explore the solution spaces more effectively and increases their convergence rates. The validation of the proposed MRPSO algorithm is demonstrated through its application for six generator systems with emission constraints for various load demand.
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paper_title: Particle Swarm Optimization for Economic Power Dispatch with Valve-Point Effects

paper_content:

In this paper, four modified versions of particle swarm optimizer (PSO) have been applied to the economic power dispatch with valve-point effects. In order to obtain the optimal solution, traditional PSO search a new position around the current position. The proposed strategies which explore the vicinity of particle's best position found so far leads to a better result. In addition, to deal with the equality constraint of the economic dispatch problems, a simple mechanism is also devised that the difference of demanded load and total generating power is evenly shared among units except the one reaching its generating limit. To show their capability, the proposed algorithms are applied to two cases with thirteen and forty generators, respectively. Comparison among evolutionary algorithm and other modified particle swarm optimization is given. The results show that the proposed algorithms indeed produce more optimal solutions in both cases.
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paper_title: A hybrid Hopfield neural network-quadratic programming approach for dynamic economic dispatch problem

paper_content:

This paper introduces a solution of the dynamic economic dispatch (DED) problem using a hybrid approach of Hopfield neural network (HNN) and quadratic programming (QP). The hybrid algorithm is based on using enhanced HNN; to solve the static part of the problem; and the QP algorithm for solving the dynamic part of the DED. This technique guarantees the global optimality of the solution due to its look-ahead capability. The new algorithm is applied and tested to an example from the literature and the solution is then compared with that obtained by some other techniques to prove the superiority and effectiveness of the proposed algorithm.
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paper_title: A fast particle swarm algorithm for solving smooth and non-smooth economic dispatch problems

paper_content:

The Economic Dispatch (ED) problem is a common task in the operational planning of a power system, which requires to be optimized. Such optimization includes two goals: (1) the minimization of the total scheduled cost and (2) the minimization of the response time. This article presents a fast Particle Swarm Optimization (PSO) approach for solving the ED problem. The proposed approach is applied to five case studies, having different size and complexity. Three of them have a smooth fuel cost, whereas the other two have non-smooth load functions, with valve-points. The experimental results indicate that the proposed approach provides good results on the test problems adopted, while requiring a lower computational time than other approaches taken from the specialized literature.
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paper_title: A New Particle Swarm Algorithm and Its Globally Convergent Modifications

paper_content:

Particle swarm optimization (PSO) is a population-based optimization technique that can be applied to a wide range of problems. Here, we first investigate the behavior of particles in the PSO using a Monte Carlo method. The results reveal the essence of the trajectory of particles during iterations and the reasons why the PSO lacks a global search ability in the last stage of iterations. Then, we report a novel PSO with a moderate-random-search strategy (MRPSO), which enhances the ability of particles to explore the solution spaces more effectively and increases their convergence rates. Furthermore, a new mutation strategy is used, which makes it easier for particles in hybrid MRPSO (HMRPSO) to find the global optimum and which also seeks a balance between the exploration of new regions and the exploitation of the already sampled regions in the solution spaces. Thirteen benchmark functions are employed to test the performance of the HMRPSO. The results show that the new PSO algorithm performs much better than other PSO algorithms for each multimodal and unimodal function. Furthermore, compared with recent evolutionary algorithms, experimental results empirically demonstrate that the proposed framework yields promising search performance.
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paper_title: Implementation of MRPSO techniques on economic load dispatch problem considering various generator constraints

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This article presents moderate-random-search strategy PSO called MRPSO to solve both convex and non-convex economic load dispatch (ELD) problem of the thermal unit. Here transmission loss is not considered. The proposed methodology can take care of ELD problems considering nonlinearities such as valve point loading, ramp rate limits, prohibited zone etc. The objective of economic load dispatch is to determine the optimal power generation of the units to meet the load demand, such that the overall cost of generation is minimized, while satisfying different operational constraints. The effectiveness of the proposed algorithms has been verified on different test systems with equality and inequality constraints. Compared with the other existing techniques demonstrates the superiority of the proposed algorithms.
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paper_title: An Extension of Particle Swarm Optimization (E-PSO) Algorithm for Solving Economic Dispatch Problem

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Producing the energy power that meets the load demands at a minimum cost while satisfying the constraints is known as economic dispatch. Economic dispatch becomes one of the most complex problems in the planning and operation of a power system that aims to determine the optimal generation scheduling at minimum cost. For that reason many optimization researches on finding an optimal solution regarding the total cost of generation have been carried out. This paper presents the implementation of the extension of the PSO (E-PSO) system in solving the continuous nonlinear function of the cost curves of the generator. In this paper, a 6-unit generation system has been applied to show the effectiveness of the E-PSO compared to the standard PSO. The results show that E-PSO is capable in solving the economic dispatch problem in term of minimizing the total cost of generation while considering the generator limits and transmission losses.
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paper_title: Economic Dispatch Problem Based on Improved Particle Swarm Optimization

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An improved particle swarm optimization (IPSO) is used to solve economic dispatch problem (EDP). The IPSO has two position updating strategies. In the early stage of iteration, the individual in the population updates the position according to its own best experience with a large probability. In the later stage of iteration, the individual updates the position according to the best experience in the population with a large probability. In addition, the IPSO introduces a mutation operator after position updating, which can increase the diversity of population and prevent the premature convergence. IPSO has been used to solve EDP with valve point effect. The experimental results show that IPSO is an effective algorithm to solve EDP.
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paper_title: An improved particle swarm optimization algorithm applied to economic dispatch

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This paper proposes a new practical optimization method applied to the economic dispatch (ED) in a power system. The proposed method is based on an improved particle swarm optimization algorithm and considers some restrict conditions of ED in a practical power system. By reinitializing them with some currently optimal values during every cycle of iteration, this proposed method can make some inactivity particles to be always within a very small area having an optimal solution. The proposed method can avoid effectively the "premature" of the classic particle swarm optimization (PSO) algorithm due to improve the cognized capacity of the classic PSO, thereby it is beneficial to obtain some optimal global solutions. The simulation results show that proposed method has some excellent characteristics of higher quality calculation precision and better computation efficiency, compared with some other PSO methods.
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paper_title: Hybrid bare-bones PSO for dynamic economic dispatch with valve-point effects

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This paper presents an efficient hybrid particle swarm optimization algorithm to solve dynamic economic dispatch problems with valve-point effects, by integrating an improved bare-bones particle swarm optimization (BBPSO) with a local searcher called directionally chaotic search (DCS). The improved BBPSO is designed as a basic level search, which can give a good direction to optimal regions, while DCS is used as a fine-tuning operator to locate optimal solution. And an adaptive disturbance factor and a new genetic operator are also incorporated into the improved BBPSO to enhance its search capability. Moreover, a heuristic handing mechanism for constraints is introduced to modify infeasible particles. Finally, the proposed algorithm is applied to the 5-, 10-, 30-unit-test power systems and several numerical functions, and a comparative study is carried out with other existing methods. Results clarify the significance of the proposed algorithm and verify its performance.
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paper_title: Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation

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Economic load dispatch (ELD) performs an important part in the economic operation of power system. The ELD problem is considered as a non-linear constrained optimisation problem. The problem becomes non-convex and non-smooth when the generators’ prohibited zones and valve-point effect are considered. The purpose of this work is to present a solution strategy to solve ELD problem in an efficient way while considering several aspects of ELD. The strategy employs a hybrid mechanism involving a quantum mechanics inspired particle swarm optimisation (PSO). The conventional PSO is modified by integrating quantum mechanics theory that redefines the particles positions and velocities in more diverse manner and therefore explores more search space. The PSO is further upgraded from a single population-based to a multi-population one. Such feature of the method delivers a fine balance between the local and global searching abilities. The simulations are carried by considering several cases of thermal units by varying different combinations of system configurations such as with/without valve-point effect, with/without network loss and for one or several hours of load demand. The results are quite promising and effective compared with several benchmark methods.
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paper_title: Locating and tracking multiple dynamic optima by a particle swarm model using speciation

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This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighborhood best values for solving multimodal optimization problems and for tracking multiple optima in a dynamic environment. In the proposed species-based particle swam optimization (SPSO), the swarm population is divided into species subpopulations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population, and then adopted as neighborhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize toward multiple optima, regardless of whether they are global or local optima. Our experiments on using the SPSO to locate multiple optima in a static environment and a dynamic SPSO (DSPSO) to track multiple changing optima in a dynamic environment have demonstrated that SPSO is very effective in dealing with multimodal optimization functions in both environments
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paper_title: Species-based Quantum Particle Swarm Optimization for economic load dispatch

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Abstract Economic load dispatch (ELD) is one of the important optimization problems in the operation of power systems which can be helpful to create effective generating management plans. In this paper, the ELD problem is discussed considering transmission network losses and practical constraints of plants such as generation ramp rate, prohibited operation zones, and valve-point effects. A new method called Species-based Quantum Particle Swarm Optimization (SQPSO), which is based on the Quantum Particle Swarm Optimization (QPSO), is proposed and applied in order to solve this problem possessing non-smooth and smooth cost functions. In the proposed intelligent technique, the particles are classified according to the output results and they explore the answers in each iteration in-group form. The new method has just one control parameter. The simulation results and the numerical investigations of various examples are compared with other conventional techniques to assess the efficiency of the proposed method. The results of the numerical investigations well depict that in spite of its simplicity, the proposed method is superior over the other techniques from standpoint of optimum answer exploitation as well as possessing appropriate and acceptable speed and stability.
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paper_title: Solving the economic dispatch problem with a modified quantum-behaved particle swarm optimization method

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Abstract In this paper, a modified quantum-behaved particle swarm optimization (QPSO) method is proposed to solve the economic dispatch (ED) problem in power systems, whose objective is to simultaneously minimize the generation cost rate while satisfying various equality and inequality constraints. The proposed method, denoted as QPSO-DM, combines the QPSO algorithm with differential mutation operation to enhance the global search ability of the algorithm. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zones, and nonsmooth cost functions are considered when the proposed method is used in practical generator operation. The feasibility of the QPSO–DM method is demonstrated by three different power systems. It is compared with the QPSO, the differential evolution (DE), the particle swarm optimization (PSO), and the genetic algorithm (GA) in terms of the solution quality, robustness and convergence property. The simulation results show that the proposed QPSO–DM method is able to obtain higher quality solutions stably and efficiently in the ED problem than any other tested optimization algorithm.
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paper_title: Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch

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Economic load dispatch (ELD) is an important topic in the operation of power plants which can help to build up effective generating management plans. The ELD problem has nonsmooth cost function with equality and inequality constraints which make it difficult to be effectively solved. Different heuristic optimization methods have been proposed to solve this problem in previous study. In this paper, quantum-inspired particle swarm optimization (QPSO) is proposed, which has stronger search ability and quicker convergence speed, not only because of the introduction of quantum computing theory, but also due to two special implementations: self-adaptive probability selection and chaotic sequences mutation. The proposed approach is tested with five standard benchmark functions and three power system cases consisting of 3, 13, and 40 thermal units. Comparisons with similar approaches including the evolutionary programming (EP), genetic algorithm (GA), immune algorithm (IA), and other versions of particle swarm optimization (PSO) are given. The promising results illustrate the efficiency of the proposed method and show that it could be used as a reliable tool for solving ELD problems.
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paper_title: Quantum particle swarm optimization for economic dispatch problem with valve-point effect

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In this paper, a new particle swarm optimization (PSO) called Quantum particle swarm optimization (QPSO) is used for solving economic load dispatch (ELD) problem with valve-point effect. The new method is based on quantum mechanics rather than the classic mechanics assumed in all previous versions of PSO and has fewer parameters and stronger search capability than the classical particle swarm optimization (CPSO), as well as is easy to implement. The algorithm optimization performance is simulated by systems possessing 13, and 40 generating units. The simulation results verify that the new method can effectively solve ELD problem and provide the solutions comparable to or better than those generated by recently reported optimization algorithms.
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paper_title: Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects

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Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.
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paper_title: A modified particle swarm optimization for economic dispatch with non-smooth cost functions

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This paper presents a new approach to economic dispatch (ED) problems with non-smooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have non-smooth cost functions with equality and inequality constraints, which makes the problem of finding the global optimum difficult when using any mathematical approaches. Since, standard PSO may converge at the early stage, in this paper, a modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. To validate the results obtained by MPSO, standard particle swarm optimization (PSO) and guaranteed convergence particle swarm optimization (GCPSO) are applied for comparison. Also, the results obtained by MPSO, PSO and GCPSO are compared with the previous approaches reported in the literature. The results show that the MPSO produces optimal or nearly optimal solutions for the study systems.
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paper_title: Solution to economic dispatch problem with valve-point loading effect by using catfish PSO algorithm

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This paper proposes application of a catfish particle swarm optimization (PSO) algorithm to economic dispatch (ED) problems. The ED problems considered in this paper include valve-point loading effect, power balance constraints, and generator limits. The conventional PSO and catfish PSO algorithms are applied to three different test systems and the solutions obtained are compared with each other and with those reported in literature. The comparison of solutions shows that catfish PSO outperforms the conventional PSO and other methods in terms of solution quality though there is a slight increase in computational time.
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paper_title: Dynamic economic dispatch using Lbest-PSO with dynamically varying sub-swarms

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Dynamic economic dispatch (DED) is one of the major planning problem in a power system. It is a non-linear optimization problem with various operational constraints, which includes the constraints of the generators operating characteristics and the system constraints. Its principal aim is to minimize the cost of power production of all the participating generators over a time horizon of 24 h, while satisfying the system constraints. This problem deals with non-convex characteristics if generation unit valve-point effects are taken into account. The paper intends to solve the DED problem with valve-point effects, using our modified form of Local-best variant of Particle Swarm Optimization (Lbest PSO) algorithm. We have tested our algorithm on 5-unit, 10-unit and 110-unit test system with non-smooth fuel cost functions to prove the effectiveness of the suggested method over different state of the art methods.
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paper_title: A genetic Lbest Particle Swarm Optimizer with dynamically varying subswarm topology

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This article presents a novel optimization technique hybridizing the concepts of Genetic Algorithm (GA) and Lbest Particle Swarm Optimization (Lbest PSO). A new topology, namely ‘Dynamically Varying Sub-swarm’ has been incorporated in the search process and some selected crossover and mutation techniques have been used for generation updating. This novel hybridized approach simultaneously ensures a robust search process, a quick convergence and a wide variety of real life applications. Simulations performed over various benchmark functions with the proposed method have been compared with other existing strong algorithms. Experimental results support the claim of proficiency of our algorithm over other existing techniques in terms of robustness, fast convergence and, most importantly its optimal search behavior.
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paper_title: Economic Load Dispatch Based on Efficient Population Utilization Strategy for Particle Swarm Optimization

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In this paper, the efficient population utilization strategy for particle swarm optimization (EPUSPSO) is proposed to solve the economic load dispatch (ELD) problem of power system. This algorithm improves the accuracy and the speed of its convergence by changing the number of particles effectively, and improving the velocity equation and position equation. In order to verify the effectiveness of the algorithm, this algorithm is tested in three different ELD cases of power system include IEEE 3-unit case, 13-unit case, and 40-unit case, and the obtained results are compared with those obtained from other algorithms using the same system parameters. The compared results show that the algorithm can find the optimal solution effectively and accurately, and avoid falling into the local optimal problem; meanwhile, faster speed can be ensured in the case.
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paper_title: Particle Swarm Based Optimal Estimation of Block Incremental Cost Curve

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Competitive electricity market (EM) requires the bid from the electricity supply companies in the required formats which are defined in the market regulations. Block (stair-case) bid and linear bid are two most commonly used bid format for both market and research purposes. In most of the EM, the generating companies (so called energy suppliers) are required to bid their power outputs in blocks with the associated price of each block. For a unit having with multiple fuel and valve point loading effect, the generating company must divide the output power of the unit into the blocks so that it can be bid into the electricity market with and/or without gaming. This paper addresses the estimation of optimal block incremental cost from the instantaneous incremental heat rate curve of a generating unit using particle swarm optimization approach. During each block, the total cost is the same to the cost obtained with the instantaneous incremental cost curve. The formulation is simple and can be used for any generating unit with minimum error at block edges. The effectiveness of the proposed method is illustrated with the case studies.
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paper_title: Calculation of Economic Dispatch of Power System Based on Improved Particle Swarm Optimization Algorithm Abstract

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For the power system economic dispatch problem, this paper takes the power system generation fuel cost as the objective function, and take into account the net loss of the power system. At the same time, it neglects the valve point effect in the process of the generation and establish power system model to meet the running power balance constraints and the motor running In this paper, the IEEE30BUS power system is chosen as an example, and this paper uses the improved particle swarm optimization algorithm to simulate the power system of the known fuel consumption parameters, and the simulation result is compared with the optimization results of the basic particle swarm optimization algorithm. The result of system simulation is: the optimization result of the traditional particle swarm optimization is that the total power is 1375.63 MW, the net loss is 11.89 MW and the total cost is 16562.98 ($/h); The optimization results obtained by the improved particle swarm optimization algorithm are that the total power is 1375.08 MW, the net loss is 10.49 MW, the total cost is 16546.86 ($/h). The net loss of the improved algorithm is reduced by 2% compared with the traditional algorithm and the total cost is reduced by 6.12 ($/h). The simulation results show that the improved particle swarm optimization algorithm can effectively solve the power system economic dispatch calculation problem.
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paper_title: Power Generation, Operation, and Control

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Topics considered include characteristics of power generation units, transmission losses, generation with limited energy supply, control of generation, and power system security. This book is a graduate-level text in electric power engineering as regards to planning, operating, and controlling large scale power generation and transmission systems. Material used was generated in the post-1966 period. Many (if not most) of the chapter problems require a digital computer. A background in steady-state power circuit analysis is required.
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paper_title: Solving the Power Economic Dispatch Problem With Generator Constraints by Random Drift Particle Swarm Optimization

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This paper proposes the random drift particle swarm optimization (RDPSO) algorithm to solve economic dispatch (ED) problems from power systems area. The RDPSO is inspired by the free electron model in metal conductors placed in an external electric field, and it employs a novel set of evolution equations that can enhance the global search ability of the algorithm. Many nonlinear characteristics of a power generator, such as the ramp rate limits, prohibited operating zones and nonsmooth cost functions are considered when the proposed method is used in practice for optimizing the generators' operation. The performance of the RDPSO method is evaluated on three different power systems, and compared with that of other optimization methods in terms of the solution quality, robustness, and convergence performance. The experimental results show that the RDPSO method performs better in solving the ED problems than any other tested optimization techniques.
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paper_title: Improved Random Drift Particle Swarm Optimization With Self-Adaptive Mechanism for Solving the Power Economic Dispatch Problem

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This paper proposes an improved version of the random drift particle swarm optimization algorithm for solving the economic dispatch problem. The improvement is achieved through adding a crossover operation followed by a greedy selection process while replacing the mean best position of the particles with the personal best position of each particle in the velocity updating equation. The improved algorithm is also augmented with a self-adaption mechanism that eliminates the need for tuning the algorithm parameters based on characteristics of the considered optimization problem. Practical features such as valve point effects, prohibited operating zones, multiple fuel options, and ramp rate limits are considered in the mathematical formulation of the economic dispatch problem. In order to demonstrate the efficacy of the proposed algorithm, five benchmark test systems are utilized. The obtained results showed that the improved random drift particle swarm optimization algorithm is capable of providing superior results compared to the original algorithm and the state of the art techniques proposed in previous literature.
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paper_title: A Multi-Agent Particle Swarm Optimization for Power System Economic Load Dispatch

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A new versatile optimization, the particle swarm optimization based on multi-agent system (MAPSO) is presented. The economic load dispatch (ELD) problem of power system can be solved by the algorithm. By competing and cooperating with the randomly selected neighbors, and adjusting its global searching ability and local exploring ability, this algorithm achieves the goal of high convergence precision and speed. To verify the effectiveness of the proposed algorithm, this algorithm is tested by three different ELD cases, including 3, 13 and 40 units IEEE cases, and the experiment results are compared with those tested by other intelligent algorithms in the same cases. The compared results show that feasible solutions can be reached effectively, local optima can be avoided and faster solution can be applied with the proposed algorithm, the algorithm for ELD problem is versatile and efficient.
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paper_title: A hybrid multi-agent based particle swarm optimization algorithm for economic power dispatch

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This paper presents a new multi-agent based hybrid particle swarm optimization technique (HMAPSO) applied to the economic power dispatch. The earlier PSO suffers from tuning of variables, randomness and uniqueness of solution. The algorithm integrates the deterministic search, the Multi-agent system (MAS), the particle swarm optimization (PSO) algorithm and the bee decision-making process. Thus making use of deterministic search, multi-agent and bee PSO, the HMAPSO realizes the purpose of optimization. The economic power dispatch problem is a non-linear constrained optimization problem. Classical optimization techniques like direct search and gradient methods fails to give the global optimum solution. Other Evolutionary algorithms provide only a good enough solution. To show the capability, the proposed algorithm is applied to two cases 13 and 40 generators, respectively. The results show that this algorithm is more accurate and robust in finding the global optimum than its counterparts.
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paper_title: Kalman-Particle Filter Used for Particle Swarm Optimization of Economic Dispatch Problem

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This paper presents an effective evolutionary method to solve the Economic Dispatch (ED) problem with units having prohibited operating zones. The Kalman filter is an efficient recursive filter that estimates the state of a dynamic system from a series of noisy measurements in theTotal Power Generation (TPG). ED is an example of a dynamic system algorithm that has been widely used for determination most economical generation profile to optimize the overall electricity prices. ED is a non-smooth problem when valve-point effects of generation units are considered. This paper applies Kalman - Particle filter (KF-PF) to the ED state estimation problem that has been optimized with Particle Swarm Optimization (PSO), with the emphasis to avoid the solution being trapped in local optimas [1], [2]. Kalman and particle filter are used to estimate TPG as state of ED problem. The performance of the KF-PF has been tested on a typical system and compared with others proposed in the literatures. The comparison results show that the efficiency of proposed approach can reach higher quality solutions.
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paper_title: A self-adaptive chaos and Kalman filter-based particle swarm optimization for economic dispatch problem

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It is challenging to obtain global minima for practical economic dispatch (ED) problem with heavy constraints. Traditional PSO is easy to fall into local optimum when it is applied to solve the ED problem; therefore, in this paper, an efficient self-adaptive chaos and Kalman filter-based particle swarm optimization algorithm (SCKF-PSO) is proposed to solve economic dispatch (ED) problem while considering minimizing the cost with various equality and inequality constraints. The algorithm adopts both the learning mechanism of PSO and the estimation strategy of Kalman filter to update the position of the particle, which can improve the convergence performance. Moreover, a novel self-adaptive chaotic strategy is utilized to increase the diversity of the population. The feasibility of SCKF-PSO algorithm is illustrated by testing on several benchmark functions and three different ED problems in power systems. The simulation results show that compared with previous approaches reported in the literature, the proposed SCKF-PSO can obtain higher quality solutions with stability and efficiency in the ED problem.
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paper_title: Comprehensive Learning Particle Swarm Optimization for economic load dispatch

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This paper presents a heuristic optimization approach to constrained economic load dispatch (ELD) problems using the Comprehensive Learning Particle Swarm Optimization (CLPSO) technique. Different non-linear characteristics of the generator such as transmission losses, prohibited operating zones and non-smoothness of cost functions are considered. The feasibility of the proposed technique is performed for two test systems with different numbers of generating units, and compared with the Differential Evolution (DE) and Particle Swarm Optimization (PSO) techniques. The findings affirmed the robustness, fast convergence and proficiency of the proposed methodology over other existing techniques.
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paper_title: A GPU accelerated PSO with application to Economic Dispatch problem

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This paper investigates the use of Graphics Processing Units (GPUs) as general purpose parallel architectures, for the acceleration of the solution of the Economic Dispatch problem (ED) via stochastic search algorithms. The Comprehensive Learning Particle Swarm Optimizer (CLPSO) is used as host process to carry out the optimization task. At every time of the evolution a parallel graphics card speeds up the optimization process by calculating, in parallel, the fitness value of all particles. Two different approaches are investigated: a fine-grained parallelism and a coarse-grained one. The results demonstrate that GPUs can be applied with success to speed up computationally intensive problems in electric energy systems.
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paper_title: Economic Dispatch of Power Systems Based on the Modified Particle Swarm Optimization Algorithm

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This paper presents a new versatile optimization algorithm called modified particle swarm optimization algorithm (MPSO) for solving the economic dispatch (ED) problem of power systems. Compared with the classical PSO algorithm, several modified operators, such as mutation operator and neighborhood magnifying operator, are employed by MPSO to ensure the algorithm search globally in theory. Based on the stochastic analysis theorem, it is proved that MPSO has global convergence property, the convergence property is independent of the initialization, and a sufficient condition for convergence is presented. This algorithm is used to solve the complicated, nonconvex, nonlinear economic dispatch problems. Several factors such as, valve-point effects of fuel cost functions, transmission capacity constraints, and system stability constraints are considered in the computation models. Numerical results show that the proposed method is feasible and efficient
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paper_title: Particle swarm optimizer for constrained economic dispatch with prohibited operating zones

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Practically, not all the operating zones of generation units are available always for load allocation due to some physical operation limitations. Accordingly, these prohibited zones divide the operating region between the minimum and the maximum generation limits into disjoint convex subsets. Units with prohibited operating zones transform the ordinary economic dispatch to a nonconvex optimization problem where the conventional Lagrangian multiplier based methods cannot be directly applied. The paper introduces the particle swarm optimizer (PSO) for solving this nonconvex economic dispatch problem. A 15-unit system with 4 units having prohibited operating zones is used for the application. The results are compared with those obtained by both conventional methods and the Hopfield neural network.
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paper_title: An Improved Attractive and Repulsive Particle Swarm Optimization for Nonconvex Economic Dispatch Problems

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Abstract: This paper presents an improved attractive and repulsive particle swarm optimization (ARPSO) algorithm for nonconvex economic dispatch problem. The ARPSO algorithm enhances the exploration and exploitation behaviors of a particle by observing a diversity factor. This paper develops an improved ARPSO by introducing a penalty factor that forces each particle to repulse from the global worst particle. The advantage of the improved ARPSO is demonstrated numerically in comparison with the basic PSO and other variation of ARPSO.
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paper_title: Economic dispatch optimization using virus-evolutionary particle swarm algorithm

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Particle swarm optimization (PSO) is a population-based stochastic optimization technique, originally developed by Eberhart and Kennedy, inspired by simulation of a social psychological metaphor instead of the survival of the fittest individual. In PSO, the system (swarm) is initialized with a population of random solutions (particles) and searches for optima using cognitive and social factors by updating generations. PSO has been successfully applied to a wide range of applications, mainly in solving continuous nonlinear optimization problems. This paper presents an improved discrete particle swarm optimization algorithm based on virus theory of evolution. Virus-evolutionary discrete particle swarm optimization (VEPSO) algorithm is proposed to simulate co-evolution of a particle swarm of candidate solutions and a virus swarm of substring representing schemata. In the co-evolutionary process, the virus propagates partial genetic information in the particle swarm by virus infection operators which enhances the horizontal search ability of particle swarm optimization algorithm. The methodology is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes in to account the valve-point loading effects.
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paper_title: ECONOMIC LOAD DISPATCH USING ?-PSO

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Abstract This paper presents a θ -particle swarm optimization ( θ -PSO) based algorithm to solve constrained economic load dispatch (ELD) problems of thermal plants. The proposed methodology easily takes care of practical constraints such as transmission losses, ramp rate limits, and prohibited operating zones, and also deals with non-smoothness of cost function arising due to the use of valve point effects. The main evaluation mechanism of classical particle swarm optimization (CPSO) is modified in the novel θ -PSO by replacing the velocity vector with a phase angle vector. So, the positions are decided by the mapping of phase angles in θ -PSO. The performance of proposed algorithm has been tested on systems possessing 6, 13, 15, and 40 generating units involving varying degree of complexity. Detailed comparisons under equitable conditions are provided with prevalent approaches to measure the efficiency of the proposed algorithm. The findings affirm that the method outperforms the existing techniques in terms of solution quality and computational efficiency and can be a promising alternative approach for solving the ELD problems in practical power system.
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paper_title: Orthogonal PSO Algorithm for Economic Dispatch of Power under Power Grid Constraints

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We propose an enhanced Particle Swarm Optimization (PSO) algorithm named Orthogonal PSO (OPSO) algorithm, for Economic Dispatch (ED) of the generated power in a smart grid environment. The equality and inequality constraints, and power balance response against mismatch between load demand and total power outputs of generating units involve nonlinear characteristics and non-smooth cost functions. The proposed OPSO algorithm has the ability to solve such complex problems of power systems including ED. The OPSO algorithm applies Orthogonal Vectors (OVs) in the d-dimensional search space. The d particles that have possible solutions move in the d-dimensional search space to form OVs. These OVs are generated and updated in each iteration and they used to guide those particles to fly in one direction toward global minimum. The OPSO algorithm is evaluated and tested through 15 generating units and its performance is compared with several other optimization methods. We found that OPSO algorithm provides better results in solving the total cost, and power constraints. Furthermore, the OPSO algorithm is succeeded to improve the PSO algorithm in terms of high solution quality, robustness and convergence.
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paper_title: A Q-learning-based swarm optimization algorithm for economic dispatch problem

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In this paper, we treat optimization problems as a kind of reinforcement learning problems regarding an optimization procedure for searching an optimal solution as a reinforcement learning procedure for finding the best policy to maximize the expected rewards. This viewpoint motivated us to propose a Q-learning-based swarm optimization (QSO) algorithm. The proposed QSO algorithm is a population-based optimization algorithm which integrates the essential properties of Q-learning and particle swarm optimization. The optimization procedure of the QSO algorithm proceeds as each individual imitates the behavior of the global best one in the swarm. The best individual is chosen based on its accumulated performance instead of its momentary performance at each evaluation. Two data sets including a set of benchmark functions and a real-world problem--the economic dispatch (ED) problem for power systems--were used to test the performance of the proposed QSO algorithm. The simulation results on the benchmark functions show that the proposed QSO algorithm is comparable to or even outperforms several existing optimization algorithms. As for the ED problem, the proposed QSO algorithm has found solutions better than all previously found solutions.
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paper_title: Power economic dispatch using particle swarm optimization

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Current market environment, ever growing difference between depleting energy resources and increasing power demand and increased expectations of customers from utility companies has made it necessary to adopt some good operational policies by electric utility companies. So the focus of utility companies has shifted towards increased customer focus, enhanced performance and to provide reliable supply at low cost. The electric power system must be operated in a way to schedule generations economically of generation facilities. In last two decades many evolutionary techniques has been developed to solve the optimization problems. Particle swarm optimization has acquired much recognition due to less memory requirement and its inherent simplicity. Particle swarm optimization technique proved to be having strong potential for solving complex and high dimensional optimization problem. PSO is free from local minimum solution convergence which is often encountered while solving nonlinear and non-convex optimization problem through conventional techniques. This paper presents a summarized view of application of PSO for solving power economic dispatch problem.
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paper_title: A Survey on Economic Load Dispatch Problem Using Particle Swarm Optimization Technique

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Economic load dispatch (ELD) problem play a vital role in the operation of power system it is the short- term determination of the optimal output of the number of electricity generation facilities, to meet the system load, at the lowest possible cost subjected to transmission and operational constraints. Traditionally economic load dispatch is done for minimizing generation cost while maintaining set of equality and inequality constraints. A particle swarm optimization is an effective computational method that optimizes problem by iteratively trying to improve a candidate solution. It is a method of determine, most efficient low cost and reliable operation of a power system by dispatching the available electricity generation resources to supply the load on the system the application of particle swarm optimization in ELD problem which is consider as one of the most complex optimization problem has been summarized in this paper.
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paper_title: Survey on Applications of Particle Swarm Optimization in Electric Power Systems

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The paper presents a survey of particle swarm optimization (PSO) applications in electric power systems. PSO, a novel population based stochastic optimizer with faster convergence speed and simpler implementation than genetic algorithm and ant colony optimization, has been successfully applied to solve electric power optimization problems such as optimal power flow, economic dispatch, reactive power dispatch, unit commitment, generation and transmission planning, maintenance scheduling, state estimation, model identification, load forecasting, control, and others. The primary objective of the paper is to provide a summary of PSO-based optimization method used in electric power system. Both recent developments and further research trends of the area are presented in detail.
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paper_title: Economic dispatch using particle swarm optimization: A review

paper_content:

Electrical power industry restructuring has created highly vibrant and competitive market that altered many aspects of the power industry. In this changed scenario, scarcity of energy resources, increasing power generation cost, environment concern, ever growing demand for electrical energy necessitate optimal economic dispatch. Practical economic dispatch (ED) problems have nonlinear, non-convex type objective function with intense equality and inequality constraints. The conventional optimization methods are not able to solve such problems as due to local optimum solution convergence. Meta-heuristic optimization techniques especially particle swarm optimization (PSO) has gained an incredible recognition as the solution algorithm for such type of ED problems in last decade. The application of PSO in ED problem, which is considered as one of the most complex optimization problem has been summarized in present paper.
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paper_title: A Survey of Particle Swarm Optimization Applications in Electric Power Systems

paper_content:

Particle swarm optimization (PSO) has received increased attention in many research fields recently. This paper presents a comprehensive coverage of different PSO applications in solving optimization problems in the area of electric power systems. It highlights the PSO key features and advantages over other various optimization algorithms. Furthermore, recent trends with regard to PSO development in this area are explored. This paper also discusses PSO possible future applications in the area of electric power systems and its potential theoretical studies.
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Title: Solution of an Economic Dispatch Problem Through Particle Swarm Optimization: A Detailed Survey - Part I

Section 1: INTRODUCTION
Description 1: Provide an overview of the economic dispatch (ED) problem, the necessity of optimization in power systems, complications introduced by various constraints, and the reasons for considering Particle Swarm Optimization (PSO) for solving the ED problem. Mention the structure of the survey.

Section 2: FORMULATION OF THE DISPATCH PROBLEM
Description 2: Detail the formulation of the single-objective ED problem, including operational and system constraints. Discuss the objective function, VPL effects, generator capacity limits, generator ramp rate limits, POZ, line flow constraints, system spinning reserve constraints, and multi-fuel options.

Section 3: OVERVIEW OF PARTICLE SWARM OPTIMIZATION (PSO)
Description 3: Present an overview of the PSO algorithm, its principles inspired by the social behaviors of animals, initialization process, and the update mechanism of velocity and position of particles. Discuss the significance of PSO, the introduction of inertia weight, and the equation modifications.

Section 4: REVIEW OF PSO APPLIED TO ECONOMIC DISPATCH PROBLEM
Description 4: Provide a detailed and comprehensive survey of the standard or classical PSO and its modified versions applied to solve the ED problem. Subsections should include variations in constriction factor, inertia component, cognitive and social components, random numbers, swarm population, and position formula. Mention different PSO variants such as CRAZYPSO, APSO, MIPSO, etc.

Section 5: ALREADY-CONDUCTED PSO BASED SURVEYS
Description 5: Offer remarks and a brief summary of the already-conducted surveys involving PSO applications to the ED problem, highlighting the limitations and objectives of these surveys. Mention notable reviews and their contributions.

Section 6: CONCLUSION
Description 6: Summarize the key findings of the survey, the significance of PSO and its modifications in solving the ED problem, and limitations of the study. Suggest future research directions and potential applications of improved PSO variants to more complex and multi-objective power system problems.