Mathematical Optimization and Algorithms for Offshore Wind Farm Design: An Overview
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paper_title: Modelling and measuring flow and wind turbine wakes in large wind farms offshore

paper_content:

Average power losses due to wind turbine wakes are of the order of 10 to 20% of total power output in large offshore wind farms. Accurately quantifying power losses due to wakes is, therefore, an important part of overall wind farm economics. The focus of this research is to compare different types of models from computational fluid dynamics (CFD) to wind farm models in terms of how accurately they represent wake losses when compared with measurements from offshore wind farms. The ultimate objective is to improve modelling of flow for large wind farms in order to optimize wind farm layouts to reduce power losses due to wakes and loads. ::: ::: The research presented is part of the EC-funded UpWind project, which aims to radically improve wind turbine and wind farm models in order to continue to improve the costs of wind energy. Reducing wake losses, or even reduce uncertainties in predicting power losses from wakes, contributes to the overall goal of reduced costs. Here, we assess the state of the art in wake and flow modelling for offshore wind farms, the focus so far has been cases at the Horns Rev wind farm, which indicate that wind farm models require modification to reduce under-prediction of wake losses while CFD models typically over-predict wake losses. Further investigation is underway to determine the causes of these discrepancies. Copyright © 2009 John Wiley & Sons, Ltd.
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paper_title: Review of recent trends in optimization techniques for solar photovoltaic–wind based hybrid energy systems

paper_content:

An update literature review on trends in optimization techniques used for the design and development of solar photovoltaic–wind based hybrid energy systems is presented. The main objective is to identify latest promising techniques for the optimization of solar photovoltaic (PV)–wind based hybrid systems. Different techniques used by researchers for the optimization of renewable based hybrid energy systems are reviewed along with PV–wind based hybrid system sizing methodology, is presented. Optimization studies during last 2.5 decades by researchers using traditional and new generation methods are analyzed and sixteen optimization methods including hybrid algorithms are presented. The trend shows that new generation artificial intelligence algorithms are mostly used during last decade as these require less computation time and have better accuracy, good convergence in comparison to traditional methods. The study suggests using hybridization of two or more algorithms to overcome the limitations of a single algorithm. Additionally some other techniques are identified for follow up research in the design of PV–wind hybrid systems. This review will be useful for researchers to face complexity and challenges in renewable energy based hybrid system research.
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paper_title: The Offshore Wind Farm Array Cable Layout Problem: A Planar Open Vehicle Routing Problem

paper_content:

In an offshore wind farm (OWF), the turbines are connected to a transformer by cable routes that cannot cross each other. Finding the minimum cost array cable layout thus amounts to a vehicle routing problem with the additional constraints that the routes must be embedded in the plane. For this problem, both exact and heuristic methods are of interest. We optimize cable layouts for real-world OWFs by a hop-indexed integer programming formulation, and develop a heuristic for computing layouts based on the Clarke and Wright savings heuristic for vehicle routing. Our heuristic computes layouts on average only 2% more expensive than the optimal layout. Finally, we present two problem extensions arising from real-world OWF cable layouts, and adapt the integer programming formulation to one of them. The thus obtained optimal layouts are up to 13% cheaper than the actually installed layouts.
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paper_title: Optimizing investments in coupled offshore wind -electrolytic hydrogen storage systems in Denmark

paper_content:

Abstract In response to electricity markets with growing levels of wind energy production and varying electricity prices, this research examines incentives for investments in integrated renewable energy power systems. A strategy for using optimization methods for a power system consisting of wind turbines, electrolyzers, and hydrogen fuel cells is explored. This research reveals the investment potential of coupling offshore wind farms with different hydrogen systems. The benefits in terms of a return on investment are demonstrated with data from the Danish electricity markets. This research also investigates the tradeoffs between selling the hydrogen directly to customers or using it as a storage medium to re-generate electricity at a time when it is more valuable. This research finds that the most beneficial configuration is to produce hydrogen at a time that complements the wind farm and sell the hydrogen directly to end users.
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paper_title: DESIGN OF WIND FARM LAYOUT FOR MAXIMUM WIND ENERGY CAPTURE

paper_content:

The paper deals with the wind farm layout optimization problem (WFLOP). The objective of the wind farm layout optimization problem is to determine the optimal placement of wind turbines within the farm. In this approach, the expected power production is maximized, taking into account eventually different other supplementary technological and functional restrictions. Because the wake effects lead to significant losses of power produced by the wind turbines, minimizing them in order to maximize the expected power production is essential. In this paper a discrete representation of wind farm is used: farm area is decomposed into a set of cells, where each cell can contain only one wind turbine. Presently, this problem is usually solved using heuristic algorithms, trying to find good enough solutions in reasonable time. In this paper, some small cases are detailed investigated, using an exact solution method to solve this problem. Some new aspects regarding the multimodal character, the existence of multiple optimal solutions of objective function, and the exact gap between the lower and upper bounds of the objective function are outlined.
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paper_title: A stochastic fleet size and mix model for maintenance operations at offshore wind farms

paper_content:

Abstract A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.
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paper_title: Solving wind farm layout optimization with mixed integer programs and constraint programs

paper_content:

The wind farm layout optimization problem is concerned with the optimal location of turbines within a fixed geographical area to maximize energy capture under stochastic wind conditions. Previously it has been modelled as a maximum diversity (or p-dispersion-sum) problem, but such a formulation cannot capture the nonlinearity of aerodynamic interactions among multiple wind turbines. We present the first constraint programming (CP) and mixed integer linear programming (MIP) models that incorporate such nonlinearity. Our empirical results indicate that the relative performance between these two models reverses when the wind scenario changes from a simple to a more complex one. We also propose an improvement to the previous maximum diversity model and demonstrate that the improved model solves more problem instances.
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paper_title: Proximity search heuristics for wind farm optimal layout

paper_content:

A heuristic framework for turbine layout optimization in a wind farm is proposed that combines ad-hoc heuristics and mixed-integer linear programming. In our framework, large-scale mixed-integer programming models are used to iteratively refine the current best solution according to the recently-proposed proximity search paradigm. Computational results on very large scale instances involving up to 20,000 potential turbine sites prove the practical viability of the overall approach.
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paper_title: Sustainable decommissioning of an offshore wind farm

paper_content:

The offshore wind industry has historically focused on setting up new projects, with the decommissioning phase receiving little attention. This can cause future problems as decommissioning needs to be planned at the beginning to prevent complications that may arise, as it implies important operations and high costs. There are numerous features that make decommissioning a challenge, such as the marine environment, the technical limitations of vessels and the lack of specific regulations that determine what should be done, increasing the uncertainty of the process. Additionally, the unique characteristics of the sites involve exclusive optimal solutions for each project. This article analyses the main operation parameters that affect the decommissioning process, identifying the benefits and drawbacks of the influencing variables. A model is designed to compare different transportation strategies, searching for cost reduction. A decommissioning methodology is been proposed based on this analysis, taking into consideration the technical aspects of the process, and minimising environmental impacts. The model forecasts that the predicted duration and costs of this process are not being adequately captured in site decommissioning plans.
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paper_title: A clustering based wind farm collector system cable layout design

paper_content:

The goal of achieving 20% wind power penetration by 2030 in the US has stimulated the installation of large scale wind farms in recent years, both on-shore and off-shore. Collector systems consolidate the power generated by turbine units distributed over the geographical area of the wind farm to a substation from where the generated power is transmitted to the electric grid. Design of a wind farm collector system must take into consideration the economics and reliability of operation. Most modern day large scale wind farms consist of hundreds of wind turbines and are generally electrically connected in a radial feeder cable configuration or daisy chains. While these configurations are generally accepted as convention, not much research has been done to analyze other cable layout configurations. This paper proposes a clustering based algorithm for cable layout of a large scale wind power plant. Comparison of the proposed method with the radial feeder cable configuration shows that real power losses in collector system are lowered and greater reliability is achieved with the proposed design. An economic analysis has also been done to compare the cost of generated energy associated with the proposed design and the conventional configuration.
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paper_title: Routing and Scheduling of Maintenance Fleet for Offshore Wind Farms

paper_content:

Reducing the operation and maintenance (O&M) cost is a necessity in current offshore wind farms so that the produced power can achieve a competitive price in the market. An offshore wind farm normally comprises a large number of turbines which demand frequent maintenance visits. In addition to making maintenance plans that avoid downtime and production losses, it is important to utilize the expensive resources, such as service vessels, in an efficient way. This article introduces the routing and scheduling problem of a maintenance fleet for offshore wind farms (RSPMFOWF), which is to determine the optimal assignments of turbines and routes to the vessels in terms of cost. Simultaneously considering the characteristics and limitations in this problem, we present the mathematical formulations for the RSPMFOWF. A computational case study is also carried out. The results provide both the optimized cost and detailed arrangements, which can be directly used in maintenance planning.
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paper_title: Wind Turbine Interference in a Wind Farm Layout Optimization Mixed Integer Linear Programming Model

paper_content:

This work develops a wind intensity interference coefficient which captures the interference caused by an upwind turbine on a downwind turbine in the same wind flow. This coefficient includes the use of a Weibull distribution to handle variability in the wind velocity, and also accounts for the geometric relationship between the turbines and the boundaries of the wind sector. This interference coefficient then forms part of a mixed integer linear program (MILP) which is used to optimise the locations of wind turbines within a wind farm site. The MILP approach is an exact method that can guarantee that the turbine locations determined by the model are optimal with respect to an a priori chosen set of possible turbine locations. Tests on an example data set (based on a demonstration case in the WindFarmer software) show, for the particular wind resource used, that interference results in a loss of power of approximately 4.2% when compared to the power production which would be predicted without accounting f...
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paper_title: Optimisation of maintenance routing and scheduling for offshore wind farms

paper_content:

An optimisation model and a solution method for maintenance routing and scheduling at offshore wind farms are proposed. The model finds the optimal schedule for maintaining the turbines and the optimal routes for the crew transfer vessels to service the turbines along with the number of technicians required for each vessel. The model takes into account multiple vessels, multiple periods (days), multiple Operation & Maintenance (O&M) bases, and multiple wind farms. We develop an algorithm based on the Dantzig–Wolfe decomposition method, where a mixed integer linear program is solved for each subset of turbines to generate all feasible routes and maintenance schedules for the vessels for each period. The routes have to consider several constraints such as weather conditions, the availability of vessels, and the number of technicians available at the O&M base. An integer linear program model is then proposed to find the optimal route configuration along with the maintenance schedules that minimise maintenance costs, including travel, technician and penalty costs. The computational experiments show that the proposed optimisation model and solution method find optimal solutions to the problem in reasonable computing times.
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paper_title: A stochastic fleet size and mix model for maintenance operations at offshore wind farms

paper_content:

Abstract A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.
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paper_title: Proximity search heuristics for wind farm optimal layout

paper_content:

A heuristic framework for turbine layout optimization in a wind farm is proposed that combines ad-hoc heuristics and mixed-integer linear programming. In our framework, large-scale mixed-integer programming models are used to iteratively refine the current best solution according to the recently-proposed proximity search paradigm. Computational results on very large scale instances involving up to 20,000 potential turbine sites prove the practical viability of the overall approach.
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paper_title: Proximity search for 0-1 mixed-integer convex programming

paper_content:

In this paper we investigate the effects of replacing the objective function of a 0-1 mixed-integer convex program (MIP) with a "proximity" one, with the aim of using a black-box solver as a refinement heuristic. Our starting observation is that enumerative MIP methods naturally tend to explore a neighborhood around the solution of a relaxation. A better heuristic performance can however be expected by searching a neighborhood of an integer solution--a result that we obtain by just modifying the objective function of the problem at hand. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, suggesting that proximity search can be quite effective in quickly refining a given feasible solution. This is particularly true when a sequence of similar MIPs has to be solved as, e.g., in a column-generation setting.
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paper_title: Proximity search heuristics for wind farm optimal layout

paper_content:

A heuristic framework for turbine layout optimization in a wind farm is proposed that combines ad-hoc heuristics and mixed-integer linear programming. In our framework, large-scale mixed-integer programming models are used to iteratively refine the current best solution according to the recently-proposed proximity search paradigm. Computational results on very large scale instances involving up to 20,000 potential turbine sites prove the practical viability of the overall approach.
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paper_title: Horns Rev Offshore Windfarm: Its Main Controller and Remote Control System

paper_content:

This paper describes the Windfarm Main Controller and the Remote Control System in the Horns Rev Offshore Windfarm. It begins with a brief description of the windfarm and proceeds to discuss the conditions for connecting the farm to the grid. The description of the Windfarm Main Controller describes the different control modes in the windfarm and shows some recorded measurements. The paper also presents the remote control system. Because of the size and location of the windfarm, it was necessary to introduce a main control concept as in conventional power plants, so to control the output and for maintenance.
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paper_title: Wind Turbine Interference in a Wind Farm Layout Optimization Mixed Integer Linear Programming Model

paper_content:

This work develops a wind intensity interference coefficient which captures the interference caused by an upwind turbine on a downwind turbine in the same wind flow. This coefficient includes the use of a Weibull distribution to handle variability in the wind velocity, and also accounts for the geometric relationship between the turbines and the boundaries of the wind sector. This interference coefficient then forms part of a mixed integer linear program (MILP) which is used to optimise the locations of wind turbines within a wind farm site. The MILP approach is an exact method that can guarantee that the turbine locations determined by the model are optimal with respect to an a priori chosen set of possible turbine locations. Tests on an example data set (based on a demonstration case in the WindFarmer software) show, for the particular wind resource used, that interference results in a loss of power of approximately 4.2% when compared to the power production which would be predicted without accounting f...
---
paper_title: The Offshore Wind Farm Array Cable Layout Problem: A Planar Open Vehicle Routing Problem

paper_content:

In an offshore wind farm (OWF), the turbines are connected to a transformer by cable routes that cannot cross each other. Finding the minimum cost array cable layout thus amounts to a vehicle routing problem with the additional constraints that the routes must be embedded in the plane. For this problem, both exact and heuristic methods are of interest. We optimize cable layouts for real-world OWFs by a hop-indexed integer programming formulation, and develop a heuristic for computing layouts based on the Clarke and Wright savings heuristic for vehicle routing. Our heuristic computes layouts on average only 2% more expensive than the optimal layout. Finally, we present two problem extensions arising from real-world OWF cable layouts, and adapt the integer programming formulation to one of them. The thus obtained optimal layouts are up to 13% cheaper than the actually installed layouts.
---
paper_title: A stochastic fleet size and mix model for maintenance operations at offshore wind farms

paper_content:

Abstract A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.
---
paper_title: Horns Rev Offshore Windfarm: Its Main Controller and Remote Control System

paper_content:

This paper describes the Windfarm Main Controller and the Remote Control System in the Horns Rev Offshore Windfarm. It begins with a brief description of the windfarm and proceeds to discuss the conditions for connecting the farm to the grid. The description of the Windfarm Main Controller describes the different control modes in the windfarm and shows some recorded measurements. The paper also presents the remote control system. Because of the size and location of the windfarm, it was necessary to introduce a main control concept as in conventional power plants, so to control the output and for maintenance.
---
paper_title: A stochastic fleet size and mix model for maintenance operations at offshore wind farms

paper_content:

Abstract A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.
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paper_title: Mixed Integer Linear Programming for new trends in wind farm cable routing

paper_content:

Abstract The efficient production of green energy plays an import role in modern economies. In this paper we address the optimization of cable connections between turbines in an offshore wind park. Different versions of this problem have been studied recently. In a previous joint project with Vattenfall BA Wind (a global leader in energy production) we have studied and modeled the main constraints arising in practical cases. Building on that model, in the present paper we address new features that have been recently proposed by Vattenfall's experts. Turbines are becoming still more customized, therefore it is important to be able to evaluate the impact of new technologies with a flexible optimization tool. We here show how some new features can effectively be modeled and solved using a Mixed-Integer Linear Programming paradigm. Computational results on a real-world case are briefly presented.
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Title: Mathematical Optimization and Algorithms for Offshore Wind Farm Design: An Overview

Section 1: Introduction
Description 1: Introduce the need for renewable energy, specifically offshore wind energy, and outline the focus of the paper on mathematical optimization techniques for wind farm design.

Section 2: Wind Park Design Phases
Description 2: Describe the complex phases involved in designing an offshore wind park, including site selection, data collection, technology selection, layout definition, foundation cost evaluation, cable routing, electrical studies, and foundation design.

Section 3: Literature Overview
Description 3: Provide a literature review of various optimization problems and methods related to offshore wind park design, covering wind farm layout, cable routing, maintenance, turbine structure optimization, energy storage, and decommissioning.

Section 4: Outline Of The Paper
Description 4: Summarize the structure of the paper, highlighting the main sections and the specific optimization tasks discussed in each.

Section 5: A Proximity Search Heuristic For Wind Farm Layout
Description 5: Detail the methods used for solving the offshore wind farm layout problem, focusing on the optimization model, the challenges due to the wake effect, and the use of a proximity search heuristic.

Section 6: Real-World Application
Description 6: Present a case study of the Borssele wind park in the Netherlands, showing the optimization results and the benefits of using mathematical optimization techniques.

Section 7: Considering Cost of Foundations
Description 7: Discuss the inclusion of foundation costs in the optimization model and the results from the Borssele wind park case study, highlighting potential savings.

Section 8: Matheuristics for Cable Routing
Description 8: Explain the optimization of inter-array cable routing, the use of matheuristics, and the handling of complex constraints such as no-cross and cable losses.

Section 9: Real-world Application
Description 9: Illustrate the application of cable routing optimization in the Horns Rev 1 wind park in Denmark, showing the cost savings and layout improvements.

Section 10: Cable Losses
Description 10: Discuss the impact of electrical resistance and energy loss in cables, and the benefits of including these losses in the optimization model.

Section 11: Jacket Foundation Optimization
Description 11: Describe the optimization of jacket foundations for offshore turbines, focusing on the selection of tube dimensions and the modeling of structural stresses.

Section 12: Preliminary Results
Description 12: Present preliminary results from applying the jacket foundation optimization model to a simplified structure, comparing the optimized and manual solutions.

Section 13: Conclusions
Description 13: Summarize the key findings, emphasize the economic benefits of mathematical optimization in offshore wind farm design, and suggest directions for future research and application in the sector.