A Survey on Forced Oscillations in Power System
---
paper_title: Analysis of forced oscillations in a multimachine power system

paper_content:

The origin of forced, low frequency oscillations introduced in power systems by low-speed diesel generators is investigated. The linear models of a multimachine power system are presented for both interconnected and autonomous systems. Particular emphasis is given to the calculation of the electromechanical oscillation frequencies. A three-machine test system exhibiting a very strong resonance is analysed. The method of analysis is based upon the computation of the frequency response of a multivariable system. Finally, the electromechanical oscillation analysis and the frequency response computation are applied to the electric power system of the island of Crete, where a number of large low-speed diesel engine driven generators have recently been installed. >
---
paper_title: Application of ambient analysis techniques for the estimation of electromechanical oscillations from measured PMU data in four different power systems

paper_content:

The application of advanced signal processing techniques to power system measurement data for the estimation of dynamic properties has been a research subject for over two decades. Several techniques have been applied to transient (or ringdown) data, ambient data, and to probing data. Some of these methodologies have been included in off-line analysis software, and are now being incorporated into software tools used in control rooms for monitoring the near real-time behavior of power system dynamics. In this paper we illustrate the practical application of some ambient analysis methods for electromechanical mode estimation in different power systems. We apply these techniques to phasor measurement unit (PMU) data from stored archives of several hours originating from the US Eastern Interconnection (EI), the Western Electricity Coordinating Council (WECC), the Nordic Power System, and time-synchronized Frequency Disturbance Recorder (FDR) data from Nigeria. It is shown that available signal processing tools are readily applicable for analysis of different power systems, regardless of their specific dynamic characteristics. The discussions and results in this paper are of value to power system operators and planners as they provide information of the applicability of these techniques via readily available signal processing tools, and in addition, it is shown how to critically analyze the results obtained with these methods.
---
paper_title: Overview of algorithms for estimating swing modes from measured responses

paper_content:

Linear-system formulations are often used to describe power-system small-signal electromechanical dynamic properties. Over the past two decades, many techniques have been developed to conduct modal analysis using only actual-system measurements. Some techniques are appropriate for transient signals, others are for ambient signal conditions, and some are for conditions where a known probing signal is exciting the system. An overview of many of the more successful analysis techniques is presented. The theoretical background for these methods is summarized as well as application properties. Examples include computer simulations and actual system experiments from the western North American power system. Analysis goals center on estimating the modal frequency and damping.
---
paper_title: Effects of forced oscillations on spectral-based mode-shape estimation

paper_content:

The impact of forced oscillations on estimating electromechanical mode-shape from time-synchronized phasor measurements is assessed. The mode-shape algorithm is mathematically derived while including a forced-oscillation component. This provides a basis of a hypothesis of how the forced oscillation impacts the algorithm. The hypothesis is tested via a four-machine simulation.
---
paper_title: Model validation for the August 10, 1996 WSCC system outage

paper_content:

A major power outage occurred in Western North America on August 10, 1996. In this paper, the authors describe the simulation of this disturbance using a transient stability program. Initially, the sequence of events was simulated using the standard WSCC dynamic database, and the simulations did not agree with the disturbance recordings. Several model additions and data modifications were made before the simulations approximated the disturbance recordings. These model changes are discussed in the paper.
---
paper_title: Initial results in the detection and estimation of forced oscillations in power systems

paper_content:

With the phasor measurement unit (PMU) networks that have been developed to improve utilities' wide-area situational awareness, it is now possible to obtain high-fidelity observations of forced oscillations (FOs). Due to the large variation in their amplitudes, reliable methods for detecting forced oscillations and estimating their parameters are needed. In this paper, an algorithm designed for the detection and estimation of sinusoids in white Gaussian noise is modified for the colored noise environment of power systems. A novel time-localization algorithm based on the cross-correlation estimator is proposed to estimate the start and end points of a forced oscillation, and an estimator for the forced oscillation's amplitude dependent on these location estimates is developed. Using a simple model, the algorithms are shown to be capable of detecting a forced oscillation, estimating its frequency, locating it within the data, and estimating its amplitude.
---
paper_title: Response of Large Power Systems to Cyclic Load Variations

paper_content:

A method is presented for finding the response of a large power system to cyclic load variations. The waveform of the load variation is represented as a Fourier series. The power system is represented by a set of first-order, linear differential equations. These are solved to give the response of the system to each harmonic component, and the results combined to give the total response. Results from a sample problem are given as an example.
---
paper_title: Analysis of forced oscillations in a multimachine power system

paper_content:

The origin of forced, low frequency oscillations introduced in power systems by low-speed diesel generators is investigated. The linear models of a multimachine power system are presented for both interconnected and autonomous systems. Particular emphasis is given to the calculation of the electromechanical oscillation frequencies. A three-machine test system exhibiting a very strong resonance is analysed. The method of analysis is based upon the computation of the frequency response of a multivariable system. Finally, the electromechanical oscillation analysis and the frequency response computation are applied to the electric power system of the island of Crete, where a number of large low-speed diesel engine driven generators have recently been installed. >
---
paper_title: Frequency domain analysis of power system forced oscillations

paper_content:

A frequency domain approach is used to analyse power system forced low frequency oscillations. The gain characteristics of a closed loop transfer function, Gd(s)= Δδ/ΔPd, which reflects the effect of disturbances on power angle oscillations, are shown to be crucial in identifying the frequency ranges in which amplified oscillatory disturbances can occur. It is shown that tuning power system stabilisers (PSS), based on eigenvalue analysis, lack the insight gained from the explicit evaluation of the Gd(s) gain response. The proposed approach identifies a risky situation which could not be detected on an eigenvalue pattern. For weakly connected systems, the inherent negative damping effects, along with the PSS derivative feedback action, result in a situation where a PSS, tuned to locate the eigenvalues corresponding to the natural mode ωn at well damped locations, can still cause a hazardous situation. While flattening the |Gd(jω)| peak at ωn, the derivative supplementary excitation feedback loops can create another peak which may match oscillatory tie-line disturbances, thereby causing amplified oscillations. The paper also proposes a dynamic gain reduction scheme which can overcome this situation by decoupling the negative damping effects while accentuating the stabilising effects of the PSS derivative feedback. It is shown that a considerable reduction in the tie-line mode oscillations can be achieved. Generalisation to multimachine networks is straightforward. An Appendix is included to describe a systematic derivation of a polynomial matrix that evaluates disturbance rejection/attenuation functions in a general multi-machine environment.
---
paper_title: Limit-induced stable limit cycles in power systems

paper_content:

Heavily loaded power systems are susceptible to Hopf bifurcations, and consequent oscillatory instability. The onset of instability can be predicted by small disturbance (eigen-value) analysis, but the ensuring behaviour may depend strongly on nonlinearities within the system. In particular, physical limits place bounds on the divergent behaviour of states. This paper explores the situation where generator field-voltage limits capture behaviour, giving rise to a stable (though non-smooth) limit cycle. It is shown that shooting methods can be adapted to solve for such non-smooth limit-induced limit cycles. By continuing branches of limit-induced and smooth limit cycles, the paper established the co-existence of equilibria, smooth and non-smooth limit cycles. Furthermore, it is shown that when branches of limit-induced and smooth limit cycles merge, the limit cycles are annihilated at a grazing bifurcation.
---
paper_title: Effects of forced oscillations on spectral-based mode-shape estimation

paper_content:

The impact of forced oscillations on estimating electromechanical mode-shape from time-synchronized phasor measurements is assessed. The mode-shape algorithm is mathematically derived while including a forced-oscillation component. This provides a basis of a hypothesis of how the forced oscillation impacts the algorithm. The hypothesis is tested via a four-machine simulation.
---
paper_title: Synchronized Phasor Data for Analyzing Wind Power Plant Dynamic Behavior and Model Validation

paper_content:

The U.S. power industry is undertaking several initiatives that will improve the operations of the power grid. One of those is the implementation of 'wide area measurements' using phasor measurement units (PMUs) to dynamically monitor the operations and the status of the network and provide advanced situational awareness and stability assessment. This project seeks to obtain PMU data from wind power plants and grid reference points and develop software tools to analyze and visualize synchrophasor data for the purpose of better understanding wind power plant dynamic behaviors under normal and contingency conditions.
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paper_title: Studies on power systems that are subjected to cyclic loads

paper_content:

Simulation and control studies are carried out on a power system that is subjected to a cyclic load. The simulation method, which is based on singular perturbations, produces accurate results with reduced computation time compared to existing techniques such as the Van Ness method. A suboptimal controller is designed on the basis of slow and fast modes. Its performance is comparable to that of an optimal controller, while its design is much easier. >
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paper_title: Initial Results in Using a Self-Coherence Method for Detecting Sustained Oscillations

paper_content:

This paper develops a self-coherence method for detecting sustained oscillations using phasor measurement unit (PMU) data. Sustained oscillations decrease system performance and introduce potential reliability issues. Timely detection of the oscillations at an early stage provides the opportunity for taking remedial reaction. Using high-speed time-synchronized PMU data, this paper details a self-coherence method for detecting sustained oscillation, even when the oscillation amplitude is lower than ambient noise. Simulation and field measurement data are used to evaluate the proposed method's performance. It is shown that the proposed method can detect sustained oscillations and estimate oscillation frequencies with a low signal-to-noise ratio. Comparison with a power spectral density method also shows that the proposed self-coherence method performs better.
---
paper_title: An energy-based methodology for locating the source of forced oscillations in power systems

paper_content:

Recently, several power grids of China came across low frequency oscillations which are difficult to explain by the traditional negative damping mechanism. Some researchers suggest that those oscillations be caused by external periodic disturbances according to the forced oscillation mechanism. It takes no doubt that the oscillation source location (means locating the disturbances) is imperative and decisive to eliminate such a kind of oscillations. This paper proposes a location methodology based on Energy Supply on Port derived from the Port-Controlled Hamiltonian theory. By calculating the energy injected to the network at corresponding ports, the oscillation sources can be effectively located, even in complicated systems containing various kinds of control devices such as governors and exciters. Different from the traditional methodology based on eigen-analysis, the proposed methodology is naturally decentralized without the dependency on global measurements. Case studies on the standard 4-machine 2-area system and the IEEE-118 bus system show the effectiveness and efficiency of the proposed methodology.
---
paper_title: Inter-Area Resonance in Power Systems From Forced Oscillations

paper_content:

This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems.
---
paper_title: Power System Stability and Control

paper_content:

Part I: Characteristics of Modern Power Systems. Introduction to the Power System Stability Problem. Part II: Synchronous Machine Theory and Modelling. Synchronous Machine Parameters. Synchronous Machine Representation in Stability Studies. AC Transmission. Power System Loads. Excitation in Stability Studies. Prime Mover and Energy Supply Systems. High-Voltage Direct-Current Transmission. Control of Active Power and Reactive Power. Part III: Small Signal Stability. Transient Stability. Voltage Stability. Subsynchronous Machine Representation in Stability Studies. AC Transmission. Power System Loads. Excitation in Stability Studies. Prime Mover and Energy Supply Systems, High-Voltage Direct-Current Transmission. Control of Active Power and Reactive Power. Part III: Small Signal Stability. Transient Stability. Voltage Stability. Subsynchronous Oscillations. Mid-Term and Long-Term Stability. Methods of Improving System Stability.
---
paper_title: Response of Large Power Systems to Cyclic Load Variations

paper_content:

A method is presented for finding the response of a large power system to cyclic load variations. The waveform of the load variation is represented as a Fourier series. The power system is represented by a set of first-order, linear differential equations. These are solved to give the response of the system to each harmonic component, and the results combined to give the total response. Results from a sample problem are given as an example.
---
paper_title: Electromechanical Mode Estimation Using Recursive Adaptive Stochastic Subspace Identification

paper_content:

Measurement based algorithms for estimating low-frequency electromechanical modes serve as useful practical methods to monitor the modal properties of power system oscillations in real-time. This paper proposes a Recursive Adaptive Stochastic Subspace Identification (RASSI) algorithm for online monitoring of power system modes using wide-area synchrophasor data. The proposed method gives an online estimation of mode frequency and damping ratio as well as mode shapes using multi-channel measurement data. It exploits both the accuracy of subspace identification and fast computational capability of recursive methods. An adaptive method is proposed to enable fast tracking of modal evolution under poorly damped conditions together with low estimation variance under quasi-steady-state conditions. The algorithms are tested using simulated data from Kundur two-area test power system as well as measured data from real systems.
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paper_title: A Cross-Coherence Method for Detecting Oscillations

paper_content:

Oscillations threaten the stability of a power system. Timely detecting oscillations can improve operators' situational awareness of system stability and enable remedial reactions. To detect oscillations during their early stages, this paper proposes a cross-coherence method using multiple-channel phasor measurement unit (PMU) data. Oscillations are related to the peaks in coherence spectra and can be detected by visual inspection and setting up a threshold. Using simulation data, it is shown that the proposed coherence method can detect oscillations even under low signal-to-noise ratios. Three algorithms for estimating coherence spectra are implemented and evaluated. Their performances are compared using Monte Carlo methods. Based on the comparison, this paper makes some recommendations for proper use of the algorithms.
---
paper_title: Initial results in the detection and estimation of forced oscillations in power systems

paper_content:

With the phasor measurement unit (PMU) networks that have been developed to improve utilities' wide-area situational awareness, it is now possible to obtain high-fidelity observations of forced oscillations (FOs). Due to the large variation in their amplitudes, reliable methods for detecting forced oscillations and estimating their parameters are needed. In this paper, an algorithm designed for the detection and estimation of sinusoids in white Gaussian noise is modified for the colored noise environment of power systems. A novel time-localization algorithm based on the cross-correlation estimator is proposed to estimate the start and end points of a forced oscillation, and an estimator for the forced oscillation's amplitude dependent on these location estimates is developed. Using a simple model, the algorithms are shown to be capable of detecting a forced oscillation, estimating its frequency, locating it within the data, and estimating its amplitude.
---
paper_title: Bootstrap-based hypothesis test for detecting sustained oscillations

paper_content:

Sustained oscillations are one of major stability concerns of a power system operator. In order to take effective remedial reactions, it is preferred to detect sustained oscillations at their early stage. Previously, self-coherence spectra were used to detect sustained oscillations using phasor measurement unit (PMU) data. This paper proposes a hypothesis test using a bootstrap method to set up a threshold on the self-coherence spectra for detecting oscillations. Simulation data are used to evaluate the performance of this method. Case studies show that the proposed method can select a threshold with a predetermined false positive rate.
---
paper_title: Initial Results in Using a Self-Coherence Method for Detecting Sustained Oscillations

paper_content:

This paper develops a self-coherence method for detecting sustained oscillations using phasor measurement unit (PMU) data. Sustained oscillations decrease system performance and introduce potential reliability issues. Timely detection of the oscillations at an early stage provides the opportunity for taking remedial reaction. Using high-speed time-synchronized PMU data, this paper details a self-coherence method for detecting sustained oscillation, even when the oscillation amplitude is lower than ambient noise. Simulation and field measurement data are used to evaluate the proposed method's performance. It is shown that the proposed method can detect sustained oscillations and estimate oscillation frequencies with a low signal-to-noise ratio. Comparison with a power spectral density method also shows that the proposed self-coherence method performs better.
---
paper_title: A coherence method for detecting and analyzing oscillations

paper_content:

In this paper, a coherence method is proposed to detect and analyze forced oscillations from phasor measurement unit data. The calculation of coherence spectrum is reviewed, and forced oscillations are related to the peaks in the coherence spectrum. Using simulation and field measurement data, the proposed coherence method's performance is compared with the power spectral density method. When applied to detect and analyze forced oscillations under low signal noise ratio conditions, the proposed coherence method shows better performance.
---
paper_title: Inter-Area Resonance in Power Systems From Forced Oscillations

paper_content:

This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems.
---
paper_title: Model validation for the August 10, 1996 WSCC system outage

paper_content:

A major power outage occurred in Western North America on August 10, 1996. In this paper, the authors describe the simulation of this disturbance using a transient stability program. Initially, the sequence of events was simulated using the standard WSCC dynamic database, and the simulations did not agree with the disturbance recordings. Several model additions and data modifications were made before the simulations approximated the disturbance recordings. These model changes are discussed in the paper.
---
paper_title: Active Power Oscillation Property Classification of Electric Power Systems Based on SVM

paper_content:

Nowadays, low frequency oscillation has become a major problem threatening the security of large-scale interconnected power systems. According to generation mechanism, active power oscillation of electric power systems can be classified into two categories: free oscillation and forced oscillation. The former results from poor or negative damping ratio of power system and external periodic disturbance may lead to the latter. Thus control strategies to suppress the oscillations are totally different. Distinction from each other of those two different kinds of power oscillations becomes a precondition for suppressing the oscillations with proper measures. This paper proposes a practical approach for power oscillation classification by identifying real-time power oscillation curves. Hilbert transform is employed to obtain envelope curves of the power oscillation curves. Twenty sampling points of the envelope curve are selected as the feature matrices to train and test the supporting vector machine (SVM). The tests on the 16-machine 68-bus benchmark power system and a real power system in China indicate that the proposed oscillation classification method is of high precision.
---
paper_title: Distinguishing features of natural and forced oscillations

paper_content:

Synchronous power systems often experience two types of oscillatory responses: natural and forced. Natural oscillations are a transient response characterized by the electromechanical oscillation modes. If one or more of these modes are undamped, a sustained oscillation occurs with the system in a near unstable condition. Alternatively, forced oscillations are typically caused by some rouge input driving the system into a sustained oscillation. An example is an ill-operating power-plant steam valve oscillating in a limit-cycle. This paper examines the unique features that may allow one to distinguish between a very lightly-damped (or undamped) natural oscillation and a forced oscillation. We first provide a unique mathematical representation for forced versus natural oscillations. The model is then used to show that the noise response of the system under the undamped natural case is considerably different than under the forced case. We show a spectral approach for using this difference to distinguish between the oscillation types.
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paper_title: Data-driven diagnostics of mechanism and source of sustained oscillations

paper_content:

Sustained oscillations observed in power systems can damage equipment, degrade the power quality and increase the risks of cascading blackouts. There are several mechanisms that can give rise to oscillations, each requiring different countermeasure to suppress or eliminate the oscillation. This work develops mathematical framework for analysis of sustained oscillations and identifies statistical signatures of each mechanism, based on which a novel oscillation diagnosis method is developed via real-time processing of phasor measurement units (PMUs) data. Case studies show that the proposed method can accurately identify the exact mechanism for sustained oscillation, and meanwhile provide insightful information to locate the oscillation sources.
---
paper_title: Application of ambient analysis techniques for the estimation of electromechanical oscillations from measured PMU data in four different power systems

paper_content:

The application of advanced signal processing techniques to power system measurement data for the estimation of dynamic properties has been a research subject for over two decades. Several techniques have been applied to transient (or ringdown) data, ambient data, and to probing data. Some of these methodologies have been included in off-line analysis software, and are now being incorporated into software tools used in control rooms for monitoring the near real-time behavior of power system dynamics. In this paper we illustrate the practical application of some ambient analysis methods for electromechanical mode estimation in different power systems. We apply these techniques to phasor measurement unit (PMU) data from stored archives of several hours originating from the US Eastern Interconnection (EI), the Western Electricity Coordinating Council (WECC), the Nordic Power System, and time-synchronized Frequency Disturbance Recorder (FDR) data from Nigeria. It is shown that available signal processing tools are readily applicable for analysis of different power systems, regardless of their specific dynamic characteristics. The discussions and results in this paper are of value to power system operators and planners as they provide information of the applicability of these techniques via readily available signal processing tools, and in addition, it is shown how to critically analyze the results obtained with these methods.
---
paper_title: Oscillation monitoring from ambient PMU measurements by Frequency Domain Decomposition

paper_content:

This paper extends the method of frequency domain decomposition (FDD) towards real-time analysis of ambient PMU measurements in power systems for the purpose of oscillation monitoring. The main idea of FDD is to apply singular value decomposition (SVD) to the power density spectrum matrix. The resulting singular values correspond to individual modes under specific conditions. The damping ratio, modal frequency and the mode shape of poorly damped (with less than 5% damping ratios) oscillatory modes can be directly determined from ambient PMU measurements. The theoretical background is presented in the paper. The technique is tested on small linear systems to show its effectiveness and weaknesses. Finally, the application of FDD in power system is shown.
---
paper_title: Overview of algorithms for estimating swing modes from measured responses

paper_content:

Linear-system formulations are often used to describe power-system small-signal electromechanical dynamic properties. Over the past two decades, many techniques have been developed to conduct modal analysis using only actual-system measurements. Some techniques are appropriate for transient signals, others are for ambient signal conditions, and some are for conditions where a known probing signal is exciting the system. An overview of many of the more successful analysis techniques is presented. The theoretical background for these methods is summarized as well as application properties. Examples include computer simulations and actual system experiments from the western North American power system. Analysis goals center on estimating the modal frequency and damping.
---
paper_title: Applications of Spectral Analysis Techniques for Estimating the Nordic Grid's Low Frequency Electromechanical Oscillations*

paper_content:

For power networks such as the Nordic Grid, that have operation constraints limits imposed by the existence of low-damped electromechanical oscillations, the estimation of electromechanical mode properties is of crucial importance for providing power system control room operators with adequate indicators of the stress of their network. This article addresses the practical application of different spectral analysis techniques that can be used for the estimation of electromechanical mode properties using data emerging from real synchronized phasor measurement units (PMUs) located at both the low-voltage distribution and high-voltage transmission networks of the Nordic grid. Emphasis is made on providing systematic approaches to deal with imperfect data found in practice so that accurate estimates can be computed.
---
paper_title: Effects of forced oscillations on spectral-based mode-shape estimation

paper_content:

The impact of forced oscillations on estimating electromechanical mode-shape from time-synchronized phasor measurements is assessed. The mode-shape algorithm is mathematically derived while including a forced-oscillation component. This provides a basis of a hypothesis of how the forced oscillation impacts the algorithm. The hypothesis is tested via a four-machine simulation.
---
paper_title: An energy-based method for location of power system oscillation source

paper_content:

An energy-based method to locate oscillation sources in power systems is proposed. The energy is identical to the transient energy. The amount of energy is consistent with the oscillation amplitude, and then the component producing energy has negative contribution to the damping and is considered as the oscillation source. The consistency of energy dissipation with damping torque of a generator is proved. A method to compute energy flow in the network based on wide area measurement system data and independent of energy functions is proposed. The energy dissipation or production of a component in the system can be obtained from the net energy flow. The components producing energy are oscillation sources and emergency control actions should be taken on them. The method is validated by simulations and actual oscillation incidents analyses.
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paper_title: Spectral estimation of low-frequency oscillations in the Nordic grid using ambient synchrophasor data under the presence of forced oscillations

paper_content:

Spectral analysis applied to synchrophasor data can provide valuable information about lightly damped low-frequency modes in power systems. This paper demonstrates application of two non-parametric spectral estimators focusing on mode frequency estimation. The first one is the well-known Welch spectral estimator whereas the application of Multitaper method is proposed here. In addition, the paper discusses mode estimator tuning procedures and the estimators' performances in the presence of “forced” oscillations. The validity of the proposed application of the non-parametric estimators and tuning procedures is verified through both simulated data and PMU data originating from the high-voltage grid of the Nordic power system. Special attention is given to the analysis of the behaviour of different low frequency modes present in the Nordic grid, including that of forced oscillations.
---
paper_title: Model validation for the August 10, 1996 WSCC system outage

paper_content:

A major power outage occurred in Western North America on August 10, 1996. In this paper, the authors describe the simulation of this disturbance using a transient stability program. Initially, the sequence of events was simulated using the standard WSCC dynamic database, and the simulations did not agree with the disturbance recordings. Several model additions and data modifications were made before the simulations approximated the disturbance recordings. These model changes are discussed in the paper.
---
paper_title: Effects of forced oscillations in power system damping estimation

paper_content:

This article analyzes the impact of forced power system oscillations on mode damping estimation. Parametric (Yule-Walker) and non-parametric (Welch) methods for mode estimation are tested in the presence of forced power system oscillations. For mode damping estimation based on non-parametric methods, an application of Half Power Point method is proposed. Performances of the mode estimators are evaluated using both simulated and real synchrophasor data from the Nordic Grid. The presence of forced oscillations poses difficulties to mode damping estimators, these difficulties are identified, illustrated and explained herein.
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paper_title: Application of Phasor Measurement Unit on Locating Disturbance Source for Low-Frequency Oscillation

paper_content:

A smart power grid is an integration of the advanced measurement, communication, computer, and control techniques. Among all the state-of-the-art technologies in building a smart power grid, the phasor measurement unit (PMU) is an important and promising one. Nowadays in China, most ultrahigh- and high-voltage buses are all equipped with PMUs. This paper reports an application of PMU data on locating the disturbance source for the low-frequency oscillation that has happened several times in the interconnected big power grids in China recently. The posterior analysis by the Electric Power System Research Institute of China (CEPRI) has confirmed that these low-frequency oscillations are caused by the resonance phenomena. It is urgent to find the disturbance source in case it happens again. However, there have been no systematic and effective methods to locate the disturbance in a very large power system. The trial and error method has been implemented via the digital simulations, but in vain. To overcome this problem, a novel method is developed in this paper to locate the disturbance source with the help of PMUs. The method takes advantage of the PMU measurements to reduce the searching area for locating the disturbance source. Case studies show the efficiency of the proposed method.
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paper_title: The disturbance source identification of forced power oscillation caused by continuous cyclical load

paper_content:

The continuous cyclical load disturbances can lead to forced power oscillations of power systems. Based on the single-machine infinite-bus system, the differences in the energy conversion characteristics between the forced power oscillation and the weak damping free oscillation are analyzed and the mechanism of the forced power oscillation caused by cyclical load disturbances is presented. Using energy functions with the linear equations of motion of the rotor, the basic principles to identify the cyclical load disturbance source location of the forced power oscillation are analyzed in energy perspective. The simulation results of the New England 10-machine 39-bus system indicate the feasibility and validity of the proposed method.
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paper_title: Forced power oscillation analysis based on EEAC theory

paper_content:

The power system forced power oscillation will be excited by the continuous cyclical small power disturbances. The forced power oscillation theory can explain some low frequency oscillations that are not caused by negative damping. In this paper, the multi-machine power system forced power oscillation is analysed on the dominant oscillation mode based on EEAC theory. And then the condition on which the amplitude of forced power oscillation caused by two disturbance sources can be the maximum is studied. A method of prime mover disturbance source identification is presented and verified.
---
paper_title: An energy-based methodology for locating the source of forced oscillations in power systems

paper_content:

Recently, several power grids of China came across low frequency oscillations which are difficult to explain by the traditional negative damping mechanism. Some researchers suggest that those oscillations be caused by external periodic disturbances according to the forced oscillation mechanism. It takes no doubt that the oscillation source location (means locating the disturbances) is imperative and decisive to eliminate such a kind of oscillations. This paper proposes a location methodology based on Energy Supply on Port derived from the Port-Controlled Hamiltonian theory. By calculating the energy injected to the network at corresponding ports, the oscillation sources can be effectively located, even in complicated systems containing various kinds of control devices such as governors and exciters. Different from the traditional methodology based on eigen-analysis, the proposed methodology is naturally decentralized without the dependency on global measurements. Case studies on the standard 4-machine 2-area system and the IEEE-118 bus system show the effectiveness and efficiency of the proposed methodology.
---
paper_title: Inter-Area Resonance in Power Systems From Forced Oscillations

paper_content:

This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems.
---
paper_title: Power System Stability and Control

paper_content:

Part I: Characteristics of Modern Power Systems. Introduction to the Power System Stability Problem. Part II: Synchronous Machine Theory and Modelling. Synchronous Machine Parameters. Synchronous Machine Representation in Stability Studies. AC Transmission. Power System Loads. Excitation in Stability Studies. Prime Mover and Energy Supply Systems. High-Voltage Direct-Current Transmission. Control of Active Power and Reactive Power. Part III: Small Signal Stability. Transient Stability. Voltage Stability. Subsynchronous Machine Representation in Stability Studies. AC Transmission. Power System Loads. Excitation in Stability Studies. Prime Mover and Energy Supply Systems, High-Voltage Direct-Current Transmission. Control of Active Power and Reactive Power. Part III: Small Signal Stability. Transient Stability. Voltage Stability. Subsynchronous Oscillations. Mid-Term and Long-Term Stability. Methods of Improving System Stability.
---
paper_title: Locating method of disturbance source of forced power oscillation based on prony anyasis

paper_content:

The characteristics of modern power grid such as extreme high voltage, large capacity and interconnection network bring a lot of challenges to the security and stabilization of power system in our country. Among them, forced power oscillation is an important problem which widely exists and needs to be studied urgently. And the study of synchronizing torque and damping torque is an important method to analyze low frequency oscillation. In this paper, Firstly, the theoretical analysis of forced power oscillation based on two- machine equivalent system has been done. Secondly, A new Prony analysis of electric torque coefficient (ETC) is proposed as the old method of ETC doesn't work well. Then, the damping torque of the machine considering the engine speed regulation system is analyzed theoretically. Finally, the simulation in the four-machine two regions system is done and the results have verified the feasibility and effectiveness of the new method.
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paper_title: Electromechanical mode shape estimation based on transfer function identification using PMU measurements

paper_content:

Power system mode shapes are a key indication of how dynamic components participate in low-frequency oscillations. Traditionally, mode shapes are calculated from a linearized dynamic model. For large-scale power systems, obtaining accurate dynamic models is very difficult. Therefore, measurement-based mode shape estimation methods have certain advantages, especially for the application of real-time small signal stability monitoring. In this paper, a measurement-based mode shape identification method is proposed. The general relationship between transfer function (TF) and mode shape is derived. As an example, a least square (LS) method is implemented to estimate mode shape using an autoregressive exogenous (ARX) model. The performance of the proposed method is evaluated by Monte-Carlo studies using simulation data from a 17-machine model. The results indicate the validity of the proposed method in estimating mode shapes with reasonably good accuracy.
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paper_title: Application of ambient analysis techniques for the estimation of electromechanical oscillations from measured PMU data in four different power systems

paper_content:

The application of advanced signal processing techniques to power system measurement data for the estimation of dynamic properties has been a research subject for over two decades. Several techniques have been applied to transient (or ringdown) data, ambient data, and to probing data. Some of these methodologies have been included in off-line analysis software, and are now being incorporated into software tools used in control rooms for monitoring the near real-time behavior of power system dynamics. In this paper we illustrate the practical application of some ambient analysis methods for electromechanical mode estimation in different power systems. We apply these techniques to phasor measurement unit (PMU) data from stored archives of several hours originating from the US Eastern Interconnection (EI), the Western Electricity Coordinating Council (WECC), the Nordic Power System, and time-synchronized Frequency Disturbance Recorder (FDR) data from Nigeria. It is shown that available signal processing tools are readily applicable for analysis of different power systems, regardless of their specific dynamic characteristics. The discussions and results in this paper are of value to power system operators and planners as they provide information of the applicability of these techniques via readily available signal processing tools, and in addition, it is shown how to critically analyze the results obtained with these methods.
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paper_title: Applications of Spectral Analysis Techniques for Estimating the Nordic Grid's Low Frequency Electromechanical Oscillations*

paper_content:

For power networks such as the Nordic Grid, that have operation constraints limits imposed by the existence of low-damped electromechanical oscillations, the estimation of electromechanical mode properties is of crucial importance for providing power system control room operators with adequate indicators of the stress of their network. This article addresses the practical application of different spectral analysis techniques that can be used for the estimation of electromechanical mode properties using data emerging from real synchronized phasor measurement units (PMUs) located at both the low-voltage distribution and high-voltage transmission networks of the Nordic grid. Emphasis is made on providing systematic approaches to deal with imperfect data found in practice so that accurate estimates can be computed.
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paper_title: A Cross-Coherence Method for Detecting Oscillations

paper_content:

Oscillations threaten the stability of a power system. Timely detecting oscillations can improve operators' situational awareness of system stability and enable remedial reactions. To detect oscillations during their early stages, this paper proposes a cross-coherence method using multiple-channel phasor measurement unit (PMU) data. Oscillations are related to the peaks in coherence spectra and can be detected by visual inspection and setting up a threshold. Using simulation data, it is shown that the proposed coherence method can detect oscillations even under low signal-to-noise ratios. Three algorithms for estimating coherence spectra are implemented and evaluated. Their performances are compared using Monte Carlo methods. Based on the comparison, this paper makes some recommendations for proper use of the algorithms.
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paper_title: Initial results in the detection and estimation of forced oscillations in power systems

paper_content:

With the phasor measurement unit (PMU) networks that have been developed to improve utilities' wide-area situational awareness, it is now possible to obtain high-fidelity observations of forced oscillations (FOs). Due to the large variation in their amplitudes, reliable methods for detecting forced oscillations and estimating their parameters are needed. In this paper, an algorithm designed for the detection and estimation of sinusoids in white Gaussian noise is modified for the colored noise environment of power systems. A novel time-localization algorithm based on the cross-correlation estimator is proposed to estimate the start and end points of a forced oscillation, and an estimator for the forced oscillation's amplitude dependent on these location estimates is developed. Using a simple model, the algorithms are shown to be capable of detecting a forced oscillation, estimating its frequency, locating it within the data, and estimating its amplitude.
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paper_title: Effects of forced oscillations in power system damping estimation

paper_content:

This article analyzes the impact of forced power system oscillations on mode damping estimation. Parametric (Yule-Walker) and non-parametric (Welch) methods for mode estimation are tested in the presence of forced power system oscillations. For mode damping estimation based on non-parametric methods, an application of Half Power Point method is proposed. Performances of the mode estimators are evaluated using both simulated and real synchrophasor data from the Nordic Grid. The presence of forced oscillations poses difficulties to mode damping estimators, these difficulties are identified, illustrated and explained herein.
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paper_title: Application of Phasor Measurement Unit on Locating Disturbance Source for Low-Frequency Oscillation

paper_content:

A smart power grid is an integration of the advanced measurement, communication, computer, and control techniques. Among all the state-of-the-art technologies in building a smart power grid, the phasor measurement unit (PMU) is an important and promising one. Nowadays in China, most ultrahigh- and high-voltage buses are all equipped with PMUs. This paper reports an application of PMU data on locating the disturbance source for the low-frequency oscillation that has happened several times in the interconnected big power grids in China recently. The posterior analysis by the Electric Power System Research Institute of China (CEPRI) has confirmed that these low-frequency oscillations are caused by the resonance phenomena. It is urgent to find the disturbance source in case it happens again. However, there have been no systematic and effective methods to locate the disturbance in a very large power system. The trial and error method has been implemented via the digital simulations, but in vain. To overcome this problem, a novel method is developed in this paper to locate the disturbance source with the help of PMUs. The method takes advantage of the PMU measurements to reduce the searching area for locating the disturbance source. Case studies show the efficiency of the proposed method.
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paper_title: Active Power Oscillation Property Classification of Electric Power Systems Based on SVM

paper_content:

Nowadays, low frequency oscillation has become a major problem threatening the security of large-scale interconnected power systems. According to generation mechanism, active power oscillation of electric power systems can be classified into two categories: free oscillation and forced oscillation. The former results from poor or negative damping ratio of power system and external periodic disturbance may lead to the latter. Thus control strategies to suppress the oscillations are totally different. Distinction from each other of those two different kinds of power oscillations becomes a precondition for suppressing the oscillations with proper measures. This paper proposes a practical approach for power oscillation classification by identifying real-time power oscillation curves. Hilbert transform is employed to obtain envelope curves of the power oscillation curves. Twenty sampling points of the envelope curve are selected as the feature matrices to train and test the supporting vector machine (SVM). The tests on the 16-machine 68-bus benchmark power system and a real power system in China indicate that the proposed oscillation classification method is of high precision.
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paper_title: Initial Results in Using a Self-Coherence Method for Detecting Sustained Oscillations

paper_content:

This paper develops a self-coherence method for detecting sustained oscillations using phasor measurement unit (PMU) data. Sustained oscillations decrease system performance and introduce potential reliability issues. Timely detection of the oscillations at an early stage provides the opportunity for taking remedial reaction. Using high-speed time-synchronized PMU data, this paper details a self-coherence method for detecting sustained oscillation, even when the oscillation amplitude is lower than ambient noise. Simulation and field measurement data are used to evaluate the proposed method's performance. It is shown that the proposed method can detect sustained oscillations and estimate oscillation frequencies with a low signal-to-noise ratio. Comparison with a power spectral density method also shows that the proposed self-coherence method performs better.
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paper_title: A coherence method for detecting and analyzing oscillations

paper_content:

In this paper, a coherence method is proposed to detect and analyze forced oscillations from phasor measurement unit data. The calculation of coherence spectrum is reviewed, and forced oscillations are related to the peaks in the coherence spectrum. Using simulation and field measurement data, the proposed coherence method's performance is compared with the power spectral density method. When applied to detect and analyze forced oscillations under low signal noise ratio conditions, the proposed coherence method shows better performance.
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paper_title: Distinguishing features of natural and forced oscillations

paper_content:

Synchronous power systems often experience two types of oscillatory responses: natural and forced. Natural oscillations are a transient response characterized by the electromechanical oscillation modes. If one or more of these modes are undamped, a sustained oscillation occurs with the system in a near unstable condition. Alternatively, forced oscillations are typically caused by some rouge input driving the system into a sustained oscillation. An example is an ill-operating power-plant steam valve oscillating in a limit-cycle. This paper examines the unique features that may allow one to distinguish between a very lightly-damped (or undamped) natural oscillation and a forced oscillation. We first provide a unique mathematical representation for forced versus natural oscillations. The model is then used to show that the noise response of the system under the undamped natural case is considerably different than under the forced case. We show a spectral approach for using this difference to distinguish between the oscillation types.
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paper_title: Inter-Area Resonance in Power Systems From Forced Oscillations

paper_content:

This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems.
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paper_title: Data-driven diagnostics of mechanism and source of sustained oscillations

paper_content:

Sustained oscillations observed in power systems can damage equipment, degrade the power quality and increase the risks of cascading blackouts. There are several mechanisms that can give rise to oscillations, each requiring different countermeasure to suppress or eliminate the oscillation. This work develops mathematical framework for analysis of sustained oscillations and identifies statistical signatures of each mechanism, based on which a novel oscillation diagnosis method is developed via real-time processing of phasor measurement units (PMUs) data. Case studies show that the proposed method can accurately identify the exact mechanism for sustained oscillation, and meanwhile provide insightful information to locate the oscillation sources.
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Title: A Survey on Forced Oscillations in Power System

Section 1: Introduction
Description 1: Provide an overview of low-frequency oscillations in power systems, their classification, and the importance of understanding and mitigating forced oscillations.

Section 2: Source of Forced Oscillations
Description 2: Discuss the identification of sources of forced oscillations, their impact on power systems, and summarize reported sources and studies.

Section 3: Oscillation Detection Methods
Description 3: Review existing methods for detecting forced oscillations, including statistical and spectral analysis techniques, and discuss challenges and accuracy of these methods.

Section 4: Oscillation Classification Methods
Description 4: Outline methods used to classify oscillations into forced or free categories, highlighting machine learning and spectral approaches.

Section 5: Oscillation Source Locating Methods
Description 5: Describe techniques for locating the sources of forced oscillations within power systems, including PMU-based methods and energy-based approaches.

Section 6: Effects of Forced Oscillation on Mode Estimation Algorithms
Description 6: Examine the impacts of forced oscillations on mode estimation algorithms, discussing how they affect system stability and mode shape estimation.

Section 7: Future Opportunities for Studying Forced Oscillations
Description 7: Discuss potential future research directions and opportunities for improving detection, classification, and localization of forced oscillations in power systems.

Section 8: Conclusion
Description 8: Summarize the main findings on forced oscillations in power systems and underscore the necessity of robust methods for detection, classification, and mitigation in ensuring system stability.