Electromechanical Oscillation Modes Research Articles

Small signal stability analysis of a wind power system integrated with a multi-band supplementary damping controller

Abstract With the integration of wind turbines represented by doubly-fed induction generators (DFIG) into the power system, the inertia level of the system decreases sharply, and small disturbances can easily cause low-frequency oscillation (LFO) in the system. In this paper, we propose a multi-band supplementary damping controller (MBSDC) directly applied to the active power control link of the rotor-side converter in the wind power generation system. We establish a linearized model for DFIG integrated with the power system, calculate eigenvalues, and screen out multiple electromechanical oscillation modes to be suppressed. Based on the calculation results, an MBSDC is designed to suppress LFO, and we propose a parameter-setting algorithm to enhance the suppression effect. Taking the New England 10-generator 39-bus system containing DFIG as an example for simulation verification, the results show that the MBSDC and parameter setting algorithm designed in this paper can effectively suppress LFO.

Ambient data-driven participation factors related to oscillation modes based on subspace dynamic mode decomposition

Analyzing the connection between the variables participating in the oscillation and modes in electromechanical oscillation is particularly important for maintaining system stability. This paper proposes an ambient data-driven method based on Subspace Dynamic Mode Decomposition (Sub-DMD) to extract the Participation Factors (PFs) related to system state and algebraic variables in electromechanical oscillation modes. This method uses ambient data to calculate the low-dimensional approximate matrix of the system, and the PFs is extracted by using eigen-decomposition and mode energy. Compare the extracted PFs with the results of power generation dispatch. The effectiveness of the proposed method is demonstrated by using simulation data from IEEE 4-generator 2-area test system and IEEE 16-generator 68-bus test system.

Method to Quantify Modal Interactions Between Converter Interfaced Generators and Synchronous Generators

The aim of this paper is to quantify the interactions between the oscillation modes of power systems within the realm of small-signal stability. This paper focuses on the interactions between Converter Interfaced Generator (CIG) oscillation modes and electromechanical oscillation modes of Synchronous Generators (SGs). It is difficult to determine the modal interactions using the existing analysis such as mode sensitivity, mode loci and participation factors. This paper proposes an extension to eigenvalue sensitivity analysis in order to determine the interaction between modes and impact of the interaction on system stability. Interaction coefficients are proposed to quantify the interaction between the modes. A modified IEEE 39-bus system with CIGs is considered to carry out the proposed analysis. The analysis is carried out to investigate the impact of PLL parameters on the interaction among the oscillation modes. The analysis is also carried out considering renewable energy penetration levels of 50-70%. It is observed that the interaction between CIG and electromechanical modes of SG results in increased participation of SGs' states in CIG modes. This increased participation of SG states in CIG modes results in reduced damping of oscillations in SG states.

Assessment of Mode Shape in Power System Using TVF-EMD and Spectral Analysis

This paper presents a robust dynamic approach for the monitoring and estimation of electromechanical oscillatory modes in the power system in real-time with less computational burden. Extensive implementation of phasor measurement units (PMU) and the utilization of advanced signal processing techniques help in identifying the dynamic behaviors of oscillatory modes. Conventional nonstationary analysis techniques are computationally weak to handle a larger quantity of data. This research utilizes the time-varying filter based empirical mode decomposition method for signal decomposition, which is highly tolerant to noise and computationally more robust. Low frequency modes are estimated by analyzing the power spectral density of the most suitable decomposed mode, the selection of which is done using correlation analysis. Instantaneous mode shapes of the signals are determined using cross-power spectral density functions, which will give the operator much information about the nature of oscillations and provide proactive steps to improve the operation of the power system. The proposed approach has been tested using signals obtained from two areas Kundur system and actual PMU data recorded from Power System Operation Corporation (POSOCO) Limited of the Indian power grid. The results confirm the superior viability and adaptability of the proposed approach in estimating the electromechanical modes. The instantaneous mode shapes are analyzed accurately with less computational complexity compared to the existing nonstationary strategies which are used for power system mode estimation.

Estimation of dominant power oscillation modes based on ConvLSTM approach using synchrophasor data and cross-validation technique

This paper proposes a deep neural network approach considering performance-based cross-validation and confidence interval analysis to estimate a power system’s dominant power oscillation modes. Due to increased electricity demands, power utilities implement various generation sources in their power systems. Accordingly, a modern power system is increasingly complex as a multi-area and multi-machine power system. The electromechanical oscillation modes arise inevitably. Moreover, a major-unexpected event could excite weakly damped power oscillation modes and cause power system instability. The estimation of dominant power oscillation modes is significant for power system monitoring and control. A fast computing time of such modes estimation is essential for further actions. This paper applies the convolutional long short-term memory 2-dimension (ConvLSTM2D) approach to estimate dominant oscillation modes based on synchrophasor data. The proposed ConvLSTM2D approach provides precise estimation with a great opportunity to avoid a forced power system outage. The simulation results of the ConvLSTM2D approach show better accuracy of the dominant power oscillation modes estimated in comparison with the state-of-the-art algorithms (SOTA), i.e., long short-term memory (LSTM), gated recurrent unit (GRU), and hybrid convolutional neural networks-long short-term memory (CNN-LSTM) algorithms. The proposed approach is a systematic approach that can be adaptively improved over time. In addition, the proposed approach can be further applied to wide-area monitoring considering the stability margin of a transmission system. • A ConvLSTM approach is proposed to estimate multiple dominant power oscillation modes. • The proposed approach using time-series cross-validation provides a promising performance. • The performance of proposed approach is robust proved by confidence interval analysis. • The proposed approach can reduce model parameters and training time.

Parameter Identification of Electromechanical Oscillation Mode in Power Systems Driven by Data: A Quasi-Real-Time Method Based on Randomized-DMD-Multilayer Artificial Neural Networks

With the increase in the power system scale, the identification of electromechanical oscillation mode parameters by traditional numerical methods can no longer meet the requirements of complete real-time analysis. Therefore, a method based on machine learning (multilayer artificial neural networks) is proposed to identify the electromechanical oscillation mode parameters of the power system. This method can take the monitorable variables of the WAMS as the input of the model and the key characteristic information such as frequency and damping ratio as the output. After processing the input and output data with randomized dynamic mode decomposition (randomized-DMD), their mapping relationship can be analyzed by using the multilayer neuron architecture. The simulation results of the 4-generator 2-area system and the IEEE 16-generator 5-area system show that this method can accurately calculate the key characteristic parameters of the system without considering the change in the control parameters and after the offline training of historical data, which shows higher accuracy, stronger robustness, and sensitive online tracking ability.

Synchronizing Torque-Based Transient Stability Index of a Multimachine Interconnected Power System

Newly developed tools and techniques are continuously established to analyze and monitor power systems’ transient stability limits. In this paper, a model-based transient stability index for each generator is proposed from the synchronizing torque contributions of all other connected generators in a multi-machine interconnected power system. It is a new interpretation of the generator’s synchronizing torque coefficient (STC) in terms of electromechanical oscillation modes to consider the synchronizing torque interactions among generators. Thus, the system operator can continuously monitor the system’s available secured transient stability limit in terms of synchronizing torque more accurately, which is helpful for planning and operation studies due to the modal based index. Furthermore, the popular transient stability indicator critical clearing time (CCT), and the traditionally determined synchronizing torque values without other generator contributions, are calculated to verify and compare the performance of the proposed transient stability index. The simulations and test result discussions are performed over a western system coordinating council (WSCC) 9-bus and an extensive New England 68-bus large power test system cases. The open-source power system analysis toolbox (PSAT) on the MATLAB/Simulink environment is used to develop, simulate, validate and compare the proposed transient stability index.

Estimation of mode shape in power systems under ambient conditions using advanced signal processing approach

This paper presents a dynamic approach for the monitoring and estimation of electromechanical oscillatory modes in the power system in real time with less computational burden. Extensive implementation of phasor measurement units (PMU) and the utilization of advanced signal processing techniques help in identifying the dynamic behaviors of oscillatory modes. Conventional nonstationary analysis techniques are computationally weak to handle a larger quantity of data in real-time. This research utilizes the variational mode decomposition (VMD) for signal decomposition, which is highly tolerant to noise and computationally more robust. The predefined parameters of the VMD process are assigned using FFT analysis of the signal. The significant decomposed mode resembling the original signal is determined using the correlation coefficient method and used for low-frequency mode estimation. The spectral analysis techniques are used to determine the instantaneous mode shapes, which help to identify the source of oscillation in the power system network. The proposed methodology has been tested using signals obtained from two area Kundur system and actual PMU data recorded from Power System Operation Corporation (POSOCO) Limited of the Indian Power grid. The results confirm the superior viability and adaptability of the proposed approach. The performance comparison with other existing signal processing techniques used to estimate low-frequency modes is also presented to illustrate the effectiveness of the proposed method.

Impact analysis of COVID-19 pandemic on the electricity demand, frequency control and electromechanical oscillation modes of the Brazilian Interconnected Power System using low voltage WAMS data

COVID-19 pandemic presented unique features among the range of threats encountered over the last century. Its impact echoes throughout the world affecting societies and their patterns of behavior, hence affecting the usage of electricity and the operation of power systems. This paper provides an analysis of the impact of COVID-19 Pandemic on the electricity demand, frequency control and electromechanical oscillation modes of the Brazilian Interconnected Power System (BIPS), taking into account public data disclosed by the Brazilian Independent System Operator (BISO) and data acquired through the MedFasee Project, the Brazilian low voltage wide area monitoring system (WAMS) leaded by the Federal University of Santa Catarina. Main results indicate that the BISO has been successful on controlling the system frequency and the main electromechanical interarea modes, despite the occurrence of a significant demand reduction in the BIPS in a certain period of time due to the COVID-19 pandemic. The total time of operation in underfrequency or overfrequency registered during the months with most demand reduction is at most 20% lower than the maximum time registered in the other months studied. The damping of the modes observed in the months with demand reduction has not reached values lower than 10% and the frequencies of oscillation have varied in a range of 0.05Hz, in agreement to what has been observed in other months.

A Novel Energy Flow Analysis and Its Connection With Modal Analysis for Investigating Electromechanical Oscillations in Multi-Machine Power Systems

In this paper, a novel energy flow analysis (EFA) is proposed based on the signal reconstruction and decomposition to investigate the electromechanical oscillations. In contrast to the conventional EFA, the connection between the proposed EFA and modal analysis (MA) can be quantitatively revealed for arbitrary models of synchronous generators in multi-machine power systems. Firstly, the time-domain implementation (TDI) of the proposed EFA is designed. Specifically, the measurements at the terminal of a local generator are reconstructed through an exponential operator and then decomposed with respect to an angular frequency. Then, the mode-screened damping torque coefficient is defined to extract the damping feature with respect to an electromechanical oscillation mode. After that, the frequency-domain implementation (FDI) is derived. Specifically, the Parseval's Theorem is applied to transform the proposed EFA from the time domain to frequency domain. On this basis, the consistency between the proposed EFA and MA is strictly proved, which is applicable for arbitrary models of synchronous generators in multi-machine power systems. Additionally, the application procedure of the proposed EFA in investigating electromechanical oscillations is given. Finally, the proposed EFA are substantially demonstrated in multiple case studies.

A Comprehensive Review of Small-Signal Stability and Power Oscillation Damping through Photovoltaic Inverters

This paper focuses on the methods that ensure the rotor angle stability of electric power systems, which is most frequently analyzed with small-signal models. Over the past several decades, power system stabilizers (PSSs) for conventional excitation systems were the main tools for improving the small-signal stability of electromechanical oscillatory modes. In the last decade, power oscillation damping (POD) control implemented in photovoltaic (PV) inverters has been considered an alternative to PSSs. As PV generation undergoes massive rollout due to policy directions and renewable energy source integration activities, it could potentially be used as a source of damping, which is crucial for sustaining the rotor angle stability of the remaining in-service synchronous generators. Several studies have already been dedicated to the development of different damping strategies. This paper contributes to the existing research in power system stability by providing a comprehensive review of the effects of PV generation on small-signal stability, as well as the recent evolution of POD control through PV inverters. The features and impacts of the various ways to realize POD controllers are assessed and summarized in this paper. Currently, detailed information and discussions on the practical application of PV inverter PODs are not available. This paper is, thus, intended to initiate a relevant discussion and propose possible implementation approaches concerning the topic under study.

Damping the electromechanical oscillation modes (EOMs) in DFIG-integrated power systems with sensitivity analysis and optimization to outputs of SGs

The electromechanical oscillation modes (EOMs) are the oscillations strongly related to the synchronous generators (SGs), which are dangerous to the security of the SGs and the stability of the power system. Integration of the doubly-fed induction generators (DFIGs) causes dynamic interaction among the SGs and the DFIGs, and adds the difficulty to damp the EOMs. This paper proposes a damping scheme to the EOMs based on the sensitivity analysis and the optimization model. The novelties include, 1) The sensitivities of the electromechanical loop participation ratios related to the EOMs are newly given by the sensitivities of the participation factors. 2) Since the participation factors are composed of the eigenvectors, by introducing the magnitude and phase angle constraints, the sensitivity model of the eigenvectors is improved to find the unique solution. 3) Since the bus powers changes the bus voltages and the eigenvalues, but are not shown in the state matrix, the sensitivities of the state matrix with respect to the power outputs of the SGs are derived with the help of the Jacobian matrix in power flow analysis. 4) Based on the sensitivities, an optimization model is proposed to coordinate the outputs of the SGs and damp the EOMs of the power systems. In the numerical analysis, the accuracy of the sensitivity models is verified by comparing with the result from continuous calculation. The optimization effect is verified by the time-domain analysis. It is found that the not only the active power but also the reactive power of the SGs are effective to damp the EOMs.

Online inertia estimation for power systems with high penetration of RES using recursive parameters estimation

Low and time-changing inertia values due to the high percentage of renewable energy sources (RESs) can cause stability problems in power systems due to rapid frequency instabilities. Inertia monitoring will assist operators to apply suitable actions and more proper control methods to alleviate stability issues. Therefore, this paper proposes an online method to estimate the total inertia of a network using a recursive least-squares approach. The proposed method uses network measurements with a non-recursive system identification approach to initially estimate the network hypothesis model. Then, the recursive method is used together with time changing measurements to recursively estimate model parameters and extract online inertia estimates of the network. During the estimation, the method does not need to store previous data after each sample step; therefore, the computation burden is significantly reduced. More importantly, the technique incorporates the use of available electromechanical oscillation modes in the system, which are linked with system parameters, to determine the network inertia estimates. The applicability of the proposed method has been validated by numerical simulations of the IEEE 39-bus network and the aggregated New Zealand network with its actual inertia data.

Resilience Against Data Manipulation in Distributed Synchrophasor-Based Mode Estimation

Generators are critical components of electrical grids and have to operate synchronously. Unfortunately, faults in power grids can cause significant electro-mechanical oscillations. A number of methods to estimate these electro-mechanical oscillation modes have been proposed in the literature. With the advent of synchrophasors which enable real-time measurements over a wide-area, and in keeping with a trend towards more distributed monitoring and control applications (e.g., WAMPAC), measurement-based methods to estimate oscillation modes in a distributed manner have been proposed. Like other power system applications these distributed mode estimation approaches also face the prospect of false data injection attacks. In this paper, we introduce a mechanism, inspired by byzantine fault tolerance, for making distributed alternating direction of multipliers method of mode estimation resilient against data manipulation attacks. We evaluate our approach using IEEE 68-bus and 145-bus test systems under different attack scenarios and show that in all the scenarios considered our approach allows distributed mode estimation to converge well.

A Method to Design Power System Stabilizers in a Multi-Machine Power System Based on Single-Machine Infinite-Bus System Model

This paper proposes a method to design power system stabilizers (PSSs) based on single-machine infinite-bus system models to mitigate the risk of low-frequency electro- mechanical power oscillations in an N-machine power system. First, models of N fabricated identical-machine power systems are established for the N-machine power system. Analysis in the paper indicates that the electromechanical oscillation mode of fabricated identical-machine power systems with the least damping is of less damping than the electromechanical oscillation modes of N-machine power system. Second, it is proved that models of fabricated identical-machine power systems are dynamically equivalent to the single-machine infinite-bus system models. Finally, it is suggested that the PSSs are designed using single-machine infinite-bus system models to enhance the least damped electromechanical oscillation mode of fabricated identical-machine power systems. This eventually improves the damping of electromechanical oscillation modes of N-machine power system, thus mitigating the risk of low-frequency electromechanical power oscillations. In the paper, the proposed method is demonstrated and evaluated by using three well-known example multi-machine power systems. Effectiveness of PSSs is confirmed by the results of modal computation and simulation.

Transition from Electromechanical Dynamics to Quasi-Electromechanical Dynamics Caused by Participation of Full Converter-Based Wind Power Generation

Previous studies generally consider that the full converter-based wind power generation (FCWG) is a “decoupled” power source from the grid, which hardly participates in electromechanical oscillations. However, it was found recently that strong interaction could be induced which might incur severe resonance incidents in the electromechanical dynamic timescale. In this paper, the participation of FCWG in electromechanical dynamics is extensively investigated, and particularly, an unusual transition of the electromechanical oscillation mode (EOM) is uncovered for the first time. The detailed mathematical models of the open-loop and closed-loop power systems are firstly established, and modal analysis is employed to quantify the FCWG participation in electromechanical dynamics, with two new mode identification criteria, i.e., FCWG dynamics correlation ratio (FDCR) and quasi-electromechanical loop correlation ratio (QELCR). On this basis, the impact of different wind penetration levels and controller parameter settings on the participation of FCWG is investigated. It is revealed that if an FCWG oscillation mode (FOM) has a similar oscillation frequency to the system EOMs, there is a high possibility to induce strong interactions between FCWG dynamics and system electromechanical dynamics of the external power systems. In this circumstance, an interesting phenomenon may occur that an EOM may be dominated by FCWG dynamics, and hence is transformed into a quasi-EOM, which actively involves the participation of FCWG quasi-electromechanical state variables.

Hybrid Power System Design for Damping Electromechanical Modes of Oscillation in Grid Connected Machines

Due to the natural intermittent nature of wind and solar PV, autonomous wind/PV systems for renewable energy typically require energy storage or other sources of production to form a hybrid system. in this paper objective of the designing of a grid dynamics controller equipped with IGBT based bridge structure for stabilizing various electrical parameters on the grid system while its renewable energy-based grid integration. And the controller has to be designed with modulation technique, for both voltage and current at particular frequency following stabilization which is both simple in implementation and operation. And the comparative analysis of techniques used has to be carried out with AI-based optimization algorithms for studying its effectiveness. The results of the THD % of voltage in the system having no controller was found to be 3.32 %. in the system having adaptive neural PSO switching of grid dynamics controller, the distortion level came down to 1.96%. The hybrid system with solar wind energy was further integrated with the grid and was analyzed for the rotor angle stability in the two machines. It was concluded that out of the three controls for grid dynamics controller the artificial intelligence-based adaptive neural PSO switching was found to be best with maximum stability of machines.

Synchronised ambient data‐driven electromechanical oscillation modes extraction for interconnected power systems using the output‐only observer/Kalman filter identification method

Ambient-based oscillation modes extraction is an effective means of monitoring the small signal stability of a power system on-line. In this study, a data-driven approach based on output-only observer/Kalman filter identification (O3KID) combined with the eigensystem realisation algorithm (ERA) was proposed to extract electromechanical modes (frequency, damping ratio and mode shape) from synchronised ambient data. As a key for extracting a reduced-order state matrix using the ERA, the Markov parameters (impulse responses) are first estimated by employing O3KID on multi-channel ambient data. O3KID makes it possible to identify the modes with the ERA using only output ambient data, while ensuring the reliability of the extractions of frequencies, damping ratios and mode shapes. The performance of the proposed method was evaluated by employing the IEEE 16-generator 5-area system and measured data from a real power system. The estimation results in all cases as well as comparison results with the RDT-ERA method and NExT-ERA method indicate that the O3KID-ERA method is a promising method for ambient data-driven electromechanical oscillation modes extraction.

An optimal modal coordination strategy based on modal superposition theory to mitigate low frequency oscillation in FCWG penetrated power systems

Full converter-based wind power generation (FCWG, e.g. permanent magnet synchronous generator (PMSG)) becomes prevalent in power electronics dominated multi-machine power system (MMPS). With flexibly modified FCWG oscillation modes (FOMs), FCWG has the potential to actuate conducive dynamic interactions with electromechanical oscillation modes (EOMs) of MMPS. In this paper, a mathematical model of FCWG and MMPS is firstly derived to examine the dynamic interactions. Then a novel modal superposition theory is proposed to classify the modal interactions between FOMs and EOMs in the complex plane for the first time. The modal coupling mechanism is graphically visualized to investigate the dynamic interactions, and the eigenvalue shift index is proposed to quantify the dynamic interaction impact on critical EOM. Based on different manifestos in modal coupling mechanism and eigenvalue shift index, a novel methodology to optimize the dynamic interactions between the FCWG and MMPS is designed within the existing control frame. The optimized dynamic interactions (i.e. modal counteraction) can significantly enhance the LFO stability of MMPS, effectiveness of which is verified by both modal analysis and time domain simulations.

Modal Shift Evaluation and Optimization for Resonance Mechanism Investigation and Mitigation of Power Systems Integrated With FCWG

The integration of full converter-based wind power generation (FCWG, e.g., permanent magnet synchronous generator (PMSG)) not only introduces the PMSG oscillation modes (POMs) but also might excite severe resonances with electromechanical oscillation modes (EOMs) of the power system. In this paper, a two-open-loop-subsystem dynamic model is firstly established to investigate the interactions between the PMSG and the rest of the power system. On this basis, a modal shift evaluation (MSE) method by using bilateral damping torque analysis is proposed to accurately quantify the interaction effect of POMs and EOMs on each other and effectively explain their complex interaction process. Then two important concepts, i.e., modal shift sensitivity (MSS) with respect to various PMSG controller parameters and resonance excitation index (REI) according to a per unit open-loop modal distance indicating the intensity of modal interactions, are derived to dig the essential modal resonance mechanisms. Furthermore, by using MSS and REI as two tools, the modal interaction optimization (MIO) is conducted through POM tuning in order to prevent potential system modal resonance and enhance resonance mode damping for the first time. The optimized modal interaction is validated to be beneficial and effective for the improvement of power system resonance stability.