Estimation Of Electromechanical Modes Research Articles

Compressed-DMD for Electromechanical Mode Estimation from High-Dimensional Ambient Data

Accurate and rapid estimation of electromechanical mode plays an important role in sensing the security situation of power systems. In this paper, the Compressed Dynamic Mode Decompensation (Compressed-DMD) based estimation approach was proposed to extract the electromechanical mode from high-dimensional ambient data measured by the synchrophasor measurement unit. To improve the efficiency of DMD in processing high-dimensional ambient data under the premise of ensuring calculation accuracy, the Compressed-DMD was introduced to generate the approximation of the high-dimensional left and right singular vectors by employing the aggressive random test matrices and truncated eigendecomposition. Simulation examples of IEEE 16-generator 5-area system and real measurements verify the feasibility and effectiveness of the proposed method.

Spectral fitting approach to estimate electromechanical oscillation modes and mode shapes by using vector fitting

Wide-area monitoring systems (WAMS) based on phasor measurement units (PMUs) provide the essential information of an electric power system (EPS) in order to face the challenges of generation, operation, and planning. The PMUs are used to obtain the power system ringdown responses. These signals can be analyzed by advanced signal-processing techniques for the estimation of electromechanical modes. This paper proposes a new spectral fitting (SF) approach to estimate these electromechanical oscillation modes and mode shapes by using vector fitting (VF) under noisy conditions. This methodology combines the numerical Laplace transform (NLT) with the VF method. A participation factor is also proposed to identify and detect the system’s dominant oscillatory modes. The proposed methodology is demonstrated for a synthetic multi-component signal, a set of noisy synthetic multi-component signals, and numerical simulations of a 16-machine and 68-bus test power system. Results indicate that the proposed technique has the ability and accuracy to carry out a complete identification of electromechanical modes and mode shapes from several ringdown responses, under noisy conditions.

Electromechanical Mode Estimation in the Presence of Periodic Forced Oscillations

Electromechanical modes are inherent to any interconnected power systems which provide a measure of the small-signal stability margin of the system. A number of algorithms have been developed for the estimation of these modes using synchrophasor measurements. However, most of these algorithms are not designed to operate in the presence of forced oscillations (FO). These FOs are results of periodic rogue input driving the system. When FOs are present, estimates of system modes can be biased depending on the frequency and the amplitude of the FOs. To tackle this problem, a new algorithm is proposed in this paper to estimate system modes in the presence of FOs. In the proposed method, the over-determined modified Yule–Walker method which is used to estimate autoregressive coefficients of an autoregressive moving average (ARMA) signal model is extended to an ARMA with exogenous input (ARMAX) model that incorporates the presence of FOs. Two versions of the proposed method are included in this paper based on the requirement of the information of the duration of FOs in the signal. Results obtained by implementing the proposed algorithm on simulated data and real-world data validate the effectiveness of both versions of the proposed method.

Parameters Estimation of Electromechanical Oscillation With Incomplete Measurement Information

Effective real-time estimation of electromechanical modes of a power system is essential, since it can provide the vital stability information of the system. However, most of existing methods for parameters estimation of electromechanical oscillation are suitable for the situations with complete measurement data, which cannot take the inevitably missing data phenomenon into account. Therefore, they fail to accurately estimate the parameters of electromechanical oscillation with incomplete measurement data. To solve the aforementioned problems, based on the traditional extended Kalman filter, in this paper, by incorporating the modified innovation-based adaptive estimation method, a novel fault tolerant adaptive extended Kalman filter (FTAEKF) is developed to realize parameters estimation of electromechanical oscillation with incomplete measurement data. Finally, several simulation studies are provided to demonstrate that the proposed FTAEKF can achieve much better performance than some existing results.

Estimating electromechanical oscillation modes from synchrophasor measurements in China Southern Power Grid

This paper proposes a generalized inverse and mode assurance criterion based stochastic subspace identification (GMSSI) method to improve the electromechanical mode estimation efficiency in China Southern Power Grid (CSG). Stochastic subspace identification (SSI) is first employed to estimate the state subspace model of power system from synchrophasor measurements. Then, a model order determination criterion is proposed to estimate the model order and the state matrix of power system is obtained. To accurately separate the electromechanical modes from trivial modes, the generalized inverse of SSI is used to estimate another state matrix. Further, the mode filtering and mode assurance criterion (MAC) are developed to distinguish the electromechanical modes. Simulation data and field-measurement data from CSG are used to evaluate the performance of the proposed GMSSI method. The comparison between existing measurement-based mode estimation methods and the proposed GMSSI demonstrates that the proposed GMSSI exhibits highly accurate, efficient and robust performance in estimating electromechanical modes from both ringdown and ambient data in bulk power grid.

Simultaneous Estimation of Electromechanical Modes and Forced Oscillations

Over the past several years, great strides have been made in the effort to monitor the small-signal stability of power systems. These efforts focus on estimating electromechanical modes, which are a property of the system that dictate how generators in different parts of the system exchange energy. Though the algorithms designed for this task are powerful and important for reliable operation of the power system, they are susceptible to severe bias when forced oscillations are present in the system. Forced oscillations are fundamentally different from electromechanical oscillations in that they are the result of a rogue input to the system, rather than a property of the system itself. To address the presence of forced oscillations, the frequently used AutoRegressive Moving Average (ARMA) model is adapted to include sinusoidal inputs, resulting in the AutoRegressive Moving Average plus Sinusoid (ARMA+S) model. From this model, a new Two-Stage Least Squares algorithm is derived to incorporate the forced oscillations, thereby enabling the simultaneous estimation of the electromechanical modes and the amplitude and phase of the forced oscillations. The method is validated using simulated power system data as well as data obtained from the western North American power system and Eastern Interconnection.

Accuracy analysis of electromechanical mode estimation under ambient conditions

Electromechanical modes estimated from ambient wide area measurement systems measurements are often used as a basis for system dynamic security assessment. It is therefore important to know the accuracy of the mode estimates. There are two interesting phenomena widely reported in ambient mode estimation: (i) the accuracy of the mode parameter estimates improves under the lighter damping conditions and (ii) the frequency estimates are more accurate than the damping ratio estimates. This study aims to systematically investigate the estimation accuracy of ambient mode analysis. An analytical differentiation-based perturbation method is presented to examine the variance propagation along the mode estimation procedure. Monte Carlo simulations in the two-area system are carried out to analyse the influences of varying the mode parameters on the estimation accuracy of the inter-area mode, in which the estimated variances are served as quantitative measures of the accuracy analysis. In addition, theoretical explanations for the observations in ambient mode estimation are also provided as a supplementary. The investigations and discussion of the estimation accuracy are of value for yielding insight into the variability of the mode estimates under ambient conditions.

Estimation of Electromechanical Oscillation Parameters Using an Extended Kalman Filter

Estimation of electromechanical modes of a power system has attracted attention in the past few decades because it can provide vital information about the stability of the system. In this paper, a new state-space model is proposed for online detection of parameters of a ringdown signal using an extended Kalman filter (EKF). The proposed model can estimate both constant and time-varying parameters. Furthermore, stability analysis of the proposed model is performed to demonstrate the convergence of the parameters. Simulation results confirm the desirable performance of the proposed method for ringdown parameter estimation.

Preprocessing synchronized phasor measurement data for spectral analysis of electromechanical oscillations in the Nordic Grid

Summary Spectral analysis techniques have successfully been applied for near real-time monitoring of power system small-signal electromechanical oscillations using synchronized phasor data from PMUs. The methods used for this purpose commonly assume that random load variations adopt the distribution function of Gaussian noise. Hence, careful attention has to be paid so that the preprocessing of synchronized phasor measurements is capable of providing data with the characteristics expected for these methods to work properly. This can be viewed as a “conditioning” step in the data handling process that has an impact on the results from spectral analysis which consume this data. This article aims to revisit the crucial step of preprocessing of PMU data in a tutorial fashion. The goal is to share the authors' experience when dealing with real PMU data originating from the Nordic Grid. This article offers a systematic and detailed methodology developed by the authors which has been successfully used in studies on estimation of electromechanical modes in the Nordic Grid. Copyright © 2013 John Wiley & Sons, Ltd.

Estimation of Electromechanical Modes from Ambient PMU Data in China Southern Power Grid

Online estimation of electromechanical oscillation modes using ambient PMU data is adopted for monitoring the China Southern Power Grid (CSG). After some preprocessing steps, the ambient PMU data is processed by ARMA (Autoregressive Moving average) method, different identification results are obtained from multiple PMU sites. Then by utilization of a clustering method, oscillation modes representing the system operating conditions are derived. In this paper, we report on the preliminary results in CSG and restriction on the ambient data usage is explained. Application of ambient data analysis for oscillation event study is also proposed to judge the oscillation type by comparing the estimated damping ratio value before and during ringdown period. Some suggestions on further ambient data analysis study are also discussed.

Estimation of Electromechanical Modes of Power Systems by Transfer Function and Eigenfunction Analysis

This paper presents a method of estimating the electromechanical damping and frequency coefficients of interconnected power systems. The method combines AESOPS approach and eigenvalue analysis. Computation time is reduced by applying an approximation based on an eigenvalue sensitivity formula, which evaluates eigenvectors of the 2ng × 2ng [A(ωK)] and [A(ωK)]T matrix and thereafter use them to obtain improved estimates of the eigenvalues. Numerical results from a 16-generator system demonstrate the feasibility of the proposed method.

Application of ambient analysis techniques for the estimation of electromechanical oscillations from measured PMU data in four different power systems

AbstractThe 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. Copyright © 2010 John Wiley & Sons, Ltd.