PMU-Based Estimation of Dynamic State Jacobian Matrix and Dynamic System State Matrix in Ambient Conditions

Abstract

Abstract-In this paper, a hybrid measurement-and modelbased method is proposed which can estimate the dynamic state Jacobian matrix and the dynamic system state matrix in near real-time utilizing statistical properties extracted from PMU measurements. The proposed method can be used to detect and identify network topology changes that have not been reflected in an assumed network model. Additionally, an application of the estimated system state matrix in online dynamic stability monitoring is presented.Index Terms-dynamic state Jacobian matrix, dynamic system state matrix, phasor measurement units, topological error identification, online dynamic stability monitoring

Online Measurement-Based Estimation of Dynamic System State Matrix in Ambient Conditions

“…Suppose the system is around the steady-state operating point, the larger initialization window will give more accurate estimations. Given the study in [17], the estimation error of the algorithm in [17] does not decrease substantially as the window length increases beyond 200s for the IEEE 39-bus system. Hence, we use 200s initialization window for the same 39-bus system in this paper which shows reasonably good accuracy (See Fig.…”

“…Ideally, C and G are calculated from an infinite number of data which is impossible in practice. Hence, the sample mean x, sample covariance matrixĈ and sample correlation matrix G calculated from finite data set is typically used as follows: 17) where N is the sample size, F = [x 1 , x 2 , · · · , x N ] is a M s × N matrix assuming there are M s state variables, F i:j denotes the submatrix of F from i to j columns, 1 N is an N by 1 vector of ones, and t is the sampling time step. Finally, the system state matrix can be estimated from:…”

“…In addition, we compare the accuracy of the proposed method with that of the method developed in [17]. The method in [17] are developed based on another important property of the stationary covariance matrix C that C satisfies the Lyapunov equation in ambient condition:…”

“…In this numerical example, the estimation error defined in (32) is 3.73% using (34), which is less than that of the proposed method. Nevertheless, since the method in this paper and the one in [17] are developed based on different properties of the stochastic dynamical system (10), there is no direct and clear conclusion that which method should possess a higher accuracy, even though the method proposed in this paper requires less model information and is completely model-free.…”

Estimating Participation Factors and Mode Shapes for Electromechanical Oscillations in Ambient Conditions

“…In this paper, we will apply a novel method proposed in [11] [12] to carry out mode identifications for electromechanical oscillations, which may potentially overcome the challenges faced by the subspace methods. The proposed method is able to accurately estimate the true system state matrix and thus all the modal knowledge including frequencies, damping ratios, mode shapes, and more importantly, participation factors that carry crucial information for control.…”