Electromechanical mode shape estimation based on transfer function identification using PMU measurements

Abstract

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, measurementbased 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. 1

New algorithm for mode shape estimation based on ambient signals considering model order selection

“…Thus, the mode shape magnitude and angle information of multiple dominant interarea modes in power grids can be estimated from the variablesΨ i0 according to (14).…”

“…Some publications have offered algorithms for identifying the modal frequency and damping ratio from ambient data [6][7][8][9], which fully demonstrate that this kind of signal includes abundant information about the system. Only recently the mode shape has been considered [10][11][12][13][14]. Based on the relationship between the cross-and power spectral densities and mode shapes, an approach for estimating the mode shapes using spectral method is presented in [10].…”

“…In this case, the changes of operation modes in actual power system would inevitably cause the ineffectiveness of the prefixed filter, and influence the estimation accuracy. In [14], the transfer function method was proposed which showed that mode shape could be calculated by evaluating a transfer function, constructed between a pair of system outputs, at the mode of interest. However, as the key factors of transfer function, the selection of model order are not taken into account in these articles, this will directly affect the accuracy of the mode shape analysis results.…”

PMU-based estimation of dynamic state Jacobian matrix

“…The above factors pose great challenges to the static and dynamic security analysis for the modern power grids and make the online security analysis even more formidable. Wide adoption of phasor measurement units (PMUs) greatly facilitates online monitoring of system states and its dynamic behaviors, offering unique opportunities for the development of measurement-based security analysis methods in power system [4]- [11].…”

“…Hence, much attention has been put for measurement-based methods which are deemed to be fast and robust to parameter change. Particularly, measurement-based mode shape estimation methods have been proposed by using Prony analysis [6], spectral methods [7] [8], frequency domain decomposition [9], subspace method [5] [10], transfer function method [11], etc. Unlike these previous studies, online oscillation analysis and control technique developed in this paper relies on online estimation of the Jacobian matrix.…”