Overview of system identification for power systems from measured responses

Large interconnected power systems are arguably some of the most complicated man-made systems to understand and to characterize. The scale of the problem is immense, involving large numbers of generators, controllers, and transmission lines covering millions of square kilometers. Measurement technology has reached a point where Phasor Measurement Units (PMUs) are being widely installed in power systems all over the world. These devices provide time synchronized (via GPS) phasor measurements from throughout the power grid to Phasor Data Concentrators (PDCs) at power system control centers. These time series can be used to better characterize the system and hopefully, in the long term, to better control the system. This paper presents a tutorial on estimating power system characteristics from measured responses. About a given operating point, power system low-frequency dynamics are well modeled as a high-order, multi-input, multi-output linear system. Of primary interest is the estimation of the inter-area electromechanical modes of the system. These inter-area modes involve generators from one area of the system oscillating against generators in another area of the system. The modes are characterized by their frequency, damping, and shape. In August 1996, the western United States experienced a massive wide spread black out caused by an unstable inter-area mode, involving generators in the north swinging against generators in the south. This paper overviews the problem and examines several methods of estimating the electromechanical modes under different signal conditions. Several real-world examples are given for estimating the electromechanical modes from ambient, transient, or probing situations. When the system is probed, more general state-space and transfer-function models are estimated. Probing a power system with known inputs is challenging and is discussed in this paper. Estimation performance issues are also discussed.