State Observation of Power Systems Equipped with Phasor Measurement Units The Case of Fourth Order Flux-Decay Model
Abstract : The problem of effective use of Phasor Measurement Units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use this new measurements to reconstruct the state of the system. In this paper we provide the first solution to the problem of (globally convergent) state estimation of multimachine power systems equipped with PMUs and described by the fourth order flux-decay model. This work is a significant extension of our previous result, where this problem was solved for the simpler third order model, for which it is possible to recover algebraically part of the unknown state.Unfortunately, this property is lost in the more accurate fourth order model, and we are confronted with the problem of estimating the full state vector. The design of the observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the Dynamic Regressor Extension and Mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. Simulation results illustrate the latter fact and show the improved performance of the proposed observer with respect to a locally stable gradient-descent based observer.
? The high reporting rate (60 Hz) compared to 0.5-1 Hz in existing measuring systems creates a whole new application area which had not been possible before.
? The measurements accompanied by the precise time stamps will allow for a constellation of PMUs implemented across the transmission network to generate the synchronized measurements necessary to estimate the state of the transmission network.
? The dynamics block performs prediction using system equations while the geometry block computes the estimated measurements based on the priori states.
? A Kalman filter gain is used to correct the priori state with the error between the measurements and their estimation.
? It is widely recognized that to improve the precision of the model, it is necessary to include additional dynamic effects, leading to a fourth order model.
? Unfortunately, for this case, the algebraic reconstruction of part of the state is impossible, and we are confronted with the problem of estimating the full state vector.
? These two theoretical developments are instrumental to solve the current problem.
? In this paper we provide the first solution to the state observation problem for multimachine power systems described by the fourth order model.
• The System Identification method i) develops a linearized electromechanical model, ii) completes a parameters sub-set selection study using si8ngular values decomposition, iii) estimates the parameters of the proposed model and iv) validates its output versus the measured output.
• The objective of system identification is to use experimental or measured data as input and output of proposed model structure describing a physical system in order to estimate the proposed model parameters and order.
• However the estimation will be tested against simulation data from more sophisticated model to demonstrate the robustness of the proposed estimation.
? The vast majority of the reported results on this matter rely on the use of linear systems-based theories, e.g., the use of Kalman filters, whose performance is assessed only via simulations, see. As thoroughly discussed in . this approach suffers from several major drawbacks.
? However, the simulation results, presented, include the multimachine case, and show the improved performance of the proposed observer with respect to a locally stable gradient-descent based observer.
? We present some simulations that illustrate the performance of the observer of the states (x3, x4) of Proposition 3, which combines GPEBO with DREM.
? Simulation results illustrate the latter fact and show the improved performance of the proposed observer with respect to a locally stable gradient-descent based observer.
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