Observability Analysis for Large-Scale Power Systems Using Factor Graphs
Abstract : The state estimation algorithm estimates the values of the state variables based on the measurement model described as the system of equations. Prior to applying the state estimation algorithm, the existence and uniqueness of the solution of the underlying system of equations is determined through the observability analysis. If a unique solution does not exist, the observability analysis defines observable islands and further defines an additional set of equations (measurements) needed to determine a unique solution. For the first time, we utilise factor graphs and Gaussian belief propagation algorithm to define a novel observability analysis approach.The observable islands and placement of measurements to restore observability are identified by following the evolution of variances across the iterations of the Gaussian belief propagation algorithm over the factor graph. Due to sparsity of the underlying power network, the resulting method has the linear computational complexity (assuming a constant number of iterations) making it particularly suitable for solving large-scale systems. The method can be flexibly matched to distributed computational resources, allowing for determination of observable islands and observability restoration in a distributed fashion. Finally, we discuss performances of the proposed observability analysis using power systems whose size ranges between 1354 and 70000 buses.
? There exists a significant gap in performance between the state-of-the-art methods and the desired informative data exploration. This problem may grow as new technologies are being deployed.
? For instance, according to utility records, for the past ten years, numerous distributed power plants (wind, solar, etc.), each serving primarily a local area, have been connected to the existing grid and their presence has raised great concerns about possible reliability problems in the future electric power grids.
? Further, President Obama’s goal of putting one million electric vehicles on the road by 2015 will also contribute to the grid architecture shift; robustness of these new architectures will have to be studied.
? In this paper, we adapt GBP in order to solve the problem of observability analysis in power systems.
? We present GBP-based island detection in this subsection and extend it to GBP-based observability restoration in the next subsection.
? However, in contrast to where the Gram matrix is needed, we are solving the observability restoration problem directly over the matrix Wbc using the GBP algorithm.
? In this scenario, the problem is distributed across O(n) nodes, and, if implemented to run in parallel, it can be O(n) times faster than the centralised solution.
• The proposed graphical model is able to discover and analyze unstructured information and it has been successfully deployed in statistical physics, computer vision, error control coding, and artificial intelligence.
• Specifically, this paper shows how to model the traditional power system state estimation problem in a probabilistic manner.
• Further, the proposed approach features an approximately linear computational time unavailable in the past.
• Based on these preliminary results, we present that the proposed method can offer a major promise for scalable SE with high accuracy for the future smart grid.
? We assess our proposed method against the numerical and topological state-of-the-art methods available in the literature. In our evaluation, we explore a large set of power systems with different bus configurations. We evaluate the performance of the proposed method using power systems with 1354, 2000, 10000, 25000 and 70000 buses .
? we use box plots where we normalise execution time of each of the different state-of-the-art methods tsa by the execution time of the GBP-based approach tbp. Hence, the case tsa/tbp > 1 corresponds to the case where the GBP-based method shows better performance (i.e., lower execution time), while tsa/tbp < 1 corresponds to the case where the GBP-based method shows worse performance (i.e., higher execution time) in comparison with the state-of-theart method.
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