Optimal PMU Placement Using Modified Greedy Algorithm
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Optimal PMU Placement Using Modified Greedy Algorithm Van-khoi Tran1 · He-sheng Zhang1
Received: 23 May 2017 / Revised: 23 August 2017 / Accepted: 13 October 2017 © Brazilian Society for Automatics–SBA 2017
Abstract Phasor measurement units (PMUs) provide synchronized measurements of real-time phasors of voltages and currents. It is considered as an important element of the smart wide area measurement system used in advanced power system monitoring, protection, and control applications. This paper proposes a new approach based on a greedy algorithm to solve the optimal phasor measurement unit placement (OPP) problem in the power network. The main purpose of proposed approach is to find out a high-quality solution in a reasonable time that ensures the practicability when applying for a real power network. The OPP problem is solved under both normal operating and contingency conditions. Moreover, some other realistic aspects that may affect the OPP problem, such as PMU channel limitation, zero injection bus, the presence of conventional measurements, are also considered to solve simultaneously. The simulations on IEEE 14-bus, 30-bus, 57-bus, 118-bus test systems, and especially on a large-scale network—the Polish 2383-bus system, are presented for evaluating the feasibility of proposed approach. The results of this study showed that the proposed method is effective and feasible to solve the OPP problem for a real power network. Keywords Phasor measurement unit (PMU) · Optimal placement · Power network observability · Greedy algorithm
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Van-khoi Tran [email protected] He-sheng Zhang [email protected]
1
School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China
1 Introduction Optimal placement of Phasor Measurement Unit (PMU) is considered as an NP-hard optimization problem. There are n! n PMU !∗(n−n PMU )! combinations from n buses of the power system when the number of PMUs is n PMU . This is a large number even for a small system, so it is impossible to try all combinations for finding the best solution. Many researchers and engineers have investigated to solve this problem, and many methods have been proposed. Baldwin et al. (1993) proposed the linear model for a power system when measuring by PMUs. In this study, authors built the constraint objective function according to the numerical observability, and applied the dual search technique to solve the OPP problem with the purpose is to reduce the size of the search space for evaluating the PMU coverage in each iteration. However, it seems to be suffered from excessive calculation burden when applied to a large-scale system. The Genetic Algorithm (GA) is commonly used to generate high-quality solutions to optimization and search problems; hence, it is popularly applied to determine the minimum number and places of PMUs (Milosevic and Begovic 2003; Aminifar et al. 2009; Miljani’c et al. 2012; Mousavian and Feizollahi 2015). Milosevic and Begovic (2003) two-stage approach was proposed: the first stage estimates individual optimal
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