Optimal multistage schedualing of PMU: an ILP approach

Indian Inst. of Technol., Mumbai
IEEE Transactions on Power Delivery (Impact Factor: 1.73). 11/2008; 23(4):1812 - 1820. DOI: 10.1109/TPWRD.2008.919046
Source: IEEE Xplore


This paper addresses various aspects of optimal phasor measurement unit (PMU) placement problem. We propose a procedure for multistaging of PMU placement in a given time horizon using an integer linear programming (ILP) framework. Hitherto, modeling of zero injection constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints in an ILP framework. Minimum PMU placement problem has multiple solutions. We propose two indices, viz, BOI and SORI, to further rank these multiple solutions, where BOI is bus observability index giving a measure of number of PMUs observing a given bus and SORI is system observability redundancy index giving sum of all BOI for a system. Results on IEEE 118 bus system have been presented. Results indicate that: (1) optimal phasing of PMUs can be computed efficiently; (2) proposed method of modeling zero injection constraints improve computational performance; and (3) BOI and SORI help in improving the quality of PMU placement.

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Available from: Rajeev Gajbhiye, Apr 30, 2013
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    • "IEEE 14 bus test system has been taken as an example to demonstrate the mathematical realizability of the phasing/staging problem of PMU. The equations of the type (2)-(10) can also be formulated for the IEEE 14 bus system [7] "
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    ABSTRACT: At present time concerted efforts are being made for the implementation of smart grid technologies. PMUs play a significant role in the wide area monitoring system (WAMS). The major advantages of the WAMS include dynamic wide area measurements with faster rate and better accuracy. Observability of a complete power system with a minimum number of PMUs has always remained a challenge. This paper suggests a binary integer linear programming approach for finding out the optimal locations of PMUs in a system. Two indices viz. BOI (Bus Observability Index) and SORI (System Observability Redundancy Index) have been suggested to rank the various possible solutions of an OPP. IEEE 14, 24, 30 and New England 39 (NE 39) bus systems have been considered for simulation and the results show excellent computational efficiency of the algorithm.
    Full-text · Article · Dec 2015
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    • "This method is complex because of the non-linear formulation, and it also may not reach the optimum solution for larger case studies. Also, in [5] [6] [7] [8], linear programming has been used for this placement but they did not consider contingencies (PMU loss and line outage) at the same time. "
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    ABSTRACT: A multi-objective optimal phasor measurement unit placement model using integer linear programming is presented in this article. The proposed model simultaneously optimizes two objectives, i.e., minimization of phasor measurement unit numbers and maximization of measurement redundancy. To calculate the redundancy criteria, the single-line outage and the phasor measurement unit loss are considered simultaneously. A linear formulation is presented for both objective functions. Also herein, to address conflicting attributes and identify Pareto optimal solutions of the multi-objective optimal phasor measurement unit placement problem, a new multi-objective mathematical programming method is proposed. Finally, a new index, i.e., minimum distance to utopia point, is implemented to select the most preferred solution among the available Pareto front based options on the goal to achieve judicious decision makers. Two test systems, i.e., a modified 9-bus and an IEEE 118-bus test systems, are used to illustrate the effectiveness of the proposed framework.
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    • "This facilitates linearization of the state estimator, hence resulting in faster state estimation with better accuracy [4] [5] [6] [7]. However, installing PMUs at all buses in a network is either not feasible or undesirable for the following reasons [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]. "
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    ABSTRACT: Phasor measurement units are emerging as a potential tool for on-line power system state estimation. Incorporation of phasor measurement units to the existing power system's monitoring system is impeded by various physical and economic constraints. This article proposes a novel topological genetic algorithm for optimal placement of phasor measurement units along with existing conventional measurement units such that state estimation can be achieved with enhanced accuracy and immunity against power grid contingencies. The proposed algorithm optimally places phasor measurement units so that complete observability of the power system is achieved through them and enhanced redundancy in measurement can be accomplished through conventional measurement units. Since practical phasor measurement unit placements are accomplished in multiple horizons, intelligent sorting and phase optimization methodologies have been presented to attain maximum observability during phasing periods. Placement of phasor measurement units with multiple channel limits has also been studied in this article. The efficacy of the proposed topological genetic algorithm for optimizing the number of phasor measurement units and enhancing state estimation under various operating conditions has been validated through extensive simulation studies conducted in IEEE standard bus systems. Practical case studies have been performed in the western and southern region Indian power grids.
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