Solving the multistage PMU placement problem by integer programming and equivalent network design model

Recently, phasor measurement units (PMUs) are becoming widely used to measure the electrical waves on a power grid to determine the health of the system. Because of high expense for PMUs, it is important to place minimized number of PMUs on power grids without losing the function of maintaining system observability. In practice, with a budget limitation at each time point, the PMUs are placed in a multistage framework spanning in a long-term period, and the proposed multistage PMU placement problem is to find the placement strategies. Within each stage for some time point, the PMUs should be placed to maximize the observability and the complete observability should be ensured in the planned last stage. In this paper, the multistage PMU placement problem is formulated by a mixed integer program (MIP) with consideration of the zero-injection bus property in power systems. To improve the computational efficiency, another MIP, based on the equivalent network flow model for the PMU placement problem, is proposed. Numerical experiments on several test cases are performed to compare the two MIPs.