Optimal multi-stage PMU placement in electric power systems using Boolean algebra

Placement of phasor measurement units (PMUs) in power systems has often been formulated for achieving total network observability. In practice, however, the installation process is not implemented at once, but at several stages, because the number of available PMUs at each time period is restricted due to financial problems. This paper presents a novel integer linear programming framework for optimal multi-stage PMU placement (OMPP) over a preset schedule, in order to improve the network observability during intermediate stages, in addition to its complete observability by the end of the PMU placement process. To precisely evaluate the network observability and fully exploit the potential of circuit rules, the observability function is formulated by Boolean algebra. Next, it will be utilized to formulate the optimal PMU placement problem and then construct a unified optimization model for OMPP. As such, among various strategies for installing PMUs over the scheduled horizon, the one achieving the maximum total observability of the system during intermediate stages is found. Moreover, the unified optimization model allows for considering the network expansion scenarios as well as the diverse importance of critical buses during the installation process so that these buses may be equipped with PMUs at primary stages. Finally, to illustrate the applicability and efficiency of the proposedmethod, it is applied to several IEEE test systems and two practical large-scale power systems, and the results are studied. Copyright © 2012 John Wiley & Sons, Ltd.