This paper introduces a framework for optimal placement (OP) of phasor measurement units (PMUs) using metaheuristic algorithms in a distribution network. The voltage magnitude and phase angle obtained from PMUs were selected as the input variables for supervised learning-based pseudo-measurement modeling that outputs the voltage magnitude and phase angle of the unmeasured buses. For three, four, and five PMU installations, the metaheuristic algorithms explored 2000 combinations, corresponding to 40.32%, 5.56%, and 0.99% of all placement combinations in the 33-bus system and 3.99%, 0.25%, and 0.02% in the 69-bus system, respectively. Two metaheuristic algorithms, a genetic algorithm and particle swarm optimization, were applied; the results of the techniques were compared to random search and brute-force algorithms. Subsequently, the effects of pseudo-measurements based on optimal PMU placement were verified by state estimation. The state estimation results were compared among the pseudo-measurements generated by the optimal PMU placement, worst PMU placement, and load profile (LP). State estimation results based on OP were superior to those of LP-based pseudo-measurements. However, when pseudo-measurements based on the worst placement were used as state variables, the results were inferior to those obtained using the LP.
Supervised Learning Approach for State Estimation of Unmeasured Points of Distribution Network
