Nondominated sorting genetic algorithm for optimal phasor measurement placement

This paper considers a phasor measurement unit (PMU) placement problem requiring simultaneous optimization of two conflicting objectives, such as minimization of the number of PMUs and maximization of the measurement redundancy. The objectives are in conflict since the improvement of one of them leads to the deterioration of another. Instead of a unique optimal solution, it exists a set of best tradeoffs between competing objectives, the so-called Pareto-optimal solutions. A specially tailored nondominated sorting genetic algorithm (NSGA) for a PMU placement problem is proposed as a methodology to find these Pareto-optimal solutions. The algorithm is combined with the graph-theoretical procedure and a simple GA to reduce the initial number of the PMU's candidate locations. The NSGA parameters are carefully set by performing a number of trial runs and evaluating the NSGA performances based on the number of distinct Pareto-optimal solutions found in the particular run and distance of the obtained Pareto front from the optimal one. Illustrative results on the 39- and 118-bus IEEE systems are presented.