A hybrid algorithm based on immune BPSO and N-1 principle for PMU multi-objective optimization placement

With guaranteeing full observability of the power grid and acquiring a good balance between the cost and the capability of phasor measurement unit (PMU) placement, the observability criteria of power grid nodes and the N-l reliability principle to judge the measurement redundancy of placement schemes were proposed in this paper, and a mathematical model of multi-objective optimization for PMU placement problem was formed for both the minimum number of PMU to be equipped and the maximal measurement redundancy. An improved binary particle swarm optimization algorithm combined with the information processing mechanism of immune system was proposed to solve the multi-objective optimization problem. The proposed algorithm has both the properties of the speed advantage in binary particle swarm optimization and the diversity of antibodies in immune system, and the abilities of converging and seeking the global optimum results in later evolution process are improved observably. The number of PMU and the measurement reliability of PMU placement schemes were evaluated synthetically in the proposed multi-objective optimization method, and the optimal schemes could be rapidly achieved by the proposed method, which was demonstrated with PMU placement optimization simulation and measurement redundancy analysis using New England 39-bus system. The proposed method is more rational and flexible to compare with those normal single-objective optimization methods for PMU placement.