PMU optimal placement based on node set

The configuration of phasor measurement units (PMU) requires the least PMUs under the premise of complete network observability. The 0-1 mixed integer programming formulation has a great advantage of solving the multi-objective PMU placement problem. However, there are plenty of zero power injection nodes in power system. It's conductive to PMU placement being as "free" measurement while still brings the nonlinearity to the optimizing issue. This paper presents a conditional function which considers the condition that the zero power injection nodes are included. It could apply to the 0-1 integer programming formulation while still keeping the linearity. Besides, the method has a strong inheritance when considering the N-1 situation and could solve the N-1 optimal allocation problem when traditional methods not. At last, the method is applied to the IEEE 14 nodes and 39 nodes cases. It reduces the numbers of PMU that is needed, and embodies the superiority of this method when compared with the other methods.