Observability of Hybrid AC/DC Power Systems With Variable-Cost PMUs

The integration of high-voltage direct-current (dc) transmission lines in conventional alternating-current (ac) systems would affect the indirect measurement of phasor measurement unit (PMU) devices since the concept of phasors would not correspond to dc transmission circuits. The optimal PMU placement problem in ac/dc systems subjected to the system observability is presented in this paper by applying a mixed-integer programming model. In practice, the cost of each PMU is variable as a function of PMU measurement channels. This attribute is incorporated in the proposed model as well. In addition, the number of PMU measurement channels is deemed to be technically limited; thus, the common assumption concerning allocation of one PMU device to a single node is relaxed. The objective in the proposed optimization model is to minimize the total installation cost of PMUs when considering the observability of ac/dc transmission systems in the base case and contingency conditions. Numerical analyses are conducted for the IEEE standard test systems and a large-scale system, and the results are discussed.