Tri-objective Optimal PMU Placement including Accurate State Estimation: the Case of Distribution Systems

This paper presents a tri-objective Optimal Phasor Measurement Units (PMUs) Placement (OPP) strategy that is focused on the minimization of i) the total number of PMU channels, ii) the maximum state estimation uncertainty based only on high-rate PMU data and iii) the sensitivity of state estimation to line parameter tolerances. The proposed formulation keeps into account system observability with and without contingencies due to single-line and PMU faults. Also, it includes the effect of possible zero-injection buses and a-priori constraints on both the number of PMU channels and the type of PMU measurements performed at each bus. Due to the nonlinear combinatorial nature of the proposed OPP problem, this is solved through a custom implementation of the nondominated sorting genetic algorithm II (NSGA-II). The analysis of the proposed OPP strategy is focused on distribution systems. The placement results obtained using four test systems of a different size show that increasing the number of buses instrumented with PMUs and/or the number of PMU channels beyond given thresholds just leads to larger costs with negligible further reductions in both state estimation uncertainty and sensitivity to line parameters tolerances. Moreover, if PMUs with just two three-phase channels are used, we can avoid instrumenting between 30% and 40% of buses with just a minor impact on state estimation performance even in the case of contingencies. This percentage can be slightly increased if multi-channel PMUs are used. However, this choice generally is not profitable.