Phasor Measurement Unit Placement Considering Line Outages

Phasor measurement unit(PMU)is able to provide synchronized voltage phasor and current phasor in power system.Because of the linear relationship between system states and phasor measurements,the utilization of PMUs at buses will simplify state estimation.PMUs can measure voltage phasors at the installed bus and current phasors of connected branches at the same time.Therefore,the observability of the whole network can be ensured by installing PMUs in some buses on the premise of selecting appropriate buses to install PMUs.At present,there are a large number of researches on the investment cost,most of which analyze the observability from a deterministic perspective.In this paper,observability is considered from a probabilistic perspective,which provides a quantitative description for observability.This method can be used to evaluate different PMU placement schemes or identify weak areas that need to be strengthened.In this paper,we established the optimal PMU placement model to ensure the complete observability of the system in different scenarios,and defined the probability of observability for both buses and system.On this basis,the calculation of probability of observability in different scenarios was disscussed.Based on the analysis of wide area measurement system’s hierarchal strcuture,the availability of PMUs,transmission lines,current sensors,voltage sensors and communication lines was considered in the form of "and" when calculating the probability of observability.In order to consider the cost and observable probability of the system simultaneously,a multi-objective PMU optimal placement model was proposed with the objectives of minimizing the number of PMUs and the unobservable probability of the system,which was solved by ε-constraint method and fuzzy decision.For IEEE-24 bus system and IEEE-57 bus system,the experimental results showed that the final placement scheme is the inflection point of Pareto front.In addition,the unobservable probability of the system obtained by multi-objective optimization model was lower than that of the single objective optimization model.Besides,compared with converting the unobservable probability of the system into the constraint,transferring the number of PMUs into the constraint was more suitable to solve the multi-objective optimization model in this paper.