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This paper presents a new procedure for finding the optimal placement of the phasor measurement units (PMUs) in modern power grids to achieve full network observability under normal operating conditions, and also abnormal operating conditions such as a single line or PMU outage, while considering the availability of PMU measuring channels. The proposed modeling framework is implemented using the fuzzy binary linear programming (FBLP) technique. Linear fuzzy models are proposed for the objective function and constraints alike. The proposed procedure is applied to five benchmark systems such as the IEEE 14-bus, 30-bus, 39-bus, 57-bus, and 118-bus. The numerical results demonstrate that the proposed framework is capable of finding a fine-tuned optimal solution with a simple model and acceptable solution characteristics compared with early works in the literature. Besides, four evaluation indices are introduced to assure the various criteria under study such as the observability depth, measurement redundancy, and robustness of the method under contingencies. The results show that full network observability can be met under normal conditions using 20% PMUs penetration; however, under contingencies, approximately 50% PMUs penetration is required. The novelty of the proposed procedure has proven the capability of the proposed linear fuzzy models to find better optimal number of PMUs with lower number of channels compared to other algorithms under various operating conditions. Hence, the proposed work represents a potential tool to monitor power systems, and it will help the operators in a smart grid environment. Keywords: Binary linear programming, Fuzzy models, Observability, Optimization, Phasor measurement unit, Smart grid

A new fuzzy framework for the optimal placement of phasor measurement units under normal and abnormal conditions