A Reliability-Oriented Fuzzy Stochastic Framework in Automated Distribution Grids to Allocate $\mu$ -PMUs

This paper proposes a reliability-oriented stochastic aggregated integer linear framework for full observability of the automated distributed systems based on the <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synchrophasor units. The <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synchrophasor unit as a newly introduced high-tech device makes it possible for an accurate and high-speed measurement of the voltage and current waveforms in the distribution systems. This paper proposes a multi-stage strategy for the <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synchrophasor unit placement together with the communication system requirements in the reconfigurable distribution systems, considering the zero-injection constraints in the model. To determine the optimal topology at the end of each phase, a reliability-based cost function is developed to optimize the customer interruption costs and power losses simultaneously. In order to model the uncertainties of forecast error in the active and reactive load demands as well as the failure rate and repair rate parameters, a stochastic framework based on the fuzzy cloud theory is employed. The proposed bi-level mixed integer linear programing approach is used to co-optimize the network switching scheme as well as the optimal <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synchrophasor positions and communication infrastructure costs in the same framework. The simulation results on a practical test system verify the observability of the automated reconfigurable distribution system during the reconfiguration process.