An ILP model for stochastic placement of [formula omitted]PMUs with limited voltage and current channels in a reconfigurable distribution network

Abstract

Micro phasor measurement units (μPMUs) play a major role in the evolution of distribution networks toward the smart grids by providing precise and synchronized measurements. In this study, an integer linear programming (ILP) model for stochastic optimal μPMU placement (SOMPP) problem is formulated in order that the network would remain observable following a network reconfiguration. Furthermore, the current measurement channels are considered limited and it is also extended to voltage measurement channels, in order to be employed in cases that measurement channels are insufficient (e.g. three-phase networks). The uncertain quantities including the variability of load demands and the unreliability of lines are characterize by proper probability distribution functions (PDFs) instead of constant values, and employed in a Monte Carlo simulation (MCS) process. The most probable scenarios are obtained by a scenario reduction method, and the most probable topologies within each scenario are identified by multiple execution of reconfiguration for the reduced scenarios using the genetic algorithm (GA). Then the SOMPP model is solved for each reduced scenario using the concept of equivalent network that is also introduced in present work. A formulation for the deterministic form of the problem is also developed in order to compare the results of the SOMPP model with the deterministic one, by which the observability of all possible topologies is guaranteed with a limited number of channels. Furthermore, using the concept of voltage channels limit, the formulation of the SOMPP model is extended to include the unbalanced networks. The simulations are performed on 33-bus and 240-bus distribution networks. The numerical results revealed the relative superiority of the SOMPP model over the deterministic version and previous works in terms of decreasing the required number of μPMUs. Moreover, the effectiveness of the model in handling the random variables with unknown PDFs is also determined. The success of the reduced scenarios in representing the most general scenarios is also demonstrated by evaluating a large number of scenarios. The validation of the concept of equivalent network is also examined for multiple simulation cases.