A Value-at-Risk Based Approach for PMU Placement in Distribution Systems

Min Liu

doi:10.32604/ee.2022.016657

Abstract

With the application of phasor measurement units (PMU) in the distribution system, it is expected that the performance of the distribution system state estimation can be improved obviously with the PMU measurements into consideration. How to appropriately place the PMUs in the distribution is therefore become an important issue due to the economical consideration. According to the concept of efficient frontier, a value-at-risk based approach is proposed to make optimal placement of PMU taking account of the uncertainty of measure errors, statistical characteristics of the pseudo measurements, and reliability of the measurement instrument. The reasonability and feasibility of the proposed model is illustrated with 12-node system and IEEE-33 node system. Simulation results indicated that uncertainties of measurement error and instrument fault result in more PMU to be installed, and measurement uncertainty is the main affect factor unless the fault rate of PMU is quite high.

Highlights

State estimation (SE) is a function that takes advantage of the inherent redundancy among the available measurements in order to determine the best estimate of the system states defined as the set of all the bus voltage magnitudes and phase angles in the system [1]
Addressing the above problems, i.e., i) How to quantify the estimation accuracy with an intuitive index taking account of the uncertainties in the process of SE? ii) How to make a tradeoff between the accuracy and cost? iii) How to address the reliability problem of the measure instruments), this paper proposed a framework for the optimal allocation of phasor measurement units (PMU) in the SE of the distribution system based on the concept of efficient frontier and value at risk (VaR), and developed a Genetic Algorithm (GA) based approach to solve the proposed optimization model since genetic algorithms (GA) is a widely used optimization algorithm and has been used in the optimization of PMU configuration [23,28,29]
The horizontal axis in the figure represents the installation cost of PMU, and the longitudinal ordinate represents the lowest state estimation accuracy that can be achieved under 95% probability

Summary

Introduction

State estimation (SE) is a function that takes advantage of the inherent redundancy among the available measurements in order to determine the best estimate of the system states defined as the set of all the bus voltage magnitudes and phase angles in the system [1]. It is not economically feasible to install a lot of measure devices to monitor, protect and control the distribution system. SE is the basic function of the Distribution Management System (DMS) of the distribution grid, which provides the required state values to the advanced DMS functions such as distribution contingency analysis, optimal network reconfiguration, fault location and restoration, demand response, voltage and var control, and var optimization et al Recently, with the development of the application of phasor measurement units (PMU) in the distribution system [2–4], synchronized phasor measurements are introduced into the SE process. Since it is not possible to install the PMUs at every node in the distribution system due to the economic consideration, we have to make a tradeoff between improving SE performance and saving cost by appropriately allocating.

Methods

Results

Conclusion