Voltage stability constrained VAR planning: model simplification using statistical approximation

Abstract

This paper presents a statistical approximation procedure to simplify the voltage stability constrained VAR planning optimization model. One major source of complexity of the voltage stability constrained model is the requirement of having two sets of network variables and power flow constraints corresponding to the “normal operation” and “point of collapse (PoC)”. This effectively doubles the number of variables and constraints in the voltage stability constrained model as compared to the VAR planning model dealing solely with “normal operation” and limits on bus voltages alone. The present analysis explores the possibility to simplify the model using statistical approximation of the locus of the PoC. This approximation exploits the fact that the MINLP model utilizes only the PoC information of the nose curve. The locus can be reasonably approximated using a standard linear/quadratic ordinary least square multivariate regression model. Although the simplified model has lower computational complexity, the impact on the model results needs to be carefully examined. We have demonstrated using a high reactive power deficit contingency case for the AEP 14-bus system that the results of the simplified model are only marginally inferior to those of the globally optimal solution.