Sensitivity Analysis of Power System Reliability Indices Including Voltage and Reactive Power Constraints

This paper presents a method for sensitivity analysis of power system reliability indices with respect to voltage and reactive power limits. The method presented in this paper utilizes a linearized power flow model that accounts for voltage bounds and reactive power constraints, unlike some traditional linearized power flow models such as the DC power flow model. The linearized power flow model is incorporated with a linear programming optimization problem with an objective of minimum load curtailment. Moreover, this work developed sensitivity expressions for some of the well-known reliability indices with respect to voltage bounds and reactive power constraints. Based on the sensitivity analysis, the most vulnerable buses to voltage collapse are identified. Monte Carlo simulations have also been carried out to sample the system states. In addition, this work utilized a heuristic state space classification technique for every sampled state so that the computational time spent in calculating reliability and sensitivity indices has been reduced. The effectiveness of the proposed method is demonstrated on the standard IEEE Reliability Test System (IEEE RTS). Results have demonstrated that the proposed method can determine the most vulnerable buses to voltage collapse in the power system. Furthermore, based on the estimated reliability indices, planners can decide where to invest by trading off between reliability requirements and the cost of installing reactive power compensations to avoid voltage collapses, and thereby improving the overall reliability of the system.

I. Introduction

Electric power systems have become vulnerable to voltage collapse, due to lack of reactive power support, which has significant impact on the reliability of the entire power system. In this context, sensitivity analysis is a promising tool to asses the effect of voltage collapse on power systems reliability. Sensitivity analysis of reliability indices of composite systems with respect to system parameters such as failure and repair rates has been extensively addressed in the literature. Nonetheless, sensitivity of the reliability indices with respect to voltage and reactive power limits has not been given much attention thus far. In performing reliability studies of a given power system, a power flow solution is repeatedly carried out. In the context of power flows, the DC power flow model and linear programming with the objective of minimum load curtailment is probably the most common model used in the traditional sensitivity analysis based methods. Nevertheless, calculating the sensitivity of the reliability indices with respect to system operating constraints such as voltage and reactive power constraints requires determining Lagrange multipliers for such vital constraints. When integrating the DC power flow model into the linear programming optimization problem, the only Lagrange multipliers that are accessible are those associated with power demand, generation, and transmission lines constraints. However, in order to calculate the sensitivity of the reliability indices with respect to voltage bounds and reactive power constraints, these constraints should be modeled in the optimization problem, which is not applicable using the DC power flow model.