Voltage Stability Assessment Techniques for Modern Power Systems

Introduction

The phenomena of power system voltage stability is being continuously studied through various offline and online computer simulation programs at energy control centers. In literature, the authors have proposed and implemented various static and dynamic techniques for the assessment of voltage stability. The static voltage assessment techniques utilize the Newton-Raphson (N-R) based power flow programs, whereas the dynamic techniques requires the time domain simulation with mathematical modeling of various power system components such as automatic voltage regulators (AVRs), generators, governors, and under load tap changing transformers (ULTC) etc. (Kundur et al., 2004). Plotting the P-V/ Q-V curves for the particular load buses selected are the most widely used methods for assessment of voltage stability (Ajjarapu, 2009). Traditionally, when P-V/Q-V curves are to be plotted, the power flow solutions are executed repeatedly with increasing the loads in steps until solution diverges. The system load at which the Jacobian of N-R method becomes singular is considered as maximum loading/critical point. The problem of divergence in the power flow results are mostly due to mathematical error or if the system states reach to a critical point. Therefore, the main drawback of this method is the recognition of the critical point. The problem of divergence in power flow solutions is resolved by the continuation power flow (CPF) technique. In CPF, the power flow equations are reformulated and locally parameterized continuation technique is applied (Ajjarapu & Cristy 1992).

The voltage stability is not only about the identification of critical point, but also it is necessary to find the factors that influence it. The bus voltage sensitivity with respect to change in reactive load demand (dV/dQ) is used as a tool for assessment of voltage stability by Faltabo, Ognedal, & Carlson (1990). The modal analysis technique which is an indirect method for calculating dV/dQ sensitivities is proposed by Gao, Morison, & Kundur (1992). In order to determine the stability margin between current operating point to the critical point, several voltage stability indices (VSIs) are proposed in the literature. Recently, a comprehensive review on VSIs had been presented by Modarresi et al. (2016). Other voltage stability methods such as bifurcation analysis (Ajjarapu 1992; Dobson 1993; Alvarado, 1994), direct methods and energy function (Overbye & DeMarco, 1991) methods can be found in literature. In recent years, wide deployment of phasor measurement units (PMUs) in power systems had opened a new perspective for developing voltage stability assessment techniques. The PMUs based voltage assessment techniques can be classified into local (Corsi & Tarantu, 2008) and wide area monitoring (Glavic 2009; Beiraghi 2013). Since, PMUs capture large amount of data, therefore for large power systems, Mohammadi & Behghani (2015), Diao et al., (2009) have proposed computational intelligence based techniques such as decision trees for online voltage stability assessment. The chapter reflects the major assessment techniques that are useful for the voltage stability of power system.