رویکردی برای تحلیل پایداری ولتاژ پویا برای ادغام پارک های باد DFIG Approach to dynamic voltage stability analysis for DFIG wind parks integration

1 Introduction Nowadays, voltage stability assessment is an important issue in the power system due to blackouts in different countries [1]. The main goal of the power system operator is to run the power system without any voltage instability at the lowest cost. Voltage stability can be affected by several elements and controllers, which operate on different time scales [2]. In particular, the effects of a wind generator (WG) are undeniable. The WG equipped with induction generator absorbs reactive power. As known, most reasons for voltage collapse are based on failing to provide reactive power demands. Therefore, the proper modelling of the WG and its reactive power limits should be adequately analysed for voltage instability detection [3]. Doubly-fed induction generators (DFIGs) are employed in the most newly installed WG in a modern power system. The wind penetration level has been increased in recent times. Many studies had been carried on DFIG reactive power capability curve [4–8]. The DFIG and converter systems can provide the reactive power capability curve. As an illustration, the authors in [8] have investigated the reactive capability curve of DFIG in the rotor-side converter (RSC) and the grid-side converter (GSC). In [9], the authors show the different types of reactive capability curves in the fully rated converter (FRC), DFIG with RSC support and DFIG with RSC and GSC support. Those papers disregarded to propose a method to detect voltage instability. Most studies have investigated the WG on short-term voltage stability [8, 10], steady-state voltage stability analysis [11], lowvoltage ride through control scheme [12]. The studies still lack a detailed model considering the DFIG reactive power capability characteristics in the long-term voltage stability assessment. They also ignored to consider the dynamic behaviour of over excitation limiter (OEL) and on-load tap changer (OLTC). In order to detect voltage instability, different voltage stability indices have been proposed in the literature. The roles of these indices lie in the evaluation of voltage instability risk and the prediction of voltage collapse point. Some indices are a minimum singular value (MSV) of the power flow Jacobian, MSV of the reduced Jacobian [13] and L-index [14]. Also, there are several line stability indices that have a close relation with active power, reactive power and the voltage stability [15]. Such indices are namely: voltage collapse proximity indicator (VCPI) [16, 17] and equivalent node voltage collapse index [18]. The above-mentioned indices cannot consider the dynamic behaviour of the power system, especially in post-contingency conditions. One of the important indices in voltage stability studies is an index based on the impedance matching theorem. Different approaches were presented to calculate Thevenin equivalent impedance (TEI) such as least-squares technique [19], Tellegen’s theorem [20], adaptive algorithm [21] and recursive least-squares technique [22]. The above-mentioned methods use two successive phasor measurements to compute TEI, however, Abdelkader and Morrow [23, 24] have implemented, respectively, three and five successive phasor measurements.