Application of Information Gap Decision Theory for Solution of Voltage Stability Constrained Optimal Power Flow in the Presence of Wind Farms

This paper deals with the Voltage Stability Constrained Optimal Power Flow (VSC-OPF) problem in the presence of wind power generation uncertainty. Due to the uncertain nature of wind power generation, an approach is proposed that determines the maximum uncertainty of wind power generation for give a percentage of total cost increase. This maximunm uncertainty is determined in a way that a desired loading margin (LM), is satisfied. It is worth to note that LM is the most important measure of voltage stability which reflects the distance from the current operating point to the voltage collapse point. For this aim, Information Gap Decision Theory (IGDT) is utilized to handle the uncertainty of wind power generation and voltage stability in the proposed VSC-OPF model. The proposed model is implemented on the IEEE 39 and 118-bus standard test systems, and solved by General Algebraic Modeling System (GAMS) optimization software. In order to evaluate the effectiveness of the proposed methodology for uncertainty handling, the results obtained by IGDT technique are compared with Monte Carlo Simulations (MCS). The simulation results imply that the uncertainty radius and the desired LM have an inverse relationship, such that for a given percentage of cost increase, the radius of uncertainty decreses with respect to the increase of the desired LM.