Functional Approximation of Power System Steady-State Voltage Stability Limits by Artificial Neural Networks

Abstract

The estimation of steady-state voltage stability limits represented by the critical value of a voltage stability index (VSI) in power flow-based electric energy system models may be a very difficult task, which might render their applicability impractical. When voltage collapse is associated with a generation bus reaching one of its reactive power generation limits, critical values of VSIs based on properties of the system Jacobian are difficult to be predicted without actually solving the maximum loading problem. In this context, this paper proposes the functional approximation of power system steady-state voltage stability limits, represented by the critical values of the minimum singular value (MSV) and tangent vector norm (TVN) indices, by means of artificial neural networks (ANNs). To construct a steady-state voltage stability boundary, the maximum loading problem was solved for a normalized even distribution of generation and load increase patterns using an optimal power flow-based approach. With these collapse points, the MSV and TVN indices were calculated and then used in the training and testing processes of the ANNs. A 6-bus system was used for carrying out this study. Results show that the proposed architecture of ANNs can be readily applied to the functional approximation of these VSIs at the voltage collapse.