Neural-network representation of Voltage Stability Indices at the voltage collapse

Representing system security in power flow based system models by the scalar magnitude of a Voltage Stability Index (VSI) may be a very difficult task, which may even render the applicability of such models impractical. VSIs at voltage collapse points are difficult to predict when reactive power generation limits are taken into account in system modeling. Therefore, this paper proposes the determination of the Minimum Singular Value (MSV) and the Tangent Vector Norm (TVN) indices at the voltage collapse by means of Neural Networks (NN), being the latter a novel VSI based on the norm of the tangent vectors used in voltage collapse assessment. In order to determine voltage collapse points for different patterns of load and generation increase, an Optimal Power Flow (OPF) approach for solving the maximum loading problem was used. With these points, the MSV and TVN were calculated and used for training and testing the NNs. A small, but realistic, 6-bus system was used for carrying out this study. Results have shown that NNs can be readily applied to representing some VSIs at the voltage collapse. This approach overcomes some difficulties encountered in problems that account for system security through these VSIs.