Black-box model for on-line voltage stability assessment of power system-case study of the Finnish transmission grid

A black-box modelling approach was developed for on-line long-term voltage stability assessment. The function to be approximated is the mapping between the pre-disturbance operation point and the voltage stability margin (VSM) of the most critical contingency. The inputs are active and reactive line flows and bus voltages at a pre-disturbance operation point. Good quality data is essential for the approach. The data generation is based on load-flow computation of operation and maximum loading points. The idea of the approach is to enlarge and generalise the existing and widely used security boundary method and to take into account the uncertainty related to power system operation. The approach does not make unnecessary the traditional computation methods; rather these methods are urgently needed at the off-line computation step of data generation. The approach was applied to the equivalent of the Finnish transmission grid to ascertain the applicability and the problems on the real system. The system was studied to assess the maximum transfer capacity from Sweden to Finland in on-line. The accuracy of the multilayer perceptron (MLP) neural network (NN) was found to be the best one; other model types were a linear polynomial model (LPM) and radial basis function (RBF) NN. According to the test results the approach is applicable to a real system, however practical implementation would require a more detailed power system model that could represent the performance of the real system.