Prediction of Period-Doubling Bifurcation Based on Dynamic Recognition and Its Application to Power Systems

Abstract

In this paper, a bifurcation prediction approach is proposed based on dynamic recognition and further applied to predict the period-doubling bifurcation (PDB) of power systems. Firstly, modeling of the internal dynamics of nonlinear systems is obtained through deterministic learning (DL), and the modeling results are applied for constructing the dynamic training pattern database. Specifically, training patterns are chosen according to the hierarchical structured knowledge representation based on the qualitative property of dynamical systems, which is capable of arranging the dynamical models into a specific order in the pattern database. Then, a dynamic recognition-based bifurcation prediction approach is suggested. As a result, perturbations implying PDB on the testing patterns can be predicted through the minimum dynamic error between the training patterns and testing patterns by recalling the knowledge restored in the pattern database. Finally, the second-order single-machine to infinite bus power system model is introduced to check the effectiveness of this prediction approach, which implies PDB under small periodic parameter perturbations. The key point that determines the prediction effect mainly lies in two methods: (1) accurate approximation of the unknown system dynamics through DL guarantees the feasibility of the prediction process; (2) the qualitative property of PDB and the generalization ability of DL algorithm ensure the validity of the selected training patterns. Simulations are included to illustrate the effectiveness of the proposed approach.