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With the trend of electronization of the power system, a traditional serial numerical algorithm is more and more difficult to adapt to the demand of real-time analysis of the power system. As one of the important calculating tasks in power systems, the online solution of Lyapunov equations has attracted much attention. A recursive neural network (RNN) is more promising to become the online solver of the Lyapunov equation due to its hardware implementation capability and parallel distribution characteristics. In order to improve the performance of the traditional RNN, in this study, we have designed an efficient vectorization method and proposed a reduced-order RNN model to replace the original one. First, a new vectorization method is proposed based on the special structure of vectorized matrix, which is more efficient than the traditional Kronecker product method. Second, aiming at the expanding effect of vectorization on the problem scale, a reduced-order RNN model based on symmetry to reduce the solution scale of RNN is proposed. With regard to the accuracy and robustness, it is proved theoretically that the proposed model can maintain the same solution as that of the original model and also proved that the proposed model is suitable for the Zhang neural network (ZNN) model and the gradient neural network (GNN) model under linear or non-linear activation functions. Finally, the effectiveness and superiority of the proposed method are verified by simulation examples, three of which are standard examples of power systems.

A Reduced-Order RNN Model for Solving Lyapunov Equation Based on Efficient Vectorization Method