A Reduced-Order RNN Model for Solving Lyapunov Equation Based on Efficient Vectorization Method - Chen, Zhiying; Du, Zhaobin; Li, Feng; Xia, Chengjun (Frontiers in Energy Research, 2022)
With the trend of electronization of power system, traditional serial numerical algorithm is more and more difficult to adapt to the demand of real-time analysis of power system. As one of the important calculating tasks in power systems, the online solution of Lyapunov equations has attracted much attention. Recursive neural network (RNN) is more promising to become the online solver of Lyapunov equation due to its hardware implementation capability and parallel distribution characteristics. In order to improve the performance of the traditional RNN, this paper designs an efficient vectorization method and then proposes a reduced-order RNN model to replace the orginal one. Firstly, a new vectorization method is proposed based on the special structure of vectorized matrix, which is more efficient than the traditional Kronecker product method. Secondly, aiming at the expanding effect of vectorization on the problem scale, this paper proposes a reduced-order RNN model based on symmetry to reduce the solution scale of RNN. With regard to the accruracy and rubustness, 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 ZNN model and GNN model under linear or nonlinear 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.