Design of a multi-parameter neural proportional–integral–derivative cooperative controller for power cyber–physical systems using t-distributed stochastic neighbor embedding

With the development of Cyber-Physical Systems in power systems, real-time data acquisition and cooperative control provide new opportunities for enhancing the stability of multi-area power transmission systems. This paper proposes a Cyber-Physical Systems-based cooperative control strategy for generators, aiming to improve the stability of multi-area power transmission systems under fault conditions. A 7-machine, 29-node power Cyber-Physical Systems model is adopted, where multiple parameters, including generator stator voltage, active power, and reactive power, are collected in real time via the Cyber-Physical Systems. The t-distributed Stochastic Neighbor Embedding dimensionality reduction technique is employed to process the stator voltage error matrix, integrating local and coupled generator data to form input vectors for a neural network, which predicts optimized Proportional-Integral-Derivative control parameters. By combining multiple-parameter acquisition, t-distributed Stochastic Neighbor Embedding dimensionality reduction, and Neural Proportional-Integral-Derivative optimized control, a Multiple-parameter t-distributed Stochastic Neighbor Embedding Neural Proportional-Integral-Derivative controller is developed to achieve efficient system cooperative control. Simulation results demonstrate that, under both lossless and different packet-loss communication environments, the proposed Multiple-parameter t-distributed Stochastic Neighbor Embedding Neural Proportional-Integral-Derivative controller consistently outperforms the conventional Proportional-Integral-Derivative controller, Backpropagation Neural Network Proportional-Integral-Derivative controller, and Fuzzy Neural Network Proportional-Integral-Derivative controller. Packet-loss sensitivity analysis further confirms its robustness. In particular, the proposed controller achieves significantly lower Integral Time-weighted Absolute Error in active power and reactive power regulation than the other controllers, demonstrating superior tracking accuracy and transient control performance.