Dynamic Modeling and Adaptive Dimension Improvement Method for Smart Distribution Network Stations Based on Koopman Theory

Aiming at the dynamic characteristics and stability of smart distribution network stations under the combined effect of the uncertainty of new energy output and the control logic of power electronics, an adaptive dimensionally increasing linear dynamic modeling method based on Koopman theory is proposed. Firstly, a regional nonlinear model of an intelligent transformer integrating photovoltaic, wind power, battery, hydrogen fuel cell, and synchronous generator is constructed. The control logic of the virtual synchronous generator is then integrated to characterize the dynamic response of the power electronic interface. Secondly, by constructing a set of nonlinear observation functions, including high-order polynomials, exponents, and periodic functions, the dimensional upgrade mapping of the system state is carried out. The dynamic mode decomposition algorithm is adopted to adaptively extract the dominant dynamic modes in the dimensional upgrade space, achieving global linear approximation of complex nonlinear dynamical systems. Finally, the simulation example results show that the average RMAE error of the Koopman method proposed in this paper in voltage spatiotemporal reconstruction is 0.1419, and the maximum RMSE error is 0.1915, significantly improving the accuracy and stability of dynamic modeling.