Modeling and Analysis of State Differential Equations of Grid-Forming DFIG System Considering Taylor Expansion’s Second-Order Nonlinear Terms Based on Normal Form Theory

This paper takes the two-machine and two-zone doubly-fed induction generator system as the research object. And each machine adopts the voltage and current double loop virtual synchronous grid-forming control strategy. Based on the Normal Form theory of vector fields, the approximate time domain solutions of the nonlinear state differential equations of the system considering taylor expansion’s second-order nonlinear terms were derived. Thus the Normal Form mathematical model of the system was established. Then the differences between the first-order Linear Mode Analysis method and the second-order Nonlinear Normal Form method were compared. And the influence of the taylor expansion’s second-order nonlinear terms of the system’s state differential equations on the time domain solution of the system’s state variables was studied. Then, the electromagnetic transient simulation model, second-order nonlinear Normal Form simulation model and first-order Linear Mode Analysis simulation model of the system were built on the MATLAB/SIMULINK simulation platform. And the time domain figures of each state variable in the three models after the disturbance occurred were compared, which verifies the correctness of the established second-order Normal Form mathematical model of the system. Moreover, the simulation results show that the time domain solution of state variables obtained by the second-order Normal Form mathematical model is closer to the real solution than the first-order Linear Mode Analysis mathematical model.