Phase-locked Loop Dynamic Preserved Model Order Reduction of Doubly-Fed Wind Turbines Based on Balanced Truncation

Phase-locked loop (PLL) has gradually become an important part of system synchronization in large-scale wind farms. Although the current reduced order state space model used for real-time simulation has a wide range of applications, the traditional reduced order model mainly focuses on model accuracy and model computational complexity, and can not realize the mechanism preservation of specific links. In order to study the problems of synchronous misalignment and wide-band oscillation in large-scale wind farms, a PLL dynamic preserved model order reduction of doubly-fed wind turbines (DFWTs) based on balanced truncation is proposed in this paper. Firstly, a small-signal model of parallel doubly-fed wind turbine with full order is established. Then, the PLL is separated from the wind turbine system to form two subsystems named decoupled subsystem (PLL) and decoupled main system. Based on this, balanced truncation based on gramian is applied to the decoupled main system with the exception of complete PLL structure. Finally, the reduced order decoupled main system is combined with the decoupled subsystem to form the PLL dynamic preserved reduced order model of DFWTs. The proposed PLL preserved order reduction method of DFWTs is verified with the simulation of 20 DFWTs in parallel effectively.