Two-layer asynchronous distributed optimal voltage control for VSC-HVDC-connected large-scale wind farm clusters

• A two-layer asynchronous distributed WFC optimal voltage control scheme was designed. • Asynchronous ADMM was employed to eliminate the need for synchronous update computations for the sub-WF controllers. • An adaptive penalty factors optimization model was introduced to improve computing efficiency and accuracy. This study proposes a two-layer asynchronous distributed optimal voltage control (TADOVC) scheme for voltage source converter high voltage direct current (VSC-HVDC)-connected large-scale wind farm clusters (WFCs). First, a TADOVC scheme based on model predictive control (MPC) and asynchronous alternating direction method of the multipliers (ADMM) was introduced, where an asynchronous decentralized ADMM was employed in WFC control, which serves as the upper-level control, to eliminate the need for central controller, and the wind farm control in the lower-level employed asynchronous global ADMM to achieve global optimization of wind farms. Second, an asynchronous adaptive ADMM (A-ADMM) is proposed to eliminate the limitation of synchronous update of all variables in the control process, mitigate the impact of controller communication delay on control efficiency in WFC, and alleviate the influence of unreasonable iteration parameters on algorithm iteration speed. Furthermore, a theoretical analysis was conducted to derive the convergence conditions of asynchronous ADMM in solving the voltage optimal control problem. A WFC with 5 sub-wind farms (sub-WFs), with each sub-WF consisting of 20 wind turbines (WTs), was used to validate the proposed TADOVC scheme. The results showed that the proposed scheme could improve the computation efficiency without affecting the original problem’s optimality, while also exhibiting enhanced robustness and environmental adaptability.