Distributed Frequency Regulation Method for Power Grids Considering the Delayed Response of Virtual Power Plants

To tackle the challenges of distributed flexible resource coordination and inherent control delays in virtual power plant (VPP)-participated frequency regulation (FR) for interconnected power systems, this paper proposes a novel distributed model predictive control (DMPC)-based FR strategy with time-delay compensation. A hierarchical FR architecture is first established, incorporating analytical models of communication latency in VPP coordination and detailed electro-mechanical dynamics of generation-load systems. Through state-space augmentation techniques, we develop a delay-embedded generalized predictive model that systematically integrates historical state reconstruction and future trajectory prediction. This approach constructs a time-delay-compensated DMPC (TDC-DMPC) optimization framework that uses quadratic programming to solve the objective function and generate the optimal FR control sequences for VPP flexible load clusters. Comparative simulations on a four-area interconnected power system show that the proposed TDC-DMPC strategy achieves significant progress in frequency regulation. Operating under a 30 ms communication delay, the TDC-DMPC reduces frequency deviations by 30.5% and 18.8% compared to conventional DMPC and sequence-selective DMPC (SS-DMPC), respectively, while reducing the stabilisation time to 0.4 s—a fivefold improvement over the conventional method’s 2.2 s. Robustness analysis confirms exceptional resilience, with the system maintaining stable operation under extreme conditions, including 600 ms communication delays and 20% parameter perturbations, significantly outperforming existing methods in stress scenarios.