With the large-scale grid integration of renewable energy, the computational and communication burden of traditional centralized control systems has increased, limiting system scalability. Distributed control relies on local communication and autonomous decision-making among inverters, where each inverter adjusts its output power based on local measurements and neighboring information to achieve a global objective. However, distributed control depends on interaction and communication among independent inverters, and the presence of communication and control delays in the system can significantly degrade performance and even lead to instability. Therefore, this paper proposes a consensus active power control strategy for grid-connected inverters based on time-delay Hamiltonian systems. The strategy leverages a Casimir-like function to implement predictive compensation for control delays. Compared to traditional consensus control strategies, the proposed approach ensures the stability of renewable energy power plants over a wider range of delays and exhibits higher robustness in nonlinear scenarios such as plug-and-play and arbitrary switching. Finally, simulation experiments under various operating conditions validate the effectiveness and correctness of the proposed control strategy.