This paper proposes a fast distributed demand response U+0028 DR U+0029 algorithm for future smart grid based on primaldual interior method and Gaussian belief propagation U+0028 GaBP U+0029 solver. At the beginning of each time slot, each end-user U+002F energysupplier exchanges limited rounds of messages that are not private with its neighbors, and computes the amount of energy consumption U+002F generation locally. The proposed demand response algorithm converges rapidly to a consumption U+002F generation decision that yields the optimal social welfare when the demands of endusers are low. When the demands are high, each end-user U+002F energysupplier estimates its energy consumption U+002F generation quickly such that a sub-optimal social welfare is achieved and the power system is ensured to operate within its capacity constraints. The impact of distributed computation errors on the proposed algorithm is analyzed theoretically. The simulation results show a good performance of the proposed algorithm.

In recent years, renewable energy has received extensive attention due to its advantages of sustainability, economy, and environmental protection. However, with the rapid development of renewable energy, the problem of curtailment is becoming increasingly serious. Studying the calculation method and establishing a quantitative evaluation system of renewable energy accommodation capacity are important means to solve this problem. This paper comprehensively considers the factors affecting the accommodation of renewable energy, establishes a accommodation calculation model with the maximum accommodation of renewable energy as the optimization target based on the time series production simulation method, and uses the hybrid particle swarm optimization (PSO) algorithm to solve it. The model is verified with historical data such as load, photovoltaic (PV), and wind power in a certain region throughout the year. The experimental results verify the rationality of the renewable-energy accommodation-capacity model proposed in this paper and the correctness of the theoretical analysis. The calculation results have important reference and guiding significance for the operation and control of power-grid planning and dispatching.

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.