A physics-informed neural network surrogate model and many-objective optimization algorithm for coupled multi-energy systems in smart grids

Abstract

The scope of smart grids is progressively extending toward Integrated Energy Systems (IES) that couple electricity with gas, heating, and cooling. Due to the unsteady-state physical characteristics inherent in the transmission of gas, heat, and cooling resources, IES scheduling must not only balance multiple typical objectives but also account for the dynamic coupling of heterogeneous physical domains. To address these challenges, this paper formulates a Many-objective Optimization Model for Coupled Multi-Energy Flows (MaOCMFM) with partial differential equations (PDEs) in IES, which captures the dynamic physical behaviors of electricity, gas, heat, and cooling subsystems. Building upon this model, we propose a Probabilistic Contributing Many-objective Evolutionary Algorithm enhanced by a Physics-Informed Neural Network surrogate model (PC-MaOEA-PINN). Cubic B-spline functions are employed to achieve a continuous representation of the decision variables, while multi-physics constraints are embedded into the loss function of the surrogate model. This design enables efficient approximation of the objective function with a limited number of samples and facilitates focused exploration in critical evolutionary regions, thereby accelerating population convergence. The effectiveness of the proposed model and algorithm is validated on 9 typical scheduling days across four simulated IES scenarios.