Deep Projected Gradient Network to Accelerate Low-Carbon Economic Dispatch Considering Energy Storage

Under the strategic goals of “peak carbon emissions and carbon neutrality”, traditional methods for solving economic dispatch problems involving carbon emission trading costs, wind power, and energy storage devices lack real-time performance and are difficult to support in real-time decision-making. This paper proposes an accelerated solution framework that expands the projection gradient descent method into a Deep Projected Gradient Network (D-PGNet). The network consists of K structured layers, each layer strictly embedding differentiable projection operations corresponding to physical constraints such as power balance, unit ramp-up, and energy storage timing dynamics. This paper systematically derived the projection closed-form solutions of each constraint set to the basic subset, designed an efficient differentiable projection layer based on Dykstra alternating projection, and analyzed the differentiability and convergence properties of the network. Multiple scenario tests have shown that the optimal gap of D-PGNet results is less than 1.08%, the carbon emission deviation is less than 0.2%, the solving speed is improved by more than 64 times at most, and the maximum violation of all physical constraints is below 1.3 × 10−5 p.u.