A non-iterative distributed approximate dynamic programming algorithm for frequency security-constrained stochastic economic dispatch

• Stochastic economic dispatch model considering the system frequency security constraints. • A golden section search-based approximate linear constraint generation algorithm. • A non-iterative distributed approximate dynamic programming algorithm. • Test results show the computational efficiency of the proposed algorithm. Due to uncertainties associated with the power output of offshore wind farms, the active power balance and frequency security control of power systems with lots of offshore wind farms are highly challenging. To address this problem, in this study, a new stochastic economic dispatch model of a power system with offshore wind farms considering the system frequency security constraints is established to obtain economic and secure dispatch decisions. Furthermore, the nonlinear convexity of frequency security constraints provides considerable theoretical support for the global optimality of decision-making, and a golden section search-based approximate linear constraint generation algorithm is designed to approximate nonlinear frequency security constraints for improving computational efficiency. Next, a non-iterative distributed approximate dynamic programming algorithm based on the equivalent projection method is designed for the distributed solution of the established model. In the algorithm, first, the model is decoupled from time periods. Next, the high-dimensional feasible region of the offshore wind farm optimization model is projected into a low-dimensional feasible region and substituted into the transmission grid optimization model, and solves the models of the transmission grid and the offshore wind farms sequentially to achieve the non-iterative distributed solution. Finally, case studies on a modified IEEE 39-bus system with two offshore wind farms and an actual provincial system with seven offshore wind farms demonstrate the effectiveness and superiority of the proposed model and algorithm, reducing solution time by over 86.4% compared to the alternating direction method of multipliers-based distributed approximate dynamic programming algorithm.