A probability constrained dynamic switching optimization method for the energy dispatch strategy of hybrid power systems with renewable energy resources and uncertainty

The actual industrial process is usually an uncertain dynamic process. Probability constraints are appropriate for the industrial process modeling in uncertain environments, where constrained conditions do not require to be entirely satisfied or cannot be strictly satisfied. This paper models an energy dispatch strategy problem for hybrid power systems with renewable energy resources as a dynamic switching optimization problem with probability constraints. Finding an analytical solution of the probability constrained dynamic switching optimization problem (i.e., an infinite dimensional optimization problem) is usually very challenging because of the switching characteristic of its dynamic system and the complexity of probability constraints. To find a numerical solution, this problem is treated as a constrained nonlinear parameter optimization problem (i.e., a finite dimensional optimization problem) by using a relaxation approach, an improved sample approximation technique, two smooth approximation methods, and a control parameterization technique. The advantage of the proposed method is that the proposed method does not rely on the structure of the original problem and can be used to handle random variables with various distributions. Further, a penalty function-based intelligent optimization method is proposed for solving the resulting constrained nonlinear parameter optimization problem based on an improved limited-memory BFGS method and an improved intelligent optimization method. According to the convergence result, the penalty function-based intelligent optimization method has global convergence. Finally, two examples are adopted to demonstrate the effectiveness of the proposed approach. Numerical results show that compared with other methods, the proposed method not only can obtain a better solution with a smaller standard deviation, but also has relatively lower computational cost. Additionally, the proposed approach can achieve a stable and robust performance, when we consider the small noise disturbances in the initial system state. That is to say, an effective numerical optimization algorithm is proposed for solving the energy dispatch strategy problem for hybrid power systems with renewable energy resources. Further, a parameter setting method is also proposed by applying the sensitivity analysis approach to balance the calculation cost and the accuracy of obtained solutions.