The operator T from a domain D into the space of measurable functions is called a nonanticipating (causal) operator if the past information is independent from the future outputs. We will study the solution x(t) of a ...The operator T from a domain D into the space of measurable functions is called a nonanticipating (causal) operator if the past information is independent from the future outputs. We will study the solution x(t) of a nonlinear operator differential equation where its changes depends on the causal operator T, and semigroup of operator A(t), and all initial parameters (t0, x0) . The initial information is described x(t)=φ(t) for almost all t ≤t0 and φ(t0) =φ0. We will study the nonlinear variation of parameters (NVP) for this type of nonanticipating operator differential equations and develop Alekseev type of NVP.展开更多
Energy storage devices can effectively balance the uncertain load and significantly reduce electricity costs in the community microgrids(C-MGs) integrated with renewable energy sources. Scheduling of energy storage is...Energy storage devices can effectively balance the uncertain load and significantly reduce electricity costs in the community microgrids(C-MGs) integrated with renewable energy sources. Scheduling of energy storage is a multi-stage decision problem in which the decisions must be guaranteed to be nonanticipative and multi-stage robust(all-scenario-feasible). To satisfy these two requirements, this paper proposes a method based on a necessary and sufficient feasibility condition of scheduling decisions under the polyhedral uncertainty set. Unlike the most popular affine decision rule(ADR) based multistage robust optimization(MSRO) method, the method proposed in this paper does not require the affine decision assumption, and the feasible regions(the set of all feasible solutions) are not reduced, nor is the solution quality affected. A simple illustrative example and real-scale scheduling cases demonstrate that the proposed method can find feasible solutions when the ADR-based MSRO fails, and that it finds better solutions when both methods succeed. Comprehensive case studies for a real system are performed and the results validate the effectiveness and efficiency of the proposed method.展开更多
文摘The operator T from a domain D into the space of measurable functions is called a nonanticipating (causal) operator if the past information is independent from the future outputs. We will study the solution x(t) of a nonlinear operator differential equation where its changes depends on the causal operator T, and semigroup of operator A(t), and all initial parameters (t0, x0) . The initial information is described x(t)=φ(t) for almost all t ≤t0 and φ(t0) =φ0. We will study the nonlinear variation of parameters (NVP) for this type of nonanticipating operator differential equations and develop Alekseev type of NVP.
基金supported in part by National Key R&D Program of China (No.2022YFA1004600)Science and Technology Project of State Grid Corporation of China (No.5400-202199524A-0-5-ZN)National Natural Science Foundation of China (No.11991023)。
文摘Energy storage devices can effectively balance the uncertain load and significantly reduce electricity costs in the community microgrids(C-MGs) integrated with renewable energy sources. Scheduling of energy storage is a multi-stage decision problem in which the decisions must be guaranteed to be nonanticipative and multi-stage robust(all-scenario-feasible). To satisfy these two requirements, this paper proposes a method based on a necessary and sufficient feasibility condition of scheduling decisions under the polyhedral uncertainty set. Unlike the most popular affine decision rule(ADR) based multistage robust optimization(MSRO) method, the method proposed in this paper does not require the affine decision assumption, and the feasible regions(the set of all feasible solutions) are not reduced, nor is the solution quality affected. A simple illustrative example and real-scale scheduling cases demonstrate that the proposed method can find feasible solutions when the ADR-based MSRO fails, and that it finds better solutions when both methods succeed. Comprehensive case studies for a real system are performed and the results validate the effectiveness and efficiency of the proposed method.
