The ever-increasing integration of variable wind energy requests for a power system with high flexibility. In this paper, we formulate the real-time economic dispatch problem as a multi-stage robust program to leverage flexible resources, especially energy storage systems, in a broader timescale, and also to avoid the risk of high costs in critical scenarios. The multi-stage robust program is decomposed to the dynamic programming form and the fast robust dual dynamic programming (FRDDP) algorithm is developed to solve it efficiently. To tackle the nonconvexities caused by the inter-temporal constraints of ESSs, an estimation-correction method is developed, and measures of the approximation accuracy are presented. Comprehensive case studies comprising units up to 1371 are carried out to verify the effectiveness of the proposed model. Numerical results show that compared with the existing ones, the proposed multi-stage robust model achieves lower cost under the worst-case scenario and shows better scalability in large-scale systems.

We propose a dynamic programming (DP) model for multi-stage stochastic-robust optimization (DMSR) to solve the real-time dispatch in power grids with fast-acting (FA) units for enhancing system resilience under extreme events. The proposed approach considers an offline solution and online dispatch. In the offline solution, the T-period real-time dispatch is formulated as a T -stage DMSR model, where its solution is based on an enhanced version of the fast robust dual dynamic programming (FRDDP) algorithm. In online dispatch, the mature cost-to-go functions coupling each stage are used as per-period policies to quickly direct the state adjustment of FA units and real-time dispatch decisions. In DMSR, the scenario-based technique is employed to model contingencies in the multi-stage framework, and the uncertainty set of wind power is constructed to reduce computing complexity. Case studies on the modified IEEE 14-Bus, 118-Bus and 300-Bus systems demonstrate the effectiveness of the proposed real-time dispatch method and solution methodology.

A multi-stage robust real-time economic dispatch model (MRRTD) for power systems is proposed in this paper. The MRRTD takes the dynamic form of multi-stage robust optimization as the framework to naturally simulate the operation of equipment that is temporally coupled, e.g., utility-level energy storage systems. For normal systems, the MRRTD can work directly in short time slots with a rolling horizon. For large-scale systems, the MRRTD expands the time-slot scale and generates optimal dispatch policies. With this guidance, the real-time dispatch decision can be swiftly made thereafter. In addition, a dynamic uncertainty set based on deep learning is proposed, which can dynamically refine the covering ability for probable occurred wind power scenarios. To efficiently solve the MRRTD, a novel fast robust dual dynamic programming method is employed. The effectiveness of the proposed model and solution algorithm, especially the improved scalability compared to several other dynamic economic dispatch methods, are demonstrated by simulation results from six benchmark test cases ranging from a modified IEEE 6-bus system to a 6495-bus system.