To naturally characterize the long-time sequence coupled equipment such as energy storage systems (ESS) and to enforce the non-anticipativity of dispatch decisions under uncertain renewable energy, a multi-stage robust dynamic unit commitment (MRDUC) model is proposed in this paper. MRDUC transforms the multi-stage robust unit commitment into a dynamic programming form, which is the first attempt to combine day-ahead optimization with intra-day multi-stage robust dynamic dispatch. The unit commitment problem is solved in the pre-stage, and a simulation of intra-day multi-stage economic dispatch is done thereafter, which further refines the UC decision in an iterative way. A pre-extended -fast robust dual dynamic programming (PE-FRDDP) method is proposed to efficiently solve the MRDUC problem, which simultaneously optimizes the day-ahead UC and the intra-day decision policies. Case studies on the modified IEEE 6-Bus and 4 large-scale systems from 300 to 1888 buses demonstrate the effectiveness of the proposed model and the solution methodology.

The current state-of-the-art approach for battery state-of-health (SOH) estimation typically employs a centralized computing framework, wherein data from local battery management systems (BMSs) is aggregated and trained on a cloud server, due to limited computing resources at the BMS. However, this framework presents various challenges, including frequent data communication, latency, data security, and degraded prediction accuracy. To address these issues, this study proposes a novel adaptive multipersonalized federated learning (FL) algorithm for evaluating the SOH of multiple batteries, aggregating multiple local SOH estimation models into a global model while locally preserving battery data. The algorithm utilizes the difference of importance weights between global and local models to regulate the local loss, incorporates adaptive personalization layers with loss variation, and employs clustering techniques to form multiple global models from distinct local models, leading to a more accurate and tailored prediction. Additionally, an adaptively SOH-related differential privacy protection mechanism is integrated to enhance the protection of local battery data while ensuring robust model performance. An extensive case study has demonstrated that the adaptive multipersonalized FL algorithm outperforms other methods in terms of estimation accuracy and operational risk. Specifically, it achieves a reduction in mean absolute error by 0.14% and 6.01% compared to traditional FL and local training methods, respectively, and exhibits nearly fivefold lower operational risk compared to centralized training.

With the proliferation of electric vehicles (EVs), vehicle-to-grid (V2G) capability emerges as a potential resource for load restoration after a large disruption. This paper presents a real-time post-disaster load restoration method for the coordinated power distribution networks (PDN) and urban traffic networks (UTN) with V2G response. The multi-period restoration problem is modeled as a dynamic programming-based multi-stage robust optimization model, addressing uncertainties of renewable generation and traffic demands. It incorporates a dynamic traffic assignment scheme to characterize vehicle travels and V2G services within short time slots. Then, an improved robust dual dynamic programming algorithm is proposed to solve the multi-stage robust optimization problem. For online application, the solved value functions from each stage serve as per-period policies, leveraging knowledge of future uncertainties to quickly guide real-time load restoration through distributed resource dispatch, network reconfiguration, and V2G assignments. Numerical experiments with a 33-bus PDN and 20-road UTN, plus a real-world 91-bus PDN with 35-road UTN, validate the effectiveness of proposed restoration method.

This paper proposes a day-ahead and intra-day co-optimized resilience enhancement strategy for distribution systems with outages under extreme events, namely, dynamic programming formulated multi-stage hybrid stochastic-robust optimization (DSRO). The DSRO model is a pioneering effort to simultaneously determine the day-ahead decision and the corresponding intra-day policies for microgrids formation, via coupling the two problem with value functions. It establishes a multi-stage framework to address the anticipative challenges inherent in the widely-used two-stage model. For coping with uncertainties, discrete Markov chains are incorporated to model subsequent contingencies, and an uncertainty set for wind generation is constructed to improve computational efficiency. To efficiently solve the DSRO model, a robust dual dynamic programming (RDDP) based solution method is presented, where the relaxed inner approximation method and Lagrangian hyperplanes are employed to handle the nonconvex challenges arising from discrete recourse variables. Case studies on the modified IEEE 14-Bus and 123-Bus distribution systems demonstrate the effectiveness of the proposed model and the solution methodology.

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.

To realize the potential of the integrated electrical-heating systems (IEHS) for coping with the uncertain renewable energy, a reserve scheduling model based on the dynamic programming transformed multi-stage adaptive robust optimization (DMRO) is proposed in this paper. The DMRO model enforces the non-anticipativity of scheduling process via temporal decomposed framework, and enhances the formulation flexibility for time-coupled equipment, such as energy storage systems (ESS). The whole scheduling model is split into two problems under the decomposition constructure, which consists of a reserve interval generation (RG) problem for making the unit commitment and systems' reserve plan, and a multi-stage economic operation (EO) problem aiming with simulating the worst-case scheduling process. To obtain the global optimal, a nested Benders decomposition algorithm is employed to solve the DMRO model. Case studies on the 6-Bus-5-node IEHS and the 118-Bus-24-node IEHS demonstrate the effectiveness of the proposed model and the solution methodology.