Gilsoo Jang

This study proposes a Bayesian weather-conditioned Wasserstein distributionally robust chance-constrained framework for operating a radial distribution network with a flexible smart factory. Daily macro regimes from clearness and variability indices, hourly micro states from regime-conditioned Gaussian mixture models, and daylight blocks condition a hierarchical empirical Bayes model of photovoltaic proxy forecast errors. The posterior predictive distribution centers each context-dependent Wasserstein ambiguity set, whose radius adapts to the group sample size. The resulting voltage and line-loading margins tighten a 24-hour mixed-integer second-order cone program that co-optimizes network operation and service-constrained production tasks. For day-ahead deployment, regime forecast probabilities replace the unavailable realized label and determine a predictive mixture and an effective-count radius. In model-based validation under realized context labels, only the oracle-context benchmark meets the 5\% individual-constraint target on all 11 representative days. In the 2025 out-of-sample test, which holds out all realized 2025 error outcomes, the proposed probabilistic formulation records annual mean and worst-day daily maximum violation rates of 3.8\% and 18\%, while the oracle and top-1 assignment variants both reach 96\% on their worst days. It also operates more cost-effectively than the more conservative global and macro-only designs, which record lower annual mean rates at higher cost.

This study proposes a novel robust low-carbon electric vehicle (EV) charging management algorithm for a photovoltaic-energy storage system-equipped electric vehicle charging station utilizing mobile energy storage systems. The proposed algorithm operates within a power distribution system that incorporates the carbon emission flow (CEF) model, explicitly addressing the dual uncertainties in power and carbon prices. In the proposed study, a carbon-aware objective function is introduced to prioritize low-carbon energy supply for EVs. To address price uncertainties, the problem is modeled using the Wasserstein metric-based distributionally robust optimization model and reformulated as a computationally tractable convex counterpart. Furthermore, to resolve the computational complexity arising from the bilinear terms in the CEF model, we propose a novel convex relaxation framework: sequential binary piecewise McCormick relaxation integrated with two-dimensional projection cuts. Numerical investigations demonstrate the superiority of the proposed framework, reducing the carbon consumption at the individual EVCSs by up to 18.94%, lowering the solution time from over 7,000 s to 232.6 s with a near-zero relaxation gap. In addition, the proposed DRO framework reduces the carbon emissions by 16.5% on average compared with robust optimization while keeping the out-of-sample cost within 1.6% of the stochastic benchmark.

This study proposes a Bayesian weather-conditioned Wasserstein distributionally robust chance-constrained framework for operating a radial distribution network with a flexible smart factory. Daily macro regimes from clearness and variability indices, hourly micro states from regime-conditioned Gaussian mixture models, and daylight blocks condition a hierarchical empirical Bayes model of photovoltaic proxy forecast errors. The posterior predictive distribution centers each context-dependent Wasserstein ambiguity set, whose radius adapts to the group sample size. The resulting voltage and line-loading margins tighten a 24-hour mixed-integer second-order cone program that co-optimizes network operation and service-constrained production tasks. For day-ahead deployment, regime forecast probabilities replace the unavailable realized label and determine a predictive mixture and an effective-count radius. In model-based validation under realized context labels, only the oracle-context benchmark meets the 5\% individual-constraint target on all 11 representative days. In the 2025 out-of-sample test, which holds out all realized 2025 error outcomes, the proposed probabilistic formulation records annual mean and worst-day daily maximum violation rates of 3.8\% and 18\%, while the oracle and top-1 assignment variants both reach 96\% on their worst days. It also operates more cost-effectively than the more conservative global and macro-only designs, which record lower annual mean rates at higher cost.

The integration of photovoltaic generators introduces significant uncertainties in distribution network (DN) operations. This study presents a novel distributionally robust energy management strategy for multiple DNs, addressing inherent variabilities in renewable energy generation and load demands. To achieve the optimal energy management across the entire system under uncertainty, we introduce a novel concept: the adjusted cost-influencing participation factor (ACPF). The distribution system operator incorporates critical components such as the net power of the entire system, the locational marginal prices of the DNs, and the rated capacities of the generation units to compute the ACPF. We further reformulate the proposed distributionally robust chance constraint into a deterministic linear constraint by employing duality theory and the nested bisection search method. Comprehensive case studies on modified IEEE test systems validate the proposed methodology, demonstrating enhanced operational efficiency and reduced generation costs under various parameters and scenarios. The approach offers a robust framework for optimizing energy transactions across multiple DNs.