The increasing penetration of solar photovoltaic (PV) systems in modern distribution networks introduces significant variability, uncertainty, and spatiotemporal heterogeneity that challenge conventional data-driven modeling approaches. Existing methods predominantly rely on deterministic representations or simplified statistical summaries, which fail to capture the complex distributional structure of PV generation and its interaction with energy storage and environmental factors. To address this limitation, this paper proposes a distributionally robust data representation framework that models PV outputs as ambiguity sets of probability distributions rather than single trajectories. Leveraging Wasserstein metrics, the framework constructs data-driven uncertainty sets that explicitly encode temporal variability, cross-resource correlations, and distributional perturbations arising from weather dynamics and measurement noise. A unified modeling architecture is developed to integrate multi-source data, including PV generation, storage state-of-charge, and meteorological variables, and to extract robust statistical descriptors through worst-case expectation formulations. In addition, a generation mechanism scenario is designed to produce representative and extreme trajectories from the ambiguity sets, enabling enhanced coverage of rare but critical operating conditions such as rapid irradiance fluctuations. Wasserstein ambiguity sets are not treated as a new theory in this work; they are used as a representation layer for PV, ESS, meteorological, and load trajectories before downstream analysis. Extensive case studies on a modified IEEE 123-bus distribution system demonstrate that the proposed approach improves out-of-sample performance, reduces scenario-level standard deviation relative to deterministic representation in repeated-run evaluation, and maintains more stable error behavior under controlled distribution shifts. Furthermore, the framework achieves up to 40–50% reduction in scenario requirements while preserving high approximation quality, indicating strong computational efficiency. The validation includes confidence intervals, variance and standard deviation definitions, ablation results, sensitivity checks, and repeatability details for the modified IEEE 123-bus test system.
Liu et al. (Sun,) studied this question.