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Active distribution networks increasingly rely on stochastic optimization to manage uncertainties arising from renewable generation, flexible demand, distributed storage, electric vehicles, and local energy markets. These uncertainties affect voltage quality, congestion, operational cost, reliability, and the value of flexibility. This systematic review categorizes and evaluates uncertainty-aware stochastic optimization techniques for demand response, DER coordination, and flexibility provision in active distribution networks. It focuses on methodological transparency, thematic synthesis, and identification of research gaps. A PRISMA-guided systematic review of 31 peer-reviewed journal articles published from 2017 to 2023 was conducted. A structured search, screening, eligibility assessment, and data extraction process was used to organize the evidence. The review maps dominant stochastic frameworks, including two-stage stochastic programming, chance-constrained optimization, robust-stochastic formulations, and distributionally robust optimization. Five synthesis tables are used across the full manuscript to summarize study selection, article characteristics, method taxonomies, application mappings, and research gaps. Stochastic optimization supports secure and efficient operation of active distribution grids, but important gaps remain in scalability, real-world validation, interoperability, and regulatory integration. The review outlines an agenda for more adaptive, transparent, and implementation-ready optimization methods.

Active distribution networks face growing renewable curtailment as distributed photovoltaic and wind generation increasingly encounter voltage, congestion, and flexibility constraints. Battery storage scheduling under uncertainty has become a central operational strategy for absorbing otherwise curtailed energy and improving distribution-level renewable integration. Despite substantial growth in optimization-based storage studies, the literature remains fragmented across stochastic programming, chance-constrained optimization, robust optimization, and distributionally robust formulations. No critical review has systematically compared these paradigms for storage scheduling and curtailment reduction specifically in active distribution networks. This critical review assesses and contrasts stochastic and robust optimization models for battery storage scheduling aimed at reducing renewable curtailment in active distribution networks. It evaluates how these approaches represent uncertainty, network constraints, operational objectives, and implementation readiness. A structured critical review of 27 peer-reviewed journal articles published between 2017 and 2024 was conducted. The analysis focuses on mathematical formulations, uncertainty modeling, storage representation, curtailment objectives, network constraints, and operational applicability. Stochastic models offer strong expected-performance reasoning but often depend on scenario quality and can become computationally demanding. Robust models provide stronger protection against adverse uncertainty realizations but may become conservative when uncertainty sets are poorly calibrated, while gaps remain in real-time scheduling, multi-service operation, degradation modeling, and field validation. The choice between stochastic and robust optimization depends on operator risk preference, data availability, computational resources, and distribution network complexity. Hybrid, data-driven, and implementation-oriented methods offer promising future pathways for reducing renewable curtailment through battery storage scheduling.