Planning capacity for wind–photovoltaic (PV)–thermal–storage systems with high renewable penetration requires models that address investment costs, operational feasibility, and strict carbon limits under uncertainty. This paper presents a two-stage robust optimization model for integrated wind–PV–thermal–storage capacity expansion that guarantees carbon compliance under worst-case renewable realizations. Unlike conventional approaches that relax carbon constraints through price penalties, we enforce the annual carbon emission cap as a hard operational constraint, ensuring candidate portfolios remain feasible even under adverse renewable conditions. To reflect practical storage design, a fixed energy-to-power (E/P) ratio couples storage energy capacity with power converter ratings, preventing unrealistic storage expansions. Renewable uncertainty is captured through a Bertsimas–Sim budgeted polyhedral set defined over representative days, balancing robustness with computational tractability. A tailored decomposition framework integrates economic dispatch and carbon-compliance verification within an outer column-and-constraint generation (C&CG) loop, simultaneously certifying worst-case operating cost and minimum achievable emissions. By exploiting strong duality, we generate two families of valid inequalities iteratively: economic cuts from the Economic subproblem (Economic-SP) and carbon-feasibility cuts from the Carbon subproblem (Carbon-SP). This dual-certification approach ensures capacity plans remain both economically optimal and carbon-compliant across all uncertainty realizations. Case studies on a realistic wind–PV–thermal–storage system demonstrate that the method produces carbon-compliant, robust capacity plans with manageable computational effort, converging in 10–15 iterations. The model explicitly captures operational coupling among renewables, thermal generation, and storage, providing a decision-support tool for low-carbon power systems under deep decarbonization targets.
Yan et al. (Fri,) studied this question.