A distributionally robust bilevel optimization model for wholesale–retail electricity market design

The increasing penetration of renewable energy resources and the rising volatility of wholesale electricity prices introduce significant uncertainty into tariff design and retailer procurement decisions. Conventional tariff-setting approaches typically rely on deterministic forecasts or limited scenario analyses, which may underestimate tail risks and fail to ensure equitable cost allocation among consumers and retailers. Moreover, existing regulatory frameworks often lack an integrated mechanism for jointly considering consumer welfare, retailer profitability, and system-level financial risk exposure, particularly under distributional uncertainty. To address these tensions, we propose a two-level model in which the upper-level regulator maximizes a risk-adjusted social welfare metric that incorporates consumer surplus, retailer surplus, and penalties for variance and tail risk, while the lower-level retailers optimize their own profit given retail tariffs, wholesale procurement, and imbalance penalties. The framework embeds stochastic demand elasticity across heterogeneous consumer segments and introduces hedging portfolios composed of forwards and call options to capture realistic financial risk management strategies. Distributional robustness is incorporated through a Wasserstein ambiguity set that models uncertainty in wholesale prices, renewable availability, and demand response distributions. Methodologically, the model is reformulated as a tractable single-level mixed-integer program using Karush-Kuhn-Tucker conditions for the lower-level retailer problem, Big-M linearizations for complementarity constraints, and epigraph-based linearizations for variance and conditional value-at-risk terms. This reformulation enables efficient solution by state-of-the-art solvers and provides convergence guarantees. To enhance scalability, the model is equipped with a Benders decomposition procedure that separates scenario-based risk evaluation from tariff and hedging decisions. Computational experiments demonstrate convergence within forty iterations to sub-percent optimality, confirming tractability for realistic day-ahead instances with 24 hourly blocks and 100 stochastic scenarios. A case study based on a stylized 1,100 MW wholesale system, with ten thermal generators and five renewable sites, illustrates the economic and operational implications of alternative tariff designs. Results show that real-time pricing yields the highest expected welfare, exceeding time-of-use by nearly one million dollars per day, but also exposes consumers to bill variability of up to 25-30 percent in high-risk scenarios. Time-of-use tariffs achieve a balanced compromise, improving expected welfare by 15 percent relative to flat pricing while maintaining tail risks within manageable bounds. Flat tariffs, while stable, impose high hidden welfare losses due to inefficient resource allocation. Hedging portfolios shift markedly across regimes: forwards dominate under flat tariffs, mixed portfolios emerge under time-of-use, and option-heavy strategies prevail under real-time pricing. Shadow price analysis further reveals that affordability constraints bind most strongly in evening hours under real-time pricing, underscoring the tension between efficiency and equity. Sensitivity tests on the ambiguity radius show that welfare losses under distributional robustness are modest for flat and time-of-use tariffs but pronounced for real-time pricing, reflecting its direct exposure to tail distributions.