Strategic pricing of flexible renewable power purchase agreements: A risk-averse bilevel optimization approach with cross-period constraints

In power systems with high shares of variable renewables, spot prices are extremely volatile with frequent deep negatives, undermining renewable revenue adequacy and market-based integration. Fixed-price power purchase agreements (PPAs) cannot share this asymmetric downside risk, motivating contracts that link long-term bilateral commitments to real-time operation. This paper studies how a renewable generator should price a flexible PPA for a price-responsive large consumer to cap tail risk while keeping the consumer willing to participate. We model the problem as a Stackelberg bilevel optimization: the upper level maximizes the generator’s risk-adjusted revenue based on conditional value-at-risk (CVaR); the lower level is a mixed-integer linear program (MILP) in which consumers choose hourly between contract and spot purchases under intertemporal green-power quotas. Because lower-level binaries preclude standard Karush–Kuhn–Tucker (KKT) reformulations, we propose an adaptive two-stage search with explicit ɛ -optimality bounds, using exact hourly MILP evaluations. An 8760-hour case study combining 2024 Shandong spot prices with IEEE RTS-GMLC wind and load profiles shows that the mechanism raises the generator’s CVaR from −115 to ＋153 million CNY, turning worst-case daily losses into profits while preserving consumer participation, and also increases expected annual revenue relative to pure spot trading and a conventional fixed-price PPA. By shifting negative-price exposure from the generator to responsive demand, the quota gives regulators a tunable lever for allocating risk between the contracting parties.