A Bilevel Multi-Market Coupling Optimization Framework for Nuclear Power Integration: Joint Modeling of Energy, Reserve, and Capacity Markets

This paper develops a bilevel multi-market coupling optimization framework to analyze the strategic participation of nuclear power plants in modern electricity systems where energy, reserve, and capacity markets are simultaneously cleared. The upper-level problem represents the Independent System Operator’s objective of maximizing system-wide social welfare under network, reserve, and carbon-cap constraints, while the lower-level problem captures the nuclear operator’s profit maximization subject to ramping limits, minimum uptime requirements, fuel-cycle depletion, and deliverability restrictions. By embedding these technical constraints into a bilevel structure reformulated through tractable complementarity conditions, the model captures the interdependence of nuclear scheduling, reserve deployment, capacity commitments, and carbon compliance in a single optimization environment. The proposed framework is applied to a stylized but realistic case study with 96-h time resolution, 12-bus network topology, and detailed representations of wind variability, demand elasticity, and emission caps. The model quantifies how nuclear participation displaces 40,000 tCO2 over the horizon, raises producer surplus by 12 percent, and increases total social welfare by nearly 18 percent when all three markets are coupled, relative to an energy-only benchmark. Nuclear profitability is shown to be highly sensitive to renewable volatility, with ±20 percent swings in wind uncertainty altering profits by 0.24 million USD. Reserve deliverability emerges as the second most influential driver, while policy variables such as carbon price shifts play a smaller role. Reliability analysis based on the complementary cumulative distribution of unserved energy demonstrates that joint market clearing reduces the probability of load shedding at the 0.5 percent threshold from 8 percent in energy-only markets to 2 percent under full coupling. Overall, the study provides the first integrated modeling treatment of nuclear bidding across energy, reserve, and capacity markets within a bilevel optimization framework. By jointly considering operational constraints and policy targets, the framework reveals how nuclear power can simultaneously improve economic efficiency, enhance system reliability, and support carbon mitigation. The results highlight that nuclear’s value extends well beyond baseload energy provision, with multi-market strategies offering measurable gains for both individual operators and social welfare under conditions of uncertainty and constraint.