An ADMM-Based Method for Computing Risk-Averse Equilibrium in Capacity Markets

Uncertainty in electricity markets introduces risk for investors. High fixed cost and increased dependency on infrequent and uncertain price spikes characterize investments. The risk-averse behavior of investors might lead to poor decision-making and undermines generation adequacy. Electricity market models rarely treat the interaction of market design and risk aversion. The representation of capacity mechanisms in modeling approaches focusing on risk aversion is limited. Our contribution addresses two problems. First, we propose a stochastic market equilibrium model. Investors are represented as risk-averse agents. The conditional value-at-risk is used as risk measure. Second, we propose an algorithm based on the alternating direction method of multipliers to compute a risk-averse equilibrium. We benchmark our approach with a state-of-the-art solver relying on a mixed complementarity problem reformulation. We show that for larger case studies our proposed approach is preferable. The algorithm converges in all cases while conventional solvers fail to compute a risk-averse equilibrium. The methodology is transferable to other risk-averse equilibrium models. With reference to capacity markets, we conclude that they are more beneficial in a risk-averse market. Capacity markets result in lower total cost, while avoiding expected energy not served. This statement still holds with increased price caps in energy-only markets.