Endogenous Risk Management of Prosumers by Distributionally Robust Chance-Constrained Optimization

Abstract

Distributed renewable energy sources owned by prosumers have been considered an effective way to fortify grid resilience, and enhance sustainability. However, prosumers serve their own interests, which are affected by their risk preferences. Moreover, their objectives are unlikely to align with those of the society. In contrast to the conventional assumption of constant and exogenous risk preference, we propose an alternative modeling framework in which prosumers endogenously determine their risk attitudes through optimization in the power sector with a day-ahead market and real-time imbalance settlement. The decisions made by prosumers and other participants in the wholesale power market are expressed as a Stackelberg leader-follower game, resulting in a mathematical program with equilibrium constraints. The problem is formulated in a distributionally robust chance-constrained framework to account for renewable generation uncertainty. We show that the effect of uncertainty can be mitigated in the market <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">if</i> prosumers are allowed to optimally determine their risk attitudes. We also examine the case of price-taking prosumers, in which consistent implications are obtained. Therefore, our work highlights the fact that endogenizing risk preferences can be a useful tool for managing risk in the power market.