Forward electricity markets with uncertain supply: Cost sharing and efficiency loss

Renewable energy continues to increase its share of total US electricity production at a dramatic rate. Power derived from such resources is inherently variable and naturally incurs a balancing cost to the power system. A basic question we aim to address in this paper is, given a collection of variable energy producers, how to disentangle the individual sources of cost causation from the aggregate system cost and allocate it back to those responsible parties, so as to induce a near efficient outcome in the forward market for energy. In particular, we propose an ex post cost sharing mechanism, satisfying certain fairness axioms, to allocate to each player a share of the total system cost in proportion to her relative contribution to the aggregate system imbalance. We establish the existence and certain properties of Nash equilibria of the forward contract game under proportional cost sharing and provide an explicit characterization for the Price of Anarchy (PoA) as the number of participants in the market grows large. We also characterize a family of `worst case' prior distributions on the supply profile at which the asymptotic PoA is maximized.