An Analytical Newsvendor Framework for Risk-Averse Energy Storage Capacity Reservation under Non-Normal Uncertainty

Abstract: Energy storage operators often reserve usable capacity before uncertain market opportunities are realized, for example when a day-ahead operator commits capacity for an evening peak-spread or ancillary-service window. Price spikes, renewable forecast errors, activation calls and imbalance penalties can make the decision-relevant opportunity distribution asymmetric and heavy-tailed rather than Gaussian. This paper develops a tri-objective storage-newsvendor framework for this capacity-reservation decision. The model jointly maximizes expected profit, minimizes CVaR tail loss and minimizes maximum regret over candidate non-normal distributions. We derive a critical-fractile expected-profit solution and a finite-scenario convex scalarization that solves the three objectives together. In stylized log-NMVM experiments with matched mean and variance, a moment-matched normal policy over-reserves capacity by up to 1.337 units. In a lognormal policy comparison, the CVaR and maximum-regret policies reduce tail loss and candidate-set regret at the cost of lower expected profit.