An expectile-based framework for risk-calibrated credible capacity evaluation of virtual power plants under wind and PV forecast uncertainties

As renewable penetration continues to increase, virtual power plants (VPPs) are required to evolve from energy aggregators into high-confidence capacity providers capable of delivering firm commitments under uncertainty. The stochastic and asymmetric characteristics of wind and photovoltaic (PV) generation challenge conventional deterministic margins and chance-constrained formulations, which often lead either to excessive conservatism or elevated overcommitment risk. To address this limitation, this paper develops an expectile-based modeling framework for credible capacity evaluation of aggregated wind-PV-storage VPPs. The proposed approach explicitly captures the tail behavior of forecast errors and embeds statistical confidence directly into operational decision-making. In contrast to value-at-risk (VaR) and conditional value-at-risk (CVaR) formulations, expectile modeling introduces a continuous and convex risk measure that asymmetrically penalizes downside deviations, thereby enabling smoother and more interpretable risk calibration. The framework consists of two integrated components. First, a stochastic forecasting and uncertainty quantification module combines quantile regression and asymmetric expectile regression to generate site-specific predictive distributions. Second, a risk-adjusted optimization layer co-schedules renewable commitments and battery dispatch subject to expectile-consistent constraints. Through epigraph reformulations and asset-level derating mechanisms, the model preserves convexity and computational scalability without requiring restrictive distributional assumptions. Case studies conducted on a regional VPP portfolio demonstrate that the proposed method achieves tighter and more economically efficient commitment bounds than CVaR-based benchmarks. Specifically, commitment shortfall events are reduced by up to 73% relative to baseline quantile approaches, while maintaining up to 95% of achievable revenue across varying market conditions. The results further reveal that battery dispatch decisions naturally concentrate during periods of heightened statistical exposure, confirming the value of integrating tail-sensitive forecasting with dynamic storage coordination. Overall, the study establishes a unified, risk-calibrated, and practically implementable framework for credible capacity modeling in renewable-dominated power systems, supporting reliable participation of VPPs in capacity and reserve markets.