Probabilistic Joint Modeling of Price and Aggregated DER Flexibility for Risk-Aware Day-Ahead Bidding

Abstract

This paper proposes a probabilistic joint modeling framework for market prices and aggregated distributed energy resource (DER) flexibility in risk-aware day-ahead bidding applications. The problem is formulated within a price-based day-ahead demand response setting, where an aggregator commits flexibility bids under uncertainty in both market prices and available flexibility. To consistently represent correlated uncertainty, a joint probabilistic model of price and aggregated flexibility is developed using copula theory combined with a first-order Markov structure, enabling scalable modeling of temporal, spatial, and price-flexibility dependencies, whose goodness-of-fit is verified empirically. Based on this joint distribution, a spectral risk-aware optimization problem is formulated to determine day-ahead flexibility bids with explicit control of downside risk. The resulting problem is solved using a scenario-based linear programming approach for day-ahead coordinated resources, or using a Markov decision process (MDP)-based optimization framework when intra-day controllable resources are available. A case study involving the aggregation of thermostatically controlled loads in the ISO New England system demonstrates that neglecting correlated uncertainty can lead to a substantial underestimation of tail risk, while moderate errors in correlation parameter estimation have a limited impact on performance; these observations remain valid when intra-day controlled battery energy storage systems are included. The results highlight the importance of explicitly modeling joint price-flexibility uncertainty for effective risk-aware bidding under aggregated DER flexibility.