Towards Realistic Virtual Power Plant Operation: Behavioral Uncertainty Modeling and Robust Dispatch Through Prospect Theory and Social Network-Driven Scenario Design

The growing complexity of distribution-level virtual power plants (VPPs) demands a rethinking of how flexible demand is modeled, aggregated, and dispatched under uncertainty. Traditional optimization frameworks often rely on deterministic or homogeneous assumptions about end-user behavior, thereby overestimating controllability and underestimating risk. In this paper, we propose a behavior-aware, two-stage stochastic dispatch framework for VPPs that explicitly models heterogeneous user participation via integrated behavioral economics and social interaction structures. At the behavioral layer, user responses to demand response (DR) incentives are captured using a Prospect Theory-based utility function, parameterized by loss aversion, nonlinear gain perception, and subjective probability weighting. In parallel, social influence dynamics are modeled using a peer interaction network that modulates individual participation probabilities through local contagion effects. These two mechanisms are combined to produce a high-dimensional, time-varying participation map across user classes, including residential, commercial, and industrial actors. This probabilistic behavioral landscape is embedded within a scenario-based two-stage stochastic optimization model. The first stage determines pre-committed dispatch quantities across flexible loads, electric vehicles, and distributed storage systems, while the second stage executes real-time recourse based on realized participation trajectories. The dispatch model includes physical constraints (e.g., energy balance, network limits), behavioral fatigue, and the intertemporal coupling of flexible resources. A scenario reduction technique and the Conditional Value-at-Risk (CVaR) metric are used to ensure computational tractability and robustness against extreme behavior deviations.