Distributionally Robust Model Predictive Control for Virtual Power Plants

TL;DR

This paper introduces a distributionally robust MPC framework for virtual power plants that effectively manages electricity price uncertainty by integrating data-driven forecasting and adaptive ambiguity sets.

Contribution

It develops a novel DR-MPC approach that incorporates predictive distribution information into real-time VPP operation, improving economic performance under uncertainty.

Findings

DR-MPC outperforms standard MPC in economic gains.

Proper ambiguity radius selection is crucial for optimal performance.

The method is validated with real weather and market data from a Nordic case study.

Abstract

This paper presents a distributionally robust model predictive control (DRMPC) framework for the optimal Virtual Power Plant (VPP) operation under electricity price uncertainty. A unified VPP model is formulated that captures the interaction between buildings, battery storage, and renewable generation, all influenced by exogenous weather and market signals. The proposed approach integrates data-driven forecasting with quantile-based uncertainty quantification to construct time-varying Wasserstein ambiguity sets that adapt to forecast dispersion and distributional shifts. This yields a tractable DR-MPC formulation that incorporates predictive distribution information directly into real-time decision making. The method is evaluated using real weather and market data from a Nordic case study across two seasonal scenarios. The results show that DR-MPC improves economic performance relative to standard forecast-based MPC when the ambiguity radius is chosen appropriately, with consistent gains of up to 0.8% for small radii across both seasonal scenarios. Larger radii become overly conservative and reduce revenue, underscoring the importance of proper radius selection. These findings demonstrate the practical value of distributionally robust optimization for uncertainty-aware VPP operation.