Building Load Control using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

TL;DR

This paper develops a robust optimization framework for HVAC load control under PV generation uncertainty, introducing novel MILP reformulations and an adjustable risk-cost trade-off, validated with real data.

Contribution

It presents new MILP reformulations for distributionally robust chance constraints with RHS uncertainty and introduces an adjustable risk-averse variant for HVAC load control.

Findings

Efficient MILP reformulations for DRCC with RHS uncertainty.

Effective trade-off between operational risk and costs.

Validated approach using real-world data.

Abstract

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed-integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we utilize the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve a trade-off between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions.