Unlock the Thermal Flexibility in Integrated Energy Systems: A Robust Nodal Pricing Approach for Thermal Loads

The thermal flexibility of buildings in integrated energy systems (IES) has great potential to improve the operational economy and wind power consumption. To incentivize the thermal flexibility of buildings under uncertainties, we propose a robust nodal pricing (RNP) model for thermal loads based on the Stackelberg game approach. The RNP model adopts a bilevel framework in which the IES operator plays the leader at the upper level while the thermal load aggregators (TLA) play the followers at the lower level. The IES operator problem optimizes the heat prices and dispatch plan, which is modeled as a two-stage robust optimization problem to address the uncertainties in the renewables and the loads. The TLA problem optimizes the thermal loads of buildings to minimize the energy cost and thermal comfort loss, which is modeled as a distributionally robust chance-constrained optimization problem to address the uncertainty in outdoor temperature. Then, we convert the TLA model into deterministic quadratic programming and prove that Slater's condition holds under a mild assumption. Using it, the TLA model is equivalently converted into Karush-Kuhn-Tucker conditions, leading to a reformulation of a classical two-stage robust optimization model for the RNP model. Case studies compare different pricing methods and verify the superiority of the proposed method.