Chance-constrained bi-level optimal scheduling model for distribution network with thermal controllable load aggregators

An increasing amount of distributed renewable energy is being integrated into distribution networks to achieve decarbonization. It is essential to exploit demand-side flexible resources further to enhance system flexibility in response to the intermittency and unpredictability of renewable energy sources. This paper introduces a polytope-based aggregation method for thermostatically controlled loads (TCLs), aggregating numerous individual TCLs into a unified virtual battery via the aggregator (AGG). This approach avoids the dimensionality curse faced by the distribution system operator when directly controlling each TCL, while efficiently utilizing TCL flexibility. Subsequently, a bi-level optimization model is established, where AGGs are treated as independent stakeholders participating in the distribution network scheduling optimization through the local energy market. This model incorporates chance constraints to address the uncertainty of renewable energy sources. Finally, the distributionally robust chance constraint (DRCC) method is used to convert chance constraints into a linear form, and strong duality theory and Karush-Kuhn-Tucker conditions are applied to transform the bi-level model into a single-level model with equilibrium solutions. Case studies on the IEEE 33-bus network demonstrate that the proposed polytope-based aggregation method substantially improves computational efficiency with minimal optimality loss. Additionally, the DRCC method offers superior economic performance compared to robust and deterministic optimization approaches, while maintaining robustness.