Multi-Transmission Node DER Aggregation: Chance-Constrained Unit Commitment with Bounded Hetero-Dimensional Mixture Model for Uncertain Distribution Factors

The increasing penetration of distributed energy resources (DERs) necessitates innovative strategies, such as multi-transmission-node DER aggregation (M-DERA), to support their wide geographic aggregation for the wholesale market integration at scale. However, M-DERAs pose new challenges in estimating the nodal power proportions within the aggregation, inducing inaccurate power flow calculations in market operation tools such as unit commitment (UC). To this end, this paper proposes a novel chance-constrained UC (CCUC) model to determine system optimal operation plans with M-DERAs, in which the estimated nodal power proportions of M-DERAs, characterized by distribution factors (DFs), are considered as uncertain parameters, and power flow limits are modeled as bilinear chance constraints. A novel bounded hetero-dimensional mixture model is proposed to describe the complex distribution of DFs over multiple hetero-dimensional hyperplanes in a bounded space. With this, the bilinear chance constraints are reformulated into a scenario-based stochastic form and solved by Benders decomposition. Test results on the IEEE 24-bus and 118-bus systems show that, compared to other methods under various system operation conditions, the proposed method reduces UC costs by up to 6% and real-time economic dispatch (RTED) costs by up to 6.8%, while also lowering load shedding in RTED and transmission overloading after M-DERAs' self-dispatch which in the best case can be reduced to zero. These results validate the effectiveness of the proposed method in managing M-DERA integration while ensuring operational economics and mitigating transmission line overloading.