Distribution Network Optimization for Low-Carbon Energy Supply in Data Centers: A Boundary-Interpretable Feasible Region Method

With the proliferation of lightweight generative artificial intelligence, data centers (DCs) are increasingly deployed within distribution networks (DNs). Their highly stochastic and high-power demands pose significant challenges to achieving low-carbon and secure power supply. Thus, coordinating the operation of DNs and DCs is critical for ensuring reliable low-carbon electricity delivery. However, significant barriers persist due to the integration of numerous distributed energy resources (DERs) and operational privacy requirements among stakeholders. To enable secure coordination while safeguarding model confidentiality, a boundary-interpretable feasible region (BIFR) method is proposed in this paper. This method can capture the intrinsic relationship between the controllable variables and the boundary responses that affect both carbon emissions and system safety performance. Based on the BIFR, a bidirectional coordinated optimization mechanism for DC-DN systems is established. The mechanism determines optimization strategies for low-carbon collaborative operation according to the coupled BIFR by iterative bidirectional adjustments until convergence. This mechanism achieves efficient DC-DN coordination through minimal information exchange while preventing privacy breaches. Case studies on modified IEEE 33-bus and Caracas 141-bus distribution networks validate the effectiveness and efficiency of the proposed method.