A Virtual Contribution Theory-Based Loss Allocation Method in Power Markets

With the large-scale integration of high-penetration distributed energy resources and the transformation of terminal loads into prosumer models, the operation of active distribution networks (ADNs) has become increasingly flexible, often leading to frequent bidirectional power flows. These dynamics pose significant challenges for accurate loss calculation in ADNs and the correction of transaction outcomes between generators and consumers under power market environments. Moreover, the distinct operating structures of the spot and bilateral contract markets further increase the complexity of ADN operation and impose significant challenges on the adaptability of loss allocation (LA) mechanisms. To address these issues, this paper proposes an innovative LA method for ADNs based on Virtual Contribution Theory (VCT), applicable to both spot and bilateral contract market scenarios. By constructing virtual contribution matrices—branch-based for the spot market and transaction-based for the bilateral market—the method accurately traces and quantifies the actual contributions of each market participant under different trading models, thereby enabling reasonable, transparent, and fair loss allocation. Additionally, the method eliminates the need for complex matrix inversion required in existing approaches by leveraging basic operations on the virtual contribution matrix, thereby reducing computational complexity and significantly improving computational efficiency. Case studies on IEEE 33 and IEEE 69 systems demonstrate the effectiveness, applicability, and fairness of the proposed approach.