In a competitive electricity market, installing the Unified Power Flow Controller (UPFC) can improve power transfer capability and help market participants keep their schedules very close to preferred ones and at the same time may retain the competitive behavior of participants. Putting the UPFC in service may assist system to operate within its physical limits and reduce total generation cost associated with out-of-merit order caused by constrained transmission. However, a competitive electricity market necessitates a reliable method to allocate congestion charges, transmission usage, and transmission pricing in an unbiased, open-accessed, basis. Therefore, it is usually necessary to trace contribution of each participant to line usage and congestion charges, and then to calculate charges based on these contributions. It has been a common practice to use distribution factors to calculate these contributions. Therefore, in this paper we present a mathematical approach to allocate the contributions of UPFCs to transmission system usage using a dc-based load flow model of UPFC-inserted transmission lines, based on a previously derived dc-based injection model of UPFC-embedded lines by this author. The present paper derives relationships to model impact of UPFC on line flows and transmission usage where we present modified admittances and distribution factors that model impact of utilizing UPFC on line flows and system usage. The relationships derived show how bus voltage angles are attributed to each of changes in generation, injections of UPFC, and changes in admittance matrix caused by inserting UPFC in transmission lines. The relationships derived can be adopted for the purpose of allocating usage and payments to users of transmission network and owners of control devices used in the network. The relationships derived are applied to test systems, where the results illustrate how transmission usage is affected when UPFC is utilized. (C) 2004 Elsevier B.V. All rights reserved.