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In this paper, a novel quadratic convex optimal power flow model, namely,MDOPF, is proposed to determine the optimal dispatches of distributedgenerators. Based on the results of MDOPF, two price mechanisms, distributionlocational marginal price (DLMP) and distribution locational price (DLP), areanalyzed. For DLMP, an explicit method is developed to calculate the marginalloss that does not require a backward/forward sweep algorithm and thus reducesthe computational complexity. However, the marginal loss component in DLMP willcause over-collection of losses (OCL). To address this issue, DLP is defined,which contains two components, the energy cost component and loss component,where the loss component is determined by the proposed loss allocation method(LAM). Numerical tests show that the proposed MDOPF has a better accuracy thanexisting OPF models based on linear power flow equations. In addition, theproposed marginal loss method and DLMP algorithm have satisfactory accuracycompared with benchmarks provided by ACOPF, and the proposed DLP can eliminateOCL.

A Quadratic Convex Approximation of Optimal Power Flow in Distribution System with Application in Loss Allocation