Three-Phase DLMP Model based on Linearized Power Flow for Distribution with Application to DER Benefit Studies


The rapid development of distributed energy resources and active distribution networks has resulted in increased interest in the concept of a distribution locational marginal price (DLMP). In this paper, first, an extension of a previous DLMP model based on linearized power flow - distribution (LPF-D) is applied to provide an explicit formulation of the voltage cost component (VCC), together with the energy cost component (ECC) and the loss cost component (LCC). Then, this DLMP model is extended to include a three-phase distribution model to form the proposed three-phase DLMP (TDLMP) based on the three-phase LPF-D (TLPF-D). An imbalance cost component (ICC) is included in this three-phase DLMP model. Finally, the proposed TDLMP model is applied to various case studies to demonstrate the benefit of distributed energy resources (DERs), including distributed generation (DG) and demand response (DR). The case studies verify that the VCC and the ICC are significant components of the TDLMP in low-voltage and unbalanced distribution networks. In addition, DERs can significantly reduce the TDLMP, especially the VCC and ICC, by improving the voltages and reducing phase imbalance. Thus, the proposed TDLMP provides a quantitative framework to evaluate the economic benefits of DERs in competitive market-based distribution operations.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center

Keywords and Phrases

Distributed Energy Resources (DERs); Imbalance; Locational Marginal Price (LMP); Three-Phase Distribution LMP (TDLMP); Voltage Constraints

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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© 2021 Elsevier, All rights reserved.

Publication Date

01 Sep 2021