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This paper presents a three-phase iterative direct current optimal power flow (DCOPF) algorithm with fictitious nodal demand. Power losses and realistic distribution system operating constraints such as line flow limits and phase imbalance limits are carefully modeled in the DCOPF formulation. The definition of locational marginal prices (LMPs) is extended to three-phase distribution systems. The three-phase LMP decomposition is derived based on the Lagrangian function. The proposed algorithm is implemented in an IEEE test case and compared with three-phase alternating current optimal power flow (ACOPF) algorithm. The simulation results show that the proposed DCOPF algorithm is effective in coordinating the operations of distributed energy resources (DERs) and managing phase imbalance and thermal overloading. The proposed iterative three-phase DCOPF algorithm provides not only a computationally efficient solution but also a good approximation to the ACOPF solution.
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ACOPF for three‐phase four‐conductor distribution systems: semidefinite programming based relaxation with variable reduction and feasible solution recovery
Emerging distribution systems with a proliferation of distributed energy resources are facing with new challenges, such as voltage collapse and power flow congestion in unsymmetrical network configurations. As a fundamental tool that could help quantify these new challenges and further mitigate their impacts on the secure and economic operation of distribution systems, effective AC optimal power flow (ACOPF) models and solution approaches are in urgent need. This study focuses on ACOPF of three‐phase four‐conductor configured distribution systems, in which neutral conductors and ground resistances are modelled explicitly to reflect practical situation. In addition, by leveraging the Kirchhoff's current law (KCL) theorem and the effect of zero injections, voltage variables of neutrals and zero‐injection phases can be effectively eliminated. The ACOPF problem is formulated as a convex semidefinite programming (SDP) relaxation model in complex domain. In recognising possible solution inexactness of SDP relaxation model, a Karush–Kuhn–Tucker condition based process is further proposed to effectively recover feasible solutions to the original ACOPF problem by calculating a set of computational‐inexpensive non‐linear equations. Numerical studies on a modified IEEE 123‐bus system show the effectiveness of the proposed SDP relaxation model with variable reductions and the feasible solution recovery process for three‐phase four‐conductor configured distribution systems.
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- Award ID(s):
- 1952683
- PAR ID:
- 10570694
- Publisher / Repository:
- DOI PREFIX: 10.1049
- Date Published:
- Journal Name:
- IET Generation, Transmission & Distribution
- Volume:
- 13
- Issue:
- 2
- ISSN:
- 1751-8687
- Format(s):
- Medium: X Size: p. 266-276
- Size(s):
- p. 266-276
- Sponsoring Org:
- National Science Foundation
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