Branch Flow Model: Relaxations and Convexification—Part I
Top Cited Papers
Open Access
- 23 April 2013
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Power Systems
- Vol. 28 (3), 2554-2564
- https://doi.org/10.1109/tpwrs.2013.2255317
Abstract
We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.Keywords
Other Versions
This publication has 36 references indexed in Scilit:
- Exact convex relaxation of OPF for radial networks using branch flow modelPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2012
- Convex Models of Distribution System ReconfigurationIEEE Transactions on Power Systems, 2012
- Potential for efficiency improvement of future electric energy systems with distributed generation unitsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2010
- A Conic Quadratic Format for the Load Flow Equations of Meshed NetworksIEEE Transactions on Power Systems, 2007
- Radial Distribution Load Flow Using Conic ProgrammingIEEE Transactions on Power Systems, 2006
- Determining and Optimizing Power Loss Reduction in Distribution Feeders due to Distributed GenerationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2006
- Usefulness of DC power flow for active power flow analysisPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Reliable load flow technique for radial distribution networksIEEE Transactions on Power Systems, 1999
- On the existence and uniqueness of load flow solution for radial distribution power networksIEEE Transactions on Circuits and Systems, 1990
- New method for the analysis of distribution networksIEEE Transactions on Power Delivery, 1990