A Linear-Programming Approximation of AC Power Flows

By Carleton Coffrin, Pascal Van Hentenryck. INFORMS journal on computing, 2012

332 citations recorded by the source corpus.

Linear active-power-only power flow approximations are pervasive in the planning and control of power systems. However, AC power systems are governed by a system of nonlinear nonconvex power flow equations. Existing linear approximations fail to capture key power flow variables, including reactive power and voltage magnitudes, both of which are necessary in many applications that require voltage management and AC power flow feasibility. This paper proposes novel linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a polyhedral relaxation of the cosine terms in the AC equations as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and Matpower benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC model...

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/b11f836d7c3b682044d7305c7443b321834e1dc6

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Citations in the corpus

A General Formulation of Linear Power Flow Models: Basic Theory and Error Analysis (2019, unknown): “In [24], the power flow equations”
New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem (2015, background): “To solve for large-scale systems, one may need to turn to computationally less demanding alternatives such as quadratic convex [19], [30], [31] or linear programming relaxations [32].”
PowerModels.J1: An Open-Source Framework for Exploring Power Flow Formulations (2017, background): “, LPAC [1], IV [2], LACR [3]), to convex relaxations (e.”
Exact Convex Relaxation of Optimal Power Flow in Radial Networks (2013, methodology): “This method also does not apply to problems where reactive power flow or voltage deviations need to be optimized explicitly, e.g., power routing with FACTS devices [5] and Volt/VAR control [6].”
Bound Tightening for the Alternating Current Optimal Power Flow Problem (2016, unknown): “, [22], [23]).”
Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation (2017, methodology): “The first is to explore initializing multiperiod OPF problems using other recently developed linear and SOCP relaxations and approximations of the power flow equations, such as those in [19], [20], [35], [48], [49].”
The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms (2019, methodology): “Although PGL IB -OPF has highlighted some advantages for AC-OPF benchmarking, its network datasets are still by-in-large synthetically generated.”
A Successive Linear Programming Approach to Solving the IV-ACOPF (2016, methodology): “Other coupled models include the recent works described in [27]–[29].”
Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence (2014, methodology): “See also [21] for amore accurate linear approximation.”