14,324 research outputs found
Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility
Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted
significant interest as in several instances they provably yield the global
optimum to the original non-convex problem. If, however, the relaxation is
inexact, the obtained solution is not AC-feasible. The quality of the obtained
solution is essential for several practical applications of AC-OPF, but
detailed analyses are lacking in existing literature. This paper aims to cover
this gap. We provide an in-depth investigation of the solution characteristics
when convex relaxations are inexact, we assess the most promising AC
feasibility recovery methods for large-scale systems, and we propose two new
metrics that lead to a better understanding of the quality of the identified
solutions. We perform a comprehensive assessment on 96 different test cases,
ranging from 14 to 3120 buses, and we show the following: (i) Despite an
optimality gap of less than 1%, several test cases still exhibit substantial
distances to both AC feasibility and local optimality and the newly proposed
metrics characterize these deviations. (ii) Penalization methods fail to
recover an AC-feasible solution in 15 out of 45 cases, and using the proposed
metrics, we show that most failed test instances exhibit substantial distances
to both AC-feasibility and local optimality. For failed test instances with
small distances, we show how our proposed metrics inform a fine-tuning of
penalty weights to obtain AC-feasible solutions. (iii) The computational
benefits of warm-starting non-convex solvers have significant variation, but a
computational speedup exists in over 75% of the cases
Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem
Alternating current optimal power flow (AC OPF) is one of the most
fundamental optimization problems in electrical power systems. It can be
formulated as a semidefinite program (SDP) with rank constraints. Solving AC
OPF, that is, obtaining near optimal primal solutions as well as high quality
dual bounds for this non-convex program, presents a major computational
challenge to today's power industry for the real-time operation of large-scale
power grids. In this paper, we propose a new technique for reformulation of the
rank constraints using both principal and non-principal 2-by-2 minors of the
involved Hermitian matrix variable and characterize all such minors into three
types. We show the equivalence of these minor constraints to the physical
constraints of voltage angle differences summing to zero over three- and
four-cycles in the power network. We study second-order conic programming
(SOCP) relaxations of this minor reformulation and propose strong cutting
planes, convex envelopes, and bound tightening techniques to strengthen the
resulting SOCP relaxations. We then propose an SOCP-based spatial
branch-and-cut method to obtain the global optimum of AC OPF. Extensive
computational experiments show that the proposed algorithm significantly
outperforms the state-of-the-art SDP-based OPF solver and on a simple personal
computer is able to obtain on average a 0.71% optimality gap in no more than
720 seconds for the most challenging power system instances in the literature
New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem
As the modern transmission control and relay technologies evolve,
transmission line switching has become an important option in power system
operators' toolkits to reduce operational cost and improve system reliability.
Most recent research has relied on the DC approximation of the power flow model
in the optimal transmission switching problem. However, it is known that DC
approximation may lead to inaccurate flow solutions and also overlook stability
issues. In this paper, we focus on the optimal transmission switching problem
with the full AC power flow model, abbreviated as AC OTS. We propose a new
exact formulation for AC OTS and its mixed-integer second-order conic
programming (MISOCP) relaxation. We improve this relaxation via several types
of strong valid inequalities inspired by the recent development for the closely
related AC Optimal Power Flow (AC OPF) problem. We also propose a practical
algorithm to obtain high quality feasible solutions for the AC OTS problem.
Extensive computational experiments show that the proposed formulation and
algorithms efficiently solve IEEE standard and congested instances and lead to
significant cost benefits with provably tight bounds
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