6,396 research outputs found
A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching
It is well-known that optimizing network topology by switching on and off
transmission lines improves the efficiency of power delivery in electrical
networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that
the U.S. should "encourage, as appropriate, the deployment of advanced
transmission technologies" including "optimized transmission line
configurations". As such, many authors have studied the problem of determining
an optimal set of transmission lines to switch off to minimize the cost of
meeting a given power demand under the direct current (DC) model of power flow.
This problem is known in the literature as the Direct-Current Optimal
Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on
heuristic algorithms for generating quality solutions or on the application of
DC-OTS to crucial operational and strategic problems such as contingency
correction, real-time dispatch, and transmission expansion. The mathematical
theory of the DC-OTS problem is less well-developed. In this work, we formally
establish that DC-OTS is NP-Hard, even if the power network is a
series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's
Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new
formulation to build a cycle-induced relaxation. We characterize the convex
hull of the cycle-induced relaxation, and the characterization provides strong
valid inequalities that can be used in a cutting-plane approach to solve the
DC-OTS. We give details of a practical implementation, and we show promising
computational results on standard benchmark instances
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
Linear Optimal Power Flow Using Cycle Flows
Linear optimal power flow (LOPF) algorithms use a linearization of the
alternating current (AC) load flow equations to optimize generator dispatch in
a network subject to the loading constraints of the network branches. Common
algorithms use the voltage angles at the buses as optimization variables, but
alternatives can be computationally advantageous. In this article we provide a
review of existing methods and describe a new formulation that expresses the
loading constraints directly in terms of the flows themselves, using a
decomposition of the network graph into a spanning tree and closed cycles. We
provide a comprehensive study of the computational performance of the various
formulations, in settings that include computationally challenging applications
such as multi-period LOPF with storage dispatch and generation capacity
expansion. We show that the new formulation of the LOPF solves up to 7 times
faster than the angle formulation using a commercial linear programming solver,
while another existing cycle-based formulation solves up to 20 times faster,
with an average speed-up of factor 3 for the standard networks considered here.
If generation capacities are also optimized, the average speed-up rises to a
factor of 12, reaching up to factor 213 in a particular instance. The speed-up
is largest for networks with many buses and decentral generators throughout the
network, which is highly relevant given the rise of distributed renewable
generation and the computational challenge of operation and planning in such
networks.Comment: 11 pages, 5 figures; version 2 includes results for generation
capacity optimization; version 3 is the final accepted journal versio
Shift factor-based SCOPF topology control MIP formulations with substation configurations
Topology control (TC) is an effective tool for managing congestion, contingency events, and overload control. The majority of TC research has focused on line and transformer switching. Substation reconfiguration is an additional TC action, which consists of opening or closing breakers not in series with lines or transformers. Some reconfiguration actions can be simpler to implement than branch opening, seen as a less invasive action. This paper introduces two formulations that incorporate substation reconfiguration with branch opening in a unified TC framework. The first method starts from a topology with all candidate breakers open, and breaker closing is emulated and optimized using virtual transactions. The second method takes the opposite approach, starting from a fully closed topology and optimizing breaker openings. We provide a theoretical framework for both methods and formulate security-constrained shift factor MIP TC formulations that incorporate both breaker and branch switching. By maintaining the shift factor formulation, we take advantage of its compactness, especially in the context of contingency constraints, and by focusing on reconfiguring substations, we hope to provide system operators additional flexibility in their TC decision processes. Simulation results on a subarea of PJM illustrate the application of the two formulations to realistic systems.The work was supported in part by the Advanced Research Projects Agency-Energy, U.S. Department of Energy, under Grant DE-AR0000223 and in part by the U.S. National Science Foundation Emerging Frontiers in Research and Innovation under Grant 1038230. Paper no. TPWRS-01497-2015. (DE-AR0000223 - Advanced Research Projects Agency-Energy, U.S. Department of Energy; 1038230 - U.S. National Science Foundation Emerging Frontiers in Research and Innovation)http://buprimo.hosted.exlibrisgroup.com/primo_library/libweb/action/openurl?date=2017&issue=2&isSerivcesPage=true&spage=1179&dscnt=2&url_ctx_fmt=null&vid=BU&volume=32&institution=bosu&issn=0885-8950&id=doi:10.1109/TPWRS.2016.2574324&dstmp=1522778516872&fromLogin=truePublished versio
New Cycle-based Formulation, Cost Function, and Heuristics for DC OPF Based Controlled Islanding
This paper presents a new formulation for intentional controlled islanding
(ICI) of power transmission grids based on mixed-integer linear programming
(MILP) DC optimal power flow (OPF) model. We highlight several deficiencies of
the most well-known formulation for this problem and propose new enhancements
for their improvement. In particular, we propose a new alternative optimization
objective that may be more suitable for ICI than the minimization of load
shedding, a new set of island connectivity constraints, and a new set of
constraints for DC OPF with switching, and a new MILP heuristic to find initial
feasible solutions for ICI. It is shown that the proposed improvements help to
reduce the final optimality gaps as compared to the benchmark model on several
test instances.Comment: https://doi.org/10.1016/j.epsr.2022.10858
Transmission Expansion Planning Using Cycle Flows
The common linear optimal power flow (LOPF) formulation that underlies most
transmission expansion planning (TEP) formulations uses bus voltage angles as
auxiliary optimization variables to describe Kirchhoff's voltage law. As well
as introducing a large number of auxiliary variables, the angle-based
formulation has the disadvantage that it is not well-suited to considering the
connection of multiple disconnected networks, It is, however, possible to
circumvent these auxiliary variables and reduce the required number of
constraints by expressing Kirchhoff's voltage law directly in terms of the
power flows, based on a cycle decomposition of the network graph. In
computationally challenging benchmarks such as generation capacity expansion
with multi-period LOPF, this equivalent reformulation was shown in previous
work to reduce solving times for LOPF problems by an order of magnitude.
Allowing line capacity to be co-optimized in a discrete TEP problem makes it a
non-convex mixed-integer problem. This paper develops a novel cycle-based
reformulation for the TEP problem with LOPF and compares it to the standard
angle-based formulation. The combinatorics of the connection of multiple
disconnected networks is formalized for both formulations, a topic which has
not received attention in the literature. The cycle-based formulation is shown
to conveniently accommodate synchronization options. Since both formulations
use the big- disjunctive relaxation, useful derivations for suitable big-
values are provided. The competing formulations are benchmarked on a realistic
generation and transmission expansion model of the European transmission system
at varying spatial and temporal resolutions. The cycle-based formulation solves
up to 31 times faster for particular cases, while averaging at a speed-up of
factor 4.Comment: Accepted for ACM e-Energy 2020, 11 pages, 12 Figures, 2 Table
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