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A Bound Strengthening Method for Optimal Transmission Switching in Power Systems
- Source :
- IEEE Transactions on Power Systems. 34:280-291
- Publication Year :
- 2019
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2019.
-
Abstract
- This paper studies the optimal transmission switching (OTS) problem for power systems, where certain lines are fixed (uncontrollable) and the remaining ones are controllable via on/off switches. The goal is to identify a topology of the power grid that minimizes the cost of the system operation while satisfying the physical and operational constraints. Most of the existing methods for the problem are based on first converting the OTS into a mixed-integer linear program (MILP) or mixed-integer quadratic program (MIQP), and then iteratively solving a series of its convex relaxations. The performance of these methods depends heavily on the strength of the MILP or MIQP formulations. In this paper, it is shown that finding the strongest variable upper and lower bounds to be used in an MILP or MIQP formulation of the OTS based on the big-$M$ or McCormick inequalities is NP-hard. Furthermore, it is proven that unless P=NP, there is no constant-factor approximation algorithm for constructing these variable bounds. Despite the inherent difficulty of obtaining the strongest bounds in general, a simple bound strengthening method is presented to strengthen the convex relaxation of the problem when there exists a connected spanning subnetwork of the system with fixed lines. The proposed method can be treated as a preprocessing step that is independent of the solver to be later used for numerical calculations and can be carried out offline before initiating the solver. A remarkable speedup in the runtime of the mixed-integer solvers is obtained using the proposed bound strengthening method for medium- and large-scale real-world systems.
- Subjects :
- Mathematical optimization
Linear programming
Computer science
020209 energy
Reliability (computer networking)
Energy Engineering and Power Technology
Approximation algorithm
Topology (electrical circuits)
02 engineering and technology
Upper and lower bounds
Electric power system
Variable (computer science)
Optimization and Control (math.OC)
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Quadratic programming
Electrical and Electronic Engineering
Mathematics - Optimization and Control
Subjects
Details
- ISSN :
- 15580679 and 08858950
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Power Systems
- Accession number :
- edsair.doi.dedup.....f91c83a93c74848017dfc5f7156af6ac