The Complexity of DC-Switching Problems

Lehmann, Karsten; Grastien, Alban; Hentenryck, Pascal Van

doi:10.48550/arxiv.1411.4369

Cited by 4 publications

(5 citation statements)

References 4 publications

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“…We refer the reader to Hedman et al [14] for a survey on the benefits of transmission switching in power systems. However, the identification of an optimal topology, namely optimal transmission switching (OTS) problem, is a non-convex combinatorial optimization problem that is proved to be NP-hard [15]. Therefore, brute-force search algorithms for finding an optimal topology are often inefficient.…”

Section: Introductionmentioning

confidence: 99%

A Bound Strengthening Method for Optimal Transmission Switching in Power Systems

Fattahi

Lavaei

Atamtürk

2019

IEEE Trans. Power Syst.

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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 = N P , 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 mediumand large-scale real world systems.

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Section: Introductionmentioning

confidence: 99%

A Bound Strengthening Method for Optimal Transmission Switching in Power Systems

Fattahi

Lavaei

Atamtürk

2019

IEEE Trans. Power Syst.

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“…The Gurobi heuristic solves for the optimal TS problem described in Equations ( 1)- (9). We consider this formulation as a heuristic as there is a limit to the upper-bound of switched lines ∑ l (1 − z l ) ≤  .…”

Section: Gurobic Heuristicmentioning

confidence: 99%

“…As the SO schedules new dispatches every 5 min for the power system [8], solving for this optimised network topology and verifying as AC feasible ought to be done within that time frame. However, the computational burden of solving even the DC formulation of the TS problem in real-time prevents the adoption of TS in the control room as it is an NP-hard problem [9] [10]. To quantify the magnitude of the search space, the IEEE 118-bus test case, which is small compared to real-world power systems, has 186 lines and thus 2 186 switching possibilities.…”

Section: Introductionmentioning

confidence: 99%

Real‐time transmission switching with neural networks

Bugaje

Cremer

Štrbac

2022

IET Generation Trans & Dist

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The classical formulation of the transmission switching problem as a mixed-integer problem is intractable for large systems in real-time control settings. Several heuristics have been proposed in the past to speed up the computation time, which only limits the number of switchable lines. In this paper, a real-time switching heuristic based on neural networks that provides almost instantaneous switching actions, are presented. The findings are shown on case studies of the IEEE 118-bus test system, and the results show that the proposed heuristic is robust to out of distribution data. Additionally, the proposed heuristic has significant computational savings while all other performance metrics like accuracy are similar to state-of-the-art machine learning methods proposed for transmission switching.

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“…Under some realistic operational assumptions, the OTS formulation is often approximated as a mixed integer linear program (MILP) with big-M parameters [8], to take advantage of mature MIP solvers. Such a MILP approximation -which is still NP-hard [18][17] -is referred in the literature as the DC OTS problem. Given the computational complexity of the problem, a number of heuristic methods have been proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Data-driven Heuristics for DC optimal transmission switching problem

Li¹,

Dokka²,

Lulli³

et al. 2021

Preprint

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The goal of Optimal Transmission Switching (OTS) problem for power systems is to identify a topology of the power grid that minimizes the cost of the system operation while satisfying the operational and physical constraints. Among the most popular methods to solve OTS is to construct approximation via integer linear programming formulations, which often come with big-M inequalities. These big-M inequalities increase, considerably, the difficulty of solving the resulting formulations. Moreover, choosing big-M values optimally is as hard as solving OTS itself. In this paper, we devise two data-driven big-M bound strengthening methods which take network structure, power demands and generation costs into account. We illustrate the robustness of our methods to load changes and impressive runtime improvements of mixed-integer solvers achieved by our methods with extensive experiments on benchmark instances. The speedup by one of the proposed methods is almost 13 times with respect to the exact method.

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The Complexity of DC-Switching Problems

Cited by 4 publications

References 4 publications

A Bound Strengthening Method for Optimal Transmission Switching in Power Systems

A Bound Strengthening Method for Optimal Transmission Switching in Power Systems

Real‐time transmission switching with neural networks

Data-driven Heuristics for DC optimal transmission switching problem

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