The power edge set problem

Poirion, Pierre‐Louis; Toubaline, Sonia; d'Ambrosio, Claudia; Liberti, Leo

doi:10.1002/net.21684

Cited by 16 publications

(48 citation statements)

References 19 publications

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“…The dominant optimization method regarding the OPP problem is the Binary Integer Linear Programming (BILP) technique. The BILP model requires the minimization of the objective function with inequality constraints and binary-valued decision variables [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…Phasor measurement unit based fault location techniques are proposed in [28][29][30]. Other methods, such as an optimized extreme learning machine-based approach, use synchrophasors to ensure real-time power transient stability prediction [31].Up to now, a BILP model is written to its standard form in which the number of the constraints is equal to the number of optimization variables for the OPP problem [4][5][6][7][8][9][10]. This work introduces an underdetermined system of nonlinear equations, where the equations are fewer than the design variables for the solution of the OPP problem.…”

mentioning

confidence: 99%

“…Up to now, a BILP model is written to its standard form in which the number of the constraints is equal to the number of optimization variables for the OPP problem [4][5][6][7][8][9][10]. This work introduces an underdetermined system of nonlinear equations, where the equations are fewer than the design variables for the solution of the OPP problem.…”

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confidence: 99%

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Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming

Theodorakatos

Lytras

Babu³

2020

Energies

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This paper introduces an underdetermined nonlinear programming model where the equality constraints are fewer than the design variables defined on a compact set for the solution of the optimal Phasor Measurement Unit (PMU) placement. The minimization model is efficiently solved by a recursive quadratic programming (RQP) method. The focus of this work is on applying an RQP to attempt to find guaranteed global minima. The proposed minimization model is conducted on IEEE systems. For all simulation runs, the RQP converges superlinearly towards optimality in a finite number of iterations without to be rejected the full step-length. The simulation results indicate that the RQP finds out the minimal number and the optimal locations of PMUs to make the power system wholly observable.Energies 2020, 13, 1724 2 of 17 OPP problem is unraveled using the mixed-integer semi-definite programming approach subjected to linear matrix inequality. This technique is based on numerical observability, whereas most of the other techniques are based on topological observability, which may or may not ensure numerical observability to be executed successfully for state estimation. In [16,17], mixed-integer linear programming and nonlinear programming techniques are compared to check their suitability for networks of different sizes.Stochastic algorithms have also been used for the OPP problem. A recursive tabu search is suggested in [18], which has been claimed superior to multiple Tabu search and higher observability. Binary particle swarm optimization (BPSO) algorithm is developed for the solution of the OPP problem in [19]. In [20], the authors proposed a BPSO algorithm to minimize the number of substations in which installations must be performed for making all voltage levels observable while being subject to various practical constraints. Authors of [21] proposed the binary gravitational search algorithm to solve the OPP problem. Authors in [22], presented a modified binary Cuckoo optimization algorithm for the solution of the OPP problem with maximum redundancy. Genetic algorithms (GA) have been applied to determine the optimal allocation of PMUs in [23,24].Accurate knowledge of transmission system parameters, such as series impedance, optimizes distance relay settings and impedance-based fault location. A new method is developed to measure transmission line impedances and admittances from synchronized phasor measurements in [25].A new on-line method for estimating transmission line constants of a power system is proposed in [26]. In [27], a new State Estimation (SE) framework is proposed for processing Remote Terminal Unit (RTU) and PMU measurements separately in order to leave the traditional weighted least square (WLS)-based SE software unchanged. Phasor measurement unit based fault location techniques are proposed in [28][29][30]. Other methods, such as an optimized extreme learning machine-based approach, use synchrophasors to ensure real-time power transient stability prediction [31].Up to now, a BILP model is written to its st...

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming

Theodorakatos

Lytras

Babu³

2020

Energies

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“…The authors discussed the consideration of a restricted version of R2 in (Emami et al, 2008). In (Poirion et al, 2016), we studied this problem from a practical point of view. We rst proposed a naturally iterative index binary linear model that turns out to be too large for practical purposes.…”

Section: Introductionmentioning

confidence: 99%

Complexity and inapproximability results for the Power Edge Set problem

et al. 2017

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We consider the single channel PMU placement problem called the Power Edge Set (PES) problem. In this variant of the PMU placement problem, (single channel) PMUs are placed on the edges of an electrical network. Such a PMU measures the current along the edge on which it is placed and the voltage at its two endpoints. The objective is to nd the minimum placement of PMUs in the network that ensures its full observability, namely measurement of all the voltages and currents. We prove that PES is NP-hard to approximate within a factor (1.12)-, for any > 0. On the positive side we prove that PES problem is solvable in polynomial time for trees and grids.Keywords PMU placement problem · Power Edge Set · NP-hardness · inapproximability This work was carried out as part of the SOGRID project (www.so-grid.com), co-funded by the French agency for Environment and Energy Management (ADEME) and developed in collaboration between participating academic and industrial partners.

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“…They also propose a linear-time algorithm on trees by performing a polynomial reduction to Path Cover. Moreover, Poirion et al [14] develop an exact method, a linear program with binary variables, indexed on the necessary iterations using propagation Rule R 1 and Rule R 2 , extended to a linear program in mixed variables, with the goal of being efficient in practice.…”

Section: Introductionmentioning

confidence: 99%

Improved Complexity for Power Edge Set Problem

Darties¹,

Château

Giroudeau

et al. 2018

Lecture Notes in Computer Science

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Abstract. We study the complexity of Power Edge Set (PES), a problem dedicated to the monitoring of an electric network. In such context we propose some new complexity results. We show that PES remains N P-hard in planar graphs with degree at most five. This result is extended to bipartite planar graphs with degree at most six. We also show that PES is hard to approximate within a factor lower than 328 /325 in the bipartite case (resp. 17/15 − ), unless P = N P, (resp. under UGC). We also show that, assuming ET H, there is no 2 o( √ n) -time algorithm and no 2 o(k) n O(1) -time parameterized algorithm, where n is the number of vertices and k the number of PMUs placed. These results improve the current best known bounds.

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The power edge set problem

Cited by 16 publications

References 19 publications

Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming

Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming

Complexity and inapproximability results for the Power Edge Set problem

Improved Complexity for Power Edge Set Problem

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