Optimal Placement of Phasor Measurement Units with Linear and Non-linear Models

Theodorakatos, Nikolaos P.; Manousakis, Νikolaos M.; Korres, George N.

doi:10.1080/15325008.2014.981319

Cited by 42 publications

(34 citation statements)

References 31 publications

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“…The same method considering conventional measurements is developed in Esmaili et al 24 Zero injection redundancy limitation and global optimal solution considering mutual buses are presented in Khajeh et al 25 Chakrabarti et al 26 propose an integer quadratic programming approach. 29,30 In Almunif and Fan, 31 MILP and NLP comparison is conducted using a simple system, and limitation of zero injection formulation for NLP is discussed. 27 Nonlinear programming (NLP) formulations are introduced in Theodorakatos et al 28 This type of formulations has been explored under several contingencies in literature.…”

Section: Introductionmentioning

confidence: 99%

“…27 Nonlinear programming (NLP) formulations are introduced in Theodorakatos et al 28 This type of formulations has been explored under several contingencies in literature. 29,30 In Almunif and Fan, 31 MILP and NLP comparison is conducted using a simple system, and limitation of zero injection formulation for NLP is discussed. However, zero injection formulation in nonlinear programming-based PMU placement has not been properly solved in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Optimal PMU placement for modeling power grid observability with mathematical programming methods

Almunif

Fan

2019

Int Trans Electr Energ Syst

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Summary Phasor measurement units (PMUs) can obtain synchronized voltage and current phasors to increase the accuracy of state estimation results. Optimal PMU placement (OPP) reduces the required number of PMUs to make the system fully observable. In this paper, two mathematical programming formulations, which are mixed integer linear programming (MILP) and nonlinear programming (NLP), for power grid observability modeling to solve the OPP problem are presented. Power flow and zero injection measurement modeling along with restricted communication facilities, PMU failure, and limited channel capacity contingencies are investigated. MILP zero injection formulation is improved to overcome the observability redundancy and optimality drawbacks. A new formulation for nonlinear programming‐based PMU placement for zero injection measurement is proposed. MILP and NLP methods are compared to illustrate the advantages and disadvantages of each method. The comparison and proposed formulations are examined on IEEE 14‐, 57‐, 118‐, 300‐bus test systems and a large 2383‐bus Polish system to demonstrate their effectiveness.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal PMU placement for modeling power grid observability with mathematical programming methods

Almunif

Fan

2019

Int Trans Electr Energ Syst

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“…References [1][2][3][4][5][6][7][8][9][10][11][24][25][26] accounted PMUs at every bus are the same cost, so the objective function of the minimum cost of PMUs corresponds to the minimum number of PMUs. However given the fact that, the cost corresponding to different PMUs are different due to the number of channels of each bus is not the same.…”

Section: Object Function For Full Network Observabilitymentioning

confidence: 99%

“…The common goal of placement method is to achieve the PSO by using the minimal number of PMUs in order the minimum cost. Integer linear programming is one of the dominant mathematical optimization technique, which is commonly used for solving effectively [1][2][3][4][5]. Heuristic and meta-heuristic search algorithms also have been attracted a lot of concerns in solving the PMU placement problem due to their good characteristics [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Optimal Placement of Phasor Measurement Unit for Observation Reliability Enhancement

Tran¹,

Zhang²,

Nguyen³

2017

Journal of Electrical Engineering and Technology

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-Phasor Measurement Unit (PMU) placement is a crucial problem for State Estimation (SE) of the power system, which can ensure that the power network is fully observed. Further, the observation reliability problem of the system has been concerned in the operation conditions. In this paper, based on modified weighted adjacent matrix (A w ), an optimal placement method is proposed to solve simultaneously two problems involving the optimal PMU placement problem and the observation reliability enhancement problem of the system. The purpose of the proposed method is to achieve both the minimum total cost and the maximum observation reliability, with a focus on increasing the security of observability, strengthening the observation reliability of buses as well as enhancing the effectiveness of redundancy. Simulations on IEEE 14, 24, 30 and 57 bus test systems are presented to justify the methodology. The results of this study show that the proposed method is not only ensuring the power network having the observability effectively but also enhancing significantly the observation reliability. Therefore, it can be a useful tool for SE of the power system.

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“…When a significant fraction of the optimization problem constraints are eliminated, the feasibility diagnosis is accelerated and speeds up the solution algorithm in finding the optimality [32][33][34][35][36]. Thus, a reduction in problem size typically translates to a reduction in total running time in comparison with past studies such as [11,12,17].The solution to such underdetermined systems is based on the Recursive Quadratic Programming (RQP) method [35]. The contribution of this work is fourfold as follows:…”

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confidence: 99%

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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Optimal Placement of Phasor Measurement Units with Linear and Non-linear Models

Cited by 42 publications

References 31 publications

Optimal PMU placement for modeling power grid observability with mathematical programming methods

Optimal PMU placement for modeling power grid observability with mathematical programming methods

Optimal Placement of Phasor Measurement Unit for Observation Reliability Enhancement

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

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