A Linear Power Flow Formulation for _newline Three-Phase Distribution Systems

2016 ◽  
Vol 31 (6) ◽  
pp. 5012-5021 ◽  
Author(s):  
Hamed Ahmadi ◽  
Jose R. Marti ◽  
Alexandra von Meier
Keyword(s):  
Power Flow ◽  
Distribution Systems ◽  
Phase Distribution ◽  
Three Phase

scholarly journals Log(v) 3LPF: A Linear Power Flow Formulation for Unbalanced Three-Phase Distribution Systems

2021 ◽  
Author(s):  
Ignacio Losada Carreño ◽  
Shammya Saha ◽  
Anna Scaglione ◽  
Daniel Arnold ◽  
Ngo Sy-Toan ◽  
...  
Keyword(s):  
Power Flow ◽  
Distribution Systems ◽  
Phase Distribution ◽  
Decomposition Methods ◽  
Efficient Computation ◽  
Flow Solver ◽  
Flow Equations ◽  
Ac Power ◽  
Three Phase ◽  
Matrix Vector

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. Log(v) 3LPF uses a logarithmic transform of the voltage phasor to linearize the AC power flow equations around the balanced case. We incorporate the modeling of ZIP loads, transformers, capacitor banks, switches and their corresponding controls and express the network equations in matrix-vector form. With scalability in mind, special attention is given to the computation of the inverse of the system admittance matrix, Ybus. We use the Sherman-Morrison-Woodbury identity for an efficient computation of the inverse of a rank-k corrected matrix and compare the performance of this method with traditional LU decomposition methods in terms of FLOPS. We showcase the solver for a variety of network sizes, ranging from tens to thousands of nodes, and compare the Log(v) 3LPF with commercial-grade software, such as OpenDSS. <br>

scholarly journals Application of Newton-Raphson method in three-phase unbalanced power flow

2021 ◽  
Author(s):  
Ali Khadem Sameni
Keyword(s):  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Phase Distribution ◽  
Renewable Energy Sources ◽  
Flow Equations ◽  
Three Phase ◽  
Newton Raphson ◽  
Raphson Method ◽  
Three Phases

Renewable energy sources are in the forefront of new energy in power systems. They are predominantly connected to distribution systems at lower voltage levels. Distribution systems have three phases and are largely unbalanced in their line parameters and loads. A large percentage of these systems suffer from severe imbalance in their phases. In the past, two methods of analysis were commonly used. The first is the 'ladder iterative technique' that consider unbalanced systems. However, this method does not possess information about the distribution system. The second method uses the 'Newton Raphson Technique' with 2N equations. It is superior since it computes a Jacobian that holds information about the distribution system. However, predominant implementations of Newton Raphson method assume that the system is balanced and they suffer from poor convergence properties. In order to overcome these difficulties, this research furthers a recent development of single phase 3N equation model of distribution systems by enlarging it to model three phase distribution systems. The Jacobian models each of the three phases using a set of 3N equations. Modeling of network components and formulation of three phase power flow equations are presented. The important characteristics of the Jacobin matrix are also presented. The method is developed and coded. It is tested on standard IEEE distribution systems with 4, 13,34,37, and 123 nodes. The results are compared with published IEEE data.

scholarly journals Application of Newton-Raphson method in three-phase unbalanced power flow

2021 ◽  
Author(s):  
Ali Khadem Sameni
Keyword(s):  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Phase Distribution ◽  
Renewable Energy Sources ◽  
Flow Equations ◽  
Three Phase ◽  
Newton Raphson ◽  
Raphson Method ◽  
Three Phases

Renewable energy sources are in the forefront of new energy in power systems. They are predominantly connected to distribution systems at lower voltage levels. Distribution systems have three phases and are largely unbalanced in their line parameters and loads. A large percentage of these systems suffer from severe imbalance in their phases. In the past, two methods of analysis were commonly used. The first is the 'ladder iterative technique' that consider unbalanced systems. However, this method does not possess information about the distribution system. The second method uses the 'Newton Raphson Technique' with 2N equations. It is superior since it computes a Jacobian that holds information about the distribution system. However, predominant implementations of Newton Raphson method assume that the system is balanced and they suffer from poor convergence properties. In order to overcome these difficulties, this research furthers a recent development of single phase 3N equation model of distribution systems by enlarging it to model three phase distribution systems. The Jacobian models each of the three phases using a set of 3N equations. Modeling of network components and formulation of three phase power flow equations are presented. The important characteristics of the Jacobin matrix are also presented. The method is developed and coded. It is tested on standard IEEE distribution systems with 4, 13,34,37, and 123 nodes. The results are compared with published IEEE data.

scholarly journals Log(v) 3LPF: A Linear Power Flow Formulation for Unbalanced Three-Phase Distribution Systems

2021 ◽  
Author(s):  
Ignacio Losada Carreño ◽  
Shammya Saha ◽  
Anna Scaglione ◽  
Daniel Arnold ◽  
Ngo Sy-Toan ◽  
...  
Keyword(s):  
Power Flow ◽  
Distribution Systems ◽  
Phase Distribution ◽  
Decomposition Methods ◽  
Efficient Computation ◽  
Flow Solver ◽  
Flow Equations ◽  
Ac Power ◽  
Three Phase ◽  
Matrix Vector

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. Log(v) 3LPF uses a logarithmic transform of the voltage phasor to linearize the AC power flow equations around the balanced case. We incorporate the modeling of ZIP loads, transformers, capacitor banks, switches and their corresponding controls and express the network equations in matrix-vector form. With scalability in mind, special attention is given to the computation of the inverse of the system admittance matrix, Ybus. We use the Sherman-Morrison-Woodbury identity for an efficient computation of the inverse of a rank-k corrected matrix and compare the performance of this method with traditional LU decomposition methods in terms of FLOPS. We showcase the solver for a variety of network sizes, ranging from tens to thousands of nodes, and compare the Log(v) 3LPF with commercial-grade software, such as OpenDSS. <br>

scholarly journals Optimal Selection of Conductors in Three-Phase Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 80
Author(s):  
John Fernando Martínez-Gil ◽  
Nicolas Alejandro Moyano-García ◽  
Oscar Danilo Montoya ◽  
Jorge Alexander Alarcon-Villamil
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Phase Distribution ◽  
Search Algorithm ◽  
Distribution Networks ◽  
Discrete Version ◽  
Optimal Selection ◽  
Flow Method ◽  
Three Phase ◽  
Selection Of

In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ− and Y−connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.

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