Three-phase power flow in power distribution networks

World Journal of Advanced Engineering Technology and Sciences, 2023

The power system network is complex. This makes it more challenging to obtain valuable information because of its hundreds of buses and transmission lines. In addition, solving the steady-state equations of the power system network requires substantial mathematical computations. The power flow analysis is a study of the electrical power system. Engineers and utility companies use it for the design, control, planning, and future improvement of the electrical power network. Power flow analysis calculates the voltage magnitude, phase angles, active and reactive power flows, losses of the power system network under various loads, and generation conditions. This paper is a tutorial article aimed to present the power flow analysis techniques of Gauss-Seidel, Newton-Raphson, and Fast-Decoupled approaches. The Power World Simulator is used to demonstrate the software implementation of the approaches. The results show that Newton Raphson and Fast Decoupled have a faster convergence. The Newton Raphson method is the popular technique used for the analysis. An illustrative example for an IEEE 3-bus system on each technique is also presented in the article.

IEEE Transactions on Power Systems, 2019

Load flow methods for distribution networks such as Backward Forward Sweep (BFS) have a good computational performance and can find solutions with accuracy. However, some studies may demand the determination of low voltage solutions, and this poses a problem for these methods since they cannot find these solutions due to convergence issues. This paper presents a load flow method based on a novel complex-valued formulation developed for distribution networks, which works well on radial topologies by using an incidence matrix to avoid complicated series element models, allow high-performance and low-voltage solution capability. The formulation is solved by Newton's method via Wirtinger's calculus. To prove the lowvoltage solution capability, both sides of QV curves, i.e., unstable and stable regions were traced on balanced and unbalanced networks. Performance tests in the IEEE test feeders show that the runtime is less than or equal to the runtime of the BFS method. Furthermore, the line R/X ratio and the number of controlled voltage node or volt-var functions do not affect the computational performance, yielding advantages over the classic Newton and BFS methods.

This paper presents a new load flow formulation to solve active and passive electric distribution networks. The fundamental idea discussed here is how to obtain the power flow solution by using the elements of a unique quasi-symmetric matrix called TRX in the iterative process. The method is formulated for singlephase balanced and three-phase unbalanced radially operated networks. It works with real variables as opposed to complex variables used in previous backward/forward sweep algorithms discussed in literature. The proposed TRX matrix constitutes a complete database by including information of network topology structure as well as branch impedances of the distribution feeder. Data arrangement is suitable to be exchanged under standard Common Information Model (CIM) under Distribution Management Systems (DMS) environment allowing an efficient computation of the state of the system for on-line and off-line study applications. The proposed methodology was applied on a group of IEEE test systems and a real distribution system of 49,000 nodes.

2021

The increase of distributed energy resources (DERs) in low voltage (LV) distribution networks requires the ability to perform an accurate power flow analysis (PFA) in unbalanced systems. The characteristics of a well performing power flow algorithm are the production of accurate results, robustness and quick convergence. The current study proposes an improvement to an already used backward-forward sweep (BFS) power flow algorithm for unbalanced three-phase distribution networks. The proposed power flow algorithm can be implemented in large systems producing accurate results in a small amount of time using as little computational resources as possible. In this version of the algorithm, the network is represented in a tree-like structure, instead of an incidence matrix, avoiding the use of redundant computations and the storing of unnecessary data. An implementation of the method was developed in Python programming language and tested for 3 IEEE feeder test cases (the 4 bus feeder, th...

International Journal of Electrical Power & Energy Systems, 2018

This paper presents an evaluation of the main convergence characteristics of multiphase power flow methods in unbalanced distribution systems. Two widely used methods for solving unbalanced power flows are analyzed: methods based on Newton-Raphson (NR) and methods based on backward forward sweep (BFS). The limits and robustness of the BFS method and NR method are tested in the following aspects: (i) variation of the X/R ratio, (ii) load's increase up to the convergence limit, (iii) load model impacts (ZIP model), and (iv) voltage regulators modeling impacts. Some models presented in the literature were implemented and tested. Tests are performed on the IEEE 34 and IEEE 123 systems. Analytical explanations are also presented.

IET Generation, Transmission & Distribution, 2014

A new continuation power flow method is proposed, which is an extension of the popular backward/forward sweep power flow (BFS) for distribution network. The different reasons for the divergence of Newton's algorithm and fixed-point iteration algorithm near the saddle node bifurcation point have been investigated extensively. Loop-analysis-based power flow (LBPF) is a revised version of BFS, which belong to fixed-point iteration algorithm and its convergence remains satisfactory in a meshed network. Based on LBPF, a tailored continuous power flow method is developed, which can be used as a voltage stability analysis tool for both radial and meshed distribution networks. Numerical test results are presented to validate the proposed procedure.

2010

This paper presents a sweep-based three-phase power flow method for solving general distribution networks that can be heavily meshed and include transformers around the meshes/loops. A load-stepping technique is proposed for solving common convergence problems of sweep-based load-flow solvers when dealing with overloaded radial sections. The proposed power-flow algorithm is based on the iterative solution of radial subsystems assembled together with the mesh equations to comply with Kirchhoff equations. The proposed method is robust and efficient for the solution of heavily loaded systems. Examples are presented for illustration.

2011 International Conference on Power Engineering, Energy and Electrical Drives, 2011

This paper proposes parallel algorithm of a general three-phase load flow calculation based on symmetrical components. The proposed algorithm comprises of two part i.e. sequence admittance matrix construction and sequence decoupled algorithm for sequence networks solver which have three independent sub-problems corresponding to positive, negative, and zero-sequence networks. These two parts are solved concurrently using multi-core parallel processing. The IEEE 8500-node test feeder is used to test the robustness of the algorithm for large system problem. The large unbalanced load connected to the center-tapped transformer solved using an iterative forward and backward sweep analysis method based on voltage drop analysis. The result showed that parallel three-phase load flow produced execution speedup and proved the ability to handle large scale problems.

IntechOpen eBooks, 2020

Power flow, or load flow, is widely used in power system operation and planning. The power flow model of a power system is built using the relevant network, load, and generation data. Outputs of the power flow model include voltages at different buses, line flows in the network, and system losses. These outputs are obtained by solving nodal power balance equations. Since these equations are nonlinear, iterative techniques such as the Newton-Raphson, the Gauss-Seidel, and the fast-decoupled methods are commonly used to solve this problem. The problem is simplified as a linear problem in the DC power flow technique. This chapter will provide an overview of different techniques used to solve the power flow problem.

Journal of Electrical Systems and Information Technology

This paper presents an improved load flow technique for a modern distribution system. The proposed load flow technique is derived from the concept of the conventional backward/forward sweep technique. The proposed technique uses linear equations based on Kirchhoff’s laws without involving matrix multiplication. The method can accommodate changes in network structure reconfiguration by involving the parent–children relationship between nodes to avoid complex renumbering of branches and nodes. The IEEE 15 bus, IEEE 33 bus and IEEE 69 bus systems were used for testing the efficacy of the proposed technique. The meshed IEEE 15 bus system was used to demonstrate the efficacy of the proposed technique under network reconfiguration scenarios. The proposed method was compared with other load flow approaches, including CIM, BFS and DLF. The results revealed that the proposed method could provide similar power flow solutions with the added advantage that it can work well under network reconfi...

This paper presents an efficient three-phase power flow algorithm for distribution network analysis. A new transformer model with various connections is implemented in the forward/backward sweep power flow method. The developed method provides an effective solution to the singularity problem of the nodal admittance submatrices appeared in some transformer configurations. Different load models and capacitor banks are also implemented with any number of phases and any connection. The proposed load flow has been tested using both the IEEE 4 and 34 node test feeders. The obtained results show that the proposed load flow is very efficient and the numerical solution is identical to that provided with the IEEE data.

ArXiv, 2020

This paper describes a simplified formulation of the Backward/Forward (BW/FW) Sweep Power Flow applied to radial distribution systems with distributed generation under positive sequence modelling. Proposed formulation was applied in an illustrative test system.

2010

Power flow is an important tool in power system planning and operational studies. The single-phase power-flow algorithms assume a balanced power system operation and a balanced power system model. There are many cases where the system unbalance cannot be ignored due to unbalanced loads, untransposed transmission lines and a combination of balanced with unbalanced networks in distribution systems. Therefore a three-phase powerflow program that deals with unbalanced power system will be a useful analytical ...

In this work, distribution system load flow analysis is formulated and tested for fundamental steady-state and harmonics power flow. For the steady-state analysis, a novel power flow formulation method for the general multiphase balanced and/or unbalanced radial distribution systems is presented. The special topology of the power distribution system has been fully exploited to facilitate obtaining a direct solution using the graph theory. Only one developed matrix used in conjunction with simple standard formulation is enough to obtain the power flow solution. This matrix is the branch-path incident matrix. A feature of using this method is that it significantly reduces the number of power flow equations, as compared to conventional methods, hence very low computation time and memory storage. The presence of nonlinear loads in the power system causes the circulation of harmonics currents in the system, leading to harmonics voltage drops. The harmonics flow analysis in this paper, uses the network techniques in conjunction with graph theory resulting in a powerful algorithm for nonlinear load flow analysis. Six pulse converters model were used to represent the nonlinear load. Two MATLAB programs have been built and used to solve for the load flow solution of standard test systems in both steady-state and harmonics cases. The results of the distribution system cases studies are presented and shows a very good resemblance with a standard results.

Energies, 2020

This paper presents an alternative solution for the power-flow analysis of power systems with distributed generation provided by heterogeneous sources. The proposed simulation approach relies on a suitable interpretation of the power network in terms of a nonlinear circuit in the phasor domain. The above circuit interpretation can be solved directly in the frequency-domain via the combination of a standard tool for circuit analysis with an iterative numerical scheme, providing directly the steady-state solution of the power-flow of a generic distribution network. At each iteration, the resulting circuit turns out to be composed by two decoupled subnetworks, a large linear part and a set of smaller nonlinear pieces accounting for the load characteristics, with evident benefits in terms of the computational time. The feasibility and strength of the proposed simulation scheme have been verified on a large benchmark consisting of the IEEE 8500-node test feeder. Then it is applied to the...