Power System

A Power Flow Method Computationally Efficient for Large-Scale Distribution Systems
A. C. Santos, M. Nanni, M. R. Mansour, A. C. B. Delbem, J. B. A. London Jr., N. G. Bretas

Abstract - Due to several factors, conventional power flow does not present a good performance in solving distribution system power flow. Thus, the Backward and Forward Sweep method is the one more utilized in this kind ofnetwork, mainly in radial distribution system. In spite of there be several variants of this method, two more utilized are Current Summation Method and Power Summation Method. In this paper is proposed a data structure that guarantees better efficiency to these methods. It is known by Node-depth Encoding, and it can improve their performance. Mainly when they are utilized in large distributionnetworks and when is necessary to run the power flow many times. It will be presented results obtained by two methods well known at the literature and these methods with node-depth encoding. The results guarantee that it can be utilized in several applications, even though in larger distribution systems. Index Terms -- Radial Distribution System, Load Flow, Forward and Backward Sweep, Node-depthEncoding.
I. NOMENCLATURE

DS : Distribution System NDE : Node-Depth Encoding TSO : Terminal-Substation Order FBS : Forward and Backward Sweep CSM : Current Summation Method CSM-NDE : Current Summation Method with NDE PSM : Power Summation Method PSM-NDE : Power Summation Method with NDE
II. INTRODUCTION

HE purpose of a power flow analysis method is to obtain the operational conditions of anelectrical network (Le., the complex phasor voltages at every network bus, as well as real and reactive power flows into every line and transformer) under the assumption of known topology, generation and load.

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This work was supported by CNPq and FAPESP. A. C. Santos - Department of Electrical Engineering / Federal Technical School of Palmas, Palmas-TO, Brazil (e-mail:augusto@?etfto.gov.br). M. Nanni - Department of Electrical Engineering - (EESC/uSP), Sao Carlos-SP, Brazil (e-mail: nanni@sel.eesc.usp.br). M. R. Mansour - Department of Electrical Engineering - (EESC/USP) Sao Carlos-SP, Brazil (e-mail: moussa@sel.eesc.usp.br). A. C. B. Delbem - Institute of Computational and Mathematics Science (ICMC/uSP), Sao Carlos-SP, Brazil (e-mail: acbd@;icmc.usp.br). 1. B. A. London Jr. -Department of Electrical Engineering (EESC/uSP), Sao Carlos-SP, Brazil (e-mail: jbalj@se1.eesc.usp.br). N. G. Bretas - Department of Electrical Engineering - (EESC/uSP), Sao Carlos-SP, Brazil (e-mail: ngbretas@sel.eesc.usp.br).

The power flow problem can be formulated through a set of non-linear algebraic equations and inequations that correspond to the Kirchhoff s laws and a set of systemoperational constraints, respectively. In the basic formulation of the power flow problem there are four variables to each network bus. Depending on the type of the bus, two variables are known (controlled variables) and the others are unknowns. These variables are: nodal voltage magnitude (V), nodal voltage angle (8), net generation of real power (P), and net injection of reactive power (Q). In someparticular situations it is necessary to modify that basic formulation, including other variables and other equality and inequality constraints. Conventional power flow methods for the solution of transmission systems, such as Newton-Raphson method [1], Fast Decoupled Power Flow method [2], and their derivatives [3-5], do not present a good performance in solving distribution system (DS) [6]. Thisoccurs because these conventional methods require matrix factorization and the matrices associated to distribution systems are ill-conditioned. Those ill-conditioned matrices are due to some particular characteristics of the distribution systems, such as: high RIX ratios (resistance/reactance), large number of distributed loads, and some parts of the network with relatively low impedances 1...