Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 1791–1808 | Cite as

An Efficient Graphical Method for Load-Flow Solution of Distribution Systems

  • Krishna MurariEmail author
  • Narayana Prasad Padhy
Research Article - Electrical Engineering


This paper presents a new and computationally efficient load-flow algorithm for ac distribution systems using graphical search technique along with matrix algebra. The proposed algorithm is equally applicable to balanced, unbalanced and meshed distribution systems. In contrast with traditional load-flow methods, the developed technique does not require any LU decomposition or bus admittance matrix. The significant feature of the algorithm lies in the formulation of path impedance matrix and loads beyond branch matrix; once formulated, it will remain unaltered for the entire operation. The reconfiguration of these matrices takes place automatically in accordance with the change in input data. Moreover, by storing all the system data in array/matrix form it hoards enormous computer memory. Because of the aforementioned reasons, the developed technique is computationally potent when applied on large-sized distribution systems. The efficacy of the proposed methodology is tested on various standard test systems. It is evident from the test results that the proposed algorithm is robust and time efficient for any size of distribution network when compared with several other existing load-flow methods.


Distribution systems Graph theory Load modeling Load flow Undirected graph 

List of symbols


Total number of branches


Total number of buses


Branch number (\(1,2,\ldots ,m\))


Node number (\(1,2,\ldots ,n\))


Voltage at node number k


Load current at bus number k

[LB] matrix

Loads beyond branch matrix

[BB] matrix

Buses beyond branch matrix

[P] matrix

Path matrix

[PI] matrix

Path impedance matrix


Impedance of branch number [b]


Total number of extreme nodes in the distribution system


Total number of power-flow paths


Complex power of load at bus k


Real power of load at bus k


Reactive power of load at bus k

\(\varepsilon \)



Maximum voltage difference


Row number of a matrix


Column number of matrix


System data matrix


Sending end node


Receiving end node


Complex power at RN node


Constant power load model


Constant current load model


Constant impedance load model


Exponential load model


Composite load model


Current through branch number b


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentIndian Institute of Technology RoorkeeRoorkeeIndia

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