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Time-Efficient Load Flow Technique for Radial Distribution Systems with Voltage-Dependent Loads

Ujjwal Ghatak(1), V. Mukherjee(2), Almoataz Y. Abdelaziz(3), Shady H. E. Abdel Aleem(4*), Hala M. Abdel Mageed(5)

(1) Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), India
(2) Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), India
(3) Faculty of Engineering and Technology Future University in Egypt Cairo, Egypt
(4) 15th of May Higher Institute of Engineering, 15th of May City, Egypt
(5) National Institute of Standards (NIS), Egypt
(*) Corresponding author



This paper presents an efficient load flow (LF) technique that exhibits an improved convergence characteristic to be employed in balanced radial distribution systems (RDSs) having voltage dependent loads (VDLs). The key enabler of this approach is the construction of load injection to bus voltage (LIBV) matrix that is utilized to carry out the backward forward sweep of power flow calculation in a single step. The bus voltages may be determined from the load injection directly by incorporating the LIBV matrix which, in turn, decreases the execution time when compared to other LF techniques. Further, a novel and generalized algorithm is proposed to construct LIBV in a fast manner. In addition, the effect of annual load growth is examined in this work. The proposed technique is tested on three balanced benchmark RDSs, which are the 30-, 33- and 118-bus systems with different VDL models. The obtained results demonstrate the effectiveness of the proposed approach compared to the results of the other approaches in the literature. Also, it is revealed that the proposed algorithm is computationally faster and more robust than the conventional LF techniques that are used to analyze distribution system having VDLs.
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Balanced Power Systems; Load Flow; Radial Distribution Systems; Voltage-Dependent Loads

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W. D. Stevenson, Elements of Power System Analysis, New Delhi, India: McGraw-Hill, 1982.

W. Tinney, C. Hart, Power Flow Solution by Newton's Method, IEEE Trans. Power Appar. Syst. PAS-86 (1967) 1449–1460.

B. Stott, O. Alsac, Fast Decoupled Load Flow, Power Appar. Syst. IEEE Trans. PAS-93 (1974) 859–869.

F. Zhang, C.. Cheng, A modified Newton method for radial distribution system power flow analysis, IEEE Trans. Power Syst. 12 (1997) 389–397.

N. Martins, Developments in the newton raphson power flow formulation based on current injections, IEEE Trans. Power Syst. 14 (1999) 1320–1326.

P. A. N. Garcia, J. L. R. Pereira, J. S. Carneiro, V. M. da Costa, N. Martins, Three-phase power flow calculations using the current injection method, IEEE Trans. Power Syst. 15 (2000) 508–514.

W. M. Lin, J. H. Teng, Three-phase distribution network fast-decoupled power flow solutions, Int. J. Electr. Power Energy Syst. 22 (2000) 375–380.

J.-H. Teng, A modified Gauss–Seidel algorithm of three-phase power flow analysis in distribution networks, Int. J. Electr. Power Energy Syst. 24 (2002) 97–102.

D. Shirmohammadi, H.W. Hong, A. Semlyen, G. X. Luo, A compensation-based power flow method for weakly meshed distribution and transmission networks, IEEE Trans. Power Syst. 3 (1988) 753–762.

Y. Zhu, K. Tomsovic, Adaptive power flow method for distribution systems with dispersed generation, IEEE Trans. Power Deliv. 17 (2002) 822–827.

M. Afsari, S. P. Singh, G. S. Raju, G. K. Rao, A fast power flow solution of radial distribution networks, Electr. Power Components Syst. 30 (2002) 1065–1074.

P. S. Nagendra Rao, R. S. Deekshit, Radial load flow for systems having distributed generation and controlled Q sources, Electr. Power Components Syst. 33 (2005) 641–655.

M. P. Selvan, K. S. Swarup, Object modeling of balanced and unbalanced distribution systems for power flow analysis, Electr. Power Components Syst. 34 (2006) 191–215.

P. Aravindhababu, R. Ashokkumar, A fast decoupled power flow for distribution systems, Electr. Power Components Syst. 36 (2008) 932–940.

R. Ranjan, B. Venkatesh, A. Chaturvedi, D. Das, Power Flow Solution of Three-Phase Unbalanced Radial Distribution Network, Electr. Power Components Syst. 32 (2004) 421–433.

J. H. Teng, A direct approach for distribution system load flow solutions, IEEE Trans. Power Deliv. 18 (2003) 882–887.

T. H. Chen, N. C. Yang, Three-phase power-flow by direct ZBR method for unbalanced radial distribution systems, Iet Gener. Transm. Distrib. 3 (2009) 903–910.

U. Eminoglu, M. H. Hocaoglu, Distribution Systems Forward/Backward Sweep-based Power Flow Algorithms: A Review and Comparison Study, Electr. Power Components Syst. 37 (2008) 91–110.

M. F. Al Hajri, M. E. El-Hawary, Exploiting the radial distribution structure in developing a fast and flexible radial power flow for unbalanced three-phase networks, IEEE Trans. Power Deliv. 25 (2010) 378–389.

S. Singh, T. Ghose, Improved radial load flow method, Int. J. Electr. Power Energy Syst. 44 (2013) 721–727.

A. B. Eltantawy, M. M. A. Salama, A novel zooming algorithm for distribution load flow analysis for smart grid, IEEE Trans. Smart Grid. 5 (2014) 1704–1711.

M. H. Haque, Load flow solution of distribution systems with voltage dependent load models, Electr. Power Syst. Res. 36 (1996) 151–156.

S. Mok, S. Elangovan, L. J. Cao, M. Salama, A new approach for power flow analysis of balanced radial distribution systems, Electr. Mach. Power Syst. 28 (2000) 325–340.

U. Eminoglu, M. H. Hocaoglu, A new power flow method for radial distribution systems including voltage dependent load models, Electr. Power Syst. Res. 76 (2005) 106–114.

B. Das, Incorporation of uncertainties in radial distribution system load flow with voltage-dependent loads, Electr. Power Components Syst. 37 (2009) 1102–1117.

S. Satyanarayana, T. Ramana, S. Sivanagaraju, G.K. Rao, An efficient load flow solution for radial distribution network including voltage dependent load models, Electr. Power Components Syst. 35 (2007) 539–551.

K. Nagaraju, S. Sivanagaraju, T. Ramana, P. V. Prasad, A novel load flow method for radial distribution systems for realistic loads, Electr. Power Components Syst. 39 (2011) 128–141.

U. Eminoglu, T.Gozel, DSPFAP: Distribution systems power flow analysis package using Matlab graphical user interface (GUI), Computer Applications in Engineering Education, 18(2010) 1–13.

T. Gozel, U.Eminoglu, M. H. Hocaoglu, A tool for voltage stability and optimization (VS&OP) in radial distribution systems using matlab Graphical User Interface (GUI), Simulation Modelling Practice and Theory, 16 (2008) 505-518.

G. B. Jasmon, L. H. C. C. Lee, Distribution network reduction for voltage stability analysis and loadflow calculations, Int. J. Electr. Power Energy Syst. 13 (1991) 9–13.

Ismael S. M., Abdel Aleem S. H. E., Abdelaziz A. Y., Zobaa A. F. State-of-the-art of hosting capacity in modern power systems with distributed generation. Renew Energy 2019;130:1002–20.

Ismael S. M., Aleem S. H. E. A., Abdelaziz A. Y. , Zobaa A. F. Practical Considerations for Optimal Conductor Reinforcement and Hosting Capacity Enhancement in Radial Distribution Systems. IEEE Access 2018;6:27268–77.

K. Muthukumar, S. Jayalalitha, M. Ramasamy, C. S. Haricharan, Optimal shunt capacitor allocation and sizing using harmony search algorithm for power loss minimization in radial distribution networks, International Journal of Development Research. 4 (2015) 537–545.

U. Ghatak, V. Mukherjee, An improved load flow technique based on load current injection for modern distribution system, Int. J. Electr. Power Energy Syst. 84 (2017) 168–181.

U. Ghatak, V. Mukherjee, A fast and efficient load flow technique for unbalanced distribution system, Int. J. Electr. Power Energy Syst. 84 (2017) 99–110.

Abul'Wafa, A network-topology-based load flow for radial distribution networks with composite and exponential load, Electr. Power Syst. Res. 91 (2012) 37–43.

Gianto, R., Hie Khwee, K., A New Method for Load Flow Solution of Electric Power Distribution System, (2016) International Review of Electrical Engineering (IREE), 11 (5), pp. 535-541.

Panyakaew, P., Power Flow Solutions by Newton-Raphson Method with Approximated Second-Order Term of Taylor Series, (2015) International Review of Electrical Engineering (IREE), 10 (6), pp. 734-746.

Muthukumar, K., Jayalalitha, S., Ramaswamy, M., PSO Embedded Artificial Bee Colony Algorithm for Optimal Shunt Capacitor Allocation and Sizing in Radial Distribution Networks with Voltage Dependent Load Models, (2015) International Review of Electrical Engineering (IREE), 10 (2), pp. 305-320.

Cresta, M., Gatta, F., Geri, A., Lamedica, R., Lauria, S., Maccioni, M., Paulucci, M., Ruvio, A., Operation of a Medium Voltage Distribution Network with a Large Penetration of Distributed Generation, (2016) International Review on Modelling and Simulations (IREMOS), 9 (4), pp. 280-287.


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