A New Load-Flow Method in Distribution Networks based on an Approximation Voltage-Dependent Load model in Extensive Presence of Distributed Generation Sources

Document Type : Research Article


1 Department of Electrical Engineering, Amirkabir University of Technology

2 Department of Electrical Eng., Amirkabir University of Technology

3 Dept. of Elect. Eng., Shahid Behshti University

4 Dept. of EE, Amirkabir University of Technology

5 Dept. of EE, Shahid Behshti University



Power-flow (PF) solution is a basic and powerful tool in power system analysis. Distribution networks (DNs), compared to transmission systems, have many fundamental distinctions that cause the conventional PF to be ineffective on these networks. This paper presents a new fast and efficient PF method which provides all different models of Distributed Generations (DGs) and their operational modes (P-V and P-Q nodes) in DNs. This study uses voltage-dependent load model instead of traditional load model (constant P-Q) which is modelled as the combination of a current source in parallel with a constant admittance. This kind of load model is closer to reality and makes the power-flow equations closer to linear conditions. To calculate the angles of the P-V buses, the numerical method (Newton-Raphson method) is applied by separating the PF equations for P-V and P-Q buses. Considering a series of approximations on the angles of these buses, the non-diagonal elements of the Jacobin matrix in Newton-Raphson method are fixed. Hence, the proposed numerical method converges toward an appropriate response in a very low number of iterations and high speed. The voltages of other buses (P-Q buses) are calculated linearly without needing any numerical methods. The presented method proves to be robust and reliable against reconfigured structures and meshed networks. Simulations have been carried out on 14-, 33- and 70-node IEEE test systems and large scale networks such as 6118-buses. The results show that the proposed method is at least 100 and 10 times faster than Gauss-Seidel and Newton-Raphson methods, respectively.


Main Subjects

[1]  CIRED preliminary report of CIRED Working Group 04, "Dispersdgeneration" Issued at the CIRED Conference in Nice, June 1999.
[2]   Etrella, A.J., "Issues, impacts and strategies for distributed generation challenged power system", Paper no. 300-12, CIGRE Symposium on impact of demand side management, integrated resource planning and distributed generation, Neptun, Romania, pp.17-19, 1997.
[3]  H. Saadat, Power Systems Analysis. New York: McGraw-Hill, 2002.
[4]  W. F. Tinney and C. E. Hart, “Power flow solution by newton’s method,” IEEE Trans. Power App. Syst., vol. PAS-86, no. 11, pp. 1449–1460, Nov. 1967.
[5]   B. Stott and O. Alsac, “Fast decoupled load flow,” IEEE Trans. Power App. Syst., vol. PAS-93, no. 3, pp. 859–869, May 1974.
[6]   W. H. Kersting, Distribution System Modelling and Analysis. Boca Raton, FL: CRC, Jan. 2012.
[7]  J. H. Teng and C. Y. Chang, "Backward/Forward Sweep-Based Harmonic Analysis Method for Distribution Systems," IEEE Transactions on Power Delivery, vol. 22, no. 3, pp. 1665-1672, July 2007.
[8]   T. Alinjak, I. Pavić and M. Stojkov, "Improvement of backward/forward sweep power flow method by using modified breadth-first search strategy," IET Generation, Transmission & Distribution, vol. 11, no. 1, pp. 102-109, 1 5 2017.
[9]  G. W. Chang, S. Y. Chu and H. L. Wang, "An Improved Backward/Forward Sweep Load Flow Algorithm for Radial Distribution Systems," IEEE Transactions on Power Systems, vol. 22, no. 2, pp. 882-884, May 2007.
[10]  D. L. Mendive, an Application of Ladder Network Theory to the Solution of Three-phase Radial Load-flow Problems. Albuquerque, NM, USA: New Mexico State University, 1975.
[11]  M. Bazrafshan and N. Gatsis, "On the solution of the three-phase load-flow in distribution networks," 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2016, pp. 303-307.
[12]  Jen-Hao Teng, "A direct approach for distribution system load flow solutions," IEEE Transactions on Power Delivery, vol. 18, no. 3, pp. 882-887, July 2003.
[13]  P. A. N. Garcia, J. L. R. Pereira, S. Carneiro, V. M. da Costa and N. Martins, "Three-phase power flow calculations using the current injection method," IEEE Transactions on Power Systems, vol. 15, no. 2, pp. 508-514, May 2000.
[14]  D. R. R. Penido, L. R. de Araujo, S. Carneiro, J. L. R. Pereira and P. A. N. Garcia, "Three-Phase Power Flow Based on Four-Conductor Current Injection Method for Unbalanced Distribution Networks," IEEE Transactions on Power Systems, vol. 23, no. 2, pp. 494-503, May 2008.
[15]   J. Marti, H. Ahmadi and L. Bashualdo, "Linear power flow formulation based on a voltage-dependent load model," IEEE PES General Meeting | Conference & Exposition, National Harbor, MD, 2014, pp. 1-1.
[16]  H. Ahmadi, J. R. Martı´ and A. von Meier, "A Linear Power Flow Formulation for Three-Phase Distribution Systems," IEEE Transactions on Power Systems, vol. 31, no. 6, pp. 5012-5021, Nov. 2016.
[17] Sadeghian, Omid, et al. "A robust data clustering method for probabilistic load flow in wind integrated radial distribution networks." International Journal of Electrical Power & Energy Systems 115 (2020): 105392.
[18] Sambaiah, Kola Sampangi, and T. Jayabarathi. "A Survey on Load/Power Flow Methods and DG Allocation Using Grasshopper Optimization Algorithm in Distribution Networks." Soft Computing for Problem Solving. Springer, Singapore, 2020. 621-630.
[19] Malakar, Tanmoy, and Ujjwal Ghatak. "An Efficient Unbalanced Load Flow for Distribution Networks." Innovations in Infrastructure. Springer, Singapore, 2019. 117-128.
 [20] Sur, Ujjal, et al. "A Modified Holomorphic Embedding Load Flow Method for Active Power Distribution Networks." 2019 IEEE Region 10 Symposium (TENSYMP). IEEE, 2019.
 [21] W El-Khattam, M.M.A Salama, "Distributed generation technologies, definitions and benefits", Electric Power Systems Research, Volume 71, Issue 2, 2004, Pages 119-128.
[22]   Thomas Ackermann, Göran Andersson, Lennart Söder, "Distributed generation: a definition", Electric Power Systems Research, Volume 57, Issue 3, 2001, Pages 195-204.
[23]  G. Pepermans, J. Driesen, D. Haeseldonckx, R. Belmans, W. D’haeseleer, "Distributed generation: definition, benefits and issues", Energy Policy, Volume 33, Issue 6, 2005, Pages 787-798.
[24]  C. S. Cheng and D. Shirmohammadi, "A three-phase power flow method for real-time distribution system analysis," IEEE Transactions on Power Systems, vol. 10, no. 2, pp. 671-679, May 1995.
[25]  S.Civanlar, J. J.Grainger, H.Yin, and S. S. H.Lee, “Distribution feeder reconfiguration for loss reduction,” IEEE Trans. Power Del., vol. 3, no. 3, pp. 1217–1223, Jul. 1988.
[26]   A. Maiti, Load Flow Analysis of Radial Distribution Network using Linear Data Structure. Jaipur Rajasthan Technical University, Kota, 2013.
[27]   D. Das, “A fuzzy multi objective approach for network reconfiguration of distribution systems,” IEEE Trans. Power Del., vol. 21, no. 1, pp. 202–209, Jan. 2006.
[28]   H. Ahmadi J. R. Martí "Minimum-loss network reconfiguration: A minimum spanning tree problem" Sustain. Energy Grids Netw. vol. 1 pp. 1-9 Mar. 2015 [online] Available: http://www.sciencedirect.com/science/article/pii/S2352467714000022.