A Technical Review on the Conventional Analytical Techniques for Optimal Load Flow Investigation on Distribution Feeder Systems Network

Authors

  • Kelechi Nworah Department of Electrical/Electronic Engineering, University of Port Harcourt, Rivers State, Nigeria
  • Eyo Sunday Abia Department of Electrical/Electronic Engineering, University of Cross River State, Calabar, Cross River State, Nigeria
  • Imoh Ime Ekanem * Department of Mechanical Engineering Technology, Akwa Ibom State Polytechnic, Ikot Osurua, Nigeria

https://doi.org/10.22105/opt.vi.70

Abstract

This technical review provides a comprehensive overview of conventional analytical techniques employed for Optimal Load Flow (OLF) investigation in distribution feeder systems. OLF is crucial for efficient power network operation, especially given the unique challenges of radial or weakly meshed distribution networks, distributed generation (DG), and dynamic load profiles. The review details the methodologies, advantages, and limitations of four key conventional methods: Newton-Raphson, Fast Decoupled Load Flow and Gauss-Seidel. While Newton-Raphson offers accuracy and fast convergence, its computational intensity can be a drawback for large systems. The Fast Decoupled Load Flow provides a quicker alternative with potential accuracy trade-offs. The Gauss-Seidel method is simple but suffers from slow and unreliable convergence. The Backward/Forward Sweep method is highlighted as particularly efficient and robust for radial distribution systems due to its non-matrix inversion approach. The study also investigates critical challenges in distribution OLF, voltage regulation, DG integration, load variability, feeder reconfiguration, and loss minimization. The conclusion emphasizes that while these conventional methods form a foundational basis, future advancements often involve their integration with advanced optimization algorithms and uncertainty management techniques to address the increasing complexities of modern smart grids.

Keywords:

Optimal load flow, distribution feeder, analytical techniques, systems network

References

  1. [1] Okachi, S. E., Ogar, V. N., Bendor, S. A., Nkpeh, E. E., Ijeoma, E, E., Acha, G. O. and Ugochukwu, P. O. (2024). Automatic Power Factor Correction of Distribution Feeder in Calabar Metropolis (A Case Study of Federal Housing Feeder). International Research Journal of Modernization in Engineering Technology and Science, 6(4), 8608-8639.

  2. [2] Afolabi, O. A., Ali, W, H., Cofie, P., Fuller, J., Obiomon, O and Kolawole, E. S. (2015). Analysis of the Load Flow Problem in Power System Planning Studies. Energy and Power Engineering 7(10) 509-523.

  3. [3] Kabalci, E. (2017). Reactive Power Compensation in AC Power Systems. In: Mahdavi Tabatabaei, N., Jafari Aghbolaghi, A., Bizon, N., Blaabjerg, F. (eds) Reactive Power Control in AC Power Systems. Power Systems. 275 - 315 Springer, Online ISBN: 978-3-319-51118-4.

  4. [4] Chakraborty, K. and Chakrabarti, A. (2015). Load Flow Studies. In: Soft Computing Techniques in Voltage Security Analysis. Energy Systems in Electrical Engineering. Springer, 11-57.

  5. [5] Broderick, R. J., Quiroz, J. E., Ellis, A., Reno, M. J., Smith, J. and Dugan, R. (2013). Time series power flow analysis for distribution connected PV generation (No. SAND2013-0537). Sandia National Lab. (SNL-NM), Albuquerque, NM (United States).

  6. [6] Karimi, M., Mokhlis, H., Naidu, K., Uddin, S. and Bakar, A. A. (2016). Photovoltaic penetration issues and impacts in distribution network-A review. Renewable and Sustainable Energy Reviews, 53, 594-605.

  7. [7] Resener, M., Haffner, S., Pereira, L. A., and Pardalos, P. M. (2018). Optimization techniques applied to planning of electric power distribution systems: a bibliographic survey. Energy Systems, 9, 473-509.

  8. [8] Thakurta, P. G., Belmans, R. and Van Hertem, D. (2015). Risk-based management of overloads caused by power injection uncertainties using power flow controlling devices. IEEE Transactions on Power Systems, 30(6), 3082-3092.

  9. [9] Haider, Z. M., Mehmood, K. K., Khan, S. U., Khan, M. O., Wadood, A. and Rhee, S. B. (2021). Optimal management of a distribution feeder during contingency and overload conditions by harnessing the flexibility of smart loads. IEEE Access, 9, 40124-40139.

  10. [10] Bottler, S. and Weindl, C. (2023). State-Space Load Flow Calculation of an Energy System with Sector-Coupling Technologies. Energies, 16(12), 4803.

  11. [11] Subedi, S., Rauniyar, M., Ishaq, S., Hansen, T. M., Tonkoski, R., Shirazi, M. and Cicilio, P. (2021). Review of methods to accelerate electromagnetic transient simulation of power systems. IEEE Access, 9, 89714-89731. Supercomputing, 69 (1), 200 - 224.

  12. [12] Awad, N. H., Ali, M. Z., Mallipeddi, R., and Suganthan, P. N. (2019). An efficient differential evolution algorithm for stochastic OPF based active–reactive power dispatch problem considering renewable generators. Applied Soft Computing, 76, 445-458.

  13. [13] Monyei, C. G., Adewumi, A. O., Obolo, M. O. and Sajou, B. (2018). Nigeria's energy poverty: Insights and implications for smart policies and framework towards a smart Nigeria electricity network. Renewable and Sustainable Energy Reviews, 81, 1582-1601.

  14. [14] Sarnari, A. J. (2019). Numerically Robust Load Flow Techniques in Power System Planning (Doctoral dissertation).

  15. [15] Ismail, B., Wahab, N. I. A., Othman, M. L., Radzi, M. A. M., Vijyakumar, K. N., and Naain, M. N. M. (2020). A comprehensive review on optimal location and sizing of reactive power compensation using hybrid-based approaches for power loss reduction, voltage stability improvement, voltage profile enhancement and loadability enhancement. IEEE Access, 8, 222733-222765.

  16. [16] Papazoglou, G. and Biskas, P. (2023). Review and comparison of genetic algorithm and particle swarm optimization in the optimal power flow problem. Energies, 16(3), 1152.

  17. [17] Arefin, A. A., Baba, M., Singh, N. S. S., Nor, N. B. M., Sheikh, M. A., Kannan, R. and Mathur, N. (2022). Review of the techniques of the data analytics and islanding detection of distribution systems using phasor measurement unit data. Electronics, 11(18), 2967.

  18. [18] Kazmi, S. A. A., Shahzad, M. K., Khan, A. Z., & Shin, D. R. (2017). Smart distribution networks: A review of modern distribution concepts from a planning perspective. Energies, 10(4), 501.

  19. [19] Theo, W. L., Lim, J. S., Ho, W. S., Hashim, H. and Lee, C. T. (2017). Review of distributed generation (DG) system planning and optimization techniques: Comparison of numerical and mathematical modelling methods. Renewable and Sustainable Energy Reviews, 67, 531-573.

  20. [20] Adefarati, T., and Bansal, R. C. (2017). Reliability assessment of distribution system with the integration of renewable distributed generation. Applied energy, 185, 158-171.

  21. [21] El-Hawary, M. E. (2014). The smart grid—state-of-the-art and future trends. Electric Power Components and Systems, 42(3-4), 239-250.

  22. [22] Krishnan, V., Ho, J., Hobbs, B. F., Liu, A. L., McCalley, J. D., Shahidehpour, M. and Zheng, Q. P. (2016). Co-optimization of electricity transmission and generation resources for planning and policy analysis: review of concepts and modeling approaches. Energy Systems, 7, 297-332.

  23. [23] Keane, A., Ochoa, L. F., Borges, C. L., Ault, G. W., Alarcon-Rodriguez, A. D., Currie, R. A. and Harrison, G. P. (2012). State-of-the-art techniques and challenges ahead for distributed generation planning and optimization. IEEE Transactions on Power Systems, 28(2), 1493-1502.

  24. [24] Viral, R. and Khatod, D. K. (2012). Optimal planning of distributed generation systems in distribution system: A review. Renewable and sustainable energy Reviews, 16(7), 5146-5165.

  25. [25] Sendin, A., Peña, I. and Angueira, P. (2014). Strategies for power line communications smart metering network deployment. Energies, 7(4), 2377-2420.

  26. [26] Yin, S. A. and Lu, C. N. (2009). Distribution feeder scheduling considering variable load profile and outage costs. IEEE Transactions on power systems, 24(2), 652-660.

  27. [27] Walling, R. A., Saint, R., Dugan, R. C., Burke, J. and Kojovic, L. A. (2008). Summary of distributed resources impact on power delivery systems. IEEE Transactions on power delivery, 23(3), 1636-1644.

  28. [28] Dugan, R. C. and McDermott, T. E. (2001). Operating conflicts for distributed generation on distribution systems. Rural Electric Power Conference. Papers Presented at the 45th Annual Conference (Cat. No. 01CH37214) (pp. A3-1). IEEE.

  29. [29] Trias, A. (2012). The holomorphic embedding load flow method. In 2012 IEEE Power and Energy Society General Meeting 1-8. IEEE.

  30. [30] Goswami, G. and Goswami, P. K. (2021). A design analysis and implementation of PI, PID and fuzzy supervised shunt APF at nonlinear load application to improve power quality and system reliability. International Journal of System Assurance Engineering and Management, 12(6), 1247-1261.

  31. [31] Yazdavar, A. H., Shaaban, M. F., El-Saadany, E. F., Salama, M. M. and Zeineldin, H. H. (2020). Optimal planning of distributed generators and shunt capacitors in isolated microgrids with nonlinear loads. IEEE Transactions on Sustainable Energy, 11(4), 2732-2744.

  32. [32] Amrr, S. M., Asghar, M. J., Ashraf, I. and Meraj, M. (2020). A comprehensive review of power flow controllers in interconnected power system networks. IEEE Access, 8, 18036-18063.

  33. [33] Vaiman, Chen, Chowdhury, Dobson, Hines, Papic and Zhang. (2011). Risk assessment of cascading outages: Methodologies and challenges. IEEE Transactions on Power Systems, 27(2), 631-641.

  34. [34] Dashti, R., Daisy, M., Mirshekali, H., Shaker, H. R. and Aliabadi, M. H. (2021). A survey of fault prediction and location methods in electrical energy distribution networks. Measurement, 184, 109947.

  35. [35] Amin, S. M. (2011). Smart grid: Overview, issues and opportunities. Advances and challenges in sensing, modeling, simulation, optimization and control. European Journal of Control, 17(5-6), 547-567.

  36. [36] Husain, T. and Ansari, M. M. (2016). Distribution Load Flow Analysis for Radial and Mesh Distribution System. International Journal of Electrical Engineering and Technology (IJEET), 7(3).

  37. [37] Moradi, M. H., Foroutan, V. B. and Abedini, M. (2017). Power flow analysis in islanded Micro-Grids via modeling different operational modes of DGs: A review and a new approach. Renewable and Sustainable Energy Reviews, 69, 248-262.

  38. [38] Shakarami, M. R., Beiranvand, H., Beiranvand, A. and Sharifipour, E. (2017). A recursive power flow method for radial distribution networks: Analysis, solvability and convergence. International Journal of Electrical Power & Energy Systems, 86, 71-80.

  39. [39] Yan, P. and Sekar, A. (2005). Analysis of radial distribution systems with embedded series FACTS devices using a fast line flow-based algorithm. IEEE Transactions on Power Systems, 20(4), 1775-1782.

  40. [40] Conejo, A. J. and Baringo, L. (2018). Power system operations. New York: Springer. 14(54).

  41. [41] De Mel, I., Klymenko, O. V., and Short, M. (2022). Balancing accuracy and complexity in optimization models of distributed energy systems and microgrids with optimal power flow: A review. Sustainable Energy Technologies and Assessments, 52, 102066.

  42. [42] Raza, M. (2014). Load Flow Calculation and Its Application. Power Factory Applications for Power System Analysis, 1-25.

  43. [43] Zad, B. B., Hasanvand, H., Lobry, J. and Vallée, F. (2015). Optimal reactive power control of DGs for voltage regulation of MV distribution systems using sensitivity analysis method and PSO algorithm. International Journal of Electrical Power & Energy Systems, 68, 52-60.

  44. [44] Kulworawanichpong, T. (2010). Simplified Newton–Raphson power-flow solution method. International Journal of electrical power & energy systems, 32(6), 551-558.

  45. [45] Lee, J. O., Kim, Y. S., & Jeon, J. H. (2022). Generic power flow algorithm for bipolar DC microgrids based on Newton–Raphson method. International Journal of Electrical Power & Energy Systems, 142, 108357.

  46. [46] Swain, A., Abdellatif, E., Mousa, A., & Pong, P. W. (2022). Sensor Technologies for Transmission and Distribution Systems: A Review of the Latest Developments. Energies, 15(19), 7339.

  47. [47] Mousa, H. H., Mahmoud, K. and Lehtonen, M. (2024). A Comprehensive Review on Recent Developments of Hosting Capacity Estimation and Optimization for Active Distribution Networks. IEEE Access.

  48. [48] Shi, Zhongtuo, Wei Yao, Zhouping Li, Lingkang Zeng, Yifan Zhao, Runfeng Zhang, Yong Tang, and Jinyu Wen. (2020). Artificial intelligence techniques for stability analysis and control in smart grids: Methodologies, applications, challenges and future directions. Applied Energy 278:115733.

  49. [49] Jereminov, M., Pandey, A., Song, H. A., Hooi, B., Faloutsos, C. and Pileggi, L. (2017). Linear load model for robust power system analysis. IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), 1-6. IEEE.

  50. [50] Pandey, A., Jereminov, M., Wagner, M. R., Bromberg, D. M., Hug, G. and Pileggi, L. (2018). Robust power flow and three-phase power flow analyses. IEEE Transactions on Power Systems, 34(1), 616-626.

  51. [51] Alayande, A. S., Jimoh, A. A. and Yusuff, A. A. (2017). Approaches for solving modern power system problems-A review. 2017 IEEE AFRICON, 1214-1219.

  52. [52] Abbasi, A. R. and Mohammadi, M. (2023). Probabilistic load flow in distribution networks: An updated and comprehensive review with a new classification proposal. Electric Power Systems Research, 222, 109497.

  53. [53] Adejumobi, I. A., Adepoju, G. A. and Hamzat, K. A. (2013). Iterative techniques for load flow study: A comparative study for Nigerian 330kv grid system as a case study. International Journal of Engineering and Advanced Technology (IJEAT), 3(1), 153-158.

  54. [54] Barrenechea, R., de Vicuña, L. G., Castilla, M., Rypin, F. and Paiva-Mata, P. (2022). Variations of the Gauss Seidel and the gauss implicit z-bus load flow methods for primary-secondary integrated distribution grids. Electric Power Systems Research, 210, 108061.

  55. [55] Alnabi, L. A., Dhaher, A. K. and Essa, M. B. (2022). Optimal Allocation of Distributed Generation with Reconfiguration by Genetic Algorithm Using Both Newton Raphson and Gauss Seidel Methods for Power Losses Minimizing. International Journal of Intelligent Engineering & Systems, 15(1).

  56. [56] Awad, M. (2023). Investigating the Best Methods to solve linear simultaneous equations and the impact on their high school students' achievement in Algebra: A case study in a private American school in Dubai (Doctoral dissertation, The British University in Dubai).

  57. [57] Montoya, O. D., Gil-González, W. and Garces, A. (2020). Numerical methods for power flow analysis in DC networks: State of the art, methods and challenges. International Journal of Electrical Power & Energy Systems, 123, 106299.

  58. [58] Rangavalli, V. and Komma Lavanya, D. (2022). Analysis of IEEE 33, 34 and 69 Bus Systems using Gauss Seidel. International Journal for Research in Applied Science and Engineering Technology, 10(6), 3867-3871.

  59. [59] Ahmadi, H., Vahidi, B., Aghaee, S. S., Hosseinian, S. H. and Mosallanejad, A. (2020). A New Load-Flow Method in Distribution Networks based on an Approximation Voltage-Dependent Load model in Extensive Presence of Distributed Generation Sources. AUT Journal of Electrical Engineering, 52(2), 133-146.

  60. [60] Teja, B. R., Murty, V. V. S. N. and Kumar, A. (2016). An efficient and simple load flow approach for radial and meshed distribution networks. International Journal of Grid and Distributed Computing, 9(2), 85-102.

  61. [61] Ghosh, S. and Sherpa, K. S. (2008). An efficient method for load− flow solution of radial distribution networks. International Journal of Electrical and Computer Engineering, 2(9), 2094-2101.

  62. [62] Visali, N., Reddy, M. S. K. and Reddy, M. S. (2014). A modified unbalanced load flow solution using branch incidence matrix. I-Manager’s Journal on Electrical Engineering, 7(3), 27.

  63. [63] Portelinha, R. K., Durce, C. C., Tortelli, O. L. and Lourenco, E. M. (2021). Fast-decoupled power flow method for integrated analysis of transmission and distribution systems. Electric Power Systems Research, 196, 107215.

  64. [64] Rafi, F. H. M., Hossain, M. J., Rahman, M. S. and Taghizadeh, S. (2020). An overview of unbalance compensation techniques using power electronic converters for active distribution systems with renewable generation. Renewable and Sustainable Energy Reviews, 125, 109812.

  65. [65] Roald, L., Misra, S., Krause, T. and Andersson, G. (2016). Corrective control to handle forecast uncertainty: A chance constrained optimal power flow. IEEE Transactions on Power Systems, 32(2), 1626-1637.

  66. [66] Kahrobaeian, A. and Mohamed, Y. A. R. I. (2013). Analysis and mitigation of low-frequency instabilities in autonomous medium-voltage converter-based microgrids with dynamic loads. IEEE Transactions on Industrial Electronics, 61(4), 1643-1658.

  67. [67] Ghiasi, M. (2018). A Detailed Study for Load Flow Analysis in Distributed Power System. International Journal of Industrial Electronics, Control and Optimization, 1(2), 153-161.

  68. [68] Guamán, W. P., Pesántez, G. N., Proaño, X. A., Pérez, E. M. and Tigse, W. V. (2021). Power Flow Solution Combining Newton-Raphson and Fast Decoupled Methods. Innovation and Research. CI3, Advances in Intelligent Systems and Computing, 1277. Springer, Cham.

  69. [69] Al‐Jaafreh, M. A. and Mokryani, G. (2019). Planning and operation of LV distribution networks: a comprehensive review. IET Energy Systems Integration, 1(3), 133-146.

  70. [70] Su, J., Lie, T. T. and Zamora, R. (2020). Integration of electric vehicles in distribution network considering dynamic power imbalance issue. IEEE Transactions on Industry Applications, 56(5), 5913-5923.

  71. [71] Táczi, I., Sinkovics, B., Vokony, I. and Hartmann, B. (2021). The challenges of low voltage distribution system state estimation-an application oriented review. Energies, 14(17) 5363.

  72. [72] Dobbe, R., van Westering, W., Liu, S., Arnold, D., Callaway, D. and Tomlin, C. (2019). Linear single-and three-phase voltage forecasting and Bayesian state estimation with limited sensing. IEEE Transactions on Power Systems, 35(3), 1674-1683.

  73. [73] Bizzarri, F., Brambilla, A., Gajani, G. S. and Banerjee, S. (2014). Simulation of real world circuits: Extending conventional analysis methods to circuits described by heterogeneous languages. IEEE Circuits and Systems Magazine, 14(4), 51-70.

  74. [74] Wang, H., Wang, Q., Tang, Y, and Ye, Y. (2022). Spatial load migration in a power system: Concept, potential and prospects. International Journal of Electrical Power and Energy Systems, 140, 107926.

  75. [75] Dashti, R., & Rouhandeh, M. (2023). Power distribution system planning framework (A comprehensive review). Energy strategy reviews, 50, 101256.

  76. [76] Islam, R., Rivin, M. A. H., Sultana, S., Asif, M. A. B., Mohammad, M., & Rahaman, M. (2025). Machine learning for power system stability and control. Results in Engineering, 105355.

  77. [77] Dawn, S., Ramakrishna, A., Ramesh, M., Das, S. S., Rao, K. D., Islam, M. M., & Selim Ustun, T. (2024). Integration of renewable energy in microgrids and smart grids in deregulated power systems: a comparative exploration. Advanced Energy and Sustainability Research, 5(10), 2400088

Published

2025-09-08

Issue

Section

Articles

How to Cite

Nworah, K., Abia, E., & Ekanem, I. (2025). A Technical Review on the Conventional Analytical Techniques for Optimal Load Flow Investigation on Distribution Feeder Systems Network. Optimality. https://doi.org/10.22105/opt.vi.70

Similar Articles

31-40 of 41

You may also start an advanced similarity search for this article.