Model of the electric network based on the fractal-cluster principle

Energy systems with a significant share of distributed generation in modern energy play an increasingly important role and contribute to the green transition. In the Ukrainian energy sector, the introduction of distributed generation also occurs under conditions of military influence on energy infrastructure facilities, which additionally forces the distribution of generation facilities across the territory of the respective regions of the country. The fundamental difference between distributed generation systems and traditional power systems with concentrated generating capacities is the consumption of energy at the place of its generation. This sets the task of reviewing the general principles of building the configuration of electrical networks. The idealized model of the branched electrical network of the power system with distributed generation is proposed in the work, which takes into account the features of systems with distributed generation. This model is based on the fractal-cluster principle of forming the configuration of electrical networks. It is proposed to build an electrical distribution network based on a regular fractal. The assumptions and limitations of the model are defined. Modeling of the structure and configuration of electrical networks was carried out. The electrical power of the underlying network cluster is determined. The basic fractal properties of the proposed idealized distribution network model are determined. Circuit solutions of unified node substations and basic network cluster are proposed.

Keywords:

distributed generation, fractal-cluster principle, electrical networks, unified substation circuits, determination of optimum voltage, configuration of electrical networks

References

[1] Aldaikh, S. O., et al.: Study of starting modes of single-phase induction motors when changing the parameters of the stator windings, phase-shifting capacitor and supply voltage. Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 14(2), 2024, 34–41 [https://doi.org/10.35784/iapgos.5928]. DOI: https://doi.org/10.35784/iapgos.5928

[2] Alhamrouni I., et al.: A Comprehensive review on the role of artificial intelligence in power system stability, control, and protection: Insights and future directions. Applied Sciences 14(14), 2024, 6214. [https://doi.org/10.3390/app14146214]. DOI: https://doi.org/10.3390/app14146214

[3] Amrane A. A., Retiere N., Riu D. M.: New modeling of electrical power networks using fractal geometry. 14th International Conference on Harmonics and Quality of Power – ICHQP 2010, Bergamo, Italy, 2010, 1–5 [https://doi.org/10.1109/ICHQP.2010.5625440]. DOI: https://doi.org/10.1109/ICHQP.2010.5625440

[4] Babič M., et al.: A new method of quantifying the complexity of fractal networks. Fractal Fract. 6, 2022, 282 [https://doi.org/10.3390/fractalfract6060282]. DOI: https://doi.org/10.3390/fractalfract6060282

[5] Budanov P. F., Brovko K. Yu.: Fractal-cluster analysis method for detecting disturbances in the operation of electric power equipment of power facilities. Visnic of the Kharkov National Technical University of Agriculture named after Peter Vasilenko. Technical sciences. Problems of energy security and energy saving in the agro-industrial complex of Ukraine 187, 2017, 92–94.

[6] Budanov P., et al.: Building a model of damage to the fractal structure of the shell of the fuel element of a nuclear reactor. Eastern-European Journal of Enterprise Technologies 4(8(118)), 2022, 60–70 [https://doi.org/10.15587/1729-4061.2022.263374]. DOI: https://doi.org/10.15587/1729-4061.2022.263374

[7] Castillo O., Melin P.: Hybrid intelligent systems for time series prediction using neural networks, fuzzy logic, and fractal theory. IEEE Transactions on Neural Networks 13(6), 2002, 1395–1408 [https://doi.org/10.1109/TNN.2002.804316]. DOI: https://doi.org/10.1109/TNN.2002.804316

[8] Florea G.: A Fractal Model for Power Smart Grids. 20th International Conference on Control Systems and Computer Science, Bucharest, Romania, 2015, 572–577 [https://doi.org/10.1109/CSCS.2015.104]. DOI: https://doi.org/10.1109/CSCS.2015.104

[9] Heshmatzadeh M., Lotfi-Neyestanak A. A., Noghanian S.: Improving Wireless Power Transfer Efficiency Using Fractal Metamaterial for Wearable Applications. IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (USNC-URSI), Portland, OR, USA, 2023, 535–536 [https://doi.org/10.1109/USNC-URSI52151.2023.10237506]. DOI: https://doi.org/10.1109/USNC-URSI52151.2023.10237506

[10] Hou H., et al.: Electric power network fractal and its relationship with power system fault. Zhaoyang Tehnički vjesnik 22(3), 2015, 623–628 [https://doi.org/10.17559/TV-20150427180553]. DOI: https://doi.org/10.17559/TV-20150427180553

[11] Huang S.-J., Lin J.-M.: Application of box counting method-based fractal geometry technique for disturbance detection in power systems. IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491), Toronto, ON, Canada 3, 2003, 1604–1608 [https://doi.org/10.1109/PES.2003.1267395]. DOI: https://doi.org/10.1109/PES.2003.1267395

[12] Khasawneh A., et al.: Optimal Determination Method of the Transposition Steps of An Extra-High Voltage Power Transmission Line. Energies 14, 2021, 6791 [https://doi.org/10.3390/en14206791]. DOI: https://doi.org/10.3390/en14206791

[13] Khomenko I. V. et al.: Electricity of Ukraine. Structure, management, innovation. NTU KhPI, LLC Planet-Print, Kharkiv 2020.

[14] Sang-Hoon Kim. Fractal structure of a white cauliflower. Journal of the Korean Physical Society 46(2), 2005, 474–477.

[15] Lezhnyuk P. D., Komar V. A., Sikorskaya O. V.: Distributed generation in the tasks of improving the energy efficiency of distribution electrical networks. VNTU, Vinnitsa 2023.

[16] Li B.-G., Yu Z.-G., Zhou Y.: Fractal and multifractal properties of a family of fractal networks. J. Stat. Mech. Theory Exp. 2, 2014, P02020 [https://doi.org/10.1088/1742-5468/2014/02/P02020]. DOI: https://doi.org/10.1088/1742-5468/2014/02/P02020

[17] Liu C., Li D.: The Chaos and Fractal Characteristics and Predication of Shearer Load Power. International Conference on Electrical and Control Engineering, Wuhan, China, 2010, 5696–5699 [https://doi.org/10.1109/iCECE.2010.1384]. DOI: https://doi.org/10.1109/iCECE.2010.1384

[18] Ma J., Wang Z.: Application of Grille Fractal in Identification of Current Transformer Saturation. Power System Technology 31(14), 2007, 84–88.

[19] Mamishev A., Russell Carl D., Benner L.: Analysis of High Impedance Faults Using Fractal Techniques. IEEE Transactions on Power Systems 11(1), 1996, 435–440 [https://doi.org/10.1109/59.486130]. DOI: https://doi.org/10.1109/59.486130

[20] Markowska K., et al.: Analysis and improvement of power quality in the onboard electrical power systems within a self-propelled floating crane. International Journal of Electrical Power & Energy Systems, 161, 2024, 110179 [https://doi.org/10.1016/j.ijepes.2024.110179]. DOI: https://doi.org/10.1016/j.ijepes.2024.110179

[21] Miroshnyk O., et al.: Investigation of Smart Grid Operation Modes with Electrical Energy Storage System. Energies 16, 2023, 2638. [https://doi.org/10.3390/en16062638]. DOI: https://doi.org/10.3390/en16062638

[22] Nurujjaman A. H., Payer A.: A Review of Fractals Properties: Mathematical Approach. Science Journal of Applied Mathematics and Statistics 5(3), 2017, 98–105 [https://doi.org/10.11648/j.sjams.20170503.11]. DOI: https://doi.org/10.11648/j.sjams.20170503.11

[23] Ortjohann E., et al.: Cluster fractal model - A flexible network model for future power systems. International Conference on Clean Electrical Power (ICCEP), June 2013, 293–297 [https://doi.org/10.1109/ICCEP.2013.6587004]. DOI: https://doi.org/10.1109/ICCEP.2013.6587004

[24] Sidqi Y., et al.: Comparing fractal indices of electric networks to roads and buildings: The case of Grenoble (France). Physica A: Statistical Mechanics and its Applications 531, 2019, 121774 [https://doi.org/10.1016/j.physa.2019.121774]. DOI: https://doi.org/10.1016/j.physa.2019.121774

[25] Song C., Havlin S., Makse H. A.: Origins of Fractality in the Growth of Complex Networks. Nat. Phys. 2 2006, 275–281 [https://doi.org/10.1038/nphys266]. DOI: https://doi.org/10.1038/nphys266

[26] Wang F., et al.: Fractal Characteristics Analysis of Blackouts in Interconnected Power Grid. IEEE Transactions on Power Systems 33(1), 1085–1086 [https://doi.org/10.1109/TPWRS.2017.2704901]. DOI: https://doi.org/10.1109/TPWRS.2017.2704901

[27] Wang Z., Ma J.: A Novel Method to Identify Inrush Current Based on Grille Fractal. Power System Technology 31(11), 2007, 63–68.

[28] Wu Z., et al.: Patrol robot path planning in nuclear power plant using an interval multi-objective particle swarm optimization algorithm. Applied Soft Computing 116, 2022, 108192 [https://doi.org/10.1016/j.asoc.2021.108192]. DOI: https://doi.org/10.1016/j.asoc.2021.108192

[29] Yang G., et al: Typical Power Quality Disturbance Identification Based on Fractal Box Dimension. International Workshop on Chaos-Fractals Theories and Applications, Shenyang, China, 2009, 412–416 [https://doi.org/10.1109/IWCFTA.2009.93]. DOI: https://doi.org/10.1109/IWCFTA.2009.93

[30] Zengping W., Jing M.: A New Adaptive Method to Identify Inrush Using Grille Fractal. IEEE Power Engineering Society General Meeting, Tampa, FL, USA, 2007, 1–5 [https://doi.org/10.1109/PES.2007.386041]. DOI: https://doi.org/10.1109/PES.2007.386041

[31] Zhu H., Ji C.: Fractal theory and its applications. Science Press, Beijing 2011.

Al_Issa, H. A., Cherniuk, A., Oliinyk, Y., Iegorov, O., Iegorova, O., Miroshnyk, O., … Halko, S. (2025). Model of the electric network based on the fractal-cluster principle. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 15(2), 110–117. https://doi.org/10.35784/iapgos.7380

Model of the electric network based on the fractal-cluster principle

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