eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Bivariate stochastic model of current harmonic analysis in the low voltage distribution grid; pp. 190–206

Full article in PDF format | 10.3176/proc.2021.2.08

Muhammad Naveed Iqbal, Lauri Kütt, Kamran Daniel, Marek Jarkovoi, Bilal Asad, Noman Shabbir


This paper presents a bottom-up bivariate analysis approach to estimate current harmonics by taking account of network and load variations. The current harmonics assessment in the presence of existing and future nonlinear loads is vital to study their impact on the distribution grid. The traditional harmonic analysis models consider only stable loads while neglecting the harmonic interaction among the devices. Modern nonlinear loads operate under different working modes and configurations. Thermal stability, harmonic cancellation, and dynamic network parameters influence the current harmonic estimations. In this paper, a probabilistic approach is presented to model harmonic emission in the low voltage distribution grid under network and load uncertainties. A case study is used to demonstrate effectiveness of the proposed model.


1. Pierce, L. W. Transformer design and application considerations for nonsinusoidal load currents. IEEE Trans. Ind. Appl., 1996, 32(3), 633–645.

2. Shareghi, M., Phung, B. T., Naderi, M. S., Blackburn, T. R. and Ambikairajah, E. Effects of current and voltage harmonics on distribution transformer losses. In Proceedings of the IEEE International Conference on Condition Monitoring and Diagnosis, Bali, Indonesia, September 23–27, 2012. IEEE, 2013, 633–636.

3. Czarnecki, L. S. Comments on active power flow and energy accounts in electrical systems with nonsinusoidal waveforms and asymmetry. IEEE Trans. Power Delivery, 1996, 11(3), 1244–1250.

4. Watson, N. R., Scott, T. L. and Hirsch, S. J. J. Implications for distribution networks of high penetration of compact fluorescent lamps. IEEE Trans. Power Delivery, 2009, 24(3), 1521–1528.

5. Clement-Nyns, K., Haesen, E. and Driesen, J. The impact of charging plug-in hybrid electric vehicles on a residential distribution grid. IEEE Trans. Power Syst., 2010, 25(1), 371–380.

6. Iqbal, M. N., Jarkovoi, M., Kütt, L. and Shabbir, N. Impact of LED thermal stability to household lighting harmonic load current modeling. In Proceedings of Electric Power Quality and Supply Reliability Conference (PQ) & Symposium on Electrical Engineering and Mechatronics (SEEM), Kärdla, Estonia, June 12–15, 2019. IEEE, 2019, 1–6.

7. Jarkovoi, M., Iqbal, M. N. and Kütt, L. Analysis of harmonic current stability and summation of LED lamps. In Proceedings of Electric Power Quality and Supply Reliability Conference (PQ) & Symposium on Electrical Engineering and Mechatronics (SEEM), Kärdla, Estonia, June 12–15, 2019. IEEE, 2019, 18957598.

8. Hansen, S., Nielsen, P. and Blaabjerg, F. Harmonic cancellation by mixing nonlinear single-phase and three-phase loads. IEEE Trans. Ind. Appl., 2000, 36(1), 152–159.

9. Chakravorty, D., Meyer, J., Schegner, P., Yanchenko, S. and Schocke, M. Impact of modern electronic equipment on the assessment of network harmonic impedance. IEEE Trans. Smart Grid, 2017, 8(1), 382–390.

10. Henao-Muñoz, A. C. and Saavedra-Montes, A. J. Comparison of two mathematical models for nonlinear residential loads. In Proceedings of the 17th International Conference on Harmonics and Quality of Power (ICHQP), Belo Horizonte, Brazil, October 16–19, 2016.

11. Blanco, A. M., Yanchenko, S., Meyer, J. and Schegner, P. Impact of supply voltage distortion on the current harmonic emission of non-linear loads. DYNA, 2015, 82(192), 150–159.

12. Koch, A. S., Myrzik, J. M. A., Wiesner, T. and Jendernalik, L. Evaluation and validation of Norton approaches for nonlinear harmonic models. InProceedings of IEEE Grenoble Conference PowerTech, Grenoble, France, June 16–20, 2013. IEEE, 2013, 1–6.

13. Almeida, C. F. M. and Kagan, N. Harmonic coupled norton equivalent model for modeling harmonic-producing loads. In Proceedings of the 14th International Conference on Harmonics and Quality of Power – ICHQP 2010, Bergamo, Italy, September 26–29, 2010. IEEE, 2010, 1–9.

14. Ahmed, E. E., Xu, W. and Zhang, G. Analyzing systems with distributed harmonic sources including the attenuation and diversity effects. IEEE Trans. Power Delivery, 2005, 20(4), 2602–2612.

15. Cunill-Sola, J. and Salichs, M. Study and characterization of waveforms from low-watt (<25 W) compact fluorescent lamps with electronic ballasts. IEEE Trans. Power Delivery, 2007, 22(4), 2305–2311.

16. Baghzouz, Y. and Tan, O. T. Probabilistic modeling of power system harmonics. IEEE Trans. Ind. Appl., 1987, IA-23(1), 173–180.

17. Ye, G., Nijhuis, M., Cuk, V. and Cobben, J. F. G. Stochastic residential harmonic source modeling for grid impact studies. Energies, 2017, 10(3), 372.

18. Salles, D., Jiang, C., Xu, W., Freitas, W. and Mazin, H. E. Assessing the collective harmonic impact of modern residential loads–Part I: methodology. IEEE Trans. Power Delivery, 2012, 27(4), 1937–1946.

19. Caramia, P., Proto, D., Russo, A. and Varilone, P. Probabilistic harmonic analysis for waveform distortion assessment of low voltage distribution systems with plug-in hybrid electric vehicles. In Proceedings of the 1st International Conference on Energy Transition in the Mediterranean Area (SyNERGY MED), Cagliari, Italy, May 28–30, 2019. IEEE, 2019, 1–6.

20. Au, M. T. and Milanović, J. V. Establishing harmonic distortion level of distribution network based on stochastic aggregate harmonic load models. IEEE Trans. Power Delivery, 2007, 22(2), 1086–1092.

21. Au, M. T. and Milanović, J. V. Stochastic assessment of harmonic distortion level of medium voltage radial distribution network. In Proceedings of the 9th International Conference on Probabilistic Methods Applied to Power Systems, Stockholm, Sweden, June 11–15, 2006. IEEE, 2007, 1–6.

22. Au, M. T. and Milanović, J. V. Development of stochastic aggregate harmonic load model based on field measurements. IEEE Trans. Power Delivery, 2007, 22(1), 323–330.

23. Jarkovoi, M., Kütt, L. and Iqbal, M. N. Probabilistic bivariate modeling of harmonic current. In Proceedings of the 19th International Conference on Harmonics and Quality of Power (ICHQP), Dubai, United Arab Emirates, July 6–7, 2020. IEEE, 2020, 1–6.

24. Nasrfard-Jahromi, F. and Mohammadi, M. Probabilistic harmonic load flow using an improved kernel density estimator. International Journal of Electrical Power and Energy Systems, 2016, 78, 292–298.

25. Ray, S. and Lindsay, B. G. The topography of multivariate normal mixtures. Ann. Stat., 2005, 33(5), 2042–2065.

26. Meyer, J. and Schegner, P. Characterization of power quality in low voltage networks based on modeling by mixture distributions. In Proceedings of the 9th International Conference on Probabilistic Methods Applied to Power Systems, PMAPS, Stockholm, Sweden, June 11–15, 2006. IEEE, 2007.

27. Botev, Z. I., Grotowski, J. F. and Kroese, D. P. Kernel density estimation via diffusion. Ann. Statist., 2010, 38(5), 2916–2957.

28. Wȩglarczyk, S. Kernel density estimation and its application. ITM Web of Conferences, 2018, 23, 00037. 20182300037

29. Nasrfard-Jahromi, F. and Mohammadi, M. A sampling-based method using an improved nonparametric density estimator for probabilistic harmonic load flow calculation. Turk. J. Elec. Eng. Comp. Sci., 2016, 24, 51113–5123.

30. Li, Z., Hu, H., Wang, Y., Tang, L., He, Z. and Gao, S. Probabilistic harmonic resonance assessment considering power system uncertainties. IEEE Trans. Power Delivery, 2018, 33(6), 2989–2998.

31. Sainz, L. and Balcells, J. Harmonic interaction influence due to current source shunt filters in networks supplying nonlinear loads. IEEE Trans. Power Delivery, 2012, 27(3), 1385–1393.

32. Barmada, S., Musolino, A., Raugi, M. and Tucci, M. Analysis of power lines uncertain parameter influence on power line communications. IEEE Trans. Power Delivery, 2007, 22(4), 2163–2171.

33. Preece, R. and Milanović, J. V. Efficient estimation of the probability of small-disturbance instability of large uncertain power systems. IEEE Trans. Power Systems, 2016, 31(2), 1063–1072.

34. Abu-Hashim, R., Burch, R., Chang, G., Grady, M., Gunther, E., Halpin, M. et al. Test systems for harmonics modeling and simulation. IEEE Trans. Power Delivery, 1999, 14(2), 579–587.

35. Morales, J. M. and Pérez-Ruiz, J. Point estimate schemes to solve the probabilistic power flow. IEEE Trans. Power Syst., 2007, 22(4), 1594–1601.

36. Pinceti, P. and Prando, D. Sensitivity of parallel harmonic filters to parameters variations. Int. J. Electr. Power Energy Syst., 2015, 68, 26–32.

37. Iqbal, M. N., Kütt, L., Asad, B., Shabbir, N. and Rasheed, I. Time-dependent variations in current harmonic emission by LED lamps in the low-voltage network. Electr. Eng., 2020, 101(25), 1277–1293.

38. Iqbal, M. N., Kütt, L., Asad, B., Vaimann, T., Rassõlkin, A. and Demidova, G. L. Time dependency of current harmonics for switch-mode power supplies. Appl. Sci., 2020, 10(21), 7806.

39. Iqbal, M. N. and Lauri, K. Impact of cable impedance on the harmonic emission of LED lamps. In Proceedings of the 21st International Scientific Conference on Electric Power Engineering (EPE), Prague, Czech Republic, October 19–21, 2020. IEEE, 2020, 1–5.

40. Sun, K., Yan, D., Hong, T. and Guo, S. Stochastic modeling of overtime occupancy and its application in building energy simulation and calibration. Build. Environ., 2014, 79, 1–12.

41. Yoshino, H., Hong, T. and Nord, N. IEA EBC annex 53: Total energy use in buildings–analysis and evaluation methods. Energy Build., 2017, 152, 124–136.

42. Sonderegger, R. C. Movers and stayers: The resident’s contribution to variation across houses in energy consumption for space heating. Energy Build., 1978, 1(3), 313–324.

43. Feng, X., Yan, D. and Hong, T. Simulation of occupancy in buildings. Energy Build., 2015, 87, 348–359.

44. Iqbal, M. N. and Kütt, L. End-user electricity consumption modelling for power quality analysis in residential building. In Proceedings of the 19th International Scientific Conference on Electric Power Engineering (EPE), Brno, Czech Republic, May 16–18, 2018. IEEE, 2018, 1–6.

45. Ofetotse, E. L., Essah, E. A. and Yao, R. Domestic energy models: complexities in defining specific tools. In Proceedings of the International Conference of SuDBE2013, Chongqing, China, October 25–28, 2013. 

46. Causone, F., Carlucci, S., Ferrando, M., Marchenko, A. and Erba, S. A data-driven procedure to model occupancy and occupantrelated electric load profiles in residential buildings for energy simulation. Energy Build., 2019, 202, 109342.

47. Tekler, Z. D., Low, R. and Blessing, L. Using smart technologies to identify occupancy and plug-in appliance interaction patterns in an office environment.IOP Conf. Ser.: Mater. Sci. Eng., 2019, 609(6), 062010.

48. Molina-Markham, A., Shenoy, P., Fu, K., Cecchet, E. and Irwin, D. Private memoirs of a smart meter. In BuildSys’10: Proceedings of the 2nd ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Buildings, Zurich, Switzerland, November 2, 2010. ACM, New York, NY, 2010, 61–66.

49. Kleiminger, W., Beckel, C. and Santini, S. Household occupancy monitoring using electricity meters. In UbiComp 2015: Proceedings of the ACM International Joint Conference on Pervasive and Ubiquitous Computing, Osaka, Japan, September 7–11, 2015. ACM, New York, NY, 2015, 975–986.

50. Richardson, I., Thomson, M. and Infield, D. A high-resolution domestic building occupancy model for energy demand simulations. Energy Build., 2008, 40(8), 1560–1566.

Back to Issue