access icon free Novelty method for the utility harmonic impedance estimation based on Gaussian mixed model

© The Institution of Engineering and Technology
Received 19/09/2019, Accepted 25/03/2020, Revised 26/02/2020, Published 27/03/2020

The accurate estimation of harmonic impedance on the utility side of a point of common coupling (PCC) is much important to harmonic control, harmonic emission level, and harmonic responsibility analysis. In this study, a novel estimation method for the utility harmonic impedance is proposed, which employs the Gaussian mixed model (GMM) to fit the measured data at a PCC, because the authors find that the statistical distribution of the measured data at a PCC is close to the Gaussian distribution. Also, in theory, GMM can approach the probability distribution of any data. In this method, the Norton equivalent circuit model at a PCC is first expressed as a GMM, and the utility harmonic impedance in the GMM is estimated by expectation maximisation iterative method. Compared to the existing estimation methods, an outstanding advantage of this method is that it is less affected by background harmonics; therefore, higher accuracy can be acquired in this method. The effectiveness and accuracy of this method are verified by simulation experiments and field data.

Inspec keywords: Gaussian processes; parameter estimation; equivalent circuits; statistical distributions; Gaussian distribution; power system harmonics; expectation-maximisation algorithm; harmonic analysis; iterative methods; electric impedance; probability

Other keywords: utility harmonic impedance estimation; Norton equivalent circuit model; harmonic control; harmonic emission level; GMM; novelty method; existing estimation methods; Gaussian mixed model; background harmonics; novel estimation method; PCC; expectation maximisation iterative method; harmonic responsibility analysis; Gaussian distribution

Subjects: Other topics in statistics; Other topics in statistics; Interpolation and function approximation (numerical analysis); Power supply quality and harmonics

References

    1. 1)
      • 1. Silva, S.R., Carrano, E.G., Uturbey, W., et al: ‘Evaluating harmonic voltage distortion in load-variating unbalanced networks using Monte Carlo simulations’, IET Gener. Transm. Distrib., 2015, 9, (9), pp. 855–865.
    2. 2)
      • 19. Zhao, X., Yang, H.: ‘A new method to calculate the utility harmonic impedance based on FastICA’, IEEE Trans. Power Deliv., 2016, 31, (1), pp. 381–388.
    3. 3)
      • 6. Yang, H., Pirotte, P., Robert, A.: ‘Harmonic emission levels of industrial loads statistical assessment’. Proc. CIGRE 1996, Paris: International Council on Large Electric Systems, Paris, France, 1996, pp. 36–306.
    4. 4)
      • 4. Zhou, L., Wu, W., Chen, Y., et al: ‘Harmonic voltage distortion damping method for parallel-connected LCL-type inverters in islanded operation’, IEEE Trans. Ind. Electron., 2018, 66, (11), pp. 9032–9044.
    5. 5)
      • 9. Salis, V., Costabeber, A., Cox, S.M., et al: ‘Experimental validation of harmonic impedance measurement and LTP Nyquist criterion for stability analysis in power converter networks’, IEEE Trans. Power Electron., 2019, 34, (8), pp. 7972–7982.
    6. 6)
      • 5. Wang, S., Liu, X., Wang, K., et al: ‘Tracing harmonic contributions of multiple distributed generations in distribution systems with uncertainty’, Int. J. Electr. Power Energy Syst., 2018, 95, pp. 585–591.
    7. 7)
      • 28. Antoneli, F., Passos, F. M., Lopes, L.R., et al: ‘A Kolmogorov–Smirnov test for the molecular clock based on Bayesian ensembles of phylogenies’, PLOS One, 2018, 13, (1), p. e0190826.
    8. 8)
      • 15. Yang, H., Porotte, P., Robert, A.: ‘Assessing the harmonic emission level from one particular customer’. Proc. Third Int. Conf. on Power Quality (ICPQ), Amsterdam, Netherlands, 1994.
    9. 9)
      • 27. Loukas, D., Katerina, S., George, Y.: ‘Capturing the effects of texting on young drivers behaviour based on copula and Gaussian mixture models’, Transp. Res. F, Traffic Psychol. Behav., 2018, 58, pp. 930–943.
    10. 10)
      • 20. Farzad, K., Saeid, E., Seyed, H.H.: ‘Method for determining utility and consumer harmonic contributions based on complex independent component analysis’, IET Gener. Transm. Distrib., 2016, 10, (2), pp. 526–534.
    11. 11)
      • 16. Hui, J., Yang, H., Lin, S., et al: ‘Assessing utility harmonic impedance based on the covariance characteristic of random vectors’, IEEE Trans. Power Deliv., 2010, 25, (3), pp. 1778–1786.
    12. 12)
      • 2. Omran, W.A., El-Goharey, H.S.K., Kazerani, M., et al: ‘Identification and measurement of harmonic pollution for radial and nonradial systems’, IEEE Trans. Power Deliv., 2009, 24, (3), pp. 1642–1650.
    13. 13)
      • 23. Xu, F., Yang, H., Zhao, J., et al: ‘Study on constraints for harmonic source determination using active power direction’, IEEE Trans. Power Deliv., 2018, 33, (6), pp. 2683–2692.
    14. 14)
      • 10. Yunyan, Z., Wei, C., Chun, D., et al: ‘A harmonic measurement mode based on partial least-squares regression method’. Electric Power Conf., Vancouver, BC, Canada, 2008, pp. 1–5.
    15. 15)
      • 25. Wang, L, Zeng, J, Hong, Y.: ‘Estimation of distribution algorithm based on copula theory’. IEEE CEC 2009, Trondheim, 2009, pp. 1057–1063.
    16. 16)
    17. 17)
      • 21. Fei, H., Honggeng, Y.: ‘Harmonic state estimation in power distribution network based on Complex independent component analysis’, Power Syst. Technol., 2014, 38, pp. 3173–3179.
    18. 18)
      • 3. Bhattacharyya, S., Cobben, S., Ribeiro, P., et al: ‘Harmonic emission limits and responsibilities at a point of connection’, IET Gener. Transm. Distrib., 2012, 6, (3), pp. 256–264.
    19. 19)
      • 13. Wang, Y., He, M. Z., Xu, W, et al: ‘Estimating harmonic impact of individual loads using multiple linear regression analysis’, Int. Trans. Electr. Energy Syst., 2016, 26, (4), pp. 809–824.
    20. 20)
      • 26. Strelen, J, Nassaj, F.: ‘Analysis and generation of random vectors with copulas’. Proc. 2007 Winter Simulation Conf. (WSC2007), Washington, 2007, pp. 488–496.
    21. 21)
      • 29. Pfajfar, T., Blazic, B., Papic, I.: ‘Methods for estimating customer voltage harmonic emission levels’. 2008 13th Int. Conf. on Harmonics and Quality of Power, Wollongong, NSW, 2008, pp. 1–6.
    22. 22)
      • 7. Gopalakrishnan, C., Prabhu, S.G., Kumar, K.U.: ‘Practical implementation of CIGRE 36.05/CIRED 2 joint WG CC02 for assessment of harmonic emission level of AC arc furnaces connected to the Tamil Nadu distribution network’, Int. J. Electr. Power Energy Syst., 2007, 29, (3), pp. 275–279.
    23. 23)
      • 17. Karimzadeh, F., Esmaeili, S., Hosseinian, S.H.: ‘A novel method for noninvasive estimation of utility harmonic impedance based on complex independent component analysis’, IEEE Trans. Power Deliv., 2015, 30, (4), pp. 1843–1852.
    24. 24)
      • 14. Hui, J., Freitas, W., Jose, C.M., et al: ‘Utility harmonic impedance measurement based on data selection’, IEEE Trans. Power Deliv., 2012, 27, (4), pp. 2193–2202.
    25. 25)
      • 12. Zang, T.L., He, Z.Y., Fu, L., et al: ‘Adaptive method for harmonic contribution assessment based on hierarchical K-means clustering and Bayesian partial least squares regression’, IET Gener. Transm. Distrib., 2016, 10, (13), pp. 3220–3227.
    26. 26)
      • 11. Xiao, X.Y., Yang, H.G.: ‘The method of estimating customers harmonic emission level based on bilinear regression’. IEEE Int. Conf. on Electric Utility Deregulation, Restructuring and Power Technologies, Proc., 2004, vol. 2, pp. 662–665.
    27. 27)
      • 22. Novey, M., Adali, T.: ‘Complex ICA by Negentropy maximization’, IEEE Trans. Neural Netw., 2008, 19, (4), pp. 596–609.
    28. 28)
      • 18. Xiao, X., Zheng, X., Wang, Y., et al: ‘A method for utility harmonic impedance estimation based on constrained complex independent component analysis’, Energies, 2018, 11, (9), p. 2247.
    29. 29)
      • 8. Alves, D.K., Ribeiro, R., Costa, F.B., et al: ‘Real-time wavelet-based grid impedance estimation method’, IEEE Trans. Ind. Electron., 2019, 66, (10), pp. 8263–8265.
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