Skip to main content
Log in

Second order sliding mode control of three-level four-leg DSTATCOM based on instantaneous symmetrical components theory

Energy Systems Aims and scope Submit manuscript

Abstract

In this paper, a second order sliding mode controller (SOSMC) is proposed to control a three-level four-leg DSTATCOM connected to three-phase four-wire distribution system. The controller is designed in synchronous reference frame using super twisting algorithm based on symmetrical components theory. The proposed DSTATCOM control is aimed for the power factor correction in both capacitive and inductive operation modes. It has also purpose the regulation of excessive neutral current in the fourth wire of the distribution utility system under unbalanced loads or asymmetrical fault in the grid cases. This paper also presents a simplified three-level three-dimensional space vector modulation (3DSVM) with DC-bus capacitor voltages balancing strategy based on the effective use of the redundant switching states of the inverter voltage vectors. The effectiveness and validity of the proposed SOSMC system and 3DSVM are maintained by computer simulation. From simulation results, the comparison between the SOSMC, first order integral SMC, and conventional PI controller shows superiority of the SOSMC with high performance under both dynamic and steady state operations even in worst cases such as fault and unbalancing loads.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Kersting, W.H.: Distribution system modeling and analysis. Power and Energy Society (2013)

  2. Singh, B., Chandra, A., Al-Haddad, K., Kothari, D.P.: Reactive power compensation and load balancing in electric power distribution systems. Int. J. Electr. Power Energy Syst. 20, 375–381 (1998)

    Article  Google Scholar 

  3. Bayliss, C.R., Hardy, B.J.: Transmission and Distribution Electrical Engineering. Elsevier (2012)

  4. Sreenivasarao, D., Agarwal, P., Das, B.: Neutral current compensation in three-phase, four-wire systems: a review. Electr. Power Syst. Res. 86, 170–180 (2012)

    Article  Google Scholar 

  5. Hingorani, N.G., Gyugyi, L.: Understanding FACTS: concepts and technology of flexible AC transmission systems. IEEE Press, Piscataway (2000)

    Google Scholar 

  6. Zhang, X.-P., Rehtanz, C., Pal, B.: Flexible AC Transmission Systems: Modelling and Control. Springer (2012)

  7. Singh, B., Al-Haddad, K., Chandra, A.: Harmonic elimination, reactive power compensation and load balancing in three-phase, four-wire electric distribution systems supplying non-linear loads. Electr. Power Syst. Res. 44, 93–100 (1998)

    Article  Google Scholar 

  8. Wu, C.J., Chiang, J.C., Yen, S.S., Liao, C.J., Yang, J.S., Guo, T.Y.: Investigation and mitigation of harmonic amplification problems caused by single-tuned filters. IEEE Trans. Power Deliv. 13, 800–806 (1998)

    Article  Google Scholar 

  9. Fukami, T., Onchi, T., Naoe, N., Hanaoka, R.: Compensation for neutral current harmonics in a three-phase four-wire system by a synchronous machine. IEEE Trans. Ind. Appl. 38, 1232–1236 (2002)

    Article  Google Scholar 

  10. Khera, P.P.: Application of zigzag transformers for reducing harmonics in the neutral conductor of low voltage distribution system. In: Conference Record of the 1990 IEEE Industry Applications Society Annual Meeting, pp. 1092–1096 (1990)

  11. Singh, B., Jayaprakash, P., Kothari, D.D.: A T-connected transformer and three-leg VSC based DSTATCOM for power quality improvement. IEEE Trans. Power Electron. 23, 2710–2718 (2008)

    Article  Google Scholar 

  12. Jayaprakash, P., Singh, B., Kothari, D.P.: Three-Phase 4-Wire DSTATCOM Based on H-Bridge VSC with a Star/Hexagon Transformer for Power Quality Improvement. In: 2008 IEEE Reg. 10 Third Int. Conf. Ind. Inf. Syst, pp. 1–6 (2008)

  13. Bouzidi, M., Benaissa, A., Barkat, S.: Hybrid direct power/current control using feedback linearization of three-level four-leg voltage source shunt active power filter. Int. J. Electr. Power Energy Syst. 61, 629–646 (2014)

    Article  Google Scholar 

  14. Hingorani, N.G.: High power electronics and flexible AC transmission system. IEEE Spectr. 30, 40–45 (1993)

    Article  Google Scholar 

  15. Kumar, P., Kumar, N., Akella, A.K.: A simulation based case study for control of DSTATCOM. ISA Trans. 53, 767–775 (2014)

    Article  Google Scholar 

  16. Yu, Q.Y.Q., Li, P.L.P., Liu, W.L.W., Xie, X.X.X.: Overview of STATCOM technologies. In: 2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies. Proceedings, pp. 647–652 (2004)

  17. Al-Haddad, K., Saha, R., Chandra, A., Singh, B.: Static synchronous compensators (STATCOM): a review. IET Power Electron. 2, 297–324 (2009)

  18. Akagi, H., Watanabe, E.H., Aredes, M.: The instantaneous power theory. In: Instantaneous Power Theory and Applications to Power Conditioning, pp. 41–107 (2007)

  19. Jou, H.-L., Wu, K.-D., Wu, J.-C., Li, C.-H., Huang, M.-S.: Novel power converter topology for three-phase four-wire hybrid power filter (2008)

  20. Iyer, S., Ghosh, A., Joshi, A.: Inverter topologies for DSTATCOM applications—a simulation study. Electr. Power Syst. Res. 75, 161–170 (2005)

    Article  Google Scholar 

  21. Sreenivasarao, D., Agarwal, P., Das, B.: Performance enhancement of a reduced rating hybrid D-STATCOM for three-phase, four-wire system. Electr. Power Syst. Res. 97, 158–171 (2013)

    Article  Google Scholar 

  22. Zhou, L.Z.L., Luo, M.L.M., Zhou, L.Z.L., Zhou, X.Z.X., Ye, Y.Y.Y.: Application of a four-leg ASVG based on 3D SVPWM in compensating the harmful currents of unbalanced system. Proc. Int. Conf. Power Syst. Technol. 2, 1045–1050 (2002)

    Article  Google Scholar 

  23. Lai, J.-S.L.J.-S., Peng, F.Z.P.F.Z.: Multilevel converters-a new breed of power converters. In: IAS ’95. Conf. Rec. 1995 IEEE Ind. Appl. Conf. Thirtieth IAS Annu. Meet, vol 3, pp. 509–517 (1995)

  24. Rodríguez, J., Lai, J.S., Peng, F.Z.: Multilevel inverters: a survey of topologies, controls, and applications. IEEE Trans. Ind. Electron. 49, 724–738 (2002)

    Article  Google Scholar 

  25. Rodríguez, J., Member, S., Bernet, S., Wu, B., Pontt, J.O., Kouro, S., Member, S.: Multilevel voltage-source-converter topologies for industrial medium-voltage drives. 54, 2930–2945 (2007)

  26. Barrena, J.A., Aurtenechea, S., Canales, J.M., Rodriguez, M.A., Marroyo, L.: Design, analysis and comparison of multilevel topologies for DSTATCOM applications. In: 2005 Eur. Conf. Power Electron. Appl, pp. 1–10 (2005)

  27. Carrara, G., Gardella, S., Marchesoni, M., Salutari, R., Sciutto, G.: A new multilevel PWM method: a theoretical analysis. IEEE Trans. Power Electron. 7, 497–505 (1992)

    Article  Google Scholar 

  28. McGrath, B.P., Holmes, D.G.: Multicarrier PWM strategies for multilevel inverters. IEEE Trans. Ind. Electron. 49, 858–867 (2002)

    Article  Google Scholar 

  29. Saeedifard, M., Iravani, R., Pou, J.: A space vector modulation strategy for a back-to-back five-level HVDC converter system. IEEE Trans. Ind. Electron. 56, 452–466 (2009)

    Article  Google Scholar 

  30. Li, X., Deng, Z., Chen, Z., Fei, Q.: Analysis and simplification of three-dimensional space vector PWM for three-phase four-leg inverters. IEEE Trans. Ind. Electron. 58, 450–464 (2011)

    Article  Google Scholar 

  31. Renge, M.M., Suryawanshi, H.M.: Three-dimensional space-vector modulation to reduce common-mode voltage for multilevel inverter. IEEE Trans. Ind. Electron. 57, 2324–2331 (2010)

    Article  Google Scholar 

  32. Zhang, R., Boroyevich, D., Prasad, V.H., Mao, H.-C., Lee, F.C., Dubovsky, S.: A three-phase inverter with a neutral leg with space vector modulation. In: Proceedings of APEC 97—Applied Power Electronics Conference, pp. 857–863 (1997)

  33. Zhang, M., Atkinson, D.J., Ji, B., Armstrong, M., Ma, M.: A near-state three-dimensional space vector modulation for a three-phase four-leg voltage source inverter. IEEE Trans. Power Electron. 29, 5715–5726 (2014)

    Article  Google Scholar 

  34. Wong, Man-Chung, Zhao, Zheng-Yi, Han, Ying-Duo, Zhao, Liang-Bing: Three-dimensional pulse-width modulation technique in three-level power inverters for three-phase four-wired system. IEEE Trans. Power Electron. 16, 418–427 (2001)

    Article  Google Scholar 

  35. Wong, M.C., Tang, J., Han, Y.D.: Cylindrical coordinate control of three-dimensional PWM technique in three-phase four-wired trilevel inverter. IEEE Trans. Power Electron. 18, 208–220 (2003)

    Article  Google Scholar 

  36. Singh, B., Solanki, J.: A comparison of control algorithms for DSTATCOM. IEEE Trans. Ind. Electron. 56, 2738–2745 (2009)

    Article  Google Scholar 

  37. Singh, B., Jayaprakash, P., Kothari, D.P.: New control approach for capacitor supported DSTATCOM in three-phase four wire distribution system under non-ideal supply voltage conditions based on synchronous reference frame theory. Int. J. Electr. Power Energy Syst. 33, 1109–1117 (2011)

    Article  Google Scholar 

  38. Sahoo, N.C., Panigrahi, B.K., Dash, P.K., Panda, G.: Application of a multivariable feedback linearization scheme for STATCOM control. Electr. Power Syst. Res. 62, 81–91 (2002)

    Article  Google Scholar 

  39. Wang, K., Crow, M.L.: Power system voltage regulation via STATCOM internal nonlinear control. IEEE Trans. Power Syst. 26, 1252–1262 (2011)

    Article  Google Scholar 

  40. Mahmud, M.A., Pota, H.R., Hossain, M.J.: Nonlinear DSTATCOM controller design for distribution network with distributed generation to enhance voltage stability. Int. J. Electr. Power Energy Syst. 53, 974–979 (2013)

    Article  Google Scholar 

  41. Eldery, M.A., El-Saadany, E.F., Salama, M.M.A.: Sliding mode controller for pulse width modulation based DSTATCOM. In: Proceedings of Canadian conference on electrical and computer engineering, CCECE ’06, pp. 2216–2219 (2006)

  42. Chong, B., Zhang, L., Waite, M.J.: Three-phase four-leg flying-capacitor multi-level inverter-based active power filter for unbalanced current operation. IET Power Electron. 6, 153–163 (2013)

    Article  Google Scholar 

  43. Balikci, A., Akpinar, E.: A three-phase four-wire static synchronous compensator with reduced number of switches for unbalanced loads. IET Power Electron. 7, 1630–1643 (2014)

    Article  Google Scholar 

  44. Mansour, A., Zhang, C., Hany, N.: Measurement of power components in balanced and unbalanced three-phase systems under nonsinusoidal operating conditions by using IEEE standard 1459–2010 and Fourier analysis. In: Technological Advances in Electrical, Electronics and Computer Engineering (TAEECE), 2013 International Conference on, pp. 166–171 (2013)

  45. Furat, M., Eker, İ.: Second-order integral sliding-mode control with experimental application. ISA Trans. 53, 1661–1669 (2014)

    Article  Google Scholar 

  46. Chiang, H.-K., Lin, W.-B., Chang, Y.-C., Fang, C.-C.: Super-twisting second-order sliding mode control for a synchronous reluctance motor. Artif. Life Robot. 16, 307–310 (2011)

    Article  Google Scholar 

  47. Young, K.D., Utkin, V.I., Özgüner, Ü.: A control engineer’s guide to sliding mode control. IEEE Trans. Control Syst. Technol. 7, 328–342 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saber Bouafia.

Appendix

Appendix

See Tables 3, 4, 5 and 6.

Table 3 Prism identification in each sector N (\(N\,=\,\)1, 2)
Table 4 Interchanging the switching states in odd sectors
Table 5 Interchanging the switching states in even sectors
Table 6 Interchanging the switching states of each tetrahedron located in same prism for sector 1 and 2, \(PR_{n}^{S} (\textit{S}\,\)=\(\,1)\;(\textit{n}\,\)=\(\,1,2,3,4), TeT_{m}^{S,P}\;(\textit{S}\,\)=\(\,1,2)\;(\textit{P}\,\)=\(\,1,2,3,4)\;(m=1,2,\ldots ,9,10)\)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bouafia, S., Benaissa, A., Barkat, S. et al. Second order sliding mode control of three-level four-leg DSTATCOM based on instantaneous symmetrical components theory. Energy Syst 9, 79–111 (2018). https://doi.org/10.1007/s12667-016-0217-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12667-016-0217-5

Keywords

Navigation