Skip to main content

Advertisement

SpringerLink
Log in

Recursive Least Squares and Sliding Mode Control for Voltage Compensation of Three-Phase Loads

  • Published:
Journal of Control, Automation and Electrical Systems Aims and scope Submit manuscript

Abstract

This paper proposes a sliding mode control method to be used in the dynamic voltage restorer (DVR) system for regulating voltages of three-phase loads. The voltages produced by the DVR’s inverter are provided by three sliding mode controllers. Each of them operates on a error resulting from the difference between the phase reference and the measured single-phase load voltage. The reference synchronization is carried out by a recursive least-square (RLS) algorithm. Moreover, a flag procedure is applied to assure that the DVR operates only on periods of time where system is in steady state. This is suitable for saving energy. The technique has been evaluated in Simulink for different sag conditions. Finally, an experimental setup of a DVR has been used to evaluate the method, and the results show the effectiveness of it.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

Abbreviations

v :

Voltage

i :

Current

\(v_{l}\) :

Measured load voltage

\(v^*_{l}\) :

Reference for each phase

\(K_{P }\) :

Proportional gain for a PI controller

\(K_{I}\) :

Integral gain for a PI controller

\(v_\mathrm{{inv}}\) :

Voltage applied by the inverter

eval :

Evaluation function

\(s_n\) :

Sliding surface

\(V_{Gm}\) :

Amplitude

\({\upalpha }_m\) :

Phase of the sinusoid

\(m{\upomega }_0\) :

Sinusoid frequency

\(\Delta t\) :

Sample period

\({{\upphi }}_n\) :

Vector of regressors

i :

Inverter

f :

Leakage

l :

Load

c :

Capacitor

\(\widehat{}\) :

Estimated value

\(*\) :

Reference value

References

  • Chen, Y.-H., Lin, C.-Y., Chen, J.-M., & Cheng, P.-T. (2012). An inrush mitigation technique of load transformers for the series voltage sag compensator. IEEE Transactions on Power Electronics, 25(8), 2211–2221.

    Article  Google Scholar 

  • Chi-Shan, Y. (2006). A discrete Fourier transform-based adaptive mimic phasor estimator for distance relaying applications. IEEE Transactions on Power Delivery, 21(4), 1836–1846.

    Article  Google Scholar 

  • Costa, F. F., Formiga, D. A., Ferreira, R. R., Sousa, T., & Costa, F. B. (2013). A recursive least-squares aided by pre-filtering for phasor-estimation in distance protection. In IEEE-PES. Powertech, Grenoble-France

  • de la O Serna, J. A., & Martinez, E. V. (2015). Included in your digital subscription smart grids part 2: Synchrophasor measurement challenges. IEEE Instrumentation & Measurement Magazine, 18(1), 13–16.

    Article  Google Scholar 

  • Dong, G., & Ojo, O. (2007). Current regulation in four-leg voltage-source converters. IEEE Transactions on Industrial Electronics, 54(4), 2095–2105.

    Article  Google Scholar 

  • Edwards, C., & Spurgeon, S. K. (1998). Sliding mode control: Theory and applications. New York, NY: Taylor & Francis systems and control book series.

    Book  MATH  Google Scholar 

  • Errabelli, R. R., Kolhatkar, Y. Y., & Das, S. P. (2006). Experimental investigation of dvr with sliding mode control. In Power India conference, 2006 IEEE (p. 5).

  • Fernandes, D. A., Costa, F. F., & Santos, E. C, Jr. (2013). Digital-scalar pwm approaches applied to four-leg voltage-source inverters. IEEE Transactions on Industrial Electronics, 60(5), 2022–2030.

    Article  Google Scholar 

  • Fernandes, D. A., Costa, F. F., & Vitorino, M. A. (2014). A method for averting saturation from series transformers of dynamic voltage restorers. IEEE Transactions on Power Delivery, 29(5), 2239–2247.

    Article  Google Scholar 

  • Goharrizi, A. Y., Hosseini, S. H., Sabahi, M., & Gharehpetian, G. B. (2012). Three-phase HFL-DVR with independently controlled phases. IEEE Transactions on Power Electronics, 27(4), 1706–1718.

    Article  Google Scholar 

  • Haroun, R., El Aroudi, A., Cid-Pastor, A., Garica, G., Olalla, C., & Martinez-Salamero, L. (2015). Impedance matching in photovoltaic systems using cascaded boost converters and sliding-mode control. IEEE Transactions on Power Electronics, 30(6), 3185–3199.

    Article  Google Scholar 

  • Jeong, H. G., Kim, W. S., Lee, K. B., Jeong, B. C., & Song, S. H. (2008). A sliding-mode approach to control the active and reactive powers for a dfig in wind turbines. In Power electronics specialists conference.

  • Jiabing, H., Nian, H., Bin, H., He, Y., & Zhu, Z. Q. (2010). Direct active and reactive power regulation of dfig using sliding-mode control approach. IEEE Transactions on Energy Conversion, 25(4), 1028–1039.

    Article  Google Scholar 

  • Kanjiya, P., Khadkikar, V., & Zeineldin, H. H. (2015). Optimal control of shunt active power filter to meet ieee std. 519 current harmonic constraints under nonideal supply condition. IEEE Transactions on Industry Applications, 62(2), 724–734.

    Google Scholar 

  • Kim, J.-H., & Sul, S.-K. (2004). A carrier-based pwm method for three-phase four-leg voltage source converters. IEEE Transactions on Power Electronics, 19(1), 66–75.

    Article  Google Scholar 

  • Lascu, C., Boldea, I., & Blaabjerg, F. (2004). Direct torque control of sensorless induction motor drives: A sliding-mode approach. IEEE Transactions on Industry Applications, 25(2), 582–590.

    Article  Google Scholar 

  • Li, X., Deng, Z., Chen, Z., & Fei, Q. (2011). Analysis and simplification of three-dimensional space vector PWM for three-phase four-leg inverters. IEEE Transactions on Industry Applications, 58(2), 450–454.

    Google Scholar 

  • Ljung, L. (1999). System identification: Theory for the user (2nd ed.). Upper Saddle River, NJ: Prentice Hall PTR.

    MATH  Google Scholar 

  • Martins, J. R. S., Fernandes, D. A., Costa, F. F., & Correia, M. B. R. (2017). Three-phase load voltage compensation based on a repetitive and least squares control system (in portuguese). Eletronica de Potencia, 22, 237–245.

    Google Scholar 

  • Mora, M. A., & Milanovic, J. V. (2012). Monitor placement for reliable estimation of voltage sags in power networks. IEEE Transactions on Power Delivery, 27(2), 936–944.

    Article  Google Scholar 

  • Naidu, S. R., & Fernandes, D. A. (2009). Dynamic voltage restorer based on 4-leg voltage source converter. IET Generation, Transmission & Distribution, 3(5), 437–447.

    Article  Google Scholar 

  • Naouar, W., Monmasson, E., Naassani, A., & Slama-Belkhodja, I. (2012). Fpga-based dynamic reconfiguration of sliding mode current controllers for synchronous machines. IEEE Transactions on Industrial Informatics, 99, 18–25.

    Google Scholar 

  • Shah, M. Z., Samar, R., & Bhatti, A. I. (2015). Guidance of air vehicles: A sliding mode approach. IEEE Transactions on Control Systems Technology, 23(1), 231–244.

    Article  Google Scholar 

  • Tan, R. H. G., & Ramachandaramurthy, V. K. (2012). Voltage sag acceptability assessment using multiple magnitude-duration function. IEEE Transactions on Power Delivery, 27(4), 1984–1990.

    Article  Google Scholar 

  • Zhang, R., Prasad, V. H., Boroyevich, D., & Lee, F. C. (2002). Three-dimensional space vector modulation for four-leg voltage-source converters. IEEE Transactions on Power Electronics, 17(3), 314–326.

    Article  Google Scholar 

Download references

Acknowledgements

Funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant No. 482736/2011-9).

Author information

Authors and Affiliations

  1. Universidade Federal do ABC, São Paulo, Brazil

    Alfeu J. Sguarezi Filho & José A. T. Altuna

  2. Universidade Federal da Paraiba, João Pessoa, Brazil

    Darlan A. Fernandes

  3. Universidade Federal da Bahia, Salvador, Brazil

    José H. Suárez & Fabiano F. Costa

Authors
  1. Alfeu J. Sguarezi Filho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Darlan A. Fernandes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José H. Suárez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fabiano F. Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. José A. T. Altuna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José A. T. Altuna.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sguarezi Filho, A.J., Fernandes, D.A., Suárez, J.H. et al. Recursive Least Squares and Sliding Mode Control for Voltage Compensation of Three-Phase Loads. J Control Autom Electr Syst 29, 769–777 (2018). https://doi.org/10.1007/s40313-018-0405-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40313-018-0405-8

Keywords

Search

Navigation