Skip to main content
Top
Published in:

06-05-2023 | Original Paper

A criterion for the Hopf bifurcation and the pathway to chaos of doubly fed induction generators

Authors: Wei Chen, Qiangqiang Li, Zhanhong Wei, Jiangtao Li, Kun Wang

Published in: Electrical Engineering | Issue 5/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Aiming at the cause of limit cycles and the pathway of chaotic oscillation by doubly fed induction generator (DFIG) as its internal parameters change, this paper proposed a method to identify limit cycles and a numerical method to identify chaotic pathways. First, a simplified four-dimensional nonlinear dynamic model of the DFIG is developed. A simple criterion for the Hopf bifurcation parameter of the DFIG is given: the Routh–Hurwitz stability criterion. In addition, the relationship between the system at critical damping and the Hopf bifurcation is obtained. Second, the stability interval of the DFIG linearized system is verified using a time-domain approach when the system has recovered from a slight disturbance. Finally, periodic, quasi-periodic, and chaotic oscillations are predicted to occur based on the largest Lyapunov exponent and power spectrum to further determine the system’s parameters. The path and threshold of the tuning parameter inducing the DFIG into chaos are obtained to provide a theoretical basis for revealing the mechanism inducing chaotic oscillations. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed method.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Liu F, Wei L, Wang HD, Li Y, Xu YY (2022) Review on oscillation mechanism and analysis methods of high proportion renewable energy power system. High Volt Eng 48(1):95–114 Liu F, Wei L, Wang HD, Li Y, Xu YY (2022) Review on oscillation mechanism and analysis methods of high proportion renewable energy power system. High Volt Eng 48(1):95–114
2.
go back to reference Xue YS, Bin ZJ (2019) Trajectory section eigenvalue method for nonlinear time-varying power system. Int J Electr Power Energy Syst 107:321–331CrossRef Xue YS, Bin ZJ (2019) Trajectory section eigenvalue method for nonlinear time-varying power system. Int J Electr Power Energy Syst 107:321–331CrossRef
3.
go back to reference Zhang DL, Wang YJ, Hu JB, Ma SC, He Q, Guo Q (2016) Impacts of PLL on the DFIG-based WTG’s electromechanical response under transient conditions: analysis and modeling. CSEE J Power Energy Syst 2(2):30–39CrossRef Zhang DL, Wang YJ, Hu JB, Ma SC, He Q, Guo Q (2016) Impacts of PLL on the DFIG-based WTG’s electromechanical response under transient conditions: analysis and modeling. CSEE J Power Energy Syst 2(2):30–39CrossRef
4.
go back to reference Prasertwong K, Mithulananthan N, Thakur D (2010) Understanding low-frequency oscillation in power systems. Int J Electr Eng Educ 47(3):248–262CrossRef Prasertwong K, Mithulananthan N, Thakur D (2010) Understanding low-frequency oscillation in power systems. Int J Electr Eng Educ 47(3):248–262CrossRef
5.
go back to reference Chen L, Lu XM, Min Y, Zhang YW, Chen Q, Zhao YM, Ben C (2018) Optimization of governor parameters to prevent frequency oscillations in power systems. IEEE Trans Power Syst 33(4):4466–4474CrossRef Chen L, Lu XM, Min Y, Zhang YW, Chen Q, Zhao YM, Ben C (2018) Optimization of governor parameters to prevent frequency oscillations in power systems. IEEE Trans Power Syst 33(4):4466–4474CrossRef
6.
go back to reference Ooi BT, Guo J, Wang X (2021) Local blackout and global power system wide blackout are caused by nonlinear negative damping. IET Gener Transm Distrib 14(26):6726–6731CrossRef Ooi BT, Guo J, Wang X (2021) Local blackout and global power system wide blackout are caused by nonlinear negative damping. IET Gener Transm Distrib 14(26):6726–6731CrossRef
7.
go back to reference Xie J, Sun W, Sun K, Wang XR (2021) A hybrid energy and mode decomposition-based method for evaluating generators damping in multi-machine power systems. IEEE Access 9:37156–37166CrossRef Xie J, Sun W, Sun K, Wang XR (2021) A hybrid energy and mode decomposition-based method for evaluating generators damping in multi-machine power systems. IEEE Access 9:37156–37166CrossRef
8.
go back to reference Peng JJ, Qi J, Yan GG, Liu K, Zhai WC, Shen MH (2022) Damping torque modeling of direct-drive wind turbine for low-frequency oscillation analysis. Electr Power Autom Equip 42(8):39–46 Peng JJ, Qi J, Yan GG, Liu K, Zhai WC, Shen MH (2022) Damping torque modeling of direct-drive wind turbine for low-frequency oscillation analysis. Electr Power Autom Equip 42(8):39–46
9.
go back to reference Yang LH, Ma XK (2012) Analysis on voltage stability of power system with doubly fed induction generator wind turbine based on bifurcation theory. Trans China Electrotech Soc 27(9):1–8 Yang LH, Ma XK (2012) Analysis on voltage stability of power system with doubly fed induction generator wind turbine based on bifurcation theory. Trans China Electrotech Soc 27(9):1–8
10.
go back to reference Babaei M, Feyzi M, Nazari Marashi A (2021) Study of bifurcation and chaos in scalar drive systems of permanent magnet synchronous machines. Int Trans Electr Energy Syst 31(9):e13023CrossRef Babaei M, Feyzi M, Nazari Marashi A (2021) Study of bifurcation and chaos in scalar drive systems of permanent magnet synchronous machines. Int Trans Electr Energy Syst 31(9):e13023CrossRef
11.
go back to reference Chen X, Hu J, Peng Z, Yuan C (2017) Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect. Nonlinear Dyn 88(1):277–292CrossRef Chen X, Hu J, Peng Z, Yuan C (2017) Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect. Nonlinear Dyn 88(1):277–292CrossRef
12.
go back to reference Gao Y, Chau KT (2004) Hopf bifurcation and chaos in synchronous reluctance motor drives. IEEE Trans Energy Conv 19(2):296–302CrossRef Gao Y, Chau KT (2004) Hopf bifurcation and chaos in synchronous reluctance motor drives. IEEE Trans Energy Conv 19(2):296–302CrossRef
13.
go back to reference Hunaish AS, Tahir FR (2021) Bifurcation and chaos in indirect field-oriented controlled induction motor drive system. Eur Phys J Plus 136(4):1–13CrossRef Hunaish AS, Tahir FR (2021) Bifurcation and chaos in indirect field-oriented controlled induction motor drive system. Eur Phys J Plus 136(4):1–13CrossRef
14.
15.
go back to reference Xue AC, Fu XY, Wang JW, Li YC, Qiao DK (2020) Switched chaotic oscillation and non-smooth bifurcation characteristics of DFIG system. Electr Power Autom Equip 40(9):170–177 Xue AC, Fu XY, Wang JW, Li YC, Qiao DK (2020) Switched chaotic oscillation and non-smooth bifurcation characteristics of DFIG system. Electr Power Autom Equip 40(9):170–177
16.
go back to reference Xue AC, Fu XY, Wang ZZ, Wang JW (2019) Analysis of sub-synchronous band oscillation in a DFIG system with non-smooth bifurcation. IEEE Access 7:183142–183149CrossRef Xue AC, Fu XY, Wang ZZ, Wang JW (2019) Analysis of sub-synchronous band oscillation in a DFIG system with non-smooth bifurcation. IEEE Access 7:183142–183149CrossRef
17.
go back to reference Hsiao-Dong C, Chih-Wen L, Varaiya PP, Wu FF, Lauby MG (1993) Chaos in a simple power system. IEEE Trans Power Syst 8(4):1407–1417CrossRef Hsiao-Dong C, Chih-Wen L, Varaiya PP, Wu FF, Lauby MG (1993) Chaos in a simple power system. IEEE Trans Power Syst 8(4):1407–1417CrossRef
18.
go back to reference Adiyaman Y, Emiroglu S, Ucar MK, Yildiz M (2020) Dynamical analysis, electronic circuit design and control application of a different chaotic system. Chaos Theory Appl 2(1):10–16 Adiyaman Y, Emiroglu S, Ucar MK, Yildiz M (2020) Dynamical analysis, electronic circuit design and control application of a different chaotic system. Chaos Theory Appl 2(1):10–16
19.
go back to reference Kamdjeu Kengne L, Mboupda Pone JR, Fotsin HB (2021) Symmetry and asymmetry induced dynamics in a memristive twin-T circuit. Int J Electron 109(2):337–366CrossRef Kamdjeu Kengne L, Mboupda Pone JR, Fotsin HB (2021) Symmetry and asymmetry induced dynamics in a memristive twin-T circuit. Int J Electron 109(2):337–366CrossRef
20.
go back to reference Wang X, Kingni ST, Volos C, Pham VT, Vo Hoang D, Jafari S (2018) A fractional system with five terms: analysis, circuit, chaos control and synchronization. Int J Electron 106(1):109–120CrossRef Wang X, Kingni ST, Volos C, Pham VT, Vo Hoang D, Jafari S (2018) A fractional system with five terms: analysis, circuit, chaos control and synchronization. Int J Electron 106(1):109–120CrossRef
21.
go back to reference Awrejcewicz J, Krysko AV, Erofeev NP, Dobriyan V, Barulina MA, Krysko VA (2018) Quantifying chaos by various computational methods. Part 1: simple systems. Entropy (Basel) 20(3):175MathSciNetCrossRef Awrejcewicz J, Krysko AV, Erofeev NP, Dobriyan V, Barulina MA, Krysko VA (2018) Quantifying chaos by various computational methods. Part 1: simple systems. Entropy (Basel) 20(3):175MathSciNetCrossRef
22.
go back to reference Emiroglu S, Uyaroglu Y, Gümüş TE (2021) Recursive backstepping control of ferroresonant chaotic oscillations consisting between grading capacitor with nonlinear inductance of voltage transformer. Eur Phys J Spec Top 230(7–8):1829–1837CrossRef Emiroglu S, Uyaroglu Y, Gümüş TE (2021) Recursive backstepping control of ferroresonant chaotic oscillations consisting between grading capacitor with nonlinear inductance of voltage transformer. Eur Phys J Spec Top 230(7–8):1829–1837CrossRef
23.
go back to reference Emiroglu S, Akgül A, Adıyaman Y et al (2021) A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization. Circuit World 48(2):265–277CrossRef Emiroglu S, Akgül A, Adıyaman Y et al (2021) A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization. Circuit World 48(2):265–277CrossRef
24.
go back to reference Jia HJ, Yu YX, Wang CS (2001) Power system chaos phenomenon and related research. Proc CSEE 21(7):26 Jia HJ, Yu YX, Wang CS (2001) Power system chaos phenomenon and related research. Proc CSEE 21(7):26
25.
go back to reference Yu Y, Mi ZQ, Liu XJ (2011) Analysis of chaos in doubly fed induction generator and sliding mode control of chaos synchronization. Acta Phys Sin 60(7):119–126 Yu Y, Mi ZQ, Liu XJ (2011) Analysis of chaos in doubly fed induction generator and sliding mode control of chaos synchronization. Acta Phys Sin 60(7):119–126
26.
go back to reference Bazanella AS, Reginatto R (2000) Robustness margins for indirect field-oriented control of induction motors. IEEE Trans Autom Control 45(6):1226–1231MathSciNetCrossRefMATH Bazanella AS, Reginatto R (2000) Robustness margins for indirect field-oriented control of induction motors. IEEE Trans Autom Control 45(6):1226–1231MathSciNetCrossRefMATH
27.
go back to reference Reginatto R, Bazanella AS (2003) Robustness of global asymptotic stability in indirect field-oriented control of induction motors. IEEE Trans Autom Control 48(7):1218–1222MathSciNetCrossRefMATH Reginatto R, Bazanella AS (2003) Robustness of global asymptotic stability in indirect field-oriented control of induction motors. IEEE Trans Autom Control 48(7):1218–1222MathSciNetCrossRefMATH
28.
go back to reference Al-Azzawi SF (2012) Stability and bifurcation of pan chaotic system by using Routh–Hurwitz and Gardan methods. Appl Math Comput 219(3):1144–1152MathSciNetMATH Al-Azzawi SF (2012) Stability and bifurcation of pan chaotic system by using Routh–Hurwitz and Gardan methods. Appl Math Comput 219(3):1144–1152MathSciNetMATH
29.
go back to reference Guo X, Liang K, Mu B, Wang P, Yang M (2020) Chaotic motion around a black hole under minimal length effects. Eur Phys J C 80(8):745. Guo X, Liang K, Mu B, Wang P, Yang M (2020) Chaotic motion around a black hole under minimal length effects. Eur Phys J C 80(8):745.
30.
go back to reference Sun M, Zhang W, Chen JE, Yao MH (2017) Subharmonic Melnikov theory for degenerate resonance systems and its application. Nonlinear Dyn 89(2):1173–1186CrossRefMATH Sun M, Zhang W, Chen JE, Yao MH (2017) Subharmonic Melnikov theory for degenerate resonance systems and its application. Nonlinear Dyn 89(2):1173–1186CrossRefMATH
31.
go back to reference Zhao ZT, Yuan XG, Zhang WZ, Niu DT, Zhang HW (2021) Dynamical modeling and analysis of hyperelastic spherical shells under dynamic loads and structural damping. Appl Math Model 95:468–483MathSciNetCrossRefMATH Zhao ZT, Yuan XG, Zhang WZ, Niu DT, Zhang HW (2021) Dynamical modeling and analysis of hyperelastic spherical shells under dynamic loads and structural damping. Appl Math Model 95:468–483MathSciNetCrossRefMATH
Metadata
Title
A criterion for the Hopf bifurcation and the pathway to chaos of doubly fed induction generators
Authors
Wei Chen
Qiangqiang Li
Zhanhong Wei
Jiangtao Li
Kun Wang
Publication date
06-05-2023
Publisher
Springer Berlin Heidelberg
Published in
Electrical Engineering / Issue 5/2023
Print ISSN: 0948-7921
Electronic ISSN: 1432-0487
DOI
https://doi.org/10.1007/s00202-023-01819-1

Other articles of this Issue 5/2023

Electrical Engineering 5/2023 Go to the issue