1. Harmonic Analysis of a DFIG for a Wind Energy Conversion System Lingling Fan, Ph.D., P.E. Assistant Professor Dept. Electrical Engineering University of South Florida Tampa, FL 33620 Linglingfan@usf.edu April 20, 2010 2010 IEEE Transmission & Distribution Conference and Exhibition New Orleans, LA

3. Outline  Objective  Principle  Case studies –Rotor injection –Unbalanced stator conditions  Conclusion

4. Objective  Develop a steady-state circuit to give quantitative analysis for harmonics in DFIG  The work is useful for understanding of –DFIG behavior during non-sinusoidal rotor injection –DFIG under unbalanced grid conditions (fault ride through)

5. Doubly Fed Induction Generator 5 fmfm RSC AC/DC Pr = sPs Ps GSC DC/AC

6. A generalized circuit for harmonic analysis in DFIG

7. Case study 1 – non-sinusoidal rotor injection

8. Frequency components in rotor voltage and stator current  Stator currents –(6n+1)f r +f m, -(6n-1)f r +f m,

9. Electromagnetic torque  Interaction of stator and rotor currents StatorI s1 (60 Hz)I s2 (-24*5 +36 Hz)Is3 (24*7 +36 Hz) RotorI r1 (24 Hz)I r2 (-24*5 Hz) I r3 (24*7 Hz) Ex: Is1, Ir2  torque (60- (-120 +36)) = 144 Hz = 6*24 Hz  6f r Is1, Ir3  torque (60- (168 +36)) = -144 Hz = -6*24 Hz  6f r

10. Torque +

12. Case study 2 – unbalanced stator conditions  Rotor injection – programmable power source –sinusoidal 3-phase  Stator phase a resistance is reduced

13. Analysis 13 Unbalanced stator currents Positive sequence (f e ) Negative sequence (-f e ) Zero sequence I r : f e -f m =sf e Rotor currents I r : -f e -f m =-(2-s)f e s: slip = 1-f m /f e f m : electric frequency corresponding to rotating speed. f e : nominal frequency 60 Hz (stator) – 50 Hz (rotating speed) = 10 Hz -60 Hz (stator) – 50 Hz (rotating speed) = -110 Hz

14. Torque PositiveNegative StatorIs1 (+60 Hz)Is2 (-60 Hz) RotorIr1 (10 Hz)Ir2 (-110 Hz) 1.Te1 Te2 – dc components 2.Te3, Te4 – pulsating components 120 Hz

15. Reference frames 15 Pos. Neg. Sequences can be separated by a dc filter!

16. Extraction scheme 16

17. Lab setup

20. Case 3 – Grid interconnected DFIG

21. Simulation results

22. Confirm simulation results with the analysis

23. Conclusion  This paper develops –A generalized steady-state DFIG circuit for harmonic analysis –A systematic method to compute torque by computing the interactions of stator and rotor currents –The sequence network based on DFIG pos, neg circuits which facilitates the analysis under unbalanced stator conditions.