2. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Gary W. Chang Paulo F. Ribeiro Department of Electrical Engineering Engineering Department National Chung Cheng University Calvin College TAIWAN USA A New Approach for Prediction of Harmonic Currents Generated by a Cluster of AC/DC Converters

3. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Outline Introduction Proposed Approach Probabilistic Model of Multiple Converters Case Study Conclusions

4. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Introduction In the past, most probabilistic or statistical approaches to estimate harmonic currents generated by a group of converters are based on deriving an analytical probabilistic harmonic current model for a single converter. To obtain an equivalent probabilistic model of a cluster of converters with more accurate operations becomes tedious and timing. Most literature show that ripple currents at the converter dc side and its effects on the ac side are ignored when predicting harmonic currents generated by multiple converters.

5. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Introduction (Continued) This paper presents a new approach to predict harmonic currents generated by multiple converters while taking the effects of ripple currents at the converter dc side into account.

6. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution Method Switching function-based approach to obtain the AC side equivalent circuit for harmonic analysis of a converter [4]

7. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution Method (Continued) Voltage and current transfer functions with firing angle variation and commutation overlap The ideal switching function, G, includes both fundamental and harmonic components

8. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution Method (Continued) The ac input current at phase a of the converter which includes effects of ripple components at its dc side becomes where I 1 and I 6h are calculated based on the equivalent circuits representing effects of dc side current components on the input current at the ac side that proposed in [4].

9. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution Proposed Solution Method (Continued) Equivalent circuit of a single converter at fundamental frequency [4]

10. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution Proposed Solution Method (Continued) Equivalent circuit of a single converter at each dc ripple frequency [4]

11. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution (Continued) Proposed Solution Method (Continued) Equivalent circuit of a cluster of converters at fundamental frequency

12. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Proposed Solution Method (Continued) Equivalent circuit of a cluster of converters at each dc ripple frequency

13. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Probabilistic Model of Multiple Converters The bivariate normal distribution model of a converter harmonic current can be obtained by calculating mean value and variance of the pdf for real part and imaginary part of the harmonic current. To avoid the complicated derivation of theoretical probabilistic model of harmonic currents generated by a cluster of converters, a statistical approach is proposed.

14. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Probabilistic Model of Multiple Converters (Continued) Bivariate normal distribution model of a cluster of converter harmonic currents

15. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU as long as the number of samples, N, is sufficiently large, Statistical approach to find the mean value and variance of harmonic currents generated by a cluster of converters Probabilistic Model of Multiple Converters (Continued)

16. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Case Study ------------------------------- R d =50 Ω L d =1 mH L c =10 mHC d =10 uF ------------------------------- Test system (10 converters) Simplified circuit of a converter Basic converter data

17. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Case Study (Continued) All converters of the test system are assumed identical. The range of each firing angle is assumed uniformly distributed from 10º to 40º. Each converter firing angle is randomly sampled 500 times. The proposed approach is validated by using Monte Carlo simulation.

18. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Case Study (Continued) Comparison of harmonic current pdf -- proposed approach (-) and Monte Carlo simulation (*)

19. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Case Study (Continued). Comparison of the harmonic current cdf with (o) and without (+) considering dc ripple using the proposed approach

20. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Conclusions Solutions obtained by the proposed approach and by Monte Carlo simulation have a good agreement. The effect of dc ripples on harmonic currents is significant. Ignoring dc ripples may result in underestimation of 5-th harmonic current and overestimation of both 7-th and 13-th harmonic currents. The proposed statistical approach is simple and computationally efficient.

21. Department of Electrical Engineering National Chung Cheng University, Taiwan IEEE ICHQP 10, 2002, Rio de Janeiro NCCU Thank You!