2. Copper Development Association K Rating of Transformers supplying Harmonic Rich Loads www.cda.org.uk

3. Copper Development Association Losses in Transformers No-load loss (‘iron loss’) – energy consumed in eddy current and hysteresis loss – present 100% of the time Load losses Resistive loss (‘copper loss’) –dependent on square of load current –important only during peak load periods Eddy current loss

4. Copper Development Association Distribution transformer efficiency standards HD 428 (538) Source: CENELEC

5. Copper Development Association Full load losses in a 100kVA C-C’ transformer Total loss = 1685 W

6. Copper Development Association Full load losses in a 100kVA C-C’ transformer Total loss = 1685 W

7. Copper Development Association Transformers supplying harmonic loads must be appropriately de-rated.  Harmonic currents, being of higher frequency, cause increased magnetic losses in the core and increased eddy current and skin effect losses in the windings.  Triple-n harmonic currents circulate in delta windings, increasing resistive losses, operating temperature and reducing effective load capacity. Effect of harmonics on transformers

8. Copper Development Association Current waveform for a typical Personal Computer

9. Copper Development Association Harmonic profile of a typical Personal Computer

10. Copper Development Association Typical harmonic profile - six-pulse controller

11. Copper Development Association Increased Eddy current losses in transformers where: P eh is the total eddy current loss P ef is the eddy current loss at fundamental frequency h is the harmonic order I h is the RMS current at harmonic h as a percentage of rated fundamental current Increase in eddy current loss can be calculated by:

12. Copper Development Association K-Rating of Transformers Two rating or de-rating systems for transformers:- American system, established by UL and manufacturers, specifies harmonic capability of transformer - known as K factor. European system, developed by IEC, defines de-rating factor for standard transformers - known as factor K.

13. Copper Development Association K-Rating of Transformers - US System where: h is the harmonic order I h is the RMS current at h in per unit of rated load current First, calculate the K factor of the load according to:

14. Copper Development Association For this typical PC load, the K factor is 11.6 (See IEE 1100-1992 for a worked example) K-Rating of Transformers - US System

15. Copper Development Association Full load losses in a 100kVA C-C’ transformer Total loss = 3245 W

16. Copper Development Association K-Rating of Transformers - US System Next, select a transformer with a higher K rating: standard ratings are 4, 9, 13, 20, 30, 40 and 50. NB - for non K-rated transformers: The K factor describes the increase in eddy current losses, not total losses. Eddy current losses at the fundamental are normally around 10 % of the resistive losses, so that a load K factor of 11.6 would require de-rating to 70 % load.

17. Copper Development Association K-Rating of Transformers - European System In Europe, the transformer de-rating factor is calculated according to the formulae in BS 7821 Part 4. The factor K is given by: e is ratio of eddy current loss (50 Hz) to resistive loss n is the harmonic order q is dependent on winding type and frequency, typically 1.5 to 1.7

18. Copper Development Association K-Rating of Transformers - European System For the same PC load, the de-rating factor is 78%

19. Copper Development Association Harmonic Diversity - K Factor

20. Copper Development Association K-Rating - Calculation software

21. Copper Development Association Full load losses in a 100kVA C-C’ transformer Total loss = 3245 W

22. Copper Development Association Effect of additional losses on life-time where T is working temperature at rated fundamental power, P f,, P k is the total power and T is the rated life-time in years

23. Copper Development Association 80% load losses in a 100kVA C-C’ transformer Total loss = 2156 W

24. Copper Development Association Effect of additional losses on life-time where T is working temperature at rated fundamental power, P f,, P k is the total power and T is the rated life-time in years

25. Copper Development Association K-Rating - Calculation software

26. Copper Development Association K-Rating - Calculation software

27. Copper Development Association Full load losses in a 100kVA C-C’ transformer Total loss = 2605 W

28. Copper Development Association Effect of additional losses on life-time where T is working temperature at rated fundamental power, P f,, P k is the total power and T is the rated life-time in years

29. Copper Development Association K-Rating - Calculation software

30. Copper Development Association K-Rating or De-rating? ‘K-rated’ transformers are designed to supply harmonic loads by : using stranded conductors to reduce eddy current losses bringing secondary winding star point connections out separately to provide a 300% neutral rating

31. Copper Development Association ‘De-rating’ a standard transformer has some disadvantages:-  primary over-current protection may be too high to protect the secondary and too low to survive the in-rush current  future increases in loading must take the de-rating fully into account  it is less efficient  the neutral star point is likely to be rated at only 100% of the phase current K-Rating or De-rating?

32. Copper Development Association Transformers supplying harmonic loads must be appropriately de-rated.  Harmonic currents, being of higher frequency, cause increased magnetic losses in the core and increased eddy current and skin effect losses in the windings.  Triple-n harmonic currents circulate in delta windings, increasing resistive losses, operating temperature and reducing effective load capacity. Effect of harmonics on transformers

33. Copper Development Association Effect of triple-n harmonics in transformers Triple-n harmonic currents circulate in delta windings - they do not propagate back onto the supply network. - but the transformer must be specified and rated to cope with the additional losses.

34. Copper Development Association www.cda.org.uk