Copper Development Association K Rating of Transformers supplying Harmonic Rich Loads .

Copper Development Association


K Rating of Transformers supplying Harmonic Rich Loads

www.cda.org.uk


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


Distribution transformer efficiency standards HD 428 (538)

Source: CENELEC

Load Losses for Distribution Transformers No-Load Losses for Distribution Transformers

RATED

POWER

OIL-FILLED (HD428) UP TO 24kV2) DRY TYPE

(HD538)

OIL-FILLED (HD428) UP TO 24kV2) DRY TYPE

(HD538)

LIST A LIST B LIST C 12kV

PRIMARY 3)

LIST A’ LIST B’ LIST C’ 12kV

PRIMARY 3)

kVA W W W W W W W W

50 1,100 1,350 875 N/A 190 145 125 N/A

100 1,750 2,150 1,475 2,000 320 260 210 440

160 2,350 3,100 2,000 2,700 460 375 300 610

250 3,250 4,200 2,750 3,500 650 530 425 820

400 4,600 6,000 3,850 4,900 930 750 610 1,150

630 /4%1) 6,500 8,400 5,400 7,300 1,300 1,030 860 1,500

630 /6% 6,750 8,700 5,600 7,600 1,200 940 800 1,370

1000 10,500 13,000 9,500 10,000 1,700 1,400 1,100 2,000

1600 17,000 20,000 14,000 14,000 2,600 2,200 1,700 2,800

2500 26,500 32,000 22,000 21,000 3,800 3,200 2,500 4,300


Full load losses in a 100kVA C-C’ transformer

12%

88%

Winding

Magnetic

Total loss = 1685 W



79%

9%

12% Resistance

Magnetic

Eddy Current

Total loss = 1685 W


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


Current waveform for a typical Personal Computer


Harmonic profile of a typical Personal Computer


Typical harmonic profile - six-pulse controller

Six pulse bridge - harmonic current

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Harmonic number

%


Increased Eddy current losses in transformers

2hh

1h

2hefeh hIPP

max

where: Peh is the total eddy current loss

Pef is the eddy current loss at fundamental frequencyh is the harmonic orderIh is the RMS current at harmonic h as a percentage of rated fundamental current

Increase in eddy current loss can be calculated by:


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.


K-Rating of Transformers - US System

2hh

1h

2hhIK

max

where: h is the harmonic order Ih is the RMS current at h in per unit of rated load current

First, calculate the K factor of the load according to:


For this typical PC load, the K factor is 11.6

(See IEE 1100-1992 for a worked example)




41%53%

6%

Resistance

Magnetic

Eddy Current

Total loss = 3245 W



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.


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:

5.0

2

2

1

2

1

11

Nn

n

nq

I

In

I

I

e

eK

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


K-Rating of Transformers - European System

For the same PC load, the de-rating factor is 78%


K Factor

0

2

4

6

8

10

12

14

16

1 2 5 10 20 41

No of Units (pairs)

K F

acto

r

Harmonic Diversity - K Factor


K-Rating - Calculation software



41%53%

6%

Resistance

Magnetic

Eddy Current

Total loss = 3245 W


CP

PttempWorking

f

k 17393.190

102t

TtimeLife

yearsTtimeLife

f

fk

P

PPt

13.02402 3.8

10

Effect of additional losses on life-time

where T is working temperature at rated fundamental power, Pf,, Pk is the total power and T is the rated life-time in years


80% load losses in a 100kVA C-C’ transformer

39%51%

10%

Resistance

Magnetic

Eddy Current

Total loss = 2156 W


CP

PttempWorking

f

k 11528.190

102t

TtimeLife

yearsTtimeLife

f

fk

P

PPt

72402 5.2

10





51%41%

8%

Resistance

Magnetic

Eddy Current

Total loss = 2605 W


CP

PttempWorking

f

k 13955.190

102t

TtimeLife

yearsTtimeLife

f

fk

P

PPt

34.12402 9.4

10




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


‘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?


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


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.



www.cda.org.uk

Copper Development Association K Rating of Transformers supplying Harmonic Rich Loads .

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