Rating of Transformers supplying Harmonic Rich Loadsgo.leonardo-energy.org/rs/europeancopper/images/transformers... · Rating of Transformers supplying Harmonic-Rich Loads. ... Rating

David Chapman

Copper Development Association

[email protected]


Rating of Transformers supplying Harmonic-Rich Loads

www.leonardo-energy.org

Copper Development Associationwww.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

– most important during high load periods

Eddy current loss



Distribution transformer efficiency standardsHD 428 & 538

Source: CENELEC

Load Losses for DistributionTransformers

No-Load Losses for DistributionTransformers

RATEDPOWER

OIL-FILLED (HD428) UP TO24kV2)

DRY TYPE(HD538)


DRY TYPE(HD538)

LIST A LIST B LIST C 12kVPRIMARY

3)

LIST A’ LIST B’ LIST C’ 12kVPRIMARY 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% 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




Source: CENELEC



RATEDPOWER


DRY TYPE(HD538)


DRY TYPE(HD538)


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% 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

BA’




Source: CENELEC



RATEDPOWER


DRY TYPE(HD538)


DRY TYPE(HD538)


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% 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

C-C’



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

12%

88%

Winding

Magnetic

Total loss = 1685 W




79%

9%

12%

Resistance

Magnetic

Eddy current(10%)

Total loss = 1685 W




84%

4%

12%

Resistance

Magnetic

Eddy Current(5%)

Total loss = 1685 W



Current waveform for a typical PC

-2.0000

-1.5000

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

0 90 180 270 360

Degrees

Curr

ent (

A)



0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Harmonic

Cur

rent

(A)

Harmonic profile of a typical PC



Typical harmonic profile - 6 pulse converter

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

%



There are two issues that affect Transformers

supplying harmonic-rich loads:

• Triple-n harmonic currents circulate in delta windings,

increasing resistive losses, operating temperature and

reducing effective load capacity

• Harmonic currents, being of higher frequency, cause

increased magnetic losses in the core and increased

eddy current and skin effect losses in the windings

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



Harmonic mitigation by transformerDelta-star transformers



There are two issues that affect Transformers

supplying harmonic-rich loads:

• Triple-n harmonic currents circulate in delta windings,

increasing resistive losses, operating temperature and

reducing effective load capacity

• Harmonic currents, being of higher frequency, cause

increased magnetic losses in the core and increased

eddy current and skin effect losses in the windings

Effect of harmonics on transformers



Increased Eddy current losses in transformers

2

1

2maxhIPP

hh

hhefeh ∑=

=

=

where: Peh is the total eddy current lossPef is the eddy current loss at fundamental frequencyh is the harmonic orderIh is the per unit RMS current at harmonic h

Increased eddy current loss can be calculated by:



K-Rating of Transformers

There are two approaches to rating transformers supplying harmonic rich load:-

• Designing for the anticipated duty - e.g.theAmerican system, established by UL and manufacturers, which specifies harmonic capabilityof the transformer - known as K-factor.

• De-rating to survive the anticipated duty - e.g. the European system, developed by IEC, which defines de-rating factor for standard transformers - known as factor K.



K-Rating of Transformers - US System

2

1

2maxhIK

hh

hh∑=

=

=

where: h is the harmonic orderIh is the RMS current at h in per unit of total current

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



For this typical PC load, the K factor is 11.6

(For worked examples see LPQI AN 3.5.2 or IEE 1100 1992)

p y

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Harmonic

Cur

rent

(A)





Next, a transformer with a higher K rating is selected from the standard range:

4, 9, 13, 20, 30, 40, 50



K-Rating of Transformers - European SystemIn 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

21

11

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

++= ∑

=

+

Nn

n

nq

IIn

II

eeK

e is ratio of eddy current loss (50 Hz) to resistive loss

n is the harmonic order

q is dependent on winding type & frequency, typically 1.5 to 1.7



K-Rating of Transformers - European System

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

p y

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Harmonic

Cur

rent

(A)



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



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

39%51%

10%

Resistance

Magnetic

Eddy Current

Total loss = 2156 W



C11528.190PP

ttempWorkingf

k °=×=×=

⎟⎠⎞

⎜⎝⎛ ∂−

×=− 10t

2TtimeLife

( )

years72402TtimeLife 5.210

PPP

tf

fk

=×=×=− −⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛ −×

−

Effect of additional losses on life-time80 % load



70% load losses in a 100kVA C-C’ transformer

38%50%

12%

Resistance

Magnetic

Eddy Current

Total loss = 1699 W



C75.900083.190PP

ttempWorkingf

k °=×=×=

⎟⎠⎞

⎜⎝⎛ ∂−

×=− 10t

2TtimeLife

( )

years382402TtimeLife 075.010

PPP

tf

fk

=×=×=− −⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛ −×

−

Effect of additional losses on life-time70 % load



The real world

Selection and management

small change in loading - large effect on lifetime.

derate then add the ‘headroom’

management practices must maintain derating

for the life of the transformer when

– adding new loads

– making changes to any harmonic filters within the

installation

David Chapman


[email protected]


www.cda.org.uk

Documents

Rating of Transformers supplying Harmonic Rich Loadsgo.leonardo-energy.org/rs/europeancopper/images/transformers... · Rating of Transformers supplying Harmonic-Rich Loads. ... Rating