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David Chapman
Copper Development Association
Copper Development Association
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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)
OIL-FILLED (HD428) UP TO24kV2)
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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)
OIL-FILLED (HD428) UP TO24kV2)
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
BA’
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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)
OIL-FILLED (HD428) UP TO24kV2)
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
C-C’
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
12%
88%
Winding
Magnetic
Total loss = 1685 W
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
79%
9%
12%
Resistance
Magnetic
Eddy current(10%)
Total loss = 1685 W
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
84%
4%
12%
Resistance
Magnetic
Eddy Current(5%)
Total loss = 1685 W
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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)
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Copper Development Associationwww.cda.org.uk
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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
%
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
Effect of triple-n harmonics in transformers
Triple-n harmonic currents circulate in delta windings - they do not propagate back onto the supply network
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
Harmonic mitigation by transformerDelta-star transformers
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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:
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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.
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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:
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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)
K-Rating of Transformers - US System
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
K-Rating of Transformers - US System
Next, a transformer with a higher K rating is selected from the standard range:
4, 9, 13, 20, 30, 40, 50
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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)
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
K-Rating - Calculation software
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
K-Rating - Calculation software
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
K-Rating - Calculation software
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
K-Rating - Calculation software
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
41%53%
6%
Resistance
Magnetic
Eddy Current
Total loss = 3245 W
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
80% load losses in a 100kVA C-C’ transformer
39%51%
10%
Resistance
Magnetic
Eddy Current
Total loss = 2156 W
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
C11528.190PP
ttempWorkingf
k °=×=×=
⎟⎠⎞
⎜⎝⎛ ∂−
×=− 10t
2TtimeLife
( )
years72402TtimeLife 5.210
PPP
tf
fk
=×=×=− −⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛ −×
−
Effect of additional losses on life-time80 % load
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
70% load losses in a 100kVA C-C’ transformer
38%50%
12%
Resistance
Magnetic
Eddy Current
Total loss = 1699 W
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
C75.900083.190PP
ttempWorkingf
k °=×=×=
⎟⎠⎞
⎜⎝⎛ ∂−
×=− 10t
2TtimeLife
( )
years382402TtimeLife 075.010
PPP
tf
fk
=×=×=− −⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛ −×
−
Effect of additional losses on life-time70 % load
www.leonardo-energy.org
Copper Development Associationwww.cda.org.uk
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
Copper Development Association
Copper Development Association
www.cda.org.uk