Rating of Transformers supplying
Harmonic-Rich Loads
David Chapman
Copper Development Association
david.chapman@copperdev.co.uk
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
– most important during high load periods
Eddy current loss
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Distribution transformer efficiency standards
HD 428 & 538
Load Losses for Distribution
Transformers
RATED
POWER
No-Load Losses for Distribution
Transformers
OIL-FILLED (HD428) UP TO
24kV2)
DRY TYPE
(HD538)
LIST A
12kV
PRIMARY
LIST B
LIST C
OIL-FILLED (HD428) UP TO
24kV2)
LIST A’
LIST B’
DRY TYPE
(HD538)
LIST C’
12kV
PRIMARY
3)
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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Distribution transformer efficiency standards
HD 428 & 538
Load Losses for Distribution
Transformers
RATED
POWER
No-Load Losses for Distribution
Transformers
OIL-FILLED (HD428) UP TO
24kV2)
DRY TYPE
(HD538)
LIST A
12kV
PRIMARY
LIST B
LIST C
OIL-FILLED (HD428) UP TO
24kV2)
LIST A’
LIST B’
DRY TYPE
(HD538)
LIST C’
12kV
PRIMARY
3)
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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Distribution transformer efficiency standards
HD 428 & 538
Load Losses for Distribution
Transformers
RATED
POWER
No-Load Losses for Distribution
Transformers
OIL-FILLED (HD428) UP TO
24kV2)
DRY TYPE
(HD538)
LIST A
12kV
PRIMARY
LIST B
LIST C
OIL-FILLED (HD428) UP TO
24kV2)
LIST A’
LIST B’
DRY TYPE
(HD538)
LIST C’
12kV
PRIMARY
3)
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’
Source: CENELEC
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
12%
Winding
Magnetic
88%
Total loss = 1685 W
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
12%
9%
Resistance
Magnetic
79%
Eddy current
(10%)
Total loss = 1685 W
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
12%
4%
Resistance
Magnetic
Eddy Current
(5%)
84%
Total loss = 1685 W
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Current waveform for a typical PC
2.0000
1.5000
1.0000
Current (A)
0.5000
0.0000
0
90
180
270
360
-0.5000
-1.0000
-1.5000
-2.0000
Degrees
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Harmonic profile of a typical PC
0.6000
0.5000
Current (A)
0.4000
0.3000
0.2000
0.1000
0.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Harmonic
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
17
Typical harmonic profile - 6 pulse converter
25
20
15
%
10
5
0
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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Effect of harmonics on 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
Copper Development Association
www.leonardo-energy.org
www.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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Harmonic mitigation by transformer
Delta-star transformers
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Effect of harmonics on 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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Increased Eddy current losses in transformers
Increased eddy current loss can be calculated by:
Peh = Pef
h = h max
∑
h =1
I h2 h 2
where:
Peh is the total eddy current loss
Pef is the eddy current loss at fundamental frequency
h
is the harmonic order
is the per unit RMS current at harmonic h
Ih
Copper Development Association
www.leonardo-energy.org
www.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.the
American system, established by UL and
manufacturers, which specifies harmonic capability
of 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.
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating of Transformers - US System
First, calculate the K factor of the load according to:
K=
h = h max
∑
h =1
I h2 h 2
where:
h is the harmonic order
Ih is the RMS current at h in per unit of total current
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating of Transformers - US System
p
y
0.6000
0.5000
Current (A)
0.4000
0.3000
0.2000
0.1000
0.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Harmonic
For this typical PC load, the K factor is 11.6
(For worked examples see LPQI AN 3.5.2 or IEE 1100 1992)
Copper Development Association
www.leonardo-energy.org
www.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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
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:
2 n=N ⎛
⎡
⎞⎤
⎛
⎞
I
e ⎛ I1 ⎞
q
n
⎜
⎟⎥
⎜
⎟
K = ⎢1 +
n
⎜
⎟ ∑
1 + e ⎝ I ⎠ n + 2 ⎜ ⎜⎝ I 1 ⎟⎠ ⎟ ⎥
⎢
⎝
⎠⎦
⎣
2
0 .5
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
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating of Transformers - European System
p
y
0.6000
0.5000
Current (A)
0.4000
0.3000
0.2000
0.1000
0.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Harmonic
For the same PC load, the de-rating factor is 78%
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Harmonic Diversity - K Factor
16
14
12
K Factor
10
8
6
4
2
0
1
2
5
10
20
41
No of Units (pairs)
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating - Calculation software
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating - Calculation software
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating - Calculation software
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
K-Rating - Calculation software
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Full load losses in a 100kVA C-C’ transformer
53%
41%
Resistance
Magnetic
Eddy Current
6%
Total loss = 3245 W
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
80% load losses in a 100kVA C-C’ transformer
51%
39%
Resistance
Magnetic
Eddy Current
10%
Total loss = 2156 W
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Effect of additional losses on life-time
80 % load
Working temp = t ×
Life − time = T × 2
Life − time = T × 2
Pk
= 90 × 1.28 = 115°C
Pf
⎛ ∂t ⎞
−⎜
⎟
⎝ 10 ⎠
⎛ (Pk − Pf ) ⎞
⎟
⎜ t×
Pf
⎟
⎜
−⎜
⎟
10
⎟⎟
⎜⎜
⎠
⎝
= 40 × 2− 2.5 = 7 years
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
70% load losses in a 100kVA C-C’ transformer
50%
38%
Resistance
Magnetic
Eddy Current
12%
Total loss = 1699 W
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
Effect of additional losses on life-time
70 % load
Working temp = t ×
Life − time = T × 2
Life − time = T × 2
Pk
= 90 × 1.0083 = 90.75°C
Pf
⎛ ∂t ⎞
−⎜
⎟
⎝ 10 ⎠
⎛ (Pk − Pf ) ⎞
⎟
⎜ t×
Pf
⎟
⎜
−⎜
⎟
10
⎟⎟
⎜⎜
⎠
⎝
= 40 × 2− 0.075 = 38 years
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
The real world
Selection and management
ƒ small change in loading - large effect on lifetime.
ƒ derate then add the ‘headroom’
ƒ management practices must maintain derating
for the life of the transformer when
– adding new loads
– making changes to any harmonic filters within the
installation
Copper Development Association
www.leonardo-energy.org
www.cda.org.uk
David Chapman
Copper Development Association
david.chapman@copperdev.co.uk
www.cda.org.uk
Copper Development Association