Transcript 5 Minute Presentation
Copper Development Association
K Rating of Transformers supplying Harmonic Rich Loads
www.cda.org.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
–
important only during peak load periods Eddy current loss Copper Development Association
Distribution transformer efficiency standards HD 428 (538)
RATED POWER kVA 50
100
160 250 400 630 /4% 1) 630 /6% 1000 1600 2500 Load Losses for Distribution Transformers OIL-FILLED (HD428) UP TO 24kV 2) DRY TYPE (HD538) LIST A LIST B LIST C W 1,100
1,750
2,350 3,250 4,600 6,500 6,750 10,500 17,000 26,500 W 1,350
2,150
3,100 4,200 6,000 8,400 8,700 13,000 20,000 32,000 W 875
1,475
2,000 2,750 3,850 5,400 5,600 9,500 14,000 22,000 12kV PRIMARY 3) W N/A
2,000
2,700 3,500 4,900 7,300 7,600 10,000 14,000 21,000 No-Load Losses for Distribution Transformers OIL-FILLED (HD428) UP TO 24kV 2) DRY TYPE (HD538) LIST A’ LIST B’ LIST C’ W 190
320
460 650 930 1,300 1,200 1,700 2,600 3,800 W 145
260
375 530 750 1,030 940 1,400 2,200 3,200 W 125
210
300 425 610 860 800 1,100 1,700 2,500 12kV PRIMARY 3) W N/A
440
610 820 1,150 1,500 1,370 2,000 2,800 4,300
Source: CENELEC
Copper Development Association
Full load losses in a 100kVA C-C’ transformer
12% 88% Winding Magnetic
Total loss = 1685 W
Copper Development Association
Full load losses in a 100kVA C-C’ transformer
12% 9% 79% Resistance Magnetic Eddy Current
Total loss = 1685 W
Copper Development Association
Effect of harmonics on transformers
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.
Copper Development Association
Current waveform for a typical Personal Computer
Desktop System
2.0000
1.5000
1.0000
0.5000
0.0000
0 -0.5000
-1.0000
-1.5000
-2.0000
90 180 270 360
Degrees Copper Development Association
Harmonic profile of a typical Personal Computer
Desktop System
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
1 2 3 4 5 6 7 8 9
Harmonic
10 11 12 13 14 15 16 17
Copper Development Association
Typical harmonic profile - six-pulse controller
Six pulse bridge - harmonic current
25 20 15
%
10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Harmonic number
16 17 18 19 20 21 22 23 24 25
Copper Development Association
Increased Eddy current losses in transformers
Increase in eddy current loss can be calculated by:
P eh P ef h h h 1 max I 2 h h 2
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 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.
Copper Development Association
K-Rating of Transformers - US System
First, calculate the K factor of the load according to:
K h h h 1 max I 2 h h 2
where: h is the harmonic order
I h
is the RMS current at h in per unit of rated load current Copper Development Association
K-Rating of Transformers - US System
Desktop System
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
1 2 3 4 5 6 7 8 9
Harmonic
10 11 12 13 14 15 16 17
For this typical PC load, the K factor is 11.6
(See IEE 1100-1992 for a worked example) Copper Development Association
Full load losses in a 100kVA C-C’ transformer
53% 41% 6% Resistance Magnetic Eddy Current
Total loss = 3245 W
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 losses, not total losses. current 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.
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:
K
1
e
1
e
I
1
I
2
n n
N
2
n q
I n 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 and frequency, typically 1.5 to 1.7
Copper Development Association
K-Rating of Transformers - European System
Desktop System
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
1 2 3 4 5 6 7 8 9
Harmonic
10 11 12 13 14 15 16 17
For the same PC load, the de-rating factor is 78% Copper Development Association
Harmonic Diversity - K Factor
K Factor
10 4 2 8 6 16 14 12 0 1 2
Copper Development Association
5
No of Units (pairs)
10 20 41
K-Rating - Calculation software
Copper Development Association
Full load losses in a 100kVA C-C’ transformer
53% 6% 41% Resistance Magnetic Eddy Current
Total loss = 3245 W
Copper Development Association
Effect of additional losses on life-time
Working temp
t
P P f k
90
1 .
93
Life
time
T Life
time
T
t
2
10
t
P k
P f P f
10
2
40
2
8 .
3
173
C
0 .
13
years where T is working temperature at rated fundamental power, P f ,, P k power and T is the rated life-time in years is the total
Copper Development Association
80% load losses in a 100kVA C-C’ transformer 51% 10% 39% Resistance Magnetic Eddy Current Total loss = 2156 W
Copper Development Association
Effect of additional losses on life-time
Working temp
t
P P f k
90
1 .
28
Life Life
time
T time
T
t
2
10
t
P k
P f P f
10 2
40
2
2 .
5 115
C
7
years where T is working temperature at rated fundamental power, P f ,, P k power and T is the rated life-time in years is the total
Copper Development Association
K-Rating - Calculation software
Copper Development Association
K-Rating - Calculation software
Copper Development Association
Full load losses in a 100kVA C-C’ transformer
41% 8% 51% Resistance Magnetic Eddy Current
Total loss = 2605 W
Copper Development Association
Effect of additional losses on life-time
Working temp
t
P P f k
90
1 .
55
Life Life
time time
T T
t
2
10
t
P k
P f P f
10
2
40
2
4 .
9
139
C
1 .
34
years where T is working temperature at rated fundamental power, P f ,, P k power and T is the rated life-time in years is the total
Copper Development Association
K-Rating - Calculation software
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 Copper Development Association
K-Rating or De-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 Copper Development Association
Effect of harmonics on transformers
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.
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.
Copper Development Association
Copper Development Association www.cda.org.uk
Copper Development Association