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Copper Development Association
Copper DevelopmentAssociation
K Rating of Transformerssupplying Harmonic Rich Loads
www.cda.org.uk
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Copper Development Association
Losses in Transformers
No-load loss (‘iron loss’)
– energy consumed in eddy current and hysteresis loss
– present 100% of the time
oad losses
!esisti"e loss (‘copper loss’)
– dependent on s#uare of load current
– important only during peak load periods
$ddy current loss
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Copper Development Association
Distribution transformer efficiency standards
HD 428 (538)
Source: CENELEC
Load Losses for Distribution Transformers No-Load Losses for Distribution Transformers
RATED
POWER
OIL-FILLED (HD42! "P TO 24#$2! DR% T%PE
(HD&'!
OIL-FILLED (HD42! "P TO 24#$2! DR% T%PE
(HD&'!
LIT A LIT ) LIT * +2#$
PRI,AR% '!
LIT A LIT ) LIT * +2#$
PRI,AR% '!
#$A W W W W W W W W
&. +/+.. +/'&. 0& N1A +. +4& +2& N1A
100 1,750 2,150 1,475 2,000 320 260 210 440
+3. 2/'&. '/+.. 2/... 2/0.. 43. '0& '.. 3+.
2&. '/2&. 4/2.. 2/0&. '/&.. 3&. &'. 42& 2.
4.. 4/3.. 3/... '/&. 4/.. '. 0&. 3+. +/+&.
3'. 14+! 3/&.. /4.. &/4.. 0/'.. +/'.. +/.'. 3. +/&..
3'. 13 3/0&. /0.. &/3.. 0/3.. +/2.. 4. .. +/'0.
+... +./&.. +'/... /&.. +./... +/0.. +/4.. +/+.. 2/...
+3.. +0/... 2./... +4/... +4/... 2/3.. 2/2.. +/0.. 2/..
2&.. 23/&.. '2/... 22/... 2+/... '/.. '/2.. 2/&.. 4/'..
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Copper Development Association
Full load losses in a 100kV !"!# transformer
12%
88%
Winding
Magnetic
Total loss $ 1%&' (
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Copper Development Association
Full load losses in a 100kV !"!# transformer
79%
9%
12% Resistance
Magnetic
Eddy Current
Total loss $ 1%&' (
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Copper Development Association
ransformers supplying harmonic loads must &eappropriately de-rated.
• 'armonic currents &eing of higher fre#uency
cause increased magnetic losses in the core and
increased eddy current and skin effect losses in
the windings.
• riple-n harmonic currents circulate in delta
windings increasing resisti"e losses operatingtemperature and reducing effecti"e load capacity.
)ffect of harmonics on transformers
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Copper Development Association
!urrent *a+eform for a typical ,ersonal !omputer
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Copper Development Association
Harmonic profile of a typical ,ersonal !omputer
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Copper Development Association
Typical harmonic profile " si-"pulse controller
)i* pulse &ridge - 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
'armonic num&er
%
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Copper Development Association
.ncreased )ddy current losses in transformers
255
+5
25ef e5 5IPP
ma6
∑==
=
where+
P eh
is the total eddy current loss
P ef is the eddy current loss at fundamental
fre#uencyh is the harmonic order
I h
is the !, current at harmonic h as a
percentage of rated fundamental current
ncrease in eddy current loss can &e calculated &y+
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Copper Development Association
K"Rating of Transformers
wo rating or de-rating systems for transformers+-
• merican system esta&lished &y / and
manufacturers specifies harmonic capa&ility of
transformer - known as K factor .
• $uropean system de"eloped &y $ defines
de-rating factor for standard transformers -
known as factor K .
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Copper Development Association
K"Rating of Transformers " / ystem
255
+5
255I7
ma6
∑==
=
where+
h is the harmonic order
I h is the !, current at h in per unit of rated load current
irst calculate the 2 factor of the load according to+
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Copper Development Association
or this typical 3 load the 2 factor is 11.4
(ee $$ 1100-1556 for a worked e*ample)
K"Rating of Transformers " / ystem
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Copper Development Association
Full load losses in a 100kV !"!# transformer
1%!"%
#%
Resistance
Magnetic
Eddy Current
Total loss $ 23' (
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Copper Development Association
K"Rating of Transformers " / ystem
Ne*t select a transformer with a higher 2 rating+standard ratings are 7 5 18 60 80 70 and 90.
N: - for non 2-rated transformers+
he 2 factor descri&es the increase in eddy current
losses not total losses.
$ddy current losses at the fundamental are normally
around 10 % of the resisti"e losses so that a load 2factor of 11.4 would re#uire de-rating to ;0 % load.
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Copper Development Association
K"Rating of Transformers " )uropean ystem
n $urope the transformer de-rating factor is calculated
according to the formulae in : ;<61 3art 7. he factor2 is gi"en &y+
&8.
2
2
+
2
+
++
++= ∑
=
+
N n
n
nq
I
I
n I
I
e
e
K
e is ratio of eddy current loss (90 '=) to resisti"e loss
n is the harmonic order
# is dependent on winding type and fre#uencytypically 1.9 to 1.;
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Copper Development Association
K"Rating of Transformers " )uropean ystem
or the same 3 load the de-rating factor is ;<%
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Copper Development Association
2 actor
0
2
4
6
8
10
12
14
16
1 2 5 10 20 41
No of /nits (pairs)
2 1
a c t o r
Harmonic Di+ersity " K Factor
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Copper Development Association
K"Rating " !alculation soft*are
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Copper Development Association
Full load losses in a 100kV !"!# transformer
1%!"%
#%
Resistance
Magnetic
Eddy Current
Total loss $ 23' (
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Copper Development Association
! ,
, t temp(orking
f
k °17393.190
∂
×
10
2
t
T time Life
yearsT time Life
f
f k
,
, , t
13.02402 3.8
10
×
)ffect of additional losses on life"time
*here T is *orking temperature at rated fundamental po*er4 , f 44 , k is the total
po*er and T is the rated life"time in years
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Copper Development Association
&05 load losses in a 100kV !"!# transformer
39%51%
10%
Resistance
Magnetic
Eddy Current
Total loss $ 21'% (
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Copper Development Association
! ,
, t temp(orking
f
k °11528.190
∂
×
10
2
t
T time Life
yearsT time Life
f
f k
,
, , t
72402 5.2
10
×
)ffect of additional losses on life"time
*here T is *orking temperature at rated fundamental po*er4 , f 44 , k is the total
po*er and T is the rated life"time in years
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Copper Development Association
K"Rating " !alculation soft*are
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Copper Development Association
K"Rating " !alculation soft*are
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Copper Development Association
Full load losses in a 100kV !"!# transformer
!1%1%
8%
Resistance
Magnetic
Eddy Current
Total loss $ 2%0' (
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Copper Development Association
! ,
, t temp(orking
f
k °13955.190
∂
×
10
2
t
T time Life
yearsT time Life
f
f k
,
, , t
34.12402 9.4
10
×
)ffect of additional losses on life"time
*here T is *orking temperature at rated fundamental po*er4 , f 44 , k is the total
po*er and T is the rated life"time in years
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Copper Development Association
K"Rating " !alculation soft*are
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Copper Development Association
K"Rating or De"rating6
‘2-rated’ transformers are designed to supply harmonic
loads &y +
• using stranded conductors to reduce eddy current
losses
• &ringing secondary winding star point connections
out separately to pro"ide a 800% neutral rating
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Copper Development Association
‘>e-rating’ a standard transformer has some
disad"antages+-
• primary o"er-current protection may &e too high
to protect the secondary and too low to sur"i"e 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 &e rated at only100% of the phase current
K"Rating or De"rating6
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Copper Development Association
ransformers supplying harmonic loads must &e
appropriately de-rated.
• 'armonic currents &eing of higher fre#uency
cause increased magnetic losses in the core and
increased eddy current and skin effect losses inthe windings.
• riple-n harmonic currents circulate in delta
windings increasing resisti"e losses operatingtemperature and reducing effecti"e load capacity.
)ffect of harmonics on transformers
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Copper Development Association
)ffect of triple"n harmonics in transformers
riple-n harmonic currents circulate in delta windings -
they do not propagate &ack onto the supply network.
- &ut the transformer must &e specified and rated to
cope with the additional losses.
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Copper Development Association
Copper DevelopmentAssociation
www.cda.org.uk