rom8 harmonic derating

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Copper Development Association

Copper DevelopmentAssociation

K Rating of Transformerssupplying Harmonic Rich Loads

www.cda.org.uk




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




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/'..




Full load losses in a 100kV !"!# transformer

12%

88%

Winding

Magnetic

Total loss $ 1%&' (





79%

9%

12% Resistance

Magnetic

Eddy Current

Total loss $ 1%&' (




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




!urrent *a+eform for a typical ,ersonal !omputer




Harmonic profile of a typical ,ersonal !omputer




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

%




.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+




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 .




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+




or this typical 3 load the 2 factor is 11.4

(ee $$ 1100-1556 for a worked e*ample)






1%!"%

#%

Resistance

Magnetic

Eddy Current

Total loss $ 23' (





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.




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.;




K"Rating of Transformers " )uropean ystem

or the same 3 load the de-rating factor is ;<%




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




K"Rating " !alculation soft*are





1%!"%

#%

Resistance

Magnetic

Eddy Current

Total loss $ 23' (




! ,

, 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




&05 load losses in a 100kV !"!# transformer

39%51%

10%

Resistance

Magnetic

Eddy Current

Total loss $ 21'% (




! ,

, t temp(orking

f

k °11528.190

∂

×

10

2

t

T time Life

yearsT time Life

f

f k

,

, , t

72402 5.2

10

×








!1%1%

8%

Resistance

Magnetic

Eddy Current

Total loss $ 2%0' (




! ,

, 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

×







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




‘>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




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




)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.




Copper DevelopmentAssociation

www.cda.org.uk

rom8 harmonic derating

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