transformers
DESCRIPTION
transformersTRANSCRIPT
1
Design, selection and operation of distribution transformers
Stefan FassbinderDeutsches KupferinstitutAm Bonneshof 5D-40474 DüsseldorfTel.: +49 211 4796-323Fax: +49 211 [email protected]
deutsch
English
2
The German Copper Institute, DKI, is the central information and advisory service dealing with all uses of copper and copper alloys. We offer our services to:
Commercial companies The skilled trades Industry R & D institutes Universities Artists and craftsmen Students Private individuals
We can be contacted by: post phone fax e-mail internet online database, or personally
3
1. Basics: “Gigantomania” or a necessity of economics?
Why build power stations in such huge units that you need such big transformers?
4
This one weighs 300t and does 600MVA...
...and this one here weighs 300g and should therefore do 600VA! But in fact it only does 6VA!
5
The coherence is given by an empirical formula
It's a law of physics: Higher energy density in larger plant
4/3*0,7 kVASkgM NFe
4/3*5,1 kVASkgM NCu
Spezifischer Kupfergehaltvon Transformatoren
1E-02kg
1E-01kg
1E+00kg
1E+01kg
1E+02kg
1E+03kg
1E+04kg
1E+05kg
1E-03kVA 1E-01kVA 1E+01kVA 1E+03kVA 1E+05kVA 1E+07kVA
Trafo-Nennleistung
Ku
pfe
r-E
insa
tz
20%
30%
40%
50%
60%
70%
80%
90%
100%
Vorgefundene Beispiel-TrafosTheoretische Herleitung
Spezifischer Kupfergehaltvon Transformatoren
1E-02kg
1E-01kg
1E+00kg
1E+01kg
1E+02kg
1E+03kg
1E+04kg
1E+05kg
1E-03kVA 1E-01kVA 1E+01kVA 1E+03kVA 1E+05kVA 1E+07kVA
Trafo-Nennleistung
Ku
pfe
r-E
insa
tz
20%
30%
40%
50%
60%
70%
80%
90%
100%
Wir
kun
gsg
rad
Vorgefundene Beispiel-TrafosTheoretische HerleitungWirkungsgrad
Specific copper contentof transformers
1E-02kg
1E-01kg
1E+00kg
1E+01kg
1E+02kg
1E+03kg
1E+04kg
1E+05kg
1E-03kVA 1E-01kVA 1E+01kVA 1E+03kVA 1E+05kVA 1E+07kVA
Transformer rated throughput
Co
pp
er
con
ten
t
20%
30%
40%
50%
60%
70%
80%
90%
100%
Example transformers foundTheoretical Deduction
Specific copper contentof transformers
1E-02kg
1E-01kg
1E+00kg
1E+01kg
1E+02kg
1E+03kg
1E+04kg
1E+05kg
1E-03kVA 1E-01kVA 1E+01kVA 1E+03kVA 1E+05kVA 1E+07kVA
Transformer rated throughput
Co
pp
er
con
ten
t
20%
30%
40%
50%
60%
70%
80%
90%
100%
Eff
icie
ncy
Example Transformers FoundTheoretical DeductionEnergy Efficiency
6
0.4kV
20kV10kV
380kV220kV110kV
50 Hz50 Hz3~3~
Structure of the public mains
27kV, nuclear21kV, e. g. coal
10kV, e. g. hydro
0.5kV, e. g. wind
7
Wooden spacers(not depicted in the following drawings)
HV winding LV winding
Current
Current 2. Designhere of a
distribution transformer
8
Yoke spanning bar
Winding spanning bolts
Yoke lamination spanning
Wooden winding spacers
HV winding
Yoke lamination
spanning boltsLV winding
Off-load tap changer
9
10
3. Operating behaviour
Equivalent circuit of a transformer:All values are referenced to one side, in this case the secondary.
Note:
Different loadsinfluence the transformer differently!
Load
RF
eX1‘ X2X
m
RCu1‘ RCu2
11
USC IN
By the way, what really is short-circuit voltage?
You apply a voltage magnitudeto the input side which is just enough to drive the short-circuit current in the output winding when shorted.
Xm AV
RF
e
RCu1‘ RCu2
X1‘ X2
12
V
By the way, what really is short-circuit power?
It doesn't really exist.
You multiply the no-load voltage by the short-circuit current.
Xm A
RF
eRCu1‘ RCu2
X1‘ X2
13
Vol
tage
acr
oss
the
load
(≈1
07%
!)
Equ
ival
ent i
nput
vol
tage
U1'
(100
%)
Inductive drop uX
Ohmic drop uR in the trans-
former
Total drop uSC in the transformer
R load (rated load) L load
Vol
tage
acr
oss
the
load
(≈9
4%)
Equ
ival
ent i
nput
vol
tage
U1'
(100
%)
Inductive drop uX
Ohmic drop uR in the trans-
former
Total drop uSC in the
transformerV
olta
ge a
cros
s th
e lo
ad (
≈99%
)
Equ
ival
ent i
nput
vol
tage
U1'
(100
%)
Inductive drop uX
Ohmic drop uR in the trans-
former
Total drop uSC in the
transformer
Inductive drop(uX = 5.916%)
Ohmic drop in the
transformer(e. g. uR = 1%)
Total drop inside the transformer(e. g. uSC = 6%)
Tricky: C load
14
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Relative Last-Admittanz Y/Y N
Rel
ativ
er L
asts
trom
I/I N
Strom bei ohmscher LastStrom bei induktiver LastStrom bei kapazitiver Last
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Relative load admittance Y/Y N
Rel
ativ
e lo
ad c
urre
ntI/I N
Current with resistive loadCurrent with inductive loadCurrent with capacitive load
Short circuit current ISC=16.7*IN
16.7*rated load
magnitude (ZSC=Zload: “half a short-circuit”)
E. g. non-detuned static Var com-pensator 1670kvaron a 100kVA transformer
Theoretical deduction of the load current
Rated load
15
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
Relative Last-Admittanz Y/Y N
Rel
ativ
er L
asts
trom
I/I N
Strom bei ohmscher Last
Strom bei induktiver LastStrom bei kapazitiver Last
Nennlast
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Relative load admittance Y/Y N Rel
ativ
e lo
ad c
urre
ntI/I N
Current with resistive load
Current with inductive loadCurrent with capacitive load
Rated load
Excerpt with the actually occurring values
16
No-load current
of a 16kV / 420V, 630kVA transformer, here excitated from the low voltage side!
RL≈400m
Ω
RF
e ≈400Ω
X1‘≈12mΩ X2≈12mΩ
Xm
>4kΩ
RCu1‘≈2mΩ RCu2 ≈2mΩ
17
Vector groups
Can the star point be loaded?
230V
400V
18
Vector groups
Can the star point be loaded?
Yes
Why?
No
U V W U V W
u v w n u v w n
19
Vector groups
Can the star point be loaded?
Approximate equivalent circuit of a Yyn vector group
RL≈400m
Ω
RF
e ≈400Ω
X1‘≈12mΩ X2≈12mΩ
Xm
>4kΩ
RCu1‘≈2mΩ RCu2 ≈2mΩ
RF
e ≈400Ω
X1‘≈12mΩ X2≈12mΩ
Xm
>4kΩ
RCu1‘≈2mΩ RCu2 ≈2mΩ
L1
N
L2
RL≈400Ω
20
Prerequisites for parallel operation:• Equal voltages of windings to be paralleled,
equal short-circuit voltage ratings,• equal vector group figures,• if input sides are not connected in parallel:
Make sure the feeding grids are in phase with each other,
• if input sides are not connected in parallel: Make sure the feeding grids have approximately equal short-circuitpowers,
• ratio of power ratings of units to beparalleled should be no greaterthan 3:1.
u X =
3.9
1%
uR = 0.9%
u SC =
4%
u X =
2.9
5%
uR = 2.7%
u SC =
4%
630 kVA transformer according to HD 428 list C
50 kVA transformer according to HD 428 list B
21
Jahr Material DickeVerlust (50Hz)
bei Induktion
1895 Eisendraht 6.00W/kg 1.0T1910 Warm gewalztes FeSi-Blech 0.35mm 2.00W/kg 1.5T1950 Kalt gewalzt, kornorientiert 0.35mm 1.00W/kg 1.5T1960 Kalt gewalzt, kornorientiert 0.30mm 0.90W/kg 1.5T1965 Kalt gewalzt, kornorientiert 0.27mm 0.84W/kg 1.5T1970 Kalt gewalztes HiB-Blech 0.30mm 0.80W/kg 1.5T1975 Amorphes Eisen 0.03mm 0.20W/kg 1.3T1980 Kalt gewalzt, kornorientiert 0.23mm 0.75W/kg 1.5T1980 Kalt gewalztes HiB 0.23mm 0.70W/kg 1.5T1983 Laser-behandeltes HiB-Blech 0.23mm 0.60W/kg 1.5T1985 Kalt gewalzt, kornorientiert 0.18mm 0.67W/kg 1.5T1987 Plasma-behandeltes HiB-Blech 0.23mm 0.60W/kg 1.5T1991 Chemisch gebeiztes HiB-Blech 0.23mm 0.60W/kg 1.5T
Year Material ThicknessLoss
(50Hz)at flux density
1895 Iron wire 6,00W/kg 1,0T1910 Warm rolled FeSi sheet 0,35mm 2,00W/kg 1,5T1950 Cold rolled, grain oriented 0,35mm 1,00W/kg 1,5T1960 Cold rolled, grain oriented 0,30mm 0,90W/kg 1,5T1965 Cold rolled, grain oriented 0,27mm 0,84W/kg 1,5T1970 Cold rolled HiB sheet 0,30mm 0,80W/kg 1,5T1975 Amorphous iron 0,03mm 0,20W/kg 1,3T1980 Cold rolled, grain oriented 0,23mm 0,75W/kg 1,5T1980 Cold rolled HiB sheet 0,23mm 0,70W/kg 1,5T1983 Laser treated HiB sheet 0,23mm 0,60W/kg 1,5T1985 Cold rolled, grain oriented 0,18mm 0,67W/kg 1,5T1987 Plasma treated HiB sheet 0,23mm 0,60W/kg 1,5T1991 Chemically etched HiB sheet 0,23mm 0,60W/kg 1,5T
4. EfficiencyDevelopment of magnetic steel
22
Nenn-Kurz-
schluss-Trocken-
trafoTrocken-
trafoleistung spg.
Schweiznach
HD538Schweiz
nach HD538
S u k Liste A Liste B Liste C 12kV OS Liste A' Liste B' Liste C' 12kV OS
50kVA 4% 1100W 1350W 875W 190W 145W 125W
100kVA 4% 1750W 2150W 1475W 1750W 2000W 320W 260W 210W 210W 440W
160kVA 4% 2350W 3100W 2000W 1800W 2700W 460W 375W 300W 250W 610W
250kVA 4% 3250W 4200W 2750W 2400W 3500W 650W 530W 425W 350W 820W
400kVA 4% 4600W 6000W 3850W 3300W 4900W 930W 750W 610W 455W 1150W
630kVA 4% 6500W 8400W 5400W 4400W 7300W 1300W 1030W 860W 635W 1500W
630kVA 6% 6750W 8700W 5600W 4400W 7600W 1200W 940W 800W 635W 1370W
1000kVA 6% 10500W 13000W 9500W 6500W 10000W 1700W 1400W 1100W 950W 2000W
1600kVA 6% 17000W 20000W 14000W 12500W 14000W 2600W 2200W 1700W 1300W 2800W
2500kVA 6% 26500W 32000W 22000W 22000W 21000W 3800W 3200W 2500W 1650W 4300W
Lastverlust
nach HD428
Leerlaufverlust
nach HD428
Öltransformator bis 24kV Öltransformator bis 24kVPower
Short-circuit
Dry transf.
Dry transf.
rating voltageSwiss
acc. to HD538
Swissacc. to HD538
S u SC List A List B List C 12kV OS List A' List B' List C' 12kV OS
50kVA 4% 1100W 1350W 875W 190W 145W 125W
100kVA 4% 1750W 2150W 1475W 1750W 2000W 320W 260W 210W 210W 440W
160kVA 4% 2350W 3100W 2000W 1800W 2700W 460W 375W 300W 250W 610W
250kVA 4% 3250W 4200W 2750W 2400W 3500W 650W 530W 425W 350W 820W
400kVA 4% 4600W 6000W 3850W 3300W 4900W 930W 750W 610W 455W 1150W
630kVA 4% 6500W 8400W 5400W 4400W 7300W 1300W 1030W 860W 635W 1500W
630kVA 6% 6750W 8700W 5600W 4400W 7600W 1200W 940W 800W 635W 1370W
1000kVA 6% 10500W 13000W 9500W 6500W 10000W 1700W 1400W 1100W 950W 2000W
1600kVA 6% 17000W 20000W 14000W 12500W 14000W 2600W 2200W 1700W 1300W 2800W
2500kVA 6% 26500W 32000W 22000W 22000W 21000W 3800W 3200W 2500W 1650W 4300W
according to HD428 according to HD428
Load loss No-load loss
Oil transformer up to 24kV Oil transformer up to 24kV
Division into classes according to thepresent HD 428
23
Nenn-rel.
Kurz-Gieß-harz-
leistung schl.- Liste DK Liste CK Liste BK Liste AK HD538 Liste E0 Liste D0 Liste C0 Liste B0 Liste A0
spg. ≤24kV ≤24kV ≤36kV ≤24kV ≤36kV ≤24kV ≤36kV ≤12kV ≤24kV ≤24kV ≤24kV ≤24kV ≤24kV
S N u k PK PK PK PK PK PK PK PK P0 Lärm P0 Lärm P0 Lärm P0 Lärm P0 Lärm
50kVA 4% 1350W 1100W 1450W 875W 1250W 750W 1050W 190W 55dB(A) 145W 50dB(A) 125W 47dB(A) 110W 42dB(A) 90W 39dB(A)
100kVA 4% 2150W 1750W 2350W 1475W 1950W 1250W 1650W 2000W 320W 59dB(A) 260W 54dB(A) 210W 49dB(A) 180W 44dB(A) 145W 41dB(A)
160kVA 4% 3100W 2350W 3350W 2000W 2550W 1700W 2150W 2700W 460W 62dB(A) 375W 57dB(A) 300W 52dB(A) 260W 47dB(A) 210W 44dB(A)
250kVA 4% 4200W 3250W 4250W 2750W 3500W 2350W 3000W 3500W 650W 65dB(A) 530W 60dB(A) 425W 55dB(A) 360W 50dB(A) 300W 47dB(A)
315kVA 4% 5000W 3900W 3250W 2800W 770W 67dB(A) 630W 61dB(A) 520W 57dB(A) 440W 52dB(A) 360W 49dB(A)
400kVA 4% 6000W 4600W 6200W 3850W 4900W 3250W 4000W 4900W 930W 68dB(A) 750W 63dB(A) 610W 58dB(A) 520W 53dB(A) 430W 50dB(A)
500kVA 4% 7200W 5500W 4600W 3900W 1100W 69dB(A) 880W 64dB(A) 720W 59dB(A) 610W 54dB(A) 510W 51dB(A)
630kVA 4% 8400W 6500W 8800W 5400W 6500W 4600W 5500W 7300W 1300W 70dB(A) 1030W 65dB(A) 860W 60dB(A) 730W 55dB(A) 600W 52dB(A)
630kVA 6% 8700W 6750W 8800W 5600W 6500W 4800W 5500W 7600W 1200W 70dB(A) 940W 65dB(A) 800W 60dB(A) 680W 55dB(A) 560W 52dB(A)
800kVA 6% 10500W 8400W 10500W 7000W 8400W 6000W 7000W 1400W 71dB(A) 1150W 66dB(A) 930W 61dB(A) 800W 56dB(A) 650W 53dB(A)
1000kVA 6% 13000W 10500W 13000W 9000W 10500W 7600W 8900W 10000W 1700W 73dB(A) 1400W 68dB(A) 1100W 63dB(A) 940W 58dB(A) 770W 55dB(A)
1250kVA 6% 16000W 13500W 16000W 11000W 13500W 9500W 11500W 2100W 74dB(A) 1750W 69dB(A) 1350W 64dB(A) 1150W 59dB(A) 950W 56dB(A)
1600kVA 6% 20000W 17000W 19200W 14000W 17000W 12000W 14500W 14000W 2600W 76dB(A) 2200W 71dB(A) 1700W 66dB(A) 1450W 61dB(A) 1200W 58dB(A)
2000kVA 6% 26000W 21000W 24000W 18000W 21000W 15000W 18000W 3100W 78dB(A) 2700W 73dB(A) 2100W 68dB(A) 1800W 63dB(A) 1450W 60dB(A)
2500kVA 6% 32000W 26500W 29400W 22000W 26500W 18500W 22500W 21000W 3500W 81dB(A) 3200W 76dB(A) 2500W 71dB(A) 2150W 66dB(A) 1750W 63dB(A)
Lastverlust Leerlaufverlust
Öltransformator ÖltransformatorPower
rel. short-
Cast resin
rating circuit List DK List CK List BK List AK HD538 List E0 List D0 List C0 List B0 List A0volt. ≤24kV ≤24kV ≤36kV ≤24kV ≤36kV ≤24kV ≤36kV ≤12kV ≤24kV ≤24kV ≤24kV ≤24kV ≤24kV
S N u k PK PK PK PK PK PK PK PK P0 Noise P0 Noise P0 Noise P0 Noise P0 Noise
50kVA 4% 1350W 1100W 1450W 875W 1250W 750W 1050W 190W 55dB(A) 145W 50dB(A) 125W 47dB(A) 110W 42dB(A) 90W 39dB(A)
100kVA 4% 2150W 1750W 2350W 1475W 1950W 1250W 1650W 2000W 320W 59dB(A) 260W 54dB(A) 210W 49dB(A) 180W 44dB(A) 145W 41dB(A)
160kVA 4% 3100W 2350W 3350W 2000W 2550W 1700W 2150W 2700W 460W 62dB(A) 375W 57dB(A) 300W 52dB(A) 260W 47dB(A) 210W 44dB(A)
250kVA 4% 4200W 3250W 4250W 2750W 3500W 2350W 3000W 3500W 650W 65dB(A) 530W 60dB(A) 425W 55dB(A) 360W 50dB(A) 300W 47dB(A)
315kVA 4% 5000W 3900W 0W 3250W 0W 2800W 770W 67dB(A) 630W 61dB(A) 520W 57dB(A) 440W 52dB(A) 360W 49dB(A)
400kVA 4% 6000W 4600W 6200W 3850W 4900W 3250W 4000W 4900W 930W 68dB(A) 750W 63dB(A) 610W 58dB(A) 520W 53dB(A) 430W 50dB(A)
500kVA 4% 7200W 5500W 4600W 3900W 1100W 69dB(A) 880W 64dB(A) 720W 59dB(A) 610W 54dB(A) 510W 51dB(A)
630kVA 4% 8400W 6500W 8800W 5400W 6500W 4600W 5500W 7300W 1300W 70dB(A) 1030W 65dB(A) 860W 60dB(A) 730W 55dB(A) 600W 52dB(A)
630kVA 6% 8700W 6750W 8800W 5600W 6500W 4800W 5500W 7600W 1200W 70dB(A) 940W 65dB(A) 800W 60dB(A) 680W 55dB(A) 560W 52dB(A)
800kVA 6% 10500W 8400W 10500W 7000W 8400W 6000W 7000W 1400W 71dB(A) 1150W 66dB(A) 930W 61dB(A) 800W 56dB(A) 650W 53dB(A)
1000kVA 6% 13000W 10500W 13000W 9000W 10500W 7600W 8900W 10000W 1700W 73dB(A) 1400W 68dB(A) 1100W 63dB(A) 940W 58dB(A) 770W 55dB(A)
1250kVA 6% 16000W 13500W 16000W 11000W 13500W 9500W 11500W 2100W 74dB(A) 1750W 69dB(A) 1350W 64dB(A) 1150W 59dB(A) 950W 56dB(A)
1600kVA 6% 20000W 17000W 19200W 14000W 17000W 12000W 14500W 14000W 2600W 76dB(A) 2200W 71dB(A) 1700W 66dB(A) 1450W 61dB(A) 1200W 58dB(A)
2000kVA 6% 26000W 21000W 24000W 18000W 21000W 15000W 18000W 3100W 78dB(A) 2700W 73dB(A) 2100W 68dB(A) 1800W 63dB(A) 1450W 60dB(A)
2500kVA 6% 32000W 26500W 29400W 22000W 26500W 18500W 22500W 21000W 3500W 81dB(A) 3200W 76dB(A) 2500W 71dB(A) 2150W 66dB(A) 1750W 63dB(A)
Load losses No-load losses
Oil-immersed transformer Oil-immersed transformer
Division into classes according to thefuture HD 428
24
98,5%
98,6%
98,7%
98,8%
98,9%
99,0%
99,1%
99,2%
99,3%
99,4%
0% 25% 50% 75% 100% 125%
Auslastungsgrad
h
Wirkungsgrad bei max. P(Fe), min. P(Cu)
Wirkungsgrad bei max. P(Cu), min. P(Fe)
98.5%
98.6%
98.7%
98.8%
98.9%
99.0%
99.1%
99.2%
99.3%
99.4%
0% 25% 50% 75% 100% 125%
Degree of loading
h
Efficiency with max. P(Fe), min. P(Cu)
Efficiency with max. P(Cu), min. P(Fe)
25
Channels / Design Measures & Weights Calculated Electrical Values Amor-
Ver-sion
betw. core & LV winding
in LV windingbetw. LV & HV winding
in HV windingstack height
width length MFe MCu Mtot PvFe PvCu Pvtot U hPrice tisa-
tion
front [mm]
long [mm]
front [mm]
long [mm]
front [mm]
long [mm]
front [mm]
long [mm]
[mm] [mm] [mm] [kg] [kg] [kg] [W] [W] [W] [V] [%] [DM] [a]
0 10 10 10 10 10 10 10 10 100 450 360 202 30,7 232,7 417 1634 2051 13 95,12 1715 ---
1 10 10 10 0 10 10 10 0 100 415 365 196 42,4 238,4 406 1343 1749 11 95,81 1823 0,924
2 10 10 0 0 10 10 10 0 100 417 342 196 46,6 242,6 406 1217 1623 10 96,10 1851 0,821
3 10 10 0 0 10 0 10 0 100 400 342 196 48,2 244,2 406 1090 1496 9 96,39 1867 0,707
4 10 10 0 0 10 10 0 0 100 406 340 196 59,9 255,9 406 874 1280 6 96,90 2008 0,981
5 10 10 0 0 0 0 0 0 100 408 335 196 65,9 261,9 406 753 1159 5 97,18 2077 1,048
6 As in 5, but with even thicker wire 100 412 341 196 71,3 267,3 406 626 1032 4 97,48 2152 1,108
7 As in 5, but with grain-oriented steel, lower stack height 80 412 311 155 64,7 219,7 223 580 803 4 98,03 2443 1,507
Data underlying the calculation:Electricity price 20 Pf/kWhWork days per year 242 dOperation hours per shift 8 hShifts 1 /d
Comparing 8 designs of a 40 kVA
transformer by Riedel transformer factory
26
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7
W
94,5
95,0
95,5
96,0
96,5
97,0
97,5
98,0
98,5%
Pvtot [W]
Efficiency
Voltage drop no load / rated load [V]
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7
V
0
500
1000
1500
2000
2500
3000
0 1 2 3 4 5 6 7
DM
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6a
Price [DM]
Amortisation [a]
Weights and measures
0
100
200
300
400
500
0 1 2 3 4 5 6 7
mm
0
50
100
150
200
250
300kg
width [mm] length [mm]
Mtot [kg] MCu [kg]
27
Jahr Material DickeVerlust (50Hz)
bei Induktion
1895 Eisendraht 6.00W/kg 1.0T1910 Warm gewalztes FeSi-Blech 0.35mm 2.00W/kg 1.5T1950 Kalt gewalzt, kornorientiert 0.35mm 1.00W/kg 1.5T1960 Kalt gewalzt, kornorientiert 0.30mm 0.90W/kg 1.5T1965 Kalt gewalzt, kornorientiert 0.27mm 0.84W/kg 1.5T1970 Kalt gewalztes HiB-Blech 0.30mm 0.80W/kg 1.5T1975 Amorphes Eisen 0.03mm 0.20W/kg 1.3T1980 Kalt gewalzt, kornorientiert 0.23mm 0.75W/kg 1.5T1980 Kalt gewalztes HiB 0.23mm 0.70W/kg 1.5T1983 Laser-behandeltes HiB-Blech 0.23mm 0.60W/kg 1.5T1985 Kalt gewalzt, kornorientiert 0.18mm 0.67W/kg 1.5T1987 Plasma-behandeltes HiB-Blech 0.23mm 0.60W/kg 1.5T1991 Chemisch gebeiztes HiB-Blech 0.23mm 0.60W/kg 1.5T
Year Material ThicknessLoss
(50Hz)at
induction1895 Iron wire 6.00W/kg 1.0T1910 Warm rolled FeSi sheet 0.35mm 2.00W/kg 1.5T1950 Cold rolled, grain oriented 0.35mm 1.00W/kg 1.5T1960 Cold rolled, grain oriented 0.30mm 0.90W/kg 1.5T1965 Cold rolled, grain oriented 0.27mm 0.84W/kg 1.5T1970 Cold rolled HiB sheet 0.30mm 0.80W/kg 1.5T1975 Amorphous iron 0.03mm 0.20W/kg 1.3T1980 Cold rolled, grain oriented 0.23mm 0.75W/kg 1.5T1980 Cold rolled HiB sheet 0.23mm 0.70W/kg 1.5T1983 Laser treated HiB sheet 0.23mm 0.60W/kg 1.5T1985 Cold rolled, grain oriented 0.18mm 0.67W/kg 1.5T1987 Plasma treated HiB sheet 0.23mm 0.60W/kg 1.5T1991 Chemically etched HiB sheet 0.23mm 0.60W/kg 1.5T
Amorphous steel could cut the no-load losses down to a fraction
However:
• bigger
• more expensive
• noisier
28
So the replacement of old transformers pays off for a variety of reasons
1958 1998(Rauscher & Stoecklin) (ABB Sécheron SA)
Geräuschpegel Abmessungen1960 58 dB (A)1970 50 dB (A)1980 46 dB (A)1990 43 dB (A)1998 38 dB (A)
Abmessungen Absolute pricesLänge Breite Höhe Volumen
mm mm mm m³1972 1710 1020 2015 3,5151998 1460 960 1735 2,432
Noise levels Dimensions1960 58 dB (A)1970 50 dB (A)1980 46 dB (A)1990 43 dB (A)1998 38 dB (A)
Dimensions Absolute pricesLength Width Height Volume
mm mm mm m³1972 1710 1020 2015 3.5151998 1460 960 1735 2.432
29
No-load loss of a 400 kVA 16 kV / 400 V distribution transformer
Improvement of efficienciesLoad loss of a 400 kVA 16 kV / 400 V distribution transformer
30
5. Too hot from “hot” loadsApparent power, TRMS voltage and TRMS current within limits – and yet it ran too hot?
Mutual influences between the trans-former and its load
31
The power loss in a transformer is:
The true power loss in a transformer is:
2
)()(
nomnomCunomFeLoss I
IPPP
2
)(
2
)(
2
)( *
nomnomnomad
nomnomCu
nomnomFeLoss I
I
f
fP
I
IP
U
UPP
2
)()()(
NNZNCuNFeV I
IPPPP
2
)(
2
)(
2
)( *
NNNZ
NNCu
NNFeV I
I
f
fP
I
IP
U
UPP
32
“supplementary” additional losses in transformers
can be calculated rapidly using the following two simple formulae:
5,0
2
2
1
2
11
Nn
n
nqh
I
In
I
I
e
eK
5,0
1
2
11
5,0
1
2
Nn
n
nNn
nn I
IIII
where:
Oh well,perhaps a practical example is clearer:
1000 compact 11W (15VA) energy-saver lamps powered by a 15kVA transformer, uSC=4%, Pad=0.1PCu
Oberschwingungen einer Sparlampe Osram Dulux 11W mit Serien-
Impedanz R =29,1W & X L=113W
U U ² I L I L² PZ /PCu
n V V² mA mA²
1 230,2 52992,0 48,5 2352,3 5,6%3 8,3 68,9 37,1 1376,4 29,5%5 10,7 114,5 20,3 412,1 24,5%7 4,3 18,5 5,3 28,1 3,3%9 1,1 1,2 3,0 9,0 1,7%
11 2,3 5,3 3,8 14,4 4,2%13 1,0 1,0 1,5 2,3 0,9%15 0,6 0,4 1,5 2,3 1,2%17 1,1 1,2 1,5 2,3 1,5%19 0,5 0,3 0,9 0,8 0,7%21 0,5 0,3 1,3 1,7 1,8%23 0,6 0,4 0,8 0,6 0,8%25 0,4 0,2 0,6 0,4 0,5%27 0,6 0,4 0,8 0,6 1,1%29 0,4 0,2 0,5 0,3 0,5%31 0,3 0,1 0,5 0,3 0,6%33 0,3 0,1 0,5 0,3 0,6%35 0,3 0,1 0,4 0,2 0,5%37 0,3 0,1 0,4 0,2 0,5%39 0,3 0,1 0,3 0,1 0,3%41 0,1 0,0 0,3 0,1 0,4%43 0,2 0,0 0,2 0,0 0,2%45 0,1 0,0 0,2 0,0 0,2%47 0,1 0,0 0,2 0,0 0,2%49 0,1 0,0 0,1 0,0 0,1%51 0,1 0,0 0,1 0,0 0,1%Anteil der Zusatz-Verluste: PZ/PCu = 81,4%
Analysis of harmonics in an 11-W Osram Dulux CFL with serial
impedance R =29.1W & X L=113W
U U ² I L I L² Pad /PCu
n V V² mA mA²
1 230.2 52992.0 48.5 2352.3 5.6%3 8.3 68.9 37.1 1376.4 29.5%5 10.7 114.5 20.3 412.1 24.5%7 4.3 18.5 5.3 28.1 3.3%9 1.1 1.2 3.0 9.0 1.7%
11 2.3 5.3 3.8 14.4 4.2%13 1.0 1.0 1.5 2.3 0.9%15 0.6 0.4 1.5 2.3 1.2%17 1.1 1.2 1.5 2.3 1.5%19 0.5 0.3 0.9 0.8 0.7%21 0.5 0.3 1.3 1.7 1.8%23 0.6 0.4 0.8 0.6 0.8%25 0.4 0.2 0.6 0.4 0.5%27 0.6 0.4 0.8 0.6 1.1%29 0.4 0.2 0.5 0.3 0.5%31 0.3 0.1 0.5 0.3 0.6%33 0.3 0.1 0.5 0.3 0.6%35 0.3 0.1 0.4 0.2 0.5%37 0.3 0.1 0.4 0.2 0.5%39 0.3 0.1 0.3 0.1 0.3%41 0.1 0.0 0.3 0.1 0.4%43 0.2 0.0 0.2 0.0 0.2%45 0.1 0.0 0.2 0.0 0.2%47 0.1 0.0 0.2 0.0 0.2%49 0.1 0.0 0.1 0.0 0.1%51 0.1 0.0 0.1 0.0 0.1%Share of additional losses Pad/PCu = 81.4%
etc.
etc.
81.4%
33
To some extent the transformer protects itself...
Always remember:
If the influence of the transformer upon the load did not exist, then the influence of the load upon the transformer would be nearly 9 times as high!
Analyse der Oberschwingungen in einer Kompaktsparlampe Osram
Dulux 11W
Oberschwingungen einer Sparlampe Osram Dulux 11W mit Serien-
Impedanz R =29,1W & X L=113W
U U ² I L I L² PZ /PCu
n V V² mA mA²
1 232,7 54149,3 48,9 2391,2 3,7%3 0,6 0,4 39,1 1528,8 21,5%5 4,4 19,4 26,4 697,0 27,3%7 2,3 5,3 20,0 400,0 30,7%9 0,1 0,0 19,2 368,6 46,7%
11 0,1 0,0 16,6 275,6 52,2%13 0,1 0,0 12,7 161,3 42,7%15 0,1 0,0 11,0 121,0 42,6%17 0,1 0,0 10,2 104,0 47,1%19 0,1 0,0 8,7 75,7 42,8%21 0,1 0,0 7,7 59,3 40,9%23 0,1 0,0 7,3 53,3 44,1%25 0,1 0,0 6,1 37,2 36,4%27 0,1 0,0 4,9 24,0 27,4%29 0,1 0,0 4,2 17,6 23,2%31 0,1 0,0 3,6 13,0 19,5%33 0,1 0,0 3,0 9,0 15,3%35 0,1 0,0 3,3 10,9 20,9%37 0,1 0,0 3,1 9,6 20,6%39 0,1 0,0 2,5 6,3 14,9%41 0,1 0,0 2,5 6,3 16,4%43 0,1 0,0 2,5 6,3 18,1%45 0,1 0,0 1,9 3,6 11,4%47 0,1 0,0 1,8 3,2 11,2%49 0,1 0,0 1,9 3,6 13,6%51 0,1 0,0 1,6 2,6 10,4%Anteil der Zusatz-Verluste: PZ/PCu = 701,7%
Harmonics measurement on an Osram Dulux 11W compact
fluorescent lamp
Analysis of harmonics in an 11-W Osram Dulux CFL with serial
impedance R =29.1W & X L=113W
U U ² I L I L² Pad /PCu
n V V² mA mA²
1 232.7 54149.3 48.9 2391.2 3.7%3 0.6 0.4 39.1 1528.8 21.5%5 4.4 19.4 26.4 697.0 27.3%7 2.3 5.3 20.0 400.0 30.7%9 0.1 0.0 19.2 368.6 46.7%
11 0.1 0.0 16.6 275.6 52.2%13 0.1 0.0 12.7 161.3 42.7%15 0.1 0.0 11.0 121.0 42.6%17 0.1 0.0 10.2 104.0 47.1%19 0.1 0.0 8.7 75.7 42.8%21 0.1 0.0 7.7 59.3 40.9%23 0.1 0.0 7.3 53.3 44.1%25 0.1 0.0 6.1 37.2 36.4%27 0.1 0.0 4.9 24.0 27.4%29 0.1 0.0 4.2 17.6 23.2%31 0.1 0.0 3.6 13.0 19.5%33 0.1 0.0 3.0 9.0 15.3%35 0.1 0.0 3.3 10.9 20.9%37 0.1 0.0 3.1 9.6 20.6%39 0.1 0.0 2.5 6.3 14.9%41 0.1 0.0 2.5 6.3 16.4%43 0.1 0.0 2.5 6.3 18.1%45 0.1 0.0 1.9 3.6 11.4%47 0.1 0.0 1.8 3.2 11.2%49 0.1 0.0 1.9 3.6 13.6%51 0.1 0.0 1.6 2.6 10.4%Share of additional losses Pad/PCu = 701.7%
etc.
etc.
701.7%
A tool is available for this, too:
The K Factor Calculator by
www.cda.org.uk
www.cda.org.uk/frontend/pubs.htm#ELECTRICAL/ENERGY%20EFFICIENCY
36
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