|
Exact voltage drop in the transformer = ( Vr Cos Φ ± Vx Sin Φ ) + (
1 / 200 )( Vx Cos Φ ± Vr Sin Φ )2 |
|
Voltage regulation at unity power factor = [ I2R02 / 0V2
] × 100% |
|
Condition for maximum voltage regulation Tan Φ = Vx / Vr |
|
Percentage voltage drop % drop = ( %R )( kW ) / kVA rating +
( %X )( kVAr ) / kVA rating |
|
Exciting conductance G0 = W / V12 Exciting susceptance B0 = √ ( Y02 – G02
) |
|
Hysteresis loss Wh = ηBmax1.6fV Where V = Volume of material η = Steinmetz hysteresis coefficient Wh α Bmax1.6f |
|
Eddy current loss We = kBmax2 f2
t2 Where Bmax = Maximum flux density f = Frequency t = Thickness of laminations We α Bmax2f2
t2 |
|
Total copper loss in the transformer WC = I12 R1
+ I22 R2 Where R1 = Resistance of primary winding R2 = Resistance of secondary winding
OR WC = I12 R01 = I22
R02 Where R01 = Total resistance as referred to
primary side R02 = Total resistance as referred to
secondary side Copper loss at half load WC α ( I / 2 )2 R = I2R
( At full load ) / 4 |
|
Effect on hysteresis loss and eddy
current loss if the flux density remains same We α f2 Wh α f Voltage equation of transformer E = 4.44fNBmax A Bmax α ( E / f ) Hysteresis loss Wh α Bmax1.6
f α ( E / f )1.6
f α ( E )1.6
f – 0.6 k ( E )1.6
f – 0.6 Eddy current loss We α Bmax2
f2 α ( E /
f )2 f2
= kE2 |
|
Percentage resistance %R = [ I1 R01 / V1
] × 100% = [ I12
R01 / I1V1 ] × 100% = [ I22
R02 / I1V1 ] × 100% = %
Copper loss at full load Percentage reactance %X = [ I1 X01 / V1
] × 100% = [ I2
X02 / V2 ] × 100% |
|
R01 = [ % R × V1 ] / [ 100 × I1
] = %
Copper loss × V1 ] / [ 100 × I1 ] R02 = [ % R × V2 ] / [ 100 × I2
] = %
Copper loss × V2 ] / [ 100 × I2 ] The percentage resistance, reactance and impedance
have same value whether it is referred to primary side or secondary side. |
|
Condition for maximum efficiency Iron loss = Copper loss Wi = I12 R01
=
I22 R02 Load corresponding to maximum efficiency I2 = √ ( Wi / R02 ) = I2full
/ I2full [ √ ( Wi / R02 ) ] = I2full
√ ( Wi / Wcu ) = I2full
√ ( Iron loss / Full load copper loss ) |
|
Efficiency at any load η = ( output
power / input power) × 100% Where Output power = ( x ) ( kVA ) ( Power factor ) Input power = ( x ) ( kVA ) ( Power factor ) + ( Wi
) + ( Wcu ) x = Ratio of actual to full load kVA |
|
kVA for maximum efficiency kVA = kVAfull ( √ Wi / Wcu
) |
|
Transformer efficiency η = 1 – ( x / Cos Φ + x ) = 1 – { ( x
/ Cos Φ ) / ( 1 + x / Cos Φ ) } Where x = Losses / V2I2 |
|
All day efficiency ηAllday = { Output in kWh / Input in kWh
} × 100% |
|
Saving in copper in auto transformer as
step down transformer Saving = k × Weight of copper in ordinary
transformer Where k = Voltage transformation ratio Power transfer inductively = ( 1 – k ) Input Power transfer conductively = k × Input |
|
Ratio of V – V connection to Delta –
Delta connection V – V Capacity / Delta – Delta Capacity = 57.7% |
|
V – V connected two transformer supply
power at Cos Φ power factor P1 = kVA Cos ( 30 – Φ ) P2 = kVA Cos ( 30 + Φ ) Where Φ = Power factor of load |
|
Rating of teaser transformer = 86.6% of Main transformer rating |
|
Sharing of load when transformer P and
transformer Q are connected in parallel SP = S ( ZQ / ZP +
ZQ ) SQ = S ( ZP / ZP +
ZQ ) Where SP = kVA rating of transformer P SQ = kVA rating of transformer Q ZP = Impedance of transformer P ZQ = Impedance of transformer Q |
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