Transformers finals

Question 1

Equation for Average Winding Temp Rise?

Answer 1

Avg winding temp rise = Avg winding temp - Ambient temp

Question 2

Equation for Hotspot Rise?

Answer 2

Hotspot Rise = Hottest spot temp - Avg winding temp

Question 3

Equation for Total Loss?

Answer 3

PLossTotal = PNLL (no load loss) + PLL (load loss)

Question 4

Equation for PNLL (no load loss)?

Answer 4

PNLL = PH (hysteresis loss) + PE (eddy loss)

Question 5

Equation for PLL (load loss)?

Answer 5

PLL = (I^2 HV + Eddies HV) + (I^2 LV + Eddies LV) + Strays

Question 6

Equation for Resistance?

Answer 6

R = (p x l) / A

where:
o l is the length of the conductor (in),
o A is the cross-sectional area of the turn (in2 ),
o ρ is the resistivity of the conductor @20°C (Ωin).
 ρ = 6.786(10-7 ) Ωin @20°C for Copper.
 ρ = 1.098(10-6 ) Ω*in @20°C for Aluminum.

Question 7

Equation for temperature correction?

Answer 7

R f = R i * (Tk + Tf) / (Tk + Ti)
* Where:
o R i – initial resistance ( Ω, mΩ, μΩ, etc.)
o R f – final resistance ( Ω, mΩ, μΩ, etc.)
o Ti – initial Temperature (°C)
o Tf – final Temperature (°C)
o Tk = 234.5 for Cu
o Tk = 225 for Al

Question 8

What are other equations for temperature correction?

Answer 8

• I^2 R f = I^2 R i * (Tk + Tf) / (Tk + Ti)
• %R f = %R i * (Tk + Tf) / (Tk + Ti),
• %R = ( P LL / S Rated ) * 100

Question 9

Equation for Eddy losses?

Answer 9

Eddy Loss = {% Eddy Loss * I^2 R} / 100

Question 10

Equation for % Eddy Loss?

Answer 10

%Eddy Loss = { (24.2 * N * A * t * f) / (EL * 60) }2 @ 75°C (basically the axial flux)

Where:
N – number of turns.
A – bare cross-sectional area of the turn (in2 ).
t – thickness of the bare conductor (in).
f – frequency of the supply (Hz).
EL – electrical length of winding (in).
Eddy Loss – Eddy loss (W)

Question 11

Equation for Strays

Answer 11

Strays = k * %X * kVA@75°C
* Where:
o Strays are Stray Losses in Watts.
o k – constant dependent on the construction of the transformer (basically comes from
experience), some factors are the type of winding (layer, foil, disc) and how close leads are to steel parts.
o %X – is the actual %X or % Reactance of the transformer.
o kVA – is the actual kVA (not VA) of the transformer 1φ or 3φ

Question 12

Equation for Impedance (%Z)?

Answer 12

%Z = √(%R^2 + %X^2 )

where
o %Z is the transformer impedance, expressed as a percentage
o %R is the transformer’s resistive component, expressed as a percentage
 is dependent on temperature.
o %X is the transformer’s reactive component, expressed as a percentage
 is not dependent on temperature

Question 13

Equation for Reactance (%X)?

Answer 13

%X = {(0.126 * f * kVA) / (V/T)2 }* (DR / heff)

%X - % reactance in % terms
f – frequency of the supply (Hz)
kVA – rating of the coil or equivalent 1φ rating of transformer
V/T – volts per turn (for either HV or LV because they are the same)
heff – generally the average electrical length of the HV and LV windings
DR – build radial factor

Question 14

Equation for DR (build radial factor)?

Answer 14

DR = {(d LV * MR LV) / 3} + (dMG * MR MG ) + {(dHV * MR HV) / 3}

DR – build radial factor
dLV - radial build of LV winding (in)
dMG - radial build of main gap (in)
dHV - radial build of HV winding (in)
MR LV – mean radius of LV winding (in)
MR MG – mean radius of main gap (in)
MR HV – mean radius of HV winding (in)

Question 15

Equation for Fault Current?

Answer 15

IFault = IRated * (100 / %Z)

Question 16

1 phase Equation for Series Current?

Answer 16

I series = I HV

Question 17

1 phase Equation for Common Current?

Answer 17

I common = ILV - IHV

Question 18

1 phase Equation for Series Voltage?

Answer 18

Vseries = VHV - VLV

Question 19

1 phase Equation for Common Voltage?

Answer 19

Vcommon = VLV

Question 20

1 phase Equation for Series Apparent Power?

Answer 20

VA series = Vseries x I series

Question 21

1 phase Equation for Common Apparent Power?

Answer 21

VA common = Vcommon x I common

Question 22

1 phase Equation for Equivalent Apparent Power?

Answer 22

VA equivalent = VA isolation rated (VA on nameplate) x (VHV - VLV) / VHV

Question 23

3 phase equation for Vphase ?

Answer 23

Vphase LV = Vline LV / root3
Vphase HV = Vline LV root3

Question 24

3 phase equation for Iphase?

Answer 24

Iphase LV = S / (root3 x VlineLV)
Iphase HV = S / (root3 x VlineHV)

Question 25

3 phase equation for series winding current?

Answer 25

Iseries = ILHV

Question 26

3 phase equation for common winding current?

Answer 26

Icommon = ILLV-ILHV

Question 27

3 phase equation for common voltage?

Answer 27

Vcommon = Vphase LV

Question 28

3 phase equation for series voltage?

Answer 28

Vseries = Vphase HV - Vphase LV

Question 29

3 phase equation for common apparent?

Answer 29

Scommon = Vcommon x Icommon X 3

Question 30

3 phase equation for series apparent?

Answer 30

Sseries = Vseries x I series x 3

Question 31

3 phase equation for equivalent apparent?

Answer 31

S equivalent = KVA isolation rated (KVA on nameplate) x (VHV - VLV) / VHV

Question 32

Equation for Efficiency?

Answer 32

%η = x * P OUT / (x * P OUT + P NLL + x2 * P LL ) *100

where
x is the fractional load on the transformer ex. x = 1/4, 1/2

P TOTAL = PLL + P NLL
P OUT = pf * S OUT