Transformers finals Flashcards
Equation for Average Winding Temp Rise?
Avg winding temp rise = Avg winding temp - Ambient temp
Equation for Hotspot Rise?
Hotspot Rise = Hottest spot temp - Avg winding temp
Equation for Total Loss?
PLossTotal = PNLL (no load loss) + PLL (load loss)
Equation for PNLL (no load loss)?
PNLL = PH (hysteresis loss) + PE (eddy loss)
Equation for PLL (load loss)?
PLL = (I^2 HV + Eddies HV) + (I^2 LV + Eddies LV) + Strays
Equation for Resistance?
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.
Equation for temperature correction?
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
What are other equations for temperature correction?
- 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
Equation for Eddy losses?
Eddy Loss = {% Eddy Loss * I^2 R} / 100
Equation for % Eddy Loss?
%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)
Equation for Strays
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
Equation for Impedance (%Z)?
%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
Equation for Reactance (%X)?
%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
Equation for DR (build radial factor)?
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)
Equation for Fault Current?
IFault = IRated * (100 / %Z)
