Tutorial # 5
U
McPherson Example 3.5
McPherson Problem 3.12
A 5 kVA single phase transformer is rated 440-220 V. Open and Short circuit data as follows:
Open Circuit Test Short Circuit Test
VOC = 220 V
VSC = 22.8 V
IOC = 1.10 A
ISC = 11.4 A
POC = 48.4 W
PSC = 52.0 W
(a) What is the efficiency of this transformer at full load, 0.8 pf? At half load with the same pf?
(b) At what load does this transformer have its maximum efficiency?
(c) Find the resistance and reactance of this transformer.
Solution:
S rated ⋅ PF
= 97.55%
S rated ⋅ PF + POC + PSC
S rated
⋅ PF
2
η HalfLoad _ PF =0.8 =
= 97.02%
S rated
PSC
⋅ PF + POC + 2
2
2
2
Remember, PCU = I R, so, at half load the current is the rated current divided by 2, the copper losses would
be the same rated divided by 4!
a) η FullLoad _ PF = 0.8 =
b) Considering the core losses constant, maximum efficiency is obtained when PCU = Pcore.
From the SC test,
R = PSC/ISC2 =0.4 Ω
At maximum efficiency,
PCU=Pcore = Imax2R
So, Imax2 = Pcore/R
Imax = 11 A
Smax = Imax V = 4840 VA
c) R = PSC/ISC2 =0.4 Ω
Z = VSC/ISC = 2
XL = sqrt(Z2-R2) = 1.95 Ω
McPherson Problem 3.17
A 10 MVA three-phase transformer ∆-Y connected is rated 110-7.2 kV. The currents given are line currents
and the voltages are line-to-line voltages. Open and Short circuit data as follows:
Open Circuit Test Short Circuit Test
VOC = 7.2 kV
VSC = 13.2 kV
IOC = 16 A
ISC = 52.5 A
POC = 72 kW
PSC = 80 kW
(a) Find the Zeqs in ohms referred to one phase of the Y connected secondary?
(b) What is the full load efficiency of this transformer at UPF?
η FullLoad _ PF =1 =
S rated ⋅ PF
= 98.5%
S rated ⋅ PF + POC + PSC