Open circuit test (iron-core and magnetising losses)
A transformer with an open circuit secondary can be modelled as shown in the circuit below. For the open circuit test case,
R1, R2, X1 and X2 can be ignored leaving just Rw (iron-core loss
resistance) and Xm (magnetising loss reactance). The open circuit test is conducted by leaving secondary winding
open, while the full rated primary voltage is applied to the primary winding. At this point Eo, Io
and Po readings are taken.
Iron-core loss as measured by the wattmeter,
\( \begin{aligned}
P_o = E_o . I_o . cos \phi_o
\end{aligned} \)
No load power factor,
\( \begin{aligned}
cos \phi_o = \frac{ P_o }{ E_o . I_o }
\end{aligned} \)
Iron-core loss current component,
\( \begin{aligned}
I_w = I_o . cos \phi_o
\end{aligned} \)
Magnetising loss current component,
\( \begin{aligned}
I_m = I_o . sin \phi_o
\end{aligned} \)
Iron-core loss resistance,
\( \begin{aligned}
R_w = \frac{ E_o }{ I_w }
\end{aligned} \)
Magnetising loss reactance,
\( \begin{aligned}
X_m = \frac{ E_o }{ I_m }
\end{aligned} \)
No load impedance,
\( \begin{aligned}
Z_o = \sqrt{ R_w^2 + X_m^2 } = R_w + jX_m
\end{aligned} \)
Open circuit measurements / calculations
Mains voltage is applied to the primary, with the secondary open circuit.
Readings of Eo, Io, and Po are taken.
\( \begin{aligned}
E_o = 240V, \text{ } I_o = 2.72A, \text{ } P_o = 53W.
\end{aligned} \)
\( \begin{aligned}
cos \phi_o = \frac{ 53 }{ 240 \times 2.72 } = 0.081
\end{aligned} \)
\( \begin{aligned}
I_w = 2.72 \times 0.081 = 0.221A
\end{aligned} \)
\( \begin{aligned}
I_m = 2.72 \times 0.997 = 2.711A
\end{aligned} \)
\( \begin{aligned}
R_w = \frac{ 240 }{ 0.221 } = 1087 \Omega
\end{aligned} \)
\( \begin{aligned}
X_m = \frac{ 240 }{ 2.711 } = 89 \Omega
\end{aligned} \)
\( \begin{aligned}
Z_o = \sqrt{ 1087^2 + 89^2 } = 1090 \Omega
\end{aligned} \)
Short circuit test (copper and eddy-current / hysteresis losses)
A transformer with a short circuit secondary can be modelled as shown in the circuit below. For the short circuit test case,
Rw and Xm can be ignored. R1 and R2 are combined together as Rc
(copper loss resistance), and X1 and X2 are combined together as Xi (eddy-current /
hysteresis loss reactance). The short circuit test is conducted by shorting the secondary winding, while the primary voltage
is gradually increased using the variac until the maximum rated primary current is reached. At this point Es,
Is and Ps readings are taken.
Copper loss as measured by the wattmeter,
\( \begin{aligned}
P_s = I_s^2 . R_c
\end{aligned} \)
Copper loss resistance,
\( \begin{aligned}
R_c = \frac{ P_s }{ I_s^2 }
\end{aligned} \)
Full load impedance,
\( \begin{aligned}
Z_s = \frac{ E_s }{ I_s }
\end{aligned} \)
Eddy-current / hysteresis loss reactance,
\( \begin{aligned}
X_i = \sqrt{ Z_s^2 - R_c^2 }
\end{aligned} \)
Full load power factor,
\( \begin{aligned}
cos \phi_s = \frac{ R_c }{ Z_s }
\end{aligned} \)
Short circuit measurements / calculations
The variac is increased until the maximum primary current is reached, with the secondary short circuit.
Readings of Es, Is, and Ps are taken.
\( \begin{aligned}
E_s = 88.7V, \text{ } I_s = 3.33A, \text{ } P_s = 186W.
\end{aligned} \)
\( \begin{aligned}
R_c = \frac{ 186 }{ 3.33^2 } = 16.8 \Omega
\end{aligned} \)
\( \begin{aligned}
Z_s = \frac{ 88.7 }{ 3.33 } = 26.6 \Omega
\end{aligned} \)
\( \begin{aligned}
X_i = \sqrt{ 26.6^2 - 16.8^2 } = 20.7 \Omega
\end{aligned} \)
\( \begin{aligned}
cos \phi_s = \frac{ 16.8 }{ 26.6 } = 0.63
\end{aligned} \)