Equivalent circuit of 5 kVA 200/400 V transformer

Method. The no-load (OC) test gives the shunt branch: $\cos\phi_0 = \frac{P_0}{V_0 I_0}$, $I_w = I_0\cos\phi_0$, $I_\mu = I_0\sin\phi_0$, $R_0 = \frac{V_0}{I_w}$, $X_0 = \frac{V_0}{I_\mu}$. The SC test gives the series branch: $Z = \frac{V_{sc}}{I_{sc}}$, $R = \frac{P_{sc}}{I_{sc}^2}$, $X = \sqrt{Z^2 - R^2}$. Values found on one side are moved to the other side by multiplying by the square of the voltage ratio.

Primary = LV side (200 V). Rated HV current $= 5000/400 = 12.5$ A, so the SC test is at full load. Factor HV to LV: $\left(\frac{200}{400}\right)^2 = 0.25$.

OC test (LV): 200 V, 1.25 A, 150 W

$$\begin{aligned} \cos\phi_0 &= \frac{150}{200 \times 1.25} = 0.6, \quad \sin\phi_0 = 0.8 \\ I_w &= 1.25 \times 0.6 = 0.75\ \text{A}, \quad I_\mu = 1.25 \times 0.8 = 1.0\ \text{A} \\ R_0 &= \frac{200}{0.75} = 266.67\ \Omega, \quad X_0 = \frac{200}{1.0} = 200\ \Omega \end{aligned}$$

These are already on the primary (LV) side.

SC test (HV): 20 V, 12.5 A, 175 W

$$\begin{aligned} Z_{02} &= \frac{20}{12.5} = 1.6\ \Omega, \quad R_{02} = \frac{175}{12.5^2} = 1.12\ \Omega \\ X_{02} &= \sqrt{1.6^2 - 1.12^2} = 1.143\ \Omega \end{aligned}$$

Referred to primary (multiply by 0.25):

$$\begin{aligned} R_{01} &= 1.12 \times 0.25 = 0.28\ \Omega \\ X_{01} &= 1.143 \times 0.25 = 0.286\ \Omega \\ Z_{01} &= 1.6 \times 0.25 = 0.4\ \Omega \end{aligned}$$

Equivalent circuit referred to primary

 I1 ->        I0                 I2'
 o-----+--------+---[ R01 ]---[ jX01 ]---o
 +     |        |                        +
     [ R0 ]  [ jX0 ]                   load
 V1    |        |                       V2'
 -     |        |                        -
 o-----+--------+------------------------o
 All values referred to primary (LV):
 R0 = 266.67 ohm, X0 = 200 ohm
 R01 = 0.28 ohm, X01 = 0.286 ohm

Answer (primary side): $R_0 = 266.67\ \Omega$, $X_0 = 200\ \Omega$, $R_{01} = 0.28\ \Omega$, $X_{01} = 0.286\ \Omega$.

(Note: the no-load power factor of 0.6 is unusually high for a real transformer, but the given data are used as stated.)