Equivalent circuit of 100 kVA 2200/220 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.

The OC test voltage (220 V) shows it was done on the LV side; the SC test voltage (90 V) and current (30 A, below the rated HV current of $100000/2200 = 45.45$ A) show it was done on the HV side. Ratio factor LV to HV: $\left(\frac{2200}{220}\right)^2 = 100$.

Shunt branch (OC test: 220 V, 10 A, 400 W on LV)

$$\begin{aligned} \cos\phi_0 &= \frac{400}{220 \times 10} = 0.1818, \quad \sin\phi_0 = 0.9833 \\ I_w &= 10 \times 0.1818 = 1.818\ \text{A}, \quad I_\mu = 10 \times 0.9833 = 9.833\ \text{A} \\ R_0 (\text{LV}) &= \frac{220}{1.818} = 121\ \Omega, \quad X_0 (\text{LV}) = \frac{220}{9.833} = 22.37\ \Omega \\ R_0 (\text{HV}) &= 121 \times 100 = 12100\ \Omega \\ X_0 (\text{HV}) &= 22.37 \times 100 = 2237.3\ \Omega \end{aligned}$$

Series branch (SC test: 90 V, 30 A, 808 W on HV)

$$\begin{aligned} Z_{01} &= \frac{90}{30} = 3\ \Omega \\ R_{01} &= \frac{808}{30^2} = 0.898\ \Omega \\ X_{01} &= \sqrt{3^2 - 0.898^2} = 2.863\ \Omega \end{aligned}$$

Equivalent circuits

Approximate equivalent circuit referred to HV (shunt branch moved to the input terminals):

 I1 ->        I0                 I2'
 o-----+--------+---[ R01 ]---[ jX01 ]---o
 +     |        |                        +
     [ R0 ]  [ jX0 ]                   load
 V1    |        |                       V2'
 -     |        |                        -
 o-----+--------+------------------------o
 All values referred to HV side:
 R0 = 12100 ohm, X0 = 2237.3 ohm
 R01 = 0.898 ohm, X01 = 2.863 ohm

The exact circuit has the series impedance split as $R_1 + jX_1$ before the shunt branch and $R_2' + jX_2'$ after it (often taken as $R_1 = R_2' = R_{01}/2$, $X_1 = X_2' = X_{01}/2$) and an ideal transformer at the output; the approximate form above is accurate enough because $I_0$ is small.

Answer (HV side): $R_0 = 12100\ \Omega$, $X_0 = 2237.3\ \Omega$, $R_{01} = 0.898\ \Omega$, $X_{01} = 2.863\ \Omega$, $Z_{01} = 3\ \Omega$.