Question

Please write neatly and clearly. Include all steps. Will like and comment

150 kVA, 2400/240 V, 60 Hz Transformer.
OC test: Voc = 240 V, loc= 15.38 A, Poc = 594 W
SC test: Vsc = 70 V, Isc = 62.5 A, Psc = 1660 W
Calculate the Xeq (in ohm up to 2 decimal places) of the approximate equivalent circuit referred to the LV side.

Answer 1

The equivalent reactance (Xeq) of the transformer referred to the LV side is calculated using the short circuit test results and is approximately 1.04 Ω.

Step-by-step explanation:

To calculate the equivalent reactance (Xeq) of the transformer referred to the low voltage (LV) side, we use the results from the short circuit (SC) test. The short circuit test gives us the values of short circuit voltage (Vsc), short circuit current (Isc), and short circuit power (Psc). Xeq is derived using the SC test values to find the impedance (Zsc), and then separating the reactive part of it, since Zsc consists of both resistance (Rsc) and reactance (Xsc). We first find Zsc by dividing the short circuit voltage by the short circuit current (Vsc/Isc) and then subtract the resistive part, which is calculated by dividing the power by the square of the short circuit current (Psc/Isc^2), from Zsc to get Xsc. These calculations are done at the SC voltage and current level.

Xeq, when referred to the LV side, requires no transformation for this particular case due to the tests already being performed on the LV side. Hence, Xsc is equivalent to Xeq.

To calculate Xeq:

1. First, calculate the impedance, Zsc = Vsc / Isc.
2. Then, calculate the resistance, Rsc = Psc / Isc^2.
3. Next, calculate the reactance, Xsc = sqrt(Zsc^2 - Rsc^2).
4. The equivalent reactance Xeq is equal to Xsc.

Substituting the given values:

1. Zsc = 70 V / 62.5 A = 1.12 Ω.
2. Rsc = 1660 W / (62.5 A)^2 = 0.4256 Ω.
3. Xsc (or Xeq) = sqrt((1.12 Ω)^2 - (0.4256 Ω)^2) = sqrt(1.2544 - 0.1810) = sqrt(1.0734) ≈ 1.04 Ω.

Therefore, the equivalent reactance Xeq referred to the LV side is approximately 1.04 Ω.