Consider a 75 kVA, 2400/240 V, 60 Hz Transformer

Understanding Transformer Parameters

To find the values you're looking for, we'll first need to understand the transformer's equivalent circuit. The given transformer has the following parameters:

• Rated apparent power (S): 75 kVA
• Primary voltage (V1): 2400 V
• Secondary voltage (V2): 240 V
• Frequency (f): 60 Hz
• Primary side impedance (ZA): 0.52 + j3.8522 referred to the primary side
• Secondary side impedance (ZB): (0.52 + j3.85) x 10^-2 referred to the secondary side

(a) Finding Primary and Secondary Currents

To find the primary and secondary currents (I1 and I2) and the rated secondary current (I2_rated), we can use the formula:

I2_rated = S / V2

I2_rated = 75,000 VA / 240 V

I2_rated = 312.5 A

Now, we can calculate the primary current (I1) using the turns ratio (a) and the rated secondary current (I2_rated):

a = V1 / V2

a = 2400 V / 240 V

a = 10

I1 = I2_rated / a

I1 = 312.5 A / 10

I1 = 31.25 A

(b) Calculating Equivalent Impedance Referred to Primary Side

The equivalent impedance referred to the primary side can be calculated as follows:

Zeq_primary = ZA + ((a^2) * ZB)

Zeq_primary = (0.52 + j3.8522) + ((10^2) * (0.52 + j3.85) x 10^-2)

Zeq_primary = 0.52 + j3.8522 + (52 + j385) x 10^-2

Zeq_primary = 0.52 + j3.8522 + 0.52 + j3.85

Separating the real and imaginary parts:

Zeq_primary = (0.52 + 0.52) + j(3.8522 + 3.85)

Zeq_primary = 1.04 + j7.7022

(c) Calculating Equivalent Resistance and Reactance

Now, we can calculate the equivalent resistance (Re) and equivalent reactance (Xeq) referred to the primary side from Zeq_primary:

Re = 1.04 ohms (real part of Zeq_primary)

Xeq = 7.7022 ohms (imaginary part of Zeq_primary)