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Problem 1

A single-phase 100-kVA, 14/2.4-kV transformer and connected to a source through a line impedance of 38.2 + j140 Ω as shown in Figure 1. The transformer’s equivalent series impedance referred to the secondary is 0.10 + j0.40 Ω. The load is 90 kW at 0.8 lagging power factor and 2300 V.
a) Find the voltage of the source.
b) Find the voltage regulation of the transformer for this load.
c) Find the efficiency of the transformer ignoring the core losses.

Problem 1 A single-phase 100-kVA, 14/2.4-kV transformer and connected to a source-example-1

1 Answer

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Answer: Your welcome!

Step-by-step explanation:

a) The voltage of the source can be calculated using the equation V_source = V_load + I_load * Z_line, where V_load is the voltage of the load, I_load is the current of the load, and Z_line is the line impedance.

Using the given values, we can calculate the voltage of the source as V_source = 2300 V + (90 kW / 0.8 PF) * (38.2 + j140 Ω) = 4576.7 V

b) The voltage regulation of the transformer is the difference between the no-load voltage and the full-load voltage, divided by the full-load voltage. The no-load voltage of the transformer can be calculated using the equation V_NL = V_source * (1 + X_L / X_m), where V_source is the voltage of the source, X_L is the leakage reactance of the transformer, and X_m is the magnetizing reactance of the transformer.

Using the given values, we can calculate the no-load voltage as V_NL = 4576.7 V * (1 + 0.40 / 0.10) = 6378.8 V

The full-load voltage of the transformer can be calculated using the equation V_FL = V_NL - I_FL * Z_eq, where V_NL is the no-load voltage, I_FL is the full-load current of the transformer, and Z_eq is the equivalent series impedance referred to the secondary of the transformer.

Using the given values, we can calculate the full-load voltage as V_FL = 6378.8 V - (90 kW / 0.8 PF) * (0.10 + j0.40 Ω) = 5777.7 V

The voltage regulation of the transformer can then be calculated as VR = (V_NL - V_FL) / V_FL = (6378.8 V - 5777.7 V) / 5777.7 V = 10.3 %

c) The efficiency of the transformer can be calculated using the equation η = (P_out / P_in) * 100, where P_out is the output power of the transformer and P_in is the input power of the transformer.

Using the given values, we can calculate the efficiency as η = (90 kW / (90 kW + (90 kW / 0.8 PF) * (0.10 + j0.40 Ω))) * 100 = 98.5 %

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