Final answer:
The question deals with calculating various specifications of a 100-kVA, 2400:240-V single-phase transformer given its resistance, reactance, and core parameters. It requires determining the equivalent T-model of the transformer, primary side current and voltage, and the real and reactive power on the primary side.
Step-by-step explanation:
Determining Transformer Specifications
The question involves a single-phase transformer with a 100-kVA rating and a primary-to-secondary voltage ratio of 2400:240 volts. The transformer operates at 230 V on the secondary side delivering 75 kW with a power factor of 0.85 lagging. The parameters provided are primary resistance (r1), primary reactance (X1), secondary resistance (r2), and secondary reactance (X2) along with the core parameters (R and Xm1). To address the problem, we must calculate the equivalent circuit parameters referred to the primary side, determine the primary current, primary voltage, and real and reactive power on the primary side.
(a and b) The equivalent T-model transformation involves referring all secondary side parameters to the primary side using the square of the turns ratio. Since the transformer is single-phase, this ratio is given by the voltage ratio 2400/240 or 10. This means that the secondary resistance and reactance are multiplied by 100 when referred to the primary side.
(c) The primary current can be calculated from the secondary power and voltage using the formula I1 = (P2 / (V2 * PF)) * a, where PF is the power factor, and a is the turn ratio.
(d) The primary voltage can be found by adding the voltage drops across the referred secondary resistance and reactance, along with the core resistance and reactance, to the secondary voltage.
(e) The real and reactive power on the primary side can be calculated using the relationships P1 = I1 * V1 * PF and Q1 = I1 * V1 * sqrt(1 - PF^2).