Question C.1: The copper loss of a 2500 kA, 13.8–4.16 kV delta–wye connect......
The copper loss of a 2500 kA, 13.8–4.16 kV delta–wye connected three-phase transformer is 4 kW on the delta side and 3 kW on the wye side. Find R_{1}, r_{1}, r_{2}, and r_{2}^{\prime} for phase values throughout. If the total reactance is 5.5%, find X_{1}, x_{1} \ x_{2}, and x_{2}^{\prime}, assuming that the reactance is divided in the same proportion as resistance.
The copper loss per phase on the 13.8 kV side = 4/3 = 1.33 kW and the current per phase = 60.4 A. Therefore, r_{1} = 0.364 ohms. Similarly for the 4.16 kV side, the copper loss = 3/3 = 1 kW, the current = 346.97 A, and r_{2} = 0.0083 ohm per phase; r_{2} referred to the primary side r_{2}^{\prime} = (0.0083)(13.8 × 4.16)² = 0.273 ohm, and R_{1} = 0.364 + 0.273 = 0.637 ohm. A 5.5% reactance on a transformer MVA base of 2.5 = 4.19 ohms referred 13.8 kV side, and then x_{1} = (4.19)(0.364)/0.637 = 2.39 ohm and x_{2}^{\prime} = 1.79 ohm. Referred to the 4.16 kV side x_{2} = 0.162 ohm. The transformer X/R ratio = 6.56.