For Problem 8.12, compute the power absorbed by the load using symmetrical components. Then verify the answer by computing directly without using symmetrical components.

Problem 8.12

A Y-connected load bank with a three-phase rating of \(500 \mathrm{kVA}\) and \(2300 \mathrm{~V}\) consists of three identical resistors of \(10.58 \Omega\). The load bank has the following applied voltages: \(V_{a b}=1840 \angle 82.8^{\circ}, V_{b c}=2760 \angle-41.4^{\circ}\), and \(V_{c a}=2300 \angle 180^{\circ} \mathrm{V}\). Determine the symmetrical components of

(a) the lineto-line voltages \(V_{a b 0}, V_{a b 1}\), and \(V_{a b 2}\),

(b) the line-to-neutral voltages \(V_{a n 0}, V_{a n 1}\), and \(V_{a n 2}\),

(c) and the line currents \(I_{a 0}, I_{a 1}\), and \(I_{a 2}\). Note that the absence of a neutral connection means that zero-sequence currents are not present.