Question

50 Points 1- A balanced delta connected load of 15 + j18 per phase is connected at the end of a three-phase line as shown in Figure 1. The line impedance is 1 + 12 12 per phase. The line is supplied from a three-phase source with a line-to-line voltage of 207.85 V rms. Taking the phase voltage Van as reference, determine: a) Current in phase a. b) Total complex power supplied from the source. c) Total complex powers of the line and the load. d) Magnitude of the line-to-line voltage at the load terminal. e) A delta connected capacitor bank is connected in parallel with the load to improve the load power factor to unity. Find the kvar and capacitance of the capacitor. do a 1+ j2 12 wm |VL| = 207.85 V ba b 15 + j18 12 со- Figure 1 Circuit for problem 1

Answer 1

zi m Lam Ivy: 207.850 15 mm 18 sce b mm ma Convert delta to start 9 Zan Zan Lac Zab Zac Zabt Zbet Zac m C b N/m Zn So now 2j mm M 21 15/35 in jo ba m 29 mem m Vana V B3 207.85 53 12020 For refrence- 1 80 Van 120 LO Ta 12020 120/-53.13 zer (1+2)(5+)6) 6+ 8) 10 Ta : 124-53.13 A CSScanned with CamScanner

.ط total complex power supplied ofrom the source * 3 Van Pan VA 3X120 20.12 L 453.13 4320 53,13 = 2592-3456 VA s. load terminal Voltage per phase Van Va - lal 1+2j) |2010- 122-53-131+4) = 93.72 4-2-93 Volt Complex power of the line 3 (Van- van) sam 34120 1 2020 – 93.722-8.93) 12 Z53:17 432 +864) VA 3 3x (43.722–2.93) (12253.13) Emplex power to the loud - 2160 + j 2592 VA d. 1 (V)u) 1(Vr)e) - B) VW): 18.13.72 = 162.39 U (C) / for unit power factor Load should be act as Resistive dyre- Realtive power of load = Capacitas bank. so rating of Capacitor = 2592 var. 2.592 KVAR CSScanned with CamScanner