Question

1- A balanced delta connected load of 15 + j18 12 per phase is connected at the end of a three-phase line as shown in Figure 1. The line impedance is 1 + j2 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. 1+ 32 12 ao a |VL = 207.85 V b. ba 15 + 18 12 со-

Answer 1

O solution. Given that, Della connected load - 15+j8 zine impedence = 1+j2 ZL. Uzs ZL - On 22 VAN = Vab ZL 27 Now, load is connected in star after- 4-1 conversion. star connected load Za 15+18 3 = 5+1(8/3) = Zy Vab= 207.85 V. 립 3 2 N 207.85 Zy a3 120 V © VAN 12070° 1 a (1+j2) +(5+593) = 15-797-37,830 UN ZL uuuuuuu = Zet Zy CS Scanned with CamScanner

6 * . complex power =-3x VX la? = 3X 120 X 15:19 237.83° = 4.4-89.73 +3 34-86'36 VA (Vc) Voltage of ZL= 1X 24 = 15.792-37.83'X Complex power of line her (1+2) = 35.3126-62 20_018.20 * VLX I û = = 35.312660 X 15.4937-23 240.64 +3 502.938 VA complex power of load = total - Line [4489.73 +3 3486-36] - [ 240.6443502.93 424.9.09 +5 2983.43 CS Scanned with CamScanner

@ Vphe at loved = ven - [XZL = 12020° – 15.79 2-37.83 x (1+52) 89.47 2-9.82 Line voltage at load = Nph x 23 = 154.96 2-9.82°, @ total complex power: 4489.13+1341-36 Q = 3486-36, For unity of compensate a a = 34 8 6 36 kV, Vph Q = 3x Xc aate Q 3XVph? 21783 x Vph ? ? Q 3-486.36 2x9x50x3 X 1202 = 257.01-4F. CS Scanned with CamScanner