Question

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Frequency= 60Hz

50 Points 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 6 ba 15 + j18 12 со- с Figure 1 Circuit for problem 1

Answer 1

Converting Delta Connected load into star connection 211 23 Z33 Zzz + ; 233= Z2 Z3 Zıt Zzt Z3 211 Z, Zz 2222 ZZZ Z + Z₂tZz Zt Z2tZ3 Given Z1 = Z2 = Z₂ = 15+j18 .: Z11 = Z22: Z33 - 리 156118 3 5+j6 ohms 120 volts re Given VL = 207.85 V (RMS) Vph = 207.85 VE Considering phase voltage reference Vph : 12020° volk i RMS) {for phase-a Drawing por phose equivalent circuit for phase-a Vow VLOAD j2 & j Ia 12010

6 Zeq = 1+ 2+ 5+ 6 = 6 + 8 ohms o Ia: 12020 122-53:13 Amps O 6+ 18 is Current in phase- 122-53-13° A Iph= I line = 6 Total complex power supplied by Source for star connection 122-53.13 A Vi-L207.85 V (or Vph: 12020ºV Total complex power supplied S = 3 Vpn Iph : 3812% 120 = 4320 VĄ power factor of supplied power = Cuph-LIph (angh) ♡ = 0-(-53.13) 53.130 power factor: cos 53.13 = 0.6 log: Pune = 1x1 = 12²x 1 = 144 watts Bline = I xj 2 = 12² x 2 = j288 VAR Total Complex power of the line Sine = 144 +j288 VA Sünel 322 VA tan! (288 639435 -power factor angle (Pine factors cos 63.4355 0.4477 lag c) $ . 744 Power

Sine : 322VA at 0.4471 log. per-phase hase equi = 122-53:13°A from valent circuit Viad: 12010- (122-53-13) (1+j2) :: VienD : 93.6-24.8 A VLOAD = 93.723 L-2.935° volts (phase) Iph Complex power of load SLOAD 3Vph Iph = 34 93.723x12 Slomp = 3.374.028 VA power factor angle -2.935 -(-53.13) - 53.13) - 50.195° cos PLOAD .. 0.6401 lag d) and Vpn (oad forminal) = 93.723 2-2.935 volts for a star connected load VL.L = V3 Vpw LVL-2= LVph + 30° ...VL-L V3 x 93-723 L-2.935+30° : VL-L (load) = 162.34 227.065" volks line voltage leads phase voltage by 30° a star connected load. NOTE : for

e) Total complea power consumed by lood. PLOAD = 3374.028% cos 50.195 Promo - 2159-974 watts GoAb = 3374.028 y sin 50.195 2592-021 VAR the power factor to unity, the delta connected capacitor bank needs to deliver equipalent amount VAR'S consumed load To bring of as by :. Scap Scap = 2592-021 -UAR KUAR of capacitor bank = 2.592 KVAR Capacitive reactance = 3 von Vph= Uph (Wad) (X) Scap Yelph: 3x 93-723 10.1665 ohms 2592021 [for a 60 Hz Power supply CE 25x60x 10.1665 0.261 mf (for 60Hz He supply