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A 500-kV, 300-km, 60-Hz three-phase lossless overhead transmission line has a series inductance of 0.97 mH/km per phase and a shunt capacitance of 0.0115 mF/km per phase. The line supplies a load of 1000 MVA at 0.8 power factor lagging and at 500 kV. The line phase constant β= 0.001259 rad/km and its surge impedance ZC=290.43 Ω, (a) Determine the capacitance/phase and total three-phase Mvars supplied by a three-phase, Delta-connected shunt-capacitor bank at the receiving end to maintain the receiving-end voltage at 500 kV when the sending end of the line is energized at 500 kV. [12 marks] (b) If series capacitive compensation of 40% is installed at the midpoint of the line, without the shunt capacitor bank at the receiving end. Compute the sending-end voltage Vs and percent voltage regulation %VR. [10 marks] Solution a) βl = (0.001259  300)(180/) = 21.64 [1 marks] The equivalent line reactance for a lossless line is given by X‘ = Zc sin βl = 290.43 sin(21.64) = 107.11 ohm [2 marks] SR(3ph)= 100036.87 = 800 MW+ j600 Mvar [1 marks] For the above operating condition, the power angle  is obtained from 800=500*500/107.11 sin [2 marks] =20.045 [1 marks] The net reactive power at the receiving end is QR(3ph) = (500*500* cos20.045 – (500) 2*cos 21.64) /107.11 [1 marks] QR(3ph) = 23.15 MVAR QC(3ph)=j23.15-j600=-j576.84 MVAR [2 marks] 2 Xc =(500) / 576.84=433.28 Ω [1 marks] 6 C=10 /(2*60*433.38)=6.1 F [1 marks] b) Xser = 0.4  X0 = 0.4(107.11) = 42.84 Ω

[2 marks]

Z’=j(X’- Xser)=j64.26 ohm Y’=j2 Zc *tan(βl /2)=j0.001316 S Bnew=j64.26 ohm Anew=1+Z’Y’/2=0.9577=D VR= 500/sqrt(3) 0=288.675 0 kV IR=S* /3VR=1000-36.87/(3*288.675 0)=1.1547-36.87 kA Vs= 326.410.47 kV VsL-L= 326.4*sqrt(3)=565.4 kV

[1 marks] [1 marks]

%VR=(565.4/0.958)-500/500 *100 %=18%

[1 marks]

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A three-phase 420-kV, 60-HZ transmision line is 463 km long and may be assumed lossless. The line is energized with 420 kV at the sending end. When the load at the receiving end is removed, the voltage at the receiving end is 700 kV, and the per phase sending end current is 646.690 A. (a) Find the phase constant β in radians per km and the surge impedance Zc in Ω. (b) Ideal reactors are to be installed at the receiving end to keep |VS| = |VR| = 420 kV when load is removed. Determine the reactance per phase and the required three-phase Mvar.