Transmission Lines1-91CHAPTER 1Problems on Nominal 'n' Method11. A 3-phase, 50 Hz, 150 km line has a resistance, inductive reactance and capacitiveshunt admittance of 0.102, 0.52 and 3x10-6 S per km per phase. If the line delivers50 MW at 110 kV and 0.8 p.f lagging, determine the sending end voltage and current.Assume a nominal- circuit for the line.(Ans. 143.55 kV (line), 306.4 A]12. A 3, 50 Hz overhead line 160 km long with 132 kV between the lines at the receivingend has the following constants.Resistance/km/conductor=0.160Inductance/km/conductor1.2 mHCapacitance/km/conductor = 0.0082 #FDetermine the voltage, current and power at the sending end when supplying a loadof 100 MVA at 0.8 p.f lagging. Using '' representation of the line.[Ans. 175.18 kV (line), 414.11 A, 0.749 lag]13. A 3-phase overhead transmission line has the following constants.Resistance/phase = 102Inductive reactance/phase = 350Capacitive admittance/phase = 3x10-4 SiemenIf the line supplied a balanced load of 40,000 kVA at 110 kV and 0.8 p.f. lagging,calculate (i) Sending end power factor (ii) regulation (iii) transmission eficiency.[Ans. (i) 0.798 lag (ii) 10% (iii) 96.38%)14. A 1 transmission line 160 km long has the following constants. Resistance/km =0.1562, reactance/km = 0.52, susceptance/km = 8.75x10-6 and receiving endvoltage = 66 kV. Using nominal method calculate the sending end voltage, sendingend current, sending end P.F when the line is delivering 15 mW at 0.8 p.f lagging.[Ans. 82.96 kV, 226.5A, 0.886 lagging]Problems on Nominal-T Method:15. A 3 transmission line delivers 20,000 kVA, p.f 0.8 lagging at 66 kv at receiving end.Each conductor has a resistance of 102 and inductive reactance of 302 and anadmittance due to capacitance between line and neutral of 4x10-4 S. Calculate thevoltage, current and p.f at the transmitting end and the efficiency of transmission, usenominal 'T' method.

11. A 3-phase, 50 Hz, 150 km line has a resistance, inductive reactance and capacitive shunt admittance of 0.102, 0.52 and 3x10-6 S per km per phase. If the line delivers 50 MW at 110 kV and 0.8 p.f lagging, determine the sending end voltage and current. Assume a nominal- circuit for the line. (Ans. 143.55 kV (line), 306.4 A]

11. A 3-phase, 50 Hz, 150 km line has a resistance, inductive reactance and capacitive shunt admittance of 0.102, 0.52 and 3x10-6 S per km per phase. If the line delivers 50 MW at 110 kV and 0.8 p.f lagging, determine the sending end voltage and current. Assume a nominal- circuit for the line. (Ans. 143.55 kV (line), 306.4 A]

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter5: Transmission Lines: Steady-state Operation

Section: Chapter Questions

Problem 5.12P

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Calculate the capacitance-to-neutral in F/m and the admittance-to-neutral in S/km for the three-phase line in Problem 4.18. Also calculate the line-charging current in kA/phase if the line is 110 km in length and is operated at 230 kV. Neglect the effect of the earth plane.
A 40-km, 220-kV, 60-Hz, three-phase overhead transmission line has a per-phase resistance of 0.15/km, a per-phase inductance of 1.3263 mH/km, and negligible shunt capacitance. Using the short line model, find the sending-end voltage, voltage regulation, sending-end power, and transmission line efficiency when the line is supplying a three-phase load of (a) 381 MVA at 0.8 power factor lagging and at 220 kV and (b) 381 MVA at 0.8 power factor leading and at 220 kV.
The 100-km, 230-kV, 60-Hz, three-phase line in Problems 4.18 and 4.39 delivers 300 M VA at 218 kv to the receiving end at full load. Using the nominal circuit, calculate the ABCD parameters, sending-end voltage, and percent voltage regulation when the receiving-end power factor is (a) 0.9 lagging, (b) unity, and (c) 0.9 leading. Assume a 50C conductor temperature to determine the resistance of this line.
A single-phase overhead transmission line consists of two solid aluminum conductors having a radius of 3 cm with a spacing 3.5 m between centers. (a) Determine the total line inductance in mH/m. (b) Given the operating frequency to be 60 Hz, find the total inductive reactance of the line in /km and in/mi. (c) If the spacing is doubled to 7 m, how does the reactance change?
Three ACSR Drake conductors are used for a three-phase overhead transmission line operating at 60 Hz. The conductor configuration is in the form of an isosceles triangle with sides of 20, 20, and 38 ft. (a) Find the capacitance-to-neutral and capacitive reactance-to-neutral for each 1-mile length of line. (b) For a line length of 175 mi and a normal operating voltage of 220 kV, determine the capacitive reactance-to-neutral for the entire line length as well as the charging current per mile and total three-phase reactive power supplied by the line capacitance.
A three-phase overhead transmission line is designed to deliver 190.5 M VA at 220 kV over a distance of 63 km, such that the total transmission line loss is not to exceed 2.5 of the rated line MVA. Given the resistivity of the conductor material to be 2.84108-m, determine the required conductor diameter and the conductor size in circular mils. Neglect power losses due to insulator leakage currents and corona.
The 500-kV, 60-Hz, three-phase line in Problems 4.20 and 4.41 has a 180-km length and delivers 1600 M W at 475 kv and at 0.95 power factor leading to the receiving end at full load. Using the nominal circuit, calculate the (a) ABCD parameters, (b) sending-end voltage and current, (c) sending-end power and power factor, (d) full-load line losses and efficiency, and (e) percent voltage regulation. Assume a 50C. conductor temperature to determine the resistance of this line.
A 60-Hz, single-phase two-wire overhead line has solid cylindrical copper conductors with a 1.5 cm diameter. The conductors are arranged in a horizontal configuration with 0.5 m spacing. Calculate in mH/km (a) the inductance of each conductor due to internal flux linkages only, (b) the inductance of each conductor due to both internal and external flux linkages, and (c) the total inductance of the line.
The capacitance of a single-circuit, three-phase transposed line with the configuration shown in Figure 4.38, including ground effect, and with conductors not equilaterally spaced is given by C20lnDeqrlnHmH8 F/mÂ line-to-neutral where Deq=D12D23D133=GMD r= conductors outside radiusHm=(H12H23H13)1/3HS=(H1H2H3)1/3 Now consider Figure 4.39 in which the configuration of a three-phase, single circuit, 345-kV line with conductors having an outside diameter of 1.065 in. is shown. Determine the capacitance to neutral in F/m, including the ground effect. Next, neglecting the effect of ground, see how the value changes.
The following parameters are based on a preliminary line design: per unitVS=1.0, VR=0.9 per unit, =5000km,Zc=320,=36.8. A three-phase power of 700 MW is to be transmitted to a substation located 315 km from the source of power. (a) Determine a nominal voltage level for the three-phase transmission line, based on the practical line-loadability equation. (b) For the voltage level obtained in part (a), determine the theoretical maximum power that can be transferred by the line.
Figure 4.34 shows double-circuit conductors' relative positions in segment I of transposition of a completely transposed three-phase overhead transmission line. The inductance is given by L=2107lnGMDGMRH/m/phase Where GMD=(DABeqDBCeqDACeq)1/3 With mean distances defined by equivalent spacings DABeq=(D12D12D12D12)1/4DBCeq=(D23D23D23D13)1/4DACeq=(D13D13D13)1/4 And GMR=[ (GMR)A(GMR)B(GMR)C ]1/3 with phase GMRs defined by (GMR)A=[ rD11 ]1/2;(GMR)B=[ rD22 ]1/2;(GMR)C=[ rD33 ]1/2 and r is the GMR of phase conductors. Now consider a 345-kV, three-phase, double-circuit line with phase-conductors GMR of 0.0588 ft and the horizontal conductor configuration shown in Figure 4.35. Determine the inductance per meter per phase in Henries (H). Calculate the inductance of just one circuit and then divide by 2 to obtain the inductance of the double circuit.
If the per-phase line loss in a 70-km-long transmission line is not to exceed 65 kW while it is delivering 100 A per phase, compute the required conductor diameter if the resistivity of the conductor material is 1.72108-m.