EE117 Representation and Performance of Transmission Lines Transmission Line Representation and Performance Levels of Transmission • • • Short Transmission Line (L < 80 km) Medium Length Transmission Line ( 80 km < 240 km) Long Transmission Line (L > 240 km) Short Transmission Line. For short lines, only the resistance and inductance are being considered. VSN  VRN 0  IZ Z  R  jX PR IR    cos 1 pfR 3 VR pfR PO PR x100  x100  Pin PS IR  PR 3 VR pfR   cos 1 pf R Transmission Line Representation and Performance Efficiency, Ploss and voltage regulation VRNL  VRFL x100 VR  VRFL Z  R  jX PR IR    cos 1 pfR 3 VR pfR PO PR x100  x100  Pin PS PR  x100 PR  PLOSS Transmission Line Representation and Performance – Nominal Pi Equivalent Circuit Medium Length Transmission Line. Analysis involves the use of lumped parameters. • Nominal Pi Equivalent Circuit Transmission Line Representation and Performance – Nominal Pi Equivalent Circuit  ZY  VSN  1  VRN  I R Z  2    ZY   ZY  I S  Y 1  VRN  1  IR   4  2    pf R  cos  R and pfS  cos  S PLOSS  3 I 2 R PR PR %  x 100  x 100 PS PR  PLOSS %VR  VRNL  VRFL x 100 VRFL VRNL  VSN  2   2  ZY    Note: Line to neutral voltages can also be used. Transmission Line Representation and Performance – Nominal T Equivalent Circuit • Nominal T Equivalent Circuit Transmission Line Representation and Performance – Nominal T Equivalent Circuit  ZY   ZY  VSN  1  V Z 1 IR  RN    2  4     ZY  I S  Y VRN  1  IR  2   pfR  cos  R PLOSS  3 I 2 S and pfS  cos  S I 2 R  R2 PR PR %  x 100  x 100 PS PR  PLOSS VRNL  VRFL %VR  x 100 VRFL VRNL  2   VS    2  ZY  Note: Line to neutral voltages can also be used. Transmission Line Representation and Performance Generalized Transmission Constant VSN  AVRN  B I R I S  C VRN  D I R Nominal Pi Circuit A  D  1 BZ VRN  DVSN  B I S I R  C VSN  A I S Nominal T Circuit ZY 2  ZY  C  Y 1  4   ZY A  D  1 2  ZY  B  Z 1  4   CY Transmission Line Long Transmission Line z  r  j  l (series impedance per unit length) y  j b  j  c (shunt admittance per unit length, g is neglected) Transmission Line Representation and Performance – Long Transmission Line Voltage and Current Relationships  VRN  Z C I R  X  VRN  Z C I R   X VSN   e  e   2 2     VRN  VRN     IR  Z   IR  Z  C  X C   X IS   e  e 2 2             where: Zc = z / y = characteristic impedance  = z y =  + j = propagation constant  = attenuation constant (neper per unit length)  = phase constant (radians per unit length) Transmission Line Representation and Performance – Long Transmission Line In hyperbolic form, VSN  VRN Cosh x  Z C I R Sinhx VRN I S  I R Cosh x  Sinh x ZC Velocity of Propagation v 2f  unit length per sec ond Incident and Reflected Wave  VRN  Z C I R  X e   2   (incident wave )  VRN  Z C I R   X e   2   (reflected wave ) Transmission Line • At infinite line, reflected wave is zero. If the line is terminated by its characteristic impedance, ZC, the reflected wave is zero. • Sometimes, ZC is called the surge impedance. However, surge i peda ce is associated with a loss less li e R a d g are zero . ZC  SIL  L C VL2 L C SIL – surge impedance loading (pf  1, resistive ) Sample Problems 1. A short, singe-phase transmission line has a total impedance of 5cis600 Ω a d supplies a total load of 120 A, 3.3 kV and 0.8 pf lagging. Calculate the sending end voltage. Answer: 3.9 kV 2. A short, three-phase transmission line with an impedance of 6 + j8 ohms per wire has a sending end and receiving end voltage of 120 and 110 kV, respectively. For a receiving end load PRE at 0.9 lagging power factor, find the active and reactive power at the receiving end. Answer:111.4 MW, 53.95 MVAR 3. A three-phase, 20 km line delivers a load of 10 MW at 11 kV. The power factor at the receiving end is 0.707 lagging. The line has a resistance of 0.02  per km and an inductive reactance of 0.07  per km per phase. Calculate the efficiency of the line. If the receiving end power factor is raised to 0.9 lagging by using static capacitor, calculate the new efficiency. Answer: 93.8 %, 96.08 % Sample Problems 4. A short three phase transmission line has an impedance per wire of (15 + j20) . The sending end voltage is 13 kV and the receiving end takes 1 MW at a lagging power factor. The current per conductor is 70 amperes. Determine the efficiency of transmission, the receiving end voltage and power factor. Answer: 81.93%, 10.08 kV, 0.8179 lagging 5. A 60 Hz, three-phase transmission line is 100 miles long. It has a total series impedance of (35 + j120)  and a shunt admittance of j930 siemen. It delivers 40 MW at 220 kV with 90% lagging power factor. Find the voltage at the sending end by : (a) short line approximation (b) the nominal π approximation (c) the nominal T approximation Also determine the voltage regulation for the given line and the power loss. Assume the sending end voltage remains constant. Answer: (a) 237.67 kV, 1.4284 MW, 8.03%; (b) 225.8 kV, 1.1642 MW, 8.67% (c) 225.10 kV, 1.5095 MW, 8.35% Sample Problems 6. A single circuit, 60 Hz, three phase transmission line has the following parameters : R = 0.30 /mile L = 2.10 milliHenry /mile C = 0.014 Farad/mile The voltage at the receiving end is 132 kV. If the line open at the receiving end, find the incident and reflected current 75 miles from the receiving end. If the line is 75 miles long and delivers 40 MW at 132 kV and 80% lagging power factor, determine the sending end voltage, current, power, and power factor. Compute for the velocity propagation. Answer: 97.8719.3, 92.461.43, 151.27 kV, 199.61 A, 42.885 MW, 0.82 lag Sample Problems 7. A short, three-phase transmission line with impedance of 6 + j10 ohms per conductor has the following loads: Load 1: Resistive load drawing 50 A Load 2: 80 A at 80% lagging power factor Load 3: Capacitor bank drawing 45 A Determine the power factor at the sending end if the receiving end voltage is 13.2 kV. Sample Problems 8. A single-circuit, 60-Hz, 3-phase, 300-km transposed transmission line composed of four ACSR per phase is in horizontal configuration. The distance between the centers of the bundle is 14 m and the spacing between the bundle conductors is 45 cm. The conductor has a diameter of 1.382 inches and GMR of 0.5592 i ches. Resista ce is 0.50 Ω/k . The load o the li e is 800 MW, 80% power factor lagging at 400 kV. Determine the: a. sending end voltage b. sending end current c. sending end power d. voltage regulation of the line e. wavelength f. velocity of propagation End of Topic