School of Electrical Engineering & Computer Science

ELEC4310 Power Systems Analysis- Tutorial-2

(Transmission Line 一 ABCD parameters)

Question 1

A 140 km, single circuit, three-phase transmission line delivers 50 MVA at 0.85 power factor lagging to the load at 132 kV (line to line). The line is composed of Drake conductors (outside diameter of 2.8 cm, and resistance = 0.075 Ω/km) with flat horizontal spacing of 3.65 m between adjacent conductors. Determine:

(a)  The series impedance and shunt admittance of the line

(b)  The ABCD constants of the line

(c)  The sending end voltage, current, real and reactive powers, and the power factor.

(d)  The percent regulation of the line.

Question 2

A three-phase, 50 Hz, completely transposed 345 kV, 200 km line has two conductors per bundle and the  following  line  constants:  z = 0.032 + j0.35Ω/km and  y = j4.2 × 10-6s/km.  Full  load  at receiving end of the line is 700 MW at 0.9 power factor lagging and at 95% of rated voltage. Assuming a medium length transmission line, determine the following:

(a)  ABCD parameters of the symmetrical π circuit

(b)  Sending end voltage Vs, current Is and real Power Ps .

(c)   Percent voltage regulation

(d)  Transmission line efficiency at full load.

Question 3

A 320 km transmission line has the following parameters at 50 Hz:

Resistance r = 0.13Ω/km per phase

Series reactance x = 0.49Ω/km per phase

Shunt susceptance b = 3.4 × 10-6s/km per phase

(a)  Determine the attenuation constant-α, wavelength-λ, and the velocity of propagation of the line at 50 Hz.

(b)  If the line is open circuited at the receiving end and the receiving end voltage is maintained at 100 kV line to line, determine the incident and reflected components of the sending end voltage and current of the line.

(c)   Hence, determine the sending voltage and current of the line.

Question 4

The general circuit constants of a double, three-phase, transposed transmission line is:

A = 0.97<0.49°

B = 52.88<74.79°Ω C = 0.0012<90.1°s

The  line is operated with a constant  receiving end voltage of 132  kV  line to  line, and one of the constant power factor values:

(a)  0.85 lagging

(b)   1.0

(c)  0.85 leading

Draw power circle diagrams to show how the sending end voltage varies as a function of the real power of the load at each of the power factor shown in (a), (b) and (c).

Question 5

A three-phase, 765-kV, 60 Hz transposed line is composed of four ACSR, 1,431,000-cmil, 45/7 Bobolink conductors per phase with flat horizontal spacing of 14 m. The conductors have a diameter of 3.625 cm and a GMR of 1.439 cm. The bundle spacing is 45 cm. The line is 400 km long, and for the purpose of this problem, a loss less line is assumed.

(a)  Determine the transmission line surge impedance Zc, phase constant- β, wavelength- λ, the Surge Impedance Loading (SIL), and the ABCD constants.

(b)  The  line delivers 2000 MVA at 0.8  power factor lagging at 735 kV. Determine the sending end quantities and voltage regulation.

(c)   Determine the receiving end quantities when 1920 MW and 600 MVAR are being transmitted at 765 kV at the sending end.

(d)  The line is terminated in a purely resistive load. Determine the sending end quantities and voltage regulation when the receiving end load resistance is 264.5 Ohm at 735 kV.

(e)  Series capacitors are installed at the midpoint of the line, providing 40% compensation. Determine the sending end quantities and the voltage regulation when the line delivers 2000 MVA at 0.8 pf lagging at 735 kV.

Question 6

A 69-kV, three-phase short transmission line is 16 km long. The line has a per phase series impedance of 0.125 + j0.4375Ω/km. Determine the sending end voltage, voltage regulation, the sending end power, and the transmission efficiency when the line delivers

(a)  70 MVA, 0.8 lagging power factor at 64 kV

(b)  120 MW, unity power factor at 64 kV

(c)  Shunt capacitors are installed at the receiving end to improve the  line  performance. The line delivers 70 MVA, 0.8 pf lagging at 64 kV. Determine the total MVAR and the capacitance per phase of the Y-connected capacitors when the sending end voltage is (i) 69 kV and (ii) 64 kV.

Question 7

A 50 HZ, 300 km, three-phase overhead transmission line has a series impedance of z = 0.8431<79.04° Ω/km and a shunt admittance of y = 5.105 × 10-6 <90° S/km.The load at the receiving end is 125 MW at unity power factor and at 215kV.

(a)  Determine the voltage, current, real and reactive power at the sending end and the  percent voltage regulation of the line. Also find the wavelength and velocity of propagation of the line.

(b)  Determine the ABCD parameters of the line when uncompensated.

(c)   For a series capacitive compensation of 70% (35% at the sending end and 35% at the receiving end), determine the ABCD parameters. Comment on the relative changes in the magnitude of B parameter with respect to the relative changes in the magnitude of A, C and D parameters. Also comment on the maximum power that can be transmitted when series compensated.

(d)  Given the uncompensated line of the problem described above, let a three-phase shunt reactor (inductor) that compensates for 70% of the total shunt admittance of the line to be connected at the receiving end of the line during no-load conditions. Determine the effect of voltage regulation with the reactor connected at no-load. Assume the reactor is removed under full-load conditions.

A 50 HZ, 400V, 400m, three-phase overhead distribution system has 250,000 all-aluminium for phase conductors and 3/0 all-aluminium for neutral conductor. The sending end voltage is balanced and fixed at 1.02pu. The receiving end loads are unbalanced, 145A 0.9 lagging for Phase-A, 135A 0.99 leading for Phase-B, and 125A 0.95 lagging for Phase-C, w.r.t 0˚, -120˚, 120˚ (voltages at the sending end). Note the neutral is grounded at the sending end but not the receiving end.

(All distances are in feet for pole top configuration.)

(a) Determine the zabcn matrix in Ω/km.

(b) Determine the ABCD parameters with the modified line model.

(c) Calculate the receiving end phase voltages, voltage unbalance percentage and neutral current.

(d) If the receiving end voltages are too low, please list two possible solutions.