**COMPUTATION OF PARAMETERS AND MODELLING OF TRANSMISSION LINES**

**1.1 AIM**

(i) To determine the positive sequence line parameters L and C per phase per kilometer of a three phase single and double circuit transmission lines for different conductor arrangements.

(ii) To understand modelling and performance of short, medium and long lines.

**1.2 OBJECTIVES**

i. To become familiar with different arrangements of conductors of a three phase single and double circuit transmission lines and to compute the GMD and GMR for different

arrangements.

ii. To compute the series inductance and shunt capacitance per phase, per km of a three phase single and double circuit overhead transmission lines with solid and bundled conductors.

iii. To become familiar with per phase equivalent of a three phase short and medium lines and to evaluate the performances for different load conditions.

iv. (a) To become familiar with the theory of long transmission line and study the effect of distributed parameters on voltage and currents, along the line, (b) calculate the surge

Impedance and surge impedance loading.

**Three Phase - Symmetrical Spacing:**

**Three Phase - Asymmetrical Transposed:**

**Nominal П-Model**

**Bundle conductors**

**Equivalent П-Model**

**1 EXERCISES:**

**1.1**A three-phase transposed line composed of one ACSR, 1,43,000 cmil, 47/7 Bobolink conductor per phase with flat horizontal spacing of 11m between phases a and b and between phases b and c. The conductors have a diameter of 3.625 cm and a GMR of

1.439 cm. The line is to be replaced by a three conductor bundle of ACSR 477,000-cmil,

26/7 Hawk conductors having the same cross sectional area of aluminum as the single conductor line. The conductors have a diameter of 2.1793 cm and a GMR of 0.8839 cm.

The new line will also have a flat horizontal configurations, but it is to be operated at a

Higher voltage and therefore the phase spacing is increased to 14m as measured from the

Centre of the bundles. The spacing between the conductors in the bundle is 45 cm.

(a) Determine the inductance and capacitance per phase per kilometer of the above two

Lines.

(b) Verify the results using the available program.

(c) Determine the percentage change in the inductance and capacitance in the bundle

Conductor system. Which system is better and why?

**1.2**A single circuit three phase transposed transmission line is composed of four ACSR 1,272,000 cmil conductors per phase with flat horizontal spacing of 14 m between

Phases a and b and between phases b and c. The bundle spacing is 45 cm. The

Conductor diameter is 3.16 cm.

a) Determine the inductance and capacitance per phase per kilometer of the line.

b) Verify the results using available program.

**1.3**A 345 kV double circuit three phase transposed line is composed of two ACSR,

1,431,000 cmil, 45/7 bobolink conductors per phase with vertical conductor configuration

as shown in Fig. 1.13. The conductors have a diameter of 1.427 in and the bundle spacing

is 18 in.

a) Find the inductance and capacitance per phase per kilometer of the line.

b) Verify the results using the available program.

c) If we change the relative phase position to acb-a’b’c’, determine the inductance and

Capacitance per unit length using available program.

d) Which relative phase position is better and why?

**1.4**A 230 kV, 60 HZ three phase transmissions is 160 km long. The per phase resistance is 0.124 Ω per km and the reactance is 0.497 Ω per km and the shunt admittance is 3.30 x 10

^{-6}∟90

^{0}seimens per km It delivers 40MW at 220 KV with 0.9 power factor lagging. Use medium line П model

i. Determine the voltage and current at sending end and also compute voltage

regulation and efficiency.

ii. Verify the results using the available program

**1.5**A three phase transmission line has a per phase impedance of Z=0.03+j0.04 Ω per km and a per phase shunt admittance of y=j4.0 x 10

^{-6}

^{ }Simens per km. The line is 200

km long. Obtain ABCD parameters of the transmission line. The line is sending 407 MW

and 7.833 MVAR at 350KV.Use medium П model

**1.6**A three phase 50 Hz, 400 kV transmission line is 250 km long. The line parameters per phase per unit length are found to be

r=0.02 Ω/km L=1.06mH/km C=0.011 µF/km

Determine the following using the program available use long line model.

(a) The sending end voltage, current and efficiency when the load at the receiving end is

640 MW at 0.8 power factor logging at 400 kV.

(b) The receiving end voltage, current, efficiency and losses when 480 MW and 320

MVAR are being transmitted at 400 kV from the sending end.

c) The sending end voltage, current and efficiency and losses when the receiving end load

Impedance is 230 Ω at 400KV

(d) The receiving end voltage when the line is open circuited and is energized with 400kV at the sending end. Also, determine the reactance and MVAR of a three phase shunt reactor to be installed at the receiving end in order to limit the no load receiving end voltage to 400 kV.

(e) The MVAR and capacitance to be installed at the receiving end for the loading

Condition in (a) to keep the receiving end voltage at 400 kV when the line is

Energized with 400 kV at the sending end.

(f) The line voltage profile along the line for the following cases: no load, rated load of

800 MW at 0.8 power factor at sending end at 400 kV, line terminated in the SIL and

Short circuited line.

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