Transmission Line Parameters

Transmission Line Parameters: Review on Inductan Inductance ce and Exampl Example e Problems

Inductance Calculations Last time we derived the formulas for approximating the inductance of transmission line. The formula are dependent on whether or not:  The conductors are solid or stranded  The conductors are bundled or not  The conductors are symmetrical space or asymmetrical spaced.

Example Problems Find inductive reactance per phase in ohms per km     

Solid conductor, symmetric spacing Bundled solid conductor, symmetric spacing Bundled solid conductor, asymmetric spacing Stranded conductor, symmetrical spacing Bundled stranded conductor, symmetric spacing

Problem Solving Hints The basic equation used to find inductance is  We need to determine what value to put in the numerator and the denominator Solution approach is to classify the problem  based on conductor and transmission line characteristics Then compute using the correct formula

Problem Solving Hints Symmetric spacing is used as GMD (Deq)



 D

Bundled must be used (calculated)

GMD (Deq) must be calculated

Not bundled 

Used

Ds

=r¶

 Ds

Solid : usually  mentioned in single dimension(diameter/r adius) 

Used r¶ as Ds

 Asymmetric spacing

Stranded  Ds

must be calculated

Example 1 Solid, single conductor with a radius of 1cm Transmission line is operate at 50Hz Find the inductive reactance per km. m

m

m

Solid conductor, symmetric spacing  Approach Determine

proper equation to calculate per phase inductance per phase inductance per km  multiply inductance by frequency in radians to find inductive reactance m

m

m

Solid conductor, symmetric spacing 1) Calculate r¶ r¶ = 0.7788 X r = 0.7788 cm 2) Find D GMD = 3¥(20)(20)(20) = D = 20 m

3) Calculate inductance L= 2 X10-7 [ln D/r¶] = 2 X10-7 ln [2000/0.7788] = 1.57 x 10-6H/m Make sure the units is consistent

Example 2  

Line is solid conductor, symmetrically spaced that is bundled This means we should use

Bundled

Solid Conductor, Symmetric

Spacing 1) calculate GMR (Ds) r¶ = 0.7788 x r= 0.7788cm GMR =1.09 x 4¥(r¶ x d3) = 1.09 x 4¥(0.7788 x (183) 

= 8.95 cm 2) Find GMD D = 20 m  3) Calculate inductance 

L = 2 x10-7 [ln D/GMR] = 2 x10-7 [ln(20/0.0895 )] = 1.08 x 10-6 H/m

Bundled

Solid Conductor, Symmetric

Spacing 4) calculate reactance XL = (2f) L= 3.39/m 

Example 3

 Are the conductors solid or stranded? Is the transmission line symmetric?  Are the conductors bundled? Solid, asymmetric and bundled Use L = 2 x 10-7 ln [ GMD/GMR]

Bundled

Solid conductor, Asymmetric

spacing 1)  What is r¶ r¶ = 0.7788 x r = 0.7788 cm 2)  What is the GMR? GMR = 1.09 x 4¥(0.7788 x (183)

= 8.95 cm 3) What is the GMD? GMD = 3¥(20)(20)(40) = 25.20m

Bundled

Solid conductor, Asymmetric

spacing GMD = 8.95cm GMR = 25.20m L = 2 x 10-7 ln [GMD/Ds] = 2 x 10-7 ln [25.20/0.0895] = 1.13 H/m XL = (2f)l = 3.54/m

Tutorial problem 1. Calculate the loop inductance per km of a single phase overhead line consisting of two conductors each 1 cm diameter and 1.2 m apart. [ 2.292mH] 2. A 3 phase transposed line has conductors of diameter 2 cm and spaced at distance of 3.65, 5.5 and 8.2m between centres. Calculate the inductance per phase per km of line length. [ 1.31mH] 3. A 3 phase 50 km long single circuit 66kV transposed overhead line has horizontal spacing with 3 m between adjacent conductors and 6 m between outer conductors. The conductor diameter is 2 cm. Find the inductance per phase. [61.85mH]

Tutorial problem 4. A 3 phase single circuit bundled conductor line with two subconductors per phase has horizontal spacing with 6.1m between the centre lines of adjacent phases. The distance between the subconductors of each phase is 30.5cm and each sub-conductor has a diameter of 2.54 cm. Find the inductance per phase per km. [0.988mH] 5. A 3-phase double circuit line has its conductors at the vertices of a regular hexagon with side 3.5m. The diameter of each conductor is 2cm. Find the inductance per phase per km.[0.596mH] 6. A 3 phase 132kV, 100km, 50Hz, single circuit line has horizontal spacing with 3.5m between adjacent conductors. The conductor is 1.2 cm. Find the line capacitance per phase and charging current per phase. [0.841F, 20.15A ]