Computation of Transmission Lines Parameters-ex1

Power system simulation lab

Dept. of EEE / TKSCT

Experiment : 01 Date :

COMPUTATION OF TRANSMISSION LINES PARAMETERS AIM: To determine the positive sequence line parameters L & C per phase per kilometer of a three phase single and double circuit transmission lions for different conductor arrangements and write a MATLAB program to determine the Line parameters. SOFTWARE REQUIRED: Mat lab COMPUTATION OF LINE PARAMETERS-THEORY GENERAL FORMULA The general formula for computing inductance per phase in mH per km of a transmission line is given by

D  L = 0.2 ln  m   Ds 

(1.1)

Where Dm = Geometric Mean Distance (GMD) Ds = Geometric Mean Radius (GMR) The expression for GMR and GMD for different arrangement of conductors of the transmission lines are given in the following section. 1. 2. 3. 4. 5. 6.

Single Phase - Two Wire System Three Phase - Symmetrical Spacing Three Phase - Asymmetrical Transposed Composite conductor lines Stranded conductors Bundle conductors.

SINGLE PHASE - TWO WIRE SYSTEM

D

Fig. 1.1. Conductor arrangement

TKSCT - Dept. of EEE

Computation Of Transmission Lines Parameters



GMD = D

(1.2)

GMR = re-1/4 = r’

(1.3)

r = radius of conductor THREE PHASE - SYMMETRICAL SPACING

D

D

D

Fig.1.2. Conductor arrangement GMD = D

(1.4)

GMR = re-1/4 = r’

(1.5)

r = radius of conductor THREE PHASE - ASYMMETRICAL TRANSPOSED A DAB DCA B DBC C

GMD = Geometric mean of the three distances of the unsymmetrical placed conductors GMD = (DAB DBC DCA) 1/3

(1.6)

GMR = re-1/4 = r’

(1.7)

r = radius of conductors





COMPOSITE CONDUCTOR LINES Composite conductor is composed of two or more elements or strands electrically in parallel. The expression derived for the inductance of composite conductors can be used for the stranded and bundled conductors and also for finding GMD and GMR of parallel transmission lines. Fig 1.4 shows a single phase line with two composite conductors.

Conductor X-with n strands

Conductor Y with m strands

Fig. 1.4. Single Phase Line with Composite Conductor The inductance of composite conductor - x., is given by

 GMD  Lx = 0.2 ln    GMRx 

(1.8)

Where GMD = [(Daa’ Dab’ … Dam’ ) …… (Dna’ Dnb’….. Dnm’ )]mn

(1.9)

GMRx = [(Daa Dab … D an) …… (Dna Dnb….. D nn)] n2

(1.10)

r’a = ra.e-1/4 The distance between elements are represented by D with respective subscripts and r’ a , and r’b and r’ n have been replaced by Daa, Dbb …… and D nn respectively for symmetry. STRANDED CONDUCTORS The GMR for the stranded conductors are generally calculated using equation (1.10). For the purpose of GMD calculation, the stranded conductors can be treated as solid conductor and the distance between any two conductors can be taken as equal to as center-tocenter distance between the stranded conductors as shown in Fig 1.5, since the distance between the conductors is high compared to the distance between the elements in a stranded conductor. This method is sufficiently accurate.





Fig. 1.5. Three Phase Line with Stranded Conductors.

BUNDLE CONDUCTORS EHV lines are constructed with bundle conductors. Bundle conductors improves power transfer capacity and reduces corona loss, radio interference and surge impedance.

d

d

d d

d

d

d

d

Fig.1.6. Examples of bundles





The GMR of a bundle conductor is normally calculated using (1.10). GMR for two sub conductor Dsb = [Ds x d] 1/2

(1.11)

GMR for three sub conductor Dsb = (Ds x d2)1/3

(1.12)

GMR for four sub conductor Dsb = 1.09 (Ds x d3)1/4

(1.13)

Where Ds is the GMR of each sub conductor and d is the bundle spacing For the purpose of GMD calculation, the bundled conductor can be treated as a solid conductor and the distance between any two conductors can be taken as equal to center tocenter distance between the bundled conductors as shown in Fig 1.7, since the distance between the conductors is high compared to bundle spacing.

Fig.1.7. Bundled conductor arrangement

CAPACITANCE A general formula for evaluating capacitance per phase in micro farad per km of a transmission line is given by

(1.14) Where





GMD is the “Geometric Mean Distance” which is the same as that defined for inductance under various cases.

GMR IS THE GEOMETRIC MEAN RADIUS AND IS DEFINED CASE BY CASE BELOW 1. Single phase two wires system (for diagram see inductance): GMD = D GMR = r (as against r’ in the case of L) 2. Three phase - symmetrical spacing (for diagram see inductance): GMD = D GMR = r in the case of solid conductor = Ds in the case of stranded conductor to be obtained from manufacturer’s data. 3. Three-phase – Asymmetrical - transposed (for diagram see Inductance): GMD = [DAB DBC DCA] 1/3

(1.15)

GMR = r ; for solid conductor GMR = Ds for stranded conductor = rb for bundled conductor where rb = [r*d] 1/2 for 2 conductor bundle rb = [r*d2] 1/3 for 3 conductor bundle (1.20) rb = 1.09 [r*d3] 1/4 for 4 conductor bundle where r = radius of each sub conductor d = bundle spacing





PROCEDURE: 1. Enter the command window of the MATLAB. 2. Create a new M – file by selecting File - New – M – File 3. Type and save the program in the editor window. 4. Execute the program by either pressing Tools – Run. 5. View the results.

EXERCISES 1)

A 50-Hz 3-phase line (transposed) composed of one ACSR moose conductor (overall Dia. = 31.8mm) per phase has flat horizontal spacing of 10m between adjacent conductors. Compare the inductive and capacitive reactance in ohms per phase of this line with that of a line (transposed) using a three-conductor bundle of ASCR lynx conductor (each having overall Dia. = 19.6mm) having 10m spacing measured from the centre of the bundles. The bundle conductors in each phase are arranged in an equilateral triangle formation with spacing between conductors in the bundle as 40m.

2)

Find the inductance and capacitance / phase / Km of double circuit 3-phase line shown in fig.1. the conductor are transposed and area of radius 0.75cm each. a c’

4m 3m

b

b’ 5.5m

3m c

a’ 4m

RESULT : Thus 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 arrangement were determined and verified with MATLAB software.





Discussion question: 1) What is meant by self GMD and mutual GMD? 2) What is proximity effect? 3) What are the advantages of bundle conductors? 4) What is the need for transposing line conductors? 5) What is critical disruptive voltage?





Program COMPUTATION OF TRANSMISSION LINES PARAMETERS

EX.No:1

clc; clear all; disp('MENU') disp('Unbundled moose conductor........>1') disp('Bundle Conductor.................>2') menu=input ('Enter your choices'); if menu==1||menu==2 d= input('Enter the over all Dia in mm:'); f=input ('Enter the frequency in Hz:'); r1=(d/2)*10^-3; % The G.M.D is equal to Dm Dm= (10*10*20)^(1/3); if menu==1 Dsl= 0.7788*r1; %GMR for ind.calculation Dsc= r1; %GMR for cap.calculation else Db= input('Enter the spacing b/w in the bundle in m:'); Dsl=(r1*0.7788*(Db)^2)^(1/3); Dsc=(r1*(.4)^2)^(1/3); end L= 2*10^-7 *log(Dm/Dsl) % (L) inductance H/m % The value of 2*pi*E =0.0555 micro.frad / km E=0.0555*10^-9; C= E/log(Dm/Dsc) % (C) capacitance F/m XL=(2*pi*f*L)*10^3 % (XL) Inductive Reactance in ohm/m/phase disp('0hm/km/phase'); XC=(1/(2*pi*f*C))*10^-3 % (XC) capacitive Reactance in ohm km /phase disp('0hm km/phase'); end

OUT PUT MENU Unbundled moose conductor........>1 Bundle Conductor.................>2 Enter your choices........1 Enter the over all Dia in mm:31.8 Enter the frequency in Hz:50 L = 1.3850e-006 C = 8.3145e-012 XL = 0.4351 ohm/km/phase XC = 3.8284e+005 ohm km/phase Enter your choices........2 Enter the over all Dia in mm:19.6 Enter the frequency in Hz:50 Enter the spacing b/w in the bundle in m.4 L = 9.5392e-007 C = 1.1843e-011 XL = 0.2997 ohm/km/phase XC = 2.6877e+005 ohm km/phase





COMPUTATION OF TRANSMISSION LINES PARAMETERS

EX.No:2

clc; clear all; r=input('Enter the radius in m:'); GMR=0.7788*r; for i=1:3 a=input('Enter the self GMR and distance b/w one phase conductor in array form:');

ds(i)=nthroot(prod(a),4); end Ds=nthroot(prod(ds),3) for i=1:3 b=input('Enter the distance b/w two conductor in array form:'); dm(i)=nthroot(prod(b),4); end Dm=nthroot(prod(dm),3) L=2*10^-7*log(Dm/Ds) disp('mH') p=input('Enter the distance d1,d4,d2,d5 in matrix form'); q=input('Enter the distance d3,d6 in matrix form'); d=((p(1)^2*p(2)^2*p(3)*p(4))/(q(1)^2*q(2))); C=.0556/log(d/r) disp('F/m')

OUT PUT Enter the radius in m:.0075 Enter the self GMR and distance b/w one phase conductor in array form:[.00584 .00584 7.21 7.21] Enter the self GMR and distance b/w one phase conductor in array form:[.00584 .00584 7.21 7.21] Enter the self GMR and distance b/w one phase conductor in array form:[.00584 .00584 5.5 5.5]

Ds = 0.1961 Enter the distance b/w two conductor in array form:[3.1 3.1 5.62 5.62] Enter the distance b/w two conductor in array form:[3.1 3.1 5.62 5.62] Enter the distance b/w two conductor in array form:[6 6 4 4] Dm = 4.4029 L = 6.2223e-007 H Enter the distance d1, d4, d2, d5 in matrix form [3.1 5.62 6 4] Enter the distance d3, d6 in matrix form [7.21 5.5] C = 0.0068 F/m



Computation of Transmission Lines Parameters-ex1

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