EHV POWER TRANSMISSION Unit: II – Calculation of Line and Ground Parameters TWO MARKS with answer
I YEAR/II SEM
EHV POWER TRANSMISSION
Unit: II – Calculation of Line and Ground
Parameters
1.
Define resistance?
It is
the property of substance which opposes the flow of current through it. The
resistance of element is denoted by the symbol “R”. It is measured in ohms (Ω).
R=ℓL/A
Where
A is the cross sectional area.
ℓ is the resistivity.
L is
the length.
2.
What are the effects of conductor
resistance in EHV line?
· Power loss in transmission caused by
I2R heating.
· Reduced current-carrying capacity of
conductor in high ambient temperature regions.
· The conductor resistance affects the attenuation of
travelling waves due to lightning and switching operations, as well as
radio-frequency energy generated by corona.
· In these cases, the resistance is computed at the
following range of frequencies: Lightning—100 to 200 kHz; Switching—1000-5000
Hz; Radio frequency—0.5 to 2 MHZ.
3. Define
standard conductors?
Conductors used for E.H.V
transmission lines are always stranded. Most common conductors use a steel core
for reinforcement of the strength of aluminium, but recently high tensile
strength aluminium is being increasingly used, replacing the steel. The former
is known as ACSR (Aluminium Conductor Steel Reinforced) and the latter ACAR
(Aluminium Conductor Alloy Reinforced).
4.
Define bundle conductors?
A
bundle conductor is a conductor made up of two or more conductors called the
sub conductors, per phase in close proximity compared with the spacing between
phases.
5.
What are the parameters consider for
modes of propagation?
(a) Velocity of
propagation, (b) attenuation, and
(c) Surge impedance.
6.
List out the properties of bundled conductors?
Bundled conductors are exclusively
used for E.H.V transmission lines. Only one line in the world, that of the
Bonneville Power Administration in the U.S.A., has used a special expanded ACSR
conductor of 2.5 inch diameter for their 525 kV line.
7. Define GMR?
A bundle of N-sub-conductors
can be replaced by a single conductor having an equivalent radius. This is
called the 'Geometric Mean Radius' or simply the 'Equivalent Radius.' It will
be shown below that its value is
req = (N.r.RN–1)1/N = r[N.(R/r)N–1]1/N
= R(N.r/R)1/N
8. Define
bundle spacing and its formula?
The spacing between adjacent
sub-conductors is termed 'Bundle Spacing' and denoted by B.
B=R/2 sin (π/N)
9. Define
bundle radius?
The radius of the pitch circle on
which the sub-conductors are located will be called the 'Bundle Radius',
denoted as R. The radius of each sub-conductor is r with diameter
d. The angle sub-tended at the centre by adjacent sub-conductors is (2p/N) radians, and it is readily seen that
R=B/2 sin (π/N)
10.
Define inductance?
It is
the property of a substance which stores energy in the form of electromagnetic
field. The Inductance of element is denoted by the symbol “L”. It is measured
in Hendry (H).
11. What are the
assumptions in bundle conductors?
· The bundle spacing (B) between adjacent sub-conductors
on the bundle radius R is very small compared to the height of H of the phase
conductor above ground.
· The total current carried by the bundle is I and that
of each sub conductor is I=I/N.
· Internal flux linkages are omitted.
12. Define
Maxwell’s co-efficient?
The inductance L=0.2 ln(2H/r) of a single
conductor located above a ground plane. The factor p=ln(2H/r) is known as
Maxwell’s coefficient.
L=0.2 (p) µH/m (or) mH/km
13. Define
capacitance?
It is the property of a substance which
stores energy in the form of electrostatic field. The capacitance of element is
denoted by the symbol “C”. It is measured in Farads (F).
C=Q/V
14. Define self
inductance?
The diagonal elements of the
inductance matrix [L]n*n represent the self-inductances.
Self
inductance (Ls) = Sum of diagonal elements/3
15.
Define mutual inductance?
The
off-diagonal elements of the inductance matrix [L]n*n represent
the mutual-inductances.
Mutual Inductance = Sum of off
diagonal elements/3
16.
What is the use of modes propagation?
· A design of carrier equipment for
speed and protection where the attenuation signals and their distortion is of
primary concern in determining the transmitter and receiver powers.
· Propagation of switching and
lightning surges on the lines which causes over voltages and control the design
of insulation clearness.
17.
What are the assumptions in potential
co-efficient for bundle conductor lines?
· The bundle dimensions B and R are
small compared to line height H.
· B and R are small compared to the
spacing S from the center of one phase to another.
18.
Define modified Clarke
transformation?
The resulting Eigen-values for both
inductance and capacitance are equal to the zero-, positive-, and negative
sequence Quantities obtained from Fortescue's transformation using phasors in
the transformation matrix. Here, we have used only real numbers to effect the
diagonalization procedure. The resulting [T] and [T]–1 are called
'Modified Clarke Transformation' matrices.
19.
Write the shorts notes on
untransposed and transposed line inductance?
The
inductance of untransposed line inductance is given by
[L]ut=0.2 * [P]
The line inductance in
transposed line is given by
[L]transposed = [Ls
Lm Lm
Lm Ls
Lm
Lm Lm
Ls]
20.
Define internal inductance and its
formula?
The
flux linkage per ampere is called inductance.
LI=µoµx/8π
LI=0.5*10-7 H/m
21.
Define external inductance and its
formula?
The
flux linkage of conductor due to external flux up to x distance is called
external inductance.
Le=0.2 ln(x/r) µH/m
x is the distance.
r is the radius of
conductor.
22.
What are the characteristics of pole
conductors?
· Velocity propagation.
· Attenuation.
· Surge impedance.
23.
What are the effects of ground
currents in system performance?
· Flow of current during short circuit
involving ground. These are confirmed to single line to ground and double line
to ground faults the system is still balanced.
· Switching operations and lightning
phenomena.
· Propagation of waves on conductors.
· Radio noise studies.
24.
Calculate the req for line
whose configuration is 400kv, N=2, d=3.18cm, B=45cm.
Given:
400kv,
N=2
D=3.18cm
r=3.18/2=1.5*10-2m
r=0.015m
B=45*10-2m
req=√r.B=(0.015*45*10-2)1/2
req=0.082m.
25.
A 345 kv line has an ACSR bluebird
conductor 1.762 inches (0.04477m) in diameter with an equivalent radius for
inductance calculation of 0.0179m. The line height is 12m. Calculate the
inductance per km length of conductor and error caused by neglecting the
internal flux linkage?
L=0.2 ln (24/0.0179)
= 1.44 mH/km
If
internal flux linkage is neglected
L=0.2 ln (24/0.02238)
= 1.3955 mH/km
Error = (1.44-1.3955)*100/1.44
=3.09%
Outer radius = 0.0179/0.02238
=0.8
For a
round solid conductor
GMR=0.7788*outer radius
=0.7788*0.8
=0.62304m.
16-MARKS
1.
A
3-phase 750 kV horizontal line has minimum height of 12 m, sag at mid span = 12
m. Phase spacing S = 15 m. Conductors are 4 × 0.035 m with bundle spacing of B =
0.4572 m. Calculate per
kilometre:
(a)
The matrix of Maxwell's Potential coefficients for an untransposed configuration.
(b)
The inductance and capacitance matrices for untransposed and transposed configurations.
(c) The zero-, positive-, and
negative-sequence inductances and capacitances for transposed line.
(d) The ground-return resistance and
inductance matrices at 750 Hz taking rs = 100ohm-metre.
For calculation take Hav =
Hmin + Sag/3.
2.
Repeat
problem 1 for a 1150-kV delta configuration of the 3-phases with average height
of 18 m for the lower conductors, 36 m for the top conductor, and spacing of 24
m between bottom conductors. Bundle radius = 0.6 m and conductor size = 6 ×
0.046 m diameter. f = 1000 Hz and rs = 50 ohm-metre.
3.
Diagonalize
the matrix
[D]=Unity 3X3 Matrix.
Give eigenvalues and eigen-vector
matrices.
4.
Discuss
the convenience offered by using modes of propagation and possible uses of this
technique.
5.
The
capacitance matrix of a 750-kV horizontal configuration line is [C]=
(a) Find the 3 eigenvalues of the
matrix, 
.
.
(b) Diagonalize the matrix
by evaluating suitable transformation matrix [T] and its inverse [T ]–1.
(c) Then prove that
[T ]–1 [C] [T ]=
Diagonal element of eigen values
6.
In
problems 1 and2 calculate the charging
current supplied. Assume full transposition and place all the capacitance at
the line entrance across the source. L =400 km.
10. In Fig. 3.18 show that the
voltage drop from A to B and B' to A add to{(Rc +
Rg) + s(Ls + Lg)} I1 + (Rg + sLm +
sLg) I2 + (Rg + sLm + sLg)
where s = the
Laplace-Transform operator.
7.
Using the transformation matrices for diagonalizing
the matrix [D], prove without multiplying, that the same transformation
matrices will diagonalizable the inductance or capacitance matrices of a
fully-transposed line of the type.[L] transposed matrix
(a) If l1, l2, l3 are the
eigenvalues of matrix [C] and given that [L][C] = [U]/g2,
prove that the eigenvalues of [L] will be m1 = 1/g2l1, m2 = 1/g2l2
and m3 = 1/g2l3. In general, prove that if l1, l2, l3 are eigenvalues of
a matrix [M], then the eigenvalues of its inverse are the reciprocals of
lamda values
8.
The
following transformation matrix is attributed to Karrenbauer.
[ T ]=
having the
three eigenvectors (1, 1, – 2),(1, – 2, 1) and(1, 1, 1)
having the
three eigenvectors (1, 1, – 2),(1, – 2, 1) and(1, 1, 1)
(a) Calculate [ T ]–1.
(b) Normalize [ T ]
and [ T ]–1.
(c) Prove that [ T ]–1
[L]t [ T ] give a diagonal matrix for the inductance of a
fully transposed line. Determine the eigenvalues of [L]t.
(d) Check that [ T ]–1
[C]t [ T ] is also diagonal where [L]t[ C
]t = [ U ]/g2.
(e) Interpret the
eigenvectors of the Karrenbauer transformation matrix.
( f ) Is this type of transformation unitary
9.
The
dimensions of a 3-phase 400-kV horizontal line are:
H
=
15 m, S = 11 m phase separation, conductor 2 × 3.18 cm dia, and B =
45.72 cm. Calculate.
(a)
the matrix of inductances per km, for untransposed
configuration, and
(b)
the same when there is complete
transposition.
10.
The
dimensions of a 3-phase 400-kV horizontal line,
are:
H = 15 m, S =
11 m phase separation, conductor 2 × 3.18 cm dia, and B = 45.72 cm.
Calculate.
(a)
the matrix of capacitance km, for untransposed
configuration, and
(b) the same when there is complete transposition.
EEE ENGINEERING NOTES
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