http://powerlearn.ee.iastate.edu --Simulator for transmission thermal limits TOWERABC: Calculates line constants for overhead three-phase, single-circuit or double-circuit, transmission lines and produces contour plots of rms V, E, and H, plus sound. It can be used for 50/60 Hz, and also for harmonic frequencies.
OVERHEAD LINES -OBJECTIVE TYPE QUESTIONS
1. The surge impedance of a 110 kV, 3-phase transmission line is 440 ohms. The surge impedance loading of the line is
Ans.: (b)
2.The capacitance and inductance per unit length of a 3-phase line, operating at 110 kV are .01 microfarad and 2.5 mH. The surge impedance of the line is
(a) 50 ohms
(b) 500 ohms
(c) 250 ohms
Ans: (b)
3. A long transmission line is energized at then sending end and is kept open circuited at the receiving end. The magnitudes of the sending end voltage Vs and of the receiving end voltage Vr satisfy the following relationship
Ans: (c)
4. Voltage regulation of a short transmission line is
Ans: (c)
5. The capacitance of an overhead line increases with
Ans: (b)
6. Shunt compensation for long EHV lines is primarily resorted to
Ans: (a)
7. Series compensation is primarily resorted to
Ans: (b)
8. Fair weather corona loss may be computed using the empirical formula given by Peterson. According to Peterson's formula corona loss is proportional to
(a) f and V2
(b) f 2 and V
where f and V are the system frequency and voltage respectively.
Ans: (a)
9. Bundled conductors are used in EHV lines primarily for
Ans: (b)
10. There are 20 discs in the string of insulators of a 3-phase 400 kV transmission line. String efficiency is 80 %. The maximum voltage across any disc is
Ans: (b)
11. Two or three sheds or petticoats are provided in pin-type insulators in order to increase
Ans: (a)
12. Pin -type insulators are use up to
Ans: (b)
13. Insulators used for transmission line at the dead -end tower are
Ans: (c)
14. Economic studies have shown that D.C. transmission is cheaper than a. c transmission for lengths
below 300 km
beyond 600 km
beyond 1200 km
Ans. b
15.Transmission voltages in the range 230 kV-765 kV are known as
Ans. b
16. Which one of the following statements is false?
As the transmission voltage increases,
Ans. c
17. The internal inductance of a solid conductor of radius r and carrying a current I is equal to
Ans. c
Ans. b
Ans. b
Ans. a
Ans .a
Ans. c
Ans. c
Ans. c
Ans. b
26. The surge impedance of a telephone line is
Ans. b
Ans. b
Ans. d
Ans. c
Ans. b
Ans. b
visual critical voltage for corona on an overhead line.
Ans. c
the switching voltage on a transmission line.
Ans. b
from a power line.
Ans. b
Ans. b
Ans. c
Ans. c
Ans. c
Ans. none of the above
Ans. a
The sheds of an insulator should be shaped
Ans. b
Ans. b
Ans. c
as that for dry flash-over
Ans. b
Ans. b
Ans. c
TOP
Gauge sizes decrease as the wire increases in size.
Number of strands = 3 n2 -3n + 1
where n = number of layers including the single central strand.
The following conductors are used.
AAC-all aluminum conductor
AAAC-all aluminum alloy conductor
ACSR-aluminum conductor steel re-inforced
ACAR-aluminum conductor alloy re-inforced
R = r l/A
R2/R1 = (T0 +T2)/ (T0 +T1)
R2 = Resistance at temperature T2
R1 = Resistance at temperature T1
T0 = Constant
= 234.5 for annealed copper of 100% conductivity
=241 for hard drawn copper of 97.3% conductivity
=228 for hard drawn aluminum of 61% conductivity
Skin effect is function of conductor size, frequency and resistance of conductor material.
Discuss the proximity effect, stranding and spiraling of conductors
Line inductance - one phase & 3-phase
Single-phase overhead line
Voltage drop in a single-phase line due to loop impedance
= 2 l (R + j
w m 0 ln (Dm/Ds)/2p) Il= line length,m
R= resistance of each conductor,m
Dm= equivalent or geometric mean distance (GMD) between conductor centres
Ds= Geometric mean radius(GMR), or self-GMD of one conductor
= 0.7788 r for cylindrical conductor
r= conductor radius
I = current
L= 2 x 10 -7 ln (Dm/Ds ) H/m
Three-phase overhead line (unsymmetrical spacing)
Dab +Dbc +Dca
Equivalent equilateral spacing=Deq = Dm = (Dab DbcDca) 1/3
In practice , conductors are transposed.
Transposition is carried out at switching stations
Average inductance per phase
L=2 x 10 -7 ln (Deq/Ds ) H/m
TOPLine capacitance, 1-phase & 3-phase
Single-phase overhead line
Cab = 2
p e 0e r/ ln (D/r) (F/m)The capacitance to neutral for a two- wire line is twice the line-to-line capacitance, Cab.
Three-phase overhead line
Line-to-neutral capacitance
Cn = 2
p e 0e r/ ln (Deq/r) (F/m)Charging current /phase =j
v Cn Vph (A/m) TOP
Effect of ground on capacitance of 3-phase line
The capacitance of a 3-phase transposed line considering ground effect is given by
Cn = 2
p e 0e r/ [ln (Deq/r) -ln (h12 h23 h31/h11h22h33)] (F/m)where h12= distance between conductor 1 and image of conductor 2, etc. Effect of ground is to increase the capacitance.
TOPEquivalent circuit for short transmission line
(up to 80 km)Note that bold symbols indicate complex quantities.
Vs =Vr + Ir Z
Is = Ir = I
Draw a phasor diagram for a short line with inductive load and with capacitive load, using Vr as the reference phasor.
Show that
Vs = SQRT[(Vr + IR Cos
f r +(or -) IX Sinf r) 2 + (IX Cos f r +(or -) IR Sinf r)2]+ sign above is for lagging p.f
- sign above is for leading p.f
f
r = angle between Vr & Irf
s = angle between Vs & Isd
= f s-f r = load angletan
d = (IX Cos f r +(or -) IR Sinf r)/ (Vr + IR Cos f r +(or -) IX Sinf r)Vs = AVr + BIr
Is = CVr +DIr
For a short line, A=1, B=Z, C=0, D=1
Line Efficiency (pu)= Vr I Cos
f r/ Vs I Cos f sVoltage regulation (pu)=(Vs-Vr)/Vr
= (VrNL- VrFL)/ VrFL
= [I(R Cos
f r -(or+) XSinf r)]/ VrFL TOPEquivalent circuit for medium length line
A T or a
p network is formed depending upon how the series impedance or the shunt admittance is lumped at a few points. See Fig.3The ABCD parameters of the nominal-T network are:
A = 1+ZY
B = Z (1+ZY/4)
C = Y
D= A
The ABCD parameters of the nominal-
p network are:A = 1+ZY/2
B = Z
C = Y (1+ZY/2)
D= A
Nominal -T and Nominal-
p networks are not equivalent electrically, as may be verified by using the Y-D transformation.Voltage regulation (pu)= ((Vs/A) - VrFL)/ VrFL
TOP (above 240 km)The solution of the voltage wave equation using the initial conditions is
V = (Cosh
g x) Vr + (Z0 Sinhg x) IrI = (Y0
Sinhg x) Vr + (Cosh g x) Irg
= sqrt (yz) = a + jba
= attenuation constant pu lengthb
= phase-shift constant pu lengthy = shunt admittance pu length
z = series impedance pu length
Z0 = surge impedance = sqrt (z/y); Y0 =1/Z0
Vs = AVr + BIr
Is = CVr +DIr
where
A = Coshg l
B = Z0Sinhg l
C = (1/Z0) Sinh g l
D = A
l= line length
Line
The exact equivalent
p circuit and the exact equivalent T circuit for a long line are shown in Fig.4The elements of the
p circuit are obtained fromZ
p = B = Z0Sinhg l = (Z Sinhg l)/ g lY
p /2 = (A-1)/B = ( Coshg l - 1)/ Z0Sinhg l = (tan(g l/2).Y/2)/(g l/2).The elements of the T circuit are obtained from
ZT/2 = (A-1)/C = (Cosh
g l-1)/ ((1/Z0) Sinh g l)ZT = 2 Z0 tanh (
g l/2) = (Z tanh (g l/2))/ (g l/2)YT = C= (1/Z0) Sinh
g l = (Y Sinh g l)/ g l TOPSurge impedance loading of lines
Incident and reflected voltages on long lines
Vs = (1/2) (Vr +Ir Zo) ea l e jb l + ((1/2) (Vr -Ir Z0) e-a l e -jb l
Is = (1/2) (VrYo +Ir) ea l e jb l + ((1/2) (VrYo -Ir) e-a l e -jb l
The first and second terms in each of the above equations refer to the incident and reflected voltages respectively.
The wavelength is defined by
l
= 2p /bThe velocity of propagation
n of the waves is given by
n
= l fl
= 6000 km at 50 Hz.When the line is terminated in its surge impedance Zr = Zo, there is no reflected wave. (Infinite line)
Surge Impedance Loading (SIL) of a transmission line
SIL = [Vr (L-L) (in kV)]2/Zo' (MW)
where Zo' = sqrt(L/C)
SIL is a measure of the maximum power that can be delivered over a line. The following factors affect the maximum power:
To increase SIL, kVr can be increased and Zo reduced by using series compensation.
The distinction between maximum power and SIL should be mentioned.
TOPThe parameter A = Cosh g l decreases with increase in line length. In such cases Vr is considerably greater than Vs, when the line is charged but unloaded. In underground cables, the effect is much more pronounced, even in short lengths. It is called the Ferranti effect. Discuss the effects of shunt compensation and reactive loading.
Advantages of bundled conductors
Disadvantages of bundled conductors
Ds = GMR of subconductors
d = distance between two sub-conductors
Dsb = GMR of bundled conductor
Dsb = (Dd) 1/2 (For a 2-conductor bundle)
Dsb = (Dd2) 1/3 (For a 3-conductor bundle)
Dsb = (Dd3) 1/4 (For a 4-conductor bundle)
Average inductance per phase of a bundled conductor,
L= 2 x 10 -7 ln (Deq/ Dsb), H/m
Deq = (D12 D23 D31)
Dij = spacing between phase i and phase j
TOPFactors affecting mechanical design of overhead lines
Factors affecting span length
There are five kinds of stresses on lines & supports
Sag and tension analysis of overhead lines
Required clearances:
The data for the following clearances of different voltage levels should be known.
Sag and tension analysis:
Factors affecting sag are:
Conductor load depends on
Effect of change in temperature:
If the conductor stress is constant and if the temperature changes, the change in length is
D l = lo. a .D t
D t = t1-to= change in temperature
D l = l1-lo = change in length
a = Coefficient of linear expansion of conductor per deg. C. I ftemperature is constant while conductor stress changes (i.e loading), the change in length is
D l = lo. D T/MA
D T =T1-To= change in tension in kg
M= modulus of elasticity of conductor
A = Metal cross-section of conductor.
Consider the following in sag & tension calculations:
Line location
These are used to provide the following
TOP
If an alternating potential is applied to two wires whose spacing is large in comparison with the diameter and the potential difference is gradually increased, a point will be reached when a faint luminous glow of violet colour will appear, and a hissing sound will be heard. This phenomenon is known as Corona. The formation of corona is accompanied by a loss of power. It causes non-sinusoidal nature of current and interference with neighbouring communication circuits.
Corona formation takes place due to ionization of a layer of air immediately surrounding the conductor. For air under ordinary conditions near sea level & without impurities, the value of potential gradient at which ionization takes place can be taken as 30kV/cm (peak).
Interference with communication circuits may be due to both electromagnetic and electrostatic action, the former producing currents, which are superposed on the true speech currents, thereby setting up distortion and the latter raising he potential of the communication circuit as a whole.
Disruptive Critical Voltage
The potential gradient , gr is maximum at the surface of the conductor, ie.
gr = V/(r ln (d/r)).
For visual corona at normal temperature & pressure,
V= 30 (r + 0.3
Ö r) ln (d/r) kV (peak)Conditions affecting corona:
Considering the above factors , the critical disruptive voltage to neutral becomes
Vc = m0g0
d r ln (d/r)m0= irregularity factor
g0=disruptive critical voltage gradient for air in kV at NTP (21.1 kV/cm ,RMS)
d
=air density factor =392 b/(273+t)b=atmospheric pressure in cm of Hg
t=temperature in deg. C
The visual critical voltage is given by
Vv = m0g0
d r (1+ 0.3/sqrt(rd ))ln (d/r)Power loss due to corona
Corona formation results in power loss. Peek's formula for corona loss is:
P= 241 [(f+25)l/
d ]sqrt(r/d) (Vph - Vc)2 10-5 kW/phwhere Vph and Vc are the effective phase and critical disruptive voltages , f is the frequency of the system, l= length in km.
Peterson's formula for corona loss is :
P = 0.000021 f V2 F /[log10(d/r)]2
P = power loss in kW per km of conductor under fair weather conditions.
f = frequency,Hz
V = line to ground voltage
D = spasing between conductors
R = radius of the condcutor
F = corona factor determined by test
Audio Noise
When corona is present on the conductors, EHV lines generate audible noise which is specially high during polluted weather. The noise is broadband , which extends from very low frequency to about 20 kHz. Corona discharges generate positive & negative ions which are alternately attracted & repelled by the periodic reversal of polarity of the a.c excitations. Their movement gives rise to sound-pressure waves at frequencies of twice the power frequency and its multiples, in addition to the broadband spectrum which is the result of random motions of the ions. Audible noise can become a serious problem from 'psychoacoustics ' point of view, leading to insanity due to loss of sleep at night to inhabitants residing close to an EHV line.
Radio Interference (RI)
Pulse type corona discharge from transmisssion line conductors gives rise to interference to radio broadcast in the range of 0.5 MHz to1.6 MHz.
Electromagnetic Effect
The emf induced in the communication circuit due to neighbouring power circuit depends on its distance with respect to the power line. The net emf induced due to electromagnetic coupling with a 3-phase line is small since the phasor sum of induced emfs tends to zero. However, the presence of certain harmonics would cause seriously high induced emfs. This problem is more serious these days since the power line current is not sinusoidal because of he use of static controllers.
Electrostatic Effect
The communication line may acquire dangerously high potential due to electroctatically induced charges. The interference between power & communication lines can be reduced considerably by transposing the conductors of bothe power & communication lines.
The communication line may require elctrostatic shilding to overcome elctrostatic interference.
TOP
Materials & types of insulators
The insulators used in connection with overhead systems employing bare conductors are composed almost invariably of glazed porecelain. Glass has also been used for medium voltgaes . The porcelain used should be ivory white ,sound, free from defects and thoroughly vitrified .
There are three types of insulators for overhead lines:
What is the difference between suspension & strain insulators?
Potential distribution over a string of insulators
Model questions
String efficiency
= S.O.V of a string of n insulators/ ( n * S.O.V of one insulator)
The string efficiency depends on the ratio= capacitance per insulator/capacitance to earth.
Methods of improving string efficiency
The string efficiency can be improved by the following methods:
m = insulator self-capacitance/capacitance to earth
This would require long cross-arms and hence is not economical.
This approach requires units of different sizes. Hence it is not generally preferred. The self-capacitance of the lowest unit has to be maximum and as we move upward , the self-capacitance should decrease progrssively.
The voltage distribution is controlled in this method by the emloyment of a grading or guard ring, which usually takes the form of a large metal ring surrounding the bottom unit and connected to the metal work at the bottom of this unit , and therefore to the line . This ring , or shield , has the effect of increasing the capacitances between the metal work and the line.
The string efficiency increases with the guard ring.
Here special features of the transformer bushing may be explained.
What is the effect of surface leakage resistance on the potential distribution across a string of insulators?
What is the effect of corona on string efficiency?
Distribution System Planning (
Moduled.xls)
This Excel spreadsheet module demonstrates the basics of distribution system planning. We select the proper conductors and the number of shunt capacitors for compensation subject to the requirements on voltage regulation, losses and fixed and operating costs. We specify the customer demands either in power or in impedance. We specify the operating costs for losses. We also specify the capital costs for various conductor line building and for capacitor placements. We have to select the best combination of conductors and capacitors to minimize cost over a certain period, normally one-year