Unit - 3

Overhead Transmission Lines and Cables

Q1) A power of 12000 MW is required to be transmitted over a distance of 1000 km at voltage levels of 400 KV, 750 KV, 1000 kV and 1200 KV, determine

i)                   possible number of circuits required with equal magnitudes for sending and receiving end voltages with 30° phase difference.

Ii)                 the currents transmitted

Iii)              the total line losses.

A1)

Omit series-capacitor compensation.

P=0.5E2/LX , MW  244.64  1150  2400  3450

a) No. Of circuits

=12000/P   50  12  6  3-4

I = E sin /√3 LX

b) Current,  kA  17.6  9.23  6.925  5.75

c) % Power loss, P  4.76  2.5  0.78  0.584

Total Power loss, MW 571  300  93.6  70

Q2) A Power of2000 MW is to be transmitted from a super thermal power station in Central India over 800 km to Delhi. Use 400 KV and 750 KV alternators. Suggest the number of circuits required with 50% series capacitor compensation and calculate the total power loss and loss per km.

A2)

With 50% of line reactance compensated, the total reactance will be half of the positive sequence reactance of the 800 km line.

P = 0.5 × 400²/400 × 0.327 = 670 MW/ckt at 400kV

And P = 0.5 × 750²/400 × 0.272 = 2860 MW/ckt at 750 Kv

	400 kV	750 kV
No. Of ckt. Required	3	1
Current per ckt., kA	667/(√3×400) =0.963	1.54
R for 800km ,  ohms	0.031×800 =4.8	=0.0136 800 =10.88
Loss per ckt, MW	3×24.8×0.9632 =69MW	3×10.88×1.542 =77.4 MW
Total power loss, MW	3×69 =207	77.4
Loss/km, kW	86.25 kW/km	97 kW/km

Q3) A 3 phase 132 KV, 50Hz, 150 km long transmission line consists of three standard aluminium conductors spaced triangularly at 3.8 m between centres. Each conductor has a diameter of 19.53 mm. The surrounding air is at temperature of 30°C and at a biometric pressure of 750 mm of Mercury. If the breakdown strength of air is 21.1 kV (rms) per cm and the surface factor is 0.85, determine the disruptive critical voltage. Also, determine the visual critical voltages for local and general Corona if the surface factors are 0.72 and 0.82 for visual Corona (10 cal) and visual Corona (general) respectively.

A3)

d=19.53mm, r=0.5d = 0.5(19.53)=9.765×10-3 m

Air density factor, =

=

D=3.8m, m0 = 0.85

G0 = 21.1 kV (rms)per cm

=21.1×1000×100  V/m

=2.11×106 V/m

The disruptive critical rms voltage per phase is given by

E0 = G0 m0 r

=2.11×106×0.85×9.765×10-3×0.9703×ln

=101.347×103 V

=101.347 kV

For local corona, mv = 0.72

The visual critical rms voltage per phase for local corona is given by

=2.11×106×0.72×9.765×10-3×0.9703[1+×ln×5.96

=112.396×103 V = 112.393 kV

For decided corona, mv = 0.82

The visual critical rms voltage per phase for decided (general) corona is given by

Ev =2.11×106×0.82×9.765×10-3×0.9703[1+×ln

=128×103 V = 128 kV

It is to be noted that there is no corona under normal working conditions since the actual operating voltage to neutral is 132/ √3 that is 76.21kV.

Q4) Conductors of a three phase transmission line are equilaterally spaced 6 m apart. The radius of each conductor is 1 cm. The air temperature is 30°C and pressure is 740 mm of Mercury. If surface factor is 0.92 and irregularity factor is 0.83, calculate the disruptive critical voltage and visual critical voltage.

A4)

E0=119.475kV(rms value) m0=0.83

=

=

Q5) Determine the Corona loss of a three phase, 220 KV, 50 Hz and 200 kilometre long transmission line of three conductors each of radius 1 cm and spaced 5m apart in an equilateral triangle formation. The air temperature is 30°C and the atmospheric pressure is 760 mm of Mercury. The surface factor or irregularity factor is 0.85.

A5)

f = 50 Hz  = =

r=1cm=0.01m  D=5m

=

En = 220/  kV = 127 kV

Pc = 472.73 kW/phase

Total corona loss = 3×472.73 kW = 1418.19 kW

Q6) Estimate the Corona loss for a three phase, 110 KV, 50 Hz, 150 km long transmission line consisting of three conductors each of 10 mm diameter and displaced 2.5 metres apart in an equilateral triangle formation. The temperature of air is 30°C and the atmospheric pressure is 750 mm of Mercury. Take the regularity factor as 0.85. Ionization of air may be assumed to take place at a maximum voltage gradient of 30 kV/cm.

A6)

d = 10mm, r= 0.5d = 5mm = 5 × 10-3 m

Air density factor, =

=

D= 2.5 m, m0 = 0.85

E0 =G0 m0 r  V/phase

=

According to peek, corona loss under fair weather conditions is given by

=

Total corona loss = 3Pc = 3×105.6 = 316.8 kW

Q7) A three phase,220 KV transmission line with conductors radius 1.3 cm is built so that Corona takes place if the line voltage exceeds 260kV (rms). Find the spacing between conductors.

A7)

Disruptive critical voltage, Vrms = = 150.11 kV

Assuming = 1 and m­0 = 1 (smooth conductor)

R = 0.013 m E0 = 150.11 kV=150.11×103 volts

150.11×103=

5.44

Deq = 0.013 × e5.44

Deq = 3 m

Q8) A Three phase equilateral line has a total Corona loss of 55kw at 110 KV and 100 KW at 114 KV. What is the disruptive critical voltage between lines? What is the Corona loss at 120 KV?

A8)

Power loss due to corona for three phases is given by

Taking , f, r and D as constants,

From (1) and (2),

E0 = 57 kV

When Vn =

From equation 1 and 3,

=196.3 kW

Line -line disruptive critical voltage

= √3 × E0

=√3 × 57

= 98.72 kV

Q9) Find the disruptive critical voltage and visual Corona voltage (local Corona as well as General Corona) for a 3 phase 220 KV line consisting of 22.26 mm diameter conductors spaced in a 6m Delta configuration. The following data can be assumed.

Temperature 25°C, pressure 73 cm of Mercury, surface factors 0.84, irregularity factor for local Corona 0.72, irregularity factor for general Corona 0.82.

A9)

r = 0.5 × 22.26 = 11.13 mm = 1.113 × 10-2 m

= = 0.9456

m0 = 0.84 D = 6m

Vd = 11.8×104 V or 118 kV per phase

Vv = 13.07 × 104 V or 130.7 kV per phase

For general visual corona mv = 0.82 and

=14.88 × 104 V or 148.8 kV/phase

Q10) Explain with neat sketch, the structure of power system.

A10)

• An electric power supply system consists of three principal components, the power station, transmission lines and distribution system.
• Electric power is generated at power stations, which are located at favorable places, generally quite away from the consumer.
• It is then transmitted over large distances to load centres with the help of conductors known as transmission lines. Finally, it is distributed to a large number of small and big consumers through a distribution network.
• The electric supply system can be broadly classified into (i) d.c. Or a.c. System (ii) overhead or underground system. Now-a- days, 3-phase, 3-wire a.c. System is universally adopted for generation and transmission of electric power as an economical proposition. However, distribution of electric power is done by 3-phase, 4-wire a.c. System.
• The underground system is more expensive than the overhead system. Therefore, in our country, overhead system is mostly adopted for transmission and distribution of electric power.
• The large network of conductor between the power station and the consumers can be broadly divided into two parts; viz; Transmission and distribution system.
• Each part can further be sub divided into two, primary transmission and secondary transmission and primary distribution and secondary distribution.

1. Generating station:

i) Generating station represents the generating station, where electric power is produced by 3 phase alternator operating in parallel.

Ii) The usual generation voltage is 11kV. The power generated at this voltage is stepped upto 132 kV, 220kV, 400 kV.

Iii)As the transmission of electric power at high voltages have so many advantages, viz; saving of conducting material, high transmission efficiency and less sine loss.

2. Primary Transmission:

i) The electric power at high voltage (say 132 kV) is transmitted by 3 phase, 3 wire overhead system to the outskirts of the city. This form the primary transmission.

3. Secondary Transmission:

i) The primary transmission line terminates at the receiving station, which usually lies at the outsides of the city at the receiving station, the voltage is reduced is reduced to 33 kV by 3 phase, 3 wire over head system to various sub stations located at the strategic points in the city. This forms secondary transmission.

4. Primary Distribution:

i) The secondary transmission line terminates at the sub station where voltage is reduced from 33 kV to 11 kV 3 phase 3 wire.

Ii) The 11 kV line runs along the important roadsides of the city. This forms the primary Distribution.

5. Secondary Distribution:

i) The electric power from primary distribution line is delivered to distribution sub stations.

Ii) These sub stations are located near the consumer localities and step down the voltage to 400 V and between any phase and neutral is 230V.

Iii) The 3 phase residential lighting load is connected between any one phase and neutral whereas 3 phase 400V motor loads are connected across 3 phase lines directly.

(v) has less corona loss and reduced interference with communication circuits.

(vii)The high voltage d.c. Transmission is free from the dielectric losses, particularly in the case of cables.

(viii) In d.c. Transmission, there are no stability problems and synchronising difficulties.

Q11) Discuss in detail the various equipment used in HVDC converter station?

A11)

Alternator (A.C Generator): It is a device which converts mechanical energy into electrical energy (Alternating Current). Convertor transformer at the sending end: It is used to side step-up the generated A.C voltage at receiving end, it steps down the HVAC into distribution voltage

Surge Arrester: It is a Protective device, used to protect the equipments during lightning.

Rectifier: In sending end converter station, rectifier converts high voltage A.C into high voltage direct current (HVDC). Rectifier at receiving end is called inverter.

Filter: Both A.C and D.C Harmonics are injected into the A.C system and D.C harmonics are injected into the D.C line. These harmonics are minimized by using A.C and D.C filters

Shunt Capacitors: To maintain the voltage at the receiving end, shunt capacitors are used.

Applications of HVDC Transmission.

 Long distance bulk power transmission

 Underground or under water cables

 Asynchronous interconnection of AC system operating at different frequencies or where independent control of system is desired

 Control and stabilization of power flows in AC ties in an integrated power system.

 Testing of HVAC cables of long length

 Electrostatic precipitation of aching in thermal power plants

 Electrostatic painting

 Cement industry and Communication systems

Q12) Explain corona formation, factors affecting corona?

A12)

Corona

When an alternating potential difference is applied across two conductors whose spacing is large as compared to their diameters, there is no apparent change in the condition of atmospheric air sur- rounding the wires if the applied voltage is low. When the applied voltage exceeds a certain value, called critical disruptive voltage, the conductors are surrounded by a faint violet glow called corona. The phenomenon of corona is accompanied by a hissing sound, production of ozone, power loss and radio interference. The higher the voltage is raised, the larger and higher the luminous envelope becomes, and greater are the sound, the power loss and the radio noise. If the applied voltage is increased to breakdown value, a flash-over will occur between the conductors due to the breakdown of air insulation. The phenomenon of violet glow, hissing noise and production of ozone gas in an overhead transmission line is known as corona. If the conductors are polished and smooth, the corona glow will be uniform throughout the length of the conductors, otherwise the rough points will appear brighter. With d.c. Voltage, there is difference in the appearance of the two wires. The positive wire has uniform glow about it, while the negative conductor has spotty glow.

(i) Corona formation

Some ionisation is always present in air due to cosmic rays, ultraviolet radiations and radioactivity. Therefore, under normal conditions, the air around the conductors contains some ionised particles (i.e., free electrons and +ve ions) and neutral molecules. When p.d. Is applied between the conductors, potential gradient is set up in the air which will have maximum value at the conductor surfaces. Under the influence of potential gradient, the existing free electrons acquire greater velocities. The greater the applied voltage, the greater the potential gradient and more is the velocity of free electrons. When the potential gradient at the conductor surface reaches about 30 kV per cm (max. Value), the velocity acquired by the free electrons is sufficient to strike a neutral molecule with enough force to dislodge one or more electrons from it. This produces another ion and one or more free electrons, which is turn are accelerated until they collide with other neutral molecules, thus producing other ions. Thus, the process of ionisation is cumulative. The result of this ionisation is that either corona is formed or spark takes place between the conductors.

Q13) List the possible factors affecting corona and also mention the methods to reduce them?

A13)

The phenomenon of corona is affected by the physical state of the atmosphere as well as by the conditions of the line. The following are the factors upon which corona depends:

(i)Atmosphere.

As corona is formed due to ionisation of air surrounding the conductors, there- fore, it is affected by the physical state of atmosphere. In the stormy weather, the number of ions is more than normal and as such corona occurs at much less voltage as compared with fair weather.

(ii) Conductor size. The corona effect depends upon the shape and conditions of the conduc- tors. The rough and irregular surface will give rise to more corona because unevenness of the surface decreases the value of breakdown voltage. Thus a stranded conductor has ir- regular surface and hence gives rise to more corona that a solid conductor.

(iii)Spacing between conductors. If the spacing between the conductors is made very large as compared to their diameters, there may not be any corona effect. It is because larger dis- tance between conductors reduces the electro-static stresses at the conductor surface, thus avoiding corona formation.

(iv)Line voltage. The line voltage greatly affects corona. If it is low, there is no change in the condition of air surrounding the conductors and hence no corona is formed. However, if the line voltage has such a value that electrostatic stresses developed at the conductor surface make the air around the conductor conducting, then corona is formed.

Methods of Reducing Corona Effect

Intense corona effects are observed at a working voltage of 33 kV or above. Therefore, careful design should be made to avoid corona on the sub-stations or bus-bars rated for 33 kV and higher voltages otherwise highly ionised air may cause flash-over in the insulators or between the phases, causing considerable damage to the equipment. The corona effects can be reduced by the following methods:

(i)By increasing conductor size. By increasing conductor size, the voltage at which corona occurs is raised and hence corona effects are considerably reduced. This is one of the reasons that ACSR conductors which have a larger cross-sectional area are used in transmission lines.

(ii)By increasing conductor spacing. By increasing the spacing between conductors, the volt- age at which corona occurs is raised and hence corona effects can be eliminated. However, spacing cannot be increased too much otherwise the cost of supporting structure (e.g., bigger cross arms and supports) may increase to a considerable extent.

Q14) Explain corona loss and power handling capacity?

A14)

Corona Power Loss

The power dissipated in the system due to the Corona discharges is called Corona loss. It is very difficult to estimate Corona loss accurately because of its extremely variable nature.

According to F. W. Peek, Jr, the Corona loss for single phase and equilaterally spaced 3 phase under fair weather conditions is given by the formula-

Where

Pc=corona power loss

f=frequency of supply in Hz

=air density factor

En=rms phase voltage (line to neutral voltage) in kV

E0=disruptive critical voltage per phase in kV (rms)

r = radius of conductor in metres.

D = spacing between conductors in metres.

For single phase line,

En = ×line voltage

For three phase line,

En = ×line voltage

The total loss of the line is the sum of the losses due to the three conductors. Peek's formula is applicable for decided visual corona. The experimental results indicate that corona takes place even when the voltage between the conductor is well below the disruptive critical voltage.

Peterson’s empirical formula for fair weather loss is

Where Pc = corona power loss

f = frequency of supply in Hz

En = voltage per phase (line to neutral voltage in kV (rms))

r = radius of conductor in metres

D = spacing between conductors in metres

The factor F is called the corona loss function. It varies with the ratio (En/E0).

Q15) When does the visual glow of corona occurs and what it is called?

A15)

Visual glow of Corona occurs at voltage higher than the disruptive critical voltage. The minimum voltage at which the visual Corona begins is termed as visual critical voltage.

According to FW peek, the actual visual Corona does not start at the disruptive critical value of voltage. The maximum value of voltage gradient responsible for starting of Corona is 3 6 V/m. But this value of the voltage gradient at the surface of the conductor will not ionize the air. The maximum value of 3 6 V/mwill cause ionization when this value is reached at a distance of  (r+0.301√r) from the conductor axis, where r is in metres.

If the maximum voltage gradient at the surface of conductor be3 6 V/m, the value of the maximum voltage gradient at any other point away from the centre would be less than this and thus there will be corona discharge at that point.

For single phase line,

If G0 = V/m

Then, 
rms volts

For three phase line,

volts/phase

If G0 = V/m

Then,    rms volts/phase

It should be noted that r, D and Deq are to be taken in metres.

mv = roughness factor or irregularity factor

mv = 1.00 for smooth conductor

mv = 0.7 to 0.75 for local corona when the effect is first visible at some places along the line.

mv = 0.8 to 0.85 for decided or general corona along the whole length of the conductor.

Q16) Derive disruptive critical voltage of singe-phase line and three-phase line?

A16)

The minimum voltage at the at which the breakdown of the insulating properties of air occurs and Corona starts is called the disruptive critical voltage.

The potential gradient corresponding to this value of the voltage is known as disruptive critical voltage gradient.

a)     Disruptive critical voltage for a single phase line

Let E = voltage between the conductors (line to line) , volts

r = radius of each conductor in m

D = spacing between the conductors, in m

= 8.854 × 10 -12 permittivity of air

The electric field intensity or voltage gradient at the conductor surface of radius r is given by

E = 2r Gr

Where Gr = V/m

Let E0 max = maximum value of disruptive critical voltage, in volts

G0 max = maximum value of disruptive critical voltage gradient in V/m

E0 max = 2r G0 max

But G0 max = 3×106 V/m

E0 max = 2r×3×106

The rms value of the disruptive critical voltage for a single phase line is given by

E0 = E0 max = × 6×106 r   V

After considering surface factor m0 and relative air density

Where r and D are in meters,

E0 = × 6×106 rm0  Volts

b) Disruptive critical voltage for a three phase line.

Let En = line to neutral voltage in volts.

(Phase voltage in volts)

Deq = equivalent spacing between the conductors in m = (Dab Dbc Dca)1/3

r = radius of each conductor in M

Then, En =

En =rGr

E0 max = r G0 max

The rms value of the disruptive voltage for a three phase line given by

E0 = E0 max =

After considering surface factor m0and relative air density where r and Deq are in meters.

Q17) Mention the needs of EHV AC transmission ad standard transmission voltages?

A17)

Need for EHV Transmission

1. Increase in size of generating units - transmission of large amounts of power over long distances is technically and economically feasible only at voltages in the EHV and UHV range.
2. Pithead steam plants and remote hydro plants - EHV Transmission Systems are needed to transmit large amount of power over long distances from these plants to load centres.
3. Surge impedance loading.
4. Transmission- The number of circuits and the land requirement for transmission decreases with the adoption of higher transmission voltage.

Line costs- The line installation cost per MW per km decreases with increase in voltage level.

The following voltage levels are recognised in India as per I5-2026 for line to line voltages of 132 KV and higher.

Nominal system Voltage kV 132 220   275   345  400   500   750

Maximum operating Voltage kV      145 245   300   362   420   525  765

When the line resistance is neglected, the power that can be transmitted depends upon

a)     the magnitudes of voltages at the ends (Es, Er).

b)    their phase difference, and

c)     the total positive sequence reactance X per phase, when the shunt capacitance admittance is neglected.

Thus,  P = EsEr sin/(L.X)

Where P = power in MW, 3 phase

Es, Er = voltages at the sending end and receiving end respectively in kV line-line

= phase difference between Es and Er

X = positive sequence reactance per phase , ohm/km

And L = line length, km