Power Transmission & Distribution

(V SEM EE)
Tutorial Sheet 1
1. A 50 km long transmission line supplies a load of 5MVA at 0.8 pf lagging at 33Kv. The efficiency
of transmission is 90%. Calculate the volume of conductor aluminum required for the line when
I. Single phase, 2-wire system is used
II. Three – phase, 3 – wire system is used
Take the resistivity of aluminum as 2.85 x 10-8 Ω-m.
2. An existing single phase ac system comprising of two overhead conductors is to be converted into 3
phase, 3 wire system by providing an additional conductor of same size. Calculate the percentage of
additional load that can be transmitted by the three phase system. If the operating line voltage and
percentage line losses remain the same in both systems?
3. What is the percentage saving in feeder copper if the line voltage in a two wire dc system be raised
from 250 V to 400V for the same power transmitted?
4. Estimate the weight of copper required to supply a load of 100MW at upf by 3 -phase, 380 KV
system over a distance of 100 km.The neutral point is earthed. The resistance of the conductor is
0.045Ω/cm2/km. The weight of copper is 0.01 kg/cm3.The efficiency of transmission can be assumed
to be 90 per cent.
5. The cost per km for each of the copper conductor of a section a cm2 for a transmission line is
Rs(2800a+1300). The load factor of the load current is 80% and the load factor of the losses is 65%.
The rate of interest and depreciation is 10% and cost of the energy is 50 paisa per kWh. Find the most
economical current density for the transmission line by the use of Kelvin’s law given. Resistivity=
1.78 x 10-8Ωm.
6. A 3-core, 11- kV cable supplies a load of 1500 KW at 0.8 pf lagging for 300 days in a year at an
average of 8 hours per day. The capital cost per km of cable is Rs 8000+20000a ( a is the cross
sectional area of cable). The resistance per km of a cable cross sectional area 1cm2 is 0.173Ω. If the
energy loss cost is 2 paisa per unit and rate of the interest and the depreciation is 12%. Calculate the
most economical current density and diameter of the conductor
7. A three phase 4 wire system is using for lighting. Compare the amount of conductor material
required with that needed for a 2-wire dc system with same lamp voltage. Assume the same losses and
balanced load. The neutral wire has half the cross section of the outers.
8. A given amount of power is to be transmitted by an overhead line. Compare the diameter and
weight of aluminum conductor with those of copper for the same power loss in the line. The following
data may be assumed
Specific resistance of aluminum = 2.85 µΩ-cm
Specific resistance of copper = 1.70 µΩ-cm
Specific gravity of aluminum = 2.71
Specific resistance of copper = 8.89
9. The cost of the two core feeder cable including installation is Rs (90a+20) per meter and the
interest and depreciation charges are 10 %. The cable is 2 km in length and the cost of the energy is 4
p per unit. The maximum current in the feeder is 250A and demand is such that the copper loss is
equivalent to what would be produced by the full current flowing in 6 months. If the resistance of a
conductor of 1sq.cm and 1 km length is 0.173 Ω. Calculate the most economical cross sectional area.
10. Compare the various supply systems on the basis of equal maximum potential difference between
any two conductors.
11. Enumerate different EHVAC and HVDC transmission lines operating in India.
 Power Transmission & Distribution
(V SEM EE)
Tutorial Sheet 2
1. The arrangement of conductors of a single-phase transmission line is shown in Fig.,
where in the forward circuit is composed of three solid wires 2.5 mm in radius and the
return circuit of two-wires of radius 5 mm placed symmetrically with respect to the
forward circuit. Find the inductance of each side of the line and that of the complete
line.

2. A single-phase 50 Hz power line is supported on a horizontal cross-arm. The spacing

between conductors is 2.5 m. A telephone line is also supported on a horizontal
cross-arm in the same horizontal plane as the power line. The conductors of the
telephone line are of solid copper spaced 0.6 m between centers. The distance
between the nearest conductors of the two lines is 20 m. Find the mutual inductance
between the circuits and the voltage per kilometer induced in the telephone line for
150 A current flowing over the power line.

3. A double-circuit three-phase line is shown in Fig. The conductors a, a’; b, b’; and c,
c’ belong to the same phase respectively. The radius of each conductor is 1.5 cm. Find
the inductance of the double-circuit line in mH/km/phase.

4. In Fig. which depicts two three-phase circuits on a steel tower there is symmetry
about the horizontal and vertical centre lines. let each three-phase circuit be
transposed by replacing a by b and then by c, so that the reactance’s of the
three-phases are equal and the GMD method of reactance calculations can be
used. Each circuit remains on its own side of the tower. Let the self GMD of a
single conductor be 1 cm. Conductors a and a’ and other corresponding phase
conductors are connected in parallel. Find the reactance per phase of the system.
5. Determine the inductance of a 3 phase, line operating at 50 Hz and the conductors are
arranged as shown in Fig. The conductor diameter is 0.7 cm.

6. Determine the inductance of the double circuit line shown in Fig. The self GMD of
the conductor is 0.007 meter.

7. Compare different types of conductors used in transmission and distribution.

 Power Transmission & Distribution
(V SEM EE)
Tutorial Sheet 3

Q1 Derive expressions of
a. the capacitance per meter length of Single phase line
b. the capacitance per phase per meter of a 3-phase line with
(i) equilateral spacing
(ii) unsymmetrical spacing. Assume transposition in (ii).

Q2. The horizontally placed conductors of a single phase line operating at 50 Hz are having
outside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The
permittivity of free space is 8.854x10-12 F/m. Find the capacitance to ground per kilometer of
each line.
Q3. A three-phase double-circuit line is shown in Fig. The diameter of each conductor is 2.0
cm. The line is transposed and carries balanced load. Find the capacitance per phase to
neutral of the line.

Q4. Find the capacitance per km per phase to neutral of a three phase line arranged as shown
in the Fig., The outside diameter of ACSR conductor is 2.50 cm. The line is transposed. Take
the effect of ground into consideration.
 Power Transmission & Distribution
(V SEM EE)
Tutorial Sheet 4

1. A single-phase 50 Hz generator supplies an inductive load of 5,000 KW at a power factor of 0.707

lagging by means of an overhead transmission line 20 km long. The line resistance and inductance are
0.0195ohm and 0.63 mH per km. The voltage at the receiving-end is required to be kept constant at 10
kV
Find (a) the sending-end voltage and voltage regulation of the line.

2. The ABCD constants for a 3-phase 220kV line are

A=D=0.94 ∠ 1.60 B=150 ∠780 and C= 0.0002 ∠900

If load at receiving end is 50MW at 0.9 pf lag supplied at rated voltage

Find (i) The sending end voltage (ii) The voltage regulation

3. A three phase 50Hz transmission line 40Km long delivers 36 MW at 0.8 pf lag at 60KV (phase).
The line constants per conductor are R=2.5Ω, L=0.1H,C=0.25µF. Shunt leakage may be neglected.
Determine the voltage, current, power factor, active power and reactive power at the sending end.
Also, determine the efficiency and regulation of the line.

4. 15000 KVA is received at 33KV at 0.85 pf lag over an 8Km three phase overhead line. Each line
has R=0.29Ωper Km and X=0.65Ωperkm. Calculate (a) the voltage at the sending end (b) the power
factor at the sending end (c)the regulation and (d) efficiency of transmission line.

5. Determine the ABCD constants of short transmission line.

 Power Transmission & Distribution
(V SEM EE)
Tutorial Sheet 5
1. A three phase 132kV transmission line is connected to a 50MW load at a power factor at 0.85 lag.
The line constants of the 80km long line are Z=96 ∠780 Ω and Y= 0.001 ∠900S. using nominal T-
circuit representation, calculate – (a) the A,B,C&D constant (b) the sending end voltage (c) sending
end current (d)sending end power factor (e) efficiency of transmission.

2. A three phase 50Hz transmission line 40km long delivers 36 MW at 0.8 pf lag at 60kV (phase). The
line constants per conductor are R=2.5Ω, L=0.1H, C=0.25µF. Shunt leakage may be neglected.
Determine the voltage, current, power factor, active power and reactive voltmeters at the sending end.
Also, determine the efficiency and regulation of the line use (a)nominal T method (b) nominal ∏
method.

3. A short 230 kV transmission line with a reactance of 18 Ω/phase supplies a load at 0.85 lagging
power factor. For a line current of 1,000 A the receiving- and sending-end voltages are to be
maintained at 230 kV Calculate (a) rating of synchronous capacitor required, (b) the load current, (c)
the load MVA.

4. A 275kV overhead transmission line has the following characteristics:

Z=12.5+j66Ω Y= 4.4 X 10-4 S
a. Calculate the ABCD constants and the surge impedance of the line
b. If the line given in above question delivers 250MW at a lagging power factor of 0.9, determine the
sending end voltage, sending end current, line charging current, efficiency of transmission and voltage
regulation.

5. What is Ferranti effect? Deduce an expression for the voltage rise of an unloaded line and what will
happen if shunt reactor compensation is provided at receiving end at no load.

6. A 50 Hz transmission line 300 km long has a total series Impedance of 40 + j125 ohms and a total
shunt admittance of 10-3 mho. The receiving-end load is 50 MW at220 kV with 0.8 lagging power
factor. Find the sending-end voltage, current, power and power factor using
(a) Short line approximation,
(b) nominal-∏ method,
(c) Exact transmission line equation
Compare the results and comment.

7. A 275 kV transmission line has the following line constants:

A = 0.85 ∠50 B = 200 ∠750
(a) Determine the power at unity power factor that can be received if the voltage profile at each end is
to be maintained at 275 kV
(b) What type and rating of compensation equipment would be required if the load is 150 MW at unity
power factor with the same voltage profile as in part (a).
(c) With the load as in part (b), what would be the receiving-end voltage if the compensation
equipment is not installed?
8. A 50 Hz, three-phase, 275kV, and 400 km transmission line has following parameters (per phase).
Resistance= 0.035 Ω/km, Inductance=1mF/km Capacitance = 0.01 pF/km
If the line is supplied at 275 kV, determine the MVA rating of a shunt reactor having negligible losses
that would be required to maintain 275kV at the receiving-end, when the line is delivering no-load.
Use nominal-∏ method.