Electrical Technology (EE11003)
Electrical Engineering Department
Indian Institute of Technology Kharagpur
Tutorial 3
1. A high-voltage generator is connected to a 3-phase wye connected load through a transmission line. Each
phase of the line has impedance 𝑍𝑍𝑙𝑙 , and the load is a balanced wye with branch impedance 𝑍𝑍. Line to line
voltage, |𝑉𝑉𝑎𝑎𝑎𝑎 | = 45𝑘𝑘𝑘𝑘(𝑟𝑟. 𝑚𝑚. 𝑠𝑠) , 𝑍𝑍𝑙𝑙 = (0.5 + 𝑗𝑗3)Ω , 𝑍𝑍 = (4.5 + 𝑗𝑗9)Ω . Find the line currents, power
consumed by the load and line losses. Draw the phasor diagram.
[Ans: 2 kA (r.m.s); 54 MW, 6 MW]
2. A balanced 3-phase a-b-c system with line-to-line voltage 𝑉𝑉𝑎𝑎𝑎𝑎 = 208∠0o V (r.m.s) supplies a balanced Δ
connected load of 3 kW with a power factor of 0.8 (lag) through a lossless transmission line. Find the line
currents. Draw the phasor diagram.
[Ans: 𝐼𝐼𝑎𝑎 = 10.41∠−66.9° A; 𝐼𝐼𝑏𝑏 = 10.41∠173.1° A; 𝐼𝐼𝑐𝑐 = 10.41∠53.1° A]
3.
A three-phase, three-wire system, with an effective line voltage 176.8 V, supplies two balanced loads,
one in Δ with per-phase impedance 15∠0° Ω, and the other in wye with per-phase impedance 10∠30° Ω.
Obtain the total power consumed by the loads.
[Ans: 8.959 kW]
4. Three identical impedances are connected in delta to a 3-phase supply of 400V. The line current is 34.5A
and the total power taken from the supply is 14.5 kW. Calculate the resistance and reactance values of
each impedance.
[Ans: 𝑅𝑅𝑝𝑝ℎ = 12.18 Ω, 𝑋𝑋𝑝𝑝ℎ = 15.96 Ω]
5. Three single phase supply, mutually displaced by 120° in time with magnitude of V volts supplying 3
single phase loads of resistance of R. What will be the total power consumed by the load for the following
cases:
Case I: Make the Supply in Υ and Load in Υ
Case II: Make the Supply in Υ and Load in Δ
Case III: Make the Supply in Δ and Load in Υ
Case IV: Make the Supply in Δ and Load in Δ
[Ans:
3𝑉𝑉 2 9𝑉𝑉 2 𝑉𝑉 2 3𝑉𝑉 2
𝑅𝑅
;
𝑅𝑅
;
𝑅𝑅
;
𝑅𝑅
]
6. A three-phase balanced wye-delta system has a line voltage of 208 V(r.m.s). The total real power absorbed
by the load is 1200 W. If the power factor angle of the load is 20° lagging, determine the magnitude of
the line current and the magnitude of the load impedance per phase in the delta.
[Ans: 3.54 A(r.m.s); (95.34+j34.70) Ω]
7. Two balanced three phase loads are supplied from the same balanced three-phase voltage source. The first
one is star-connected and consists of a resistor R1 and a capacitor C1 in series in each phase, whereas the
second one is delta connected and consists of a resistor R2 and a capacitor C2 in series in each phase. If
both the loads take the same three-phase power (P - jQ), then express (i) R2 in terms of R1, (ii) C2 in terms
of C1. Now if C1 and C2 are replaced by inductors L1 and L2 and the three-phase power is (P + jQ) then
find the relation between L1 and L2.
[Ans: (i) R2 = 3R1 (ii) C2 = C1/3, (iii) L2 = 3L1]
8. A balanced three-phase source serves three loads as follows:
Load 1: 24 kW at 0.6 lagging p.f.
Load 2: 10 kW at u.p.f
Load 3: 12 kVA at 0.8 leading p.f.
If the line voltage at the loads is 208 V(r.m.s) at 50 Hz, determine the line current and the combined power
factor of the loads. Determine the line voltage and power factor at the source if the line impedance is
𝑍𝑍𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 0.05 + 𝑗𝑗0.02 Ω.
[Ans: 139.23 A(r.m.s); 0.869(lag); 220.87 V(r.m.s); 0.873(lag)]
9. In the balanced three-phase system shown in Fig. 1, the line voltage is 34.5 kV (r.m.s) at 50 Hz. Find the
values of the capacitors C such that the total load has a power factor of 0.94 leading.
[Ans: 58.35 μF]
10. A balanced three-phase voltage source supplies a balanced three-phase load through a transmission line
having two equal segments (NM and MO), as shown in Fig. 2(a). Each segment has a resistance of 1Ω
and a reactance (at 50Hz) of 3Ω. The phase sequence of the voltage source is R-Y-B and the expression
of the R-phase voltage 𝑣𝑣𝑅𝑅 = 100𝑠𝑠𝑠𝑠𝑠𝑠(100𝜋𝜋𝜋𝜋). Each phase of the load consists of a 4Ω resistance and
9.5mH inductance in series. To form the balanced three-phase load, three of these single phase load
combination are
(i) Connected in delta,
(ii) Connected in star with the neutral point of the load shorted to ground.
For each of the above-mentioned connections, find the expression of phase voltages (with respect to
ground) at the mid-point (M) of the line.
𝒗𝒗𝑹𝑹
𝒗𝒗𝒀𝒀
𝒗𝒗𝑩𝑩
Zline/2 =
N (1+j3)Ω
M
Zline/2 =
(1+j3)Ω
Zline/2
O
4Ω
Zline/2
Balanced
3-φ load
Zline/2
9.5
mH
Zline/2
Load in
each phase
Fig. 2(a)
Fig. 2(b)
11. Calculate the readings of two wattmeters connected to measure the total power for a balanced star connected load
fed from 3 phase, 400 V (r.m.s) balanced supply with phase sequence R-Y-B. The load impedance per phase is
(20+j15) Ω. Also find the line and phase currents, power factor, total power, total reactive VA and total VA.
[Ans: IR=9.24∠−36.87°; IY=9.24∠−156.87°; IB=9.24∠83.13°; 0.8(lag); 5.123 KW; 3.842KVAR; 6.403 KVA]
Balanced 3 Phase
Induction Motor
Balanced 3
Phase Supply
12. While performing a load test on a 3-phase wound rotor induction motor by two-wattmeter method, the readings
obtained on two wattmeters were 14.2 kW and −6.1 kW and the line voltage was 440V. Calculate, i) True power
drawn by the motor; ii) Power factor; and iii) Line current.
[Ans: 8.1 kW; 0.2246(lag); 47.26 A]
13. The power input to a synchronous motor is measured by two wattmeters and both of them indicate 50 kW. If the
power factor of the motor be changed to 0.866 leading, determine the readings of two wattmeters, the total input
power remaining the same. Draw the phasor diagram for the second condition of the load.
[Ans: 𝑊𝑊1 = 33.33 𝑘𝑘𝑘𝑘, 𝑊𝑊2 = 66.67 𝑘𝑘𝑘𝑘]
14. A star connected balanced load is supplied from a 3-phase balanced supply with a line voltage of 416V at a
frequency of 50Hz. Each phase of load consists of a resistance and capacitor joined in series, and the readings of
two wattmeters connected to measure the total power supplied are 782 W and 1980 W. Calculate (a) the power
factor of the circuit, (b) the line current, and (c) the capacitance of each capacitor.
[Ans: p.f.= 0.8 leading, IL = 4.8 A, C = 106 µF]
15. The 3-phase load consumes a total power of 42 kW at 0.8 lagging power factor. The supply phase sequence is AB-C. Determine the wattmeter reading when the switch S is in positions N, B, and C respectively
[Ans: 14kW, 11.9067kW, 30.0933kW]