Introduction to Power System: Assignment One

Max. students per group 3 (Date of Submission: Wednesday , 27/11 /2024)

Chapter two: Single Phase system

1. For v(t)= 200cos(50t +45) V and i(t)= 20cos(50t-30) A . find

a. P(t), S,P and Q
b. Power factor
2. Three loads are connected in parallel across a single-phase source voltage of 240 V (RMS).
Load 1 absorbs 20 kW and 10 kVAR;
Load 2 absorbs 5 kVA at 0.9PF leading;
Load 3 absorbs 15 kW at unity power factor.
Calculate the equivalent impedance, Z, for the three parallel loads, for two cases:
a. Series combination of R and X, and (ii) parallel combination of R and X.
3. A certain single-phase load draws 5Mw at 0.7 power factor lagging Determine the reactive
power required from a parallel capacitor to bring the power factor to 0.9.
4. An inductive load consisting of R and X in parallel feeding from 3000V rms supply absorbs
288kW at a lagging power factor of 0.8. Determine R and X
5. For the following fig 1. The load is taking 30 kVA at 0.8 P.F leading
a. Find the values of R and X.
b. Determine the supply voltage V

fig 1
Chapter Two: Three Phase System
6. Calculate Va’n, Vb’n and Va’b’ (at the delta connected capacitor load) fig 2

fig 2
7. A balanced delta connected load consisting of pure resistance of 18 ohm per phase is in parallel
with a purely resistive balanced wye connected load of 12 ohm per phase as shown in the fig
 the combination is connected to a three phase balanced supply of 380V rms (line to line) via
three phase line having an inductive reactance of 4 ohm per phase. Atking the phase voltage
as reference Determine the current, real power, and reactive power from the supply

fig 3
Chapter Two: Per Unit System
8. For the following single line diagram of fig 5 Using base values of 50kVA and 400V in the
transmission line, draw the per unit circuit, and determine the per unit impedances and the
per unit source voltage. Then calculate the load current both in per unit and in amperes.
Transformer winding resistance and shunt admittance branches are neglected.
T1 T2
30 kVA Xline=2Ω
G
VG=220∟0ºV
Zload=0.9+j0.2Ω
30 kVA 20 kVA
240/480V 460/115V
XT1=0.1pu XT2=0.1pu
Fig 5
9. The one-line diagram of three-phase power system is shown below in fig 4. Select a
common base of 100 MVA and 22 kV on the generator side.
a. Draw an impedance diagram with all impedance including the load impedance marked
in per-unit.
b. The actual current flowing through the load
50 MVA 40 MVA
22/220 kV 220/11 kV
X = 10% X = 6.0%
T1 T2
1 2 4
Line 1
220 kV 66.5 MVA
X = 48.4 O 10.45 kV
X = 18.5%

G M
90 MVA
T3 T4
22 kV 3
X = 18%
Line 2
110 kV Load
57 MVA
X = 64.43 O
40 MVA 40 MVA 0.6 pf lag
22/110 kV 110/11 kV 10.45 kV
X = 6.4% X = 8.0%

Fig 4
 Chapter Three: Electrical Design of Over head Transmission line
10.A three-phase line is designed with equilateral spacing of 3m. but now It is decided to
build the line with horizontal spacing (D13=2D12=2D23). The conductors are transposed.
What should be the spacing between adjacent conductors in order to obtain the same
inductance as in the original design ( 6pt)
11.Three copper conductors of a 3-phase overhead line are arranged in a horizontal plane 6 m
apart. The diameter
of each conductor is 1·24 cm. Find the capacitance, inductance and resistance of each
conductor to neutral per 100 km of the line
12.A 20 km single phase line has two parallel conductors separated by 1·5 metres. The diameter
of each conductor is 0·823 cm. If the conductor has a resistance of 0·311Ω/km, find the loop
impedance of this line at 50 Hz.