PHYSICS PROBLEMS

Physics Problems



Physics Problems

Question 1

A balanced three-phase inductive load is supplied in the steady state by a balanced star connected three phase voltage source with a phase voltage of 120 V rms. The load draws a total power of 10 kW at a power factor of 0.9.

Calculate the rms value of the phase currents and the magnitude of the per-phase load impedance, assuming a balanced delta connected load.

Draw a phasor diagram showing the load voltages and currents in all three phases

Solution

Formula for power factor

P = VLine IPhase Cos?

Here,

VLine = Line Voltage = 3 x Vphase

IPhase = Phase current

Cos? = Power Factor = 0.9

P = Total Power = 10 kW

IPhase = = = = 30.86 A

I rms = = = 21.82<00

Pahsor Diagram

Question 2

Draw an impedance diagram for the power system shown in Fig. 1, showing all impedances in per unit on a 100 MVA base. Choose 20 kV as the voltage base for the generator. The three-phase power and line voltage ratings are as follows:

G1:

90 MVA

20 kV

X = 9 %

T1:

80 MVA

20/200 kV

X = 16 %

T2:

80 MVA

200/20 kV

X = 20 %

G2:

90 MVA

18 kV

X = 9 %

Line:

200 kV

X = 120 Ohms

Load:

200 kV

S = 48 MW + j 64 MVAR

Fig. 1 One line diagram for Question 2

Solution

Region 1 Region 2 Region 3

SB = 20 kV

So,

SB1 = SB2 = SB3 = 20 kV

Region 1

Vbase1 = 20 kV = VB1new

Region 2

Vbase2 = x 20 = 200 kV = VB2new

Region 3

Vbase3 = x 200 = 20 kV = VB3new

The corresponding base impedances in each region are

Z base1 new = = = 20? for Region 1

Z base2 new = = = 2000? for Region 2

Z base3 new = = = 20? for Region 3

As, we know that

Zpu = Zpu old ] 2

Zpu G1 new = 0.09 x 2 = j0.02Pu

Zpu T1 new = 0.16 x 2 = j160KPu

Zpu T2 new = 0.2 x 2 = j20Pu

Zpu G2 new = 0.09 x 2 = j0.024Pu

Zpu Line new = = = j0.00025pu

Impedance Diagram

Question 3

The one line diagram of a threephase power system is shown in Fig. 2. Impedances are marked in per unit on a 100 MVA, 400 kVA base. The load at bus 2 is S2 = 15.93 MW - j 33.4 MVAR, and at bus 3 is S3 = 77 MW + j14 MVAR. It is required to hold the voltage at bus 3 at 400<0 per unit, determine the voltages at buses 2 and 1.

Fig. 2 One line diagram for Question 3

Solution

Z base1 new =

100 x j0.5 =

VB1new2 = 50

VB1new = 7.07 <00 Volts

Z base2 new =

100 x j0.4 =

VB2new2 = 40

VB2new = 6.322 <00 Volts

Question 4

A balanced delta connected load of 5 + j48 Ohms per phase is connected at the end of a three-phase line, as shown in Fig. 3. The line impedance is 1 + j3 Ohms per phase. The line is supplied form a three-phase source with a line voltage of 207.85 V ...