Concept explainers
A balanced, positive-sequence wye-connected source has Van = 240
- (a) Calculate the line currents if ZAB = 40 + j15 Ω, ZBC = 60 Ω, ZCA = 18 − jl2 Ω.
- (b) Find the complex power supplied by the source.
a.
Calculate the line currents for the described circuit using PSpice.
Answer to Problem 48P
The value for the line currents
Explanation of Solution
Given data:
The phase voltage is
The transmission line impedance is
The value of the impedances
Formula used:
Write the formulae for the conversion of delta connected impedances to star connected impedances.
Here,
Write the expression for reactance of the inductor.
Here,
Write the expression for reactance of the capacitor.
Here,
Calculation:
The given unbalanced delta connected load is shown in Figure 1.
Substitute
Substitute
Substitute
The transformed circuit is shown in Figure 2.
The given balanced wye-connected source supplies the unbalanced delta connected load is shown in Figure 3.
Let us assume that the value of the angular frequency,
Calculate the frequency as follows.
Substitute
Substitute
Substitute
Substitute
The time domain representation of Figure 3 is shown in Figure 4.
PSpice Simulation:
Draw Figure 4 in PSpice as shown in Figure 5.
Provide the simulation setting as shown in Figure 6.
The obtained results are given below.
FREQ IM(V_PRINT1) IP(V_PRINT1)
1.592E-01 2.492E+01 -6.124E+00
FREQ IM(V_PRINT2) IP(V_PRINT2)
1.592E-01 9.723E+00 -1.442E+02
FREQ IM(V_PRINT3) IP(V_PRINT3)
1.592E-01 2.094E+01 1.365E+02
The obtained line currents are given below.
Conclusion:
Thus, the value for the line currents
b.
Calculate the total complex power supplied by the source.
Answer to Problem 48P
The total complex power supplied by the source is
Explanation of Solution
Calculation:
Write the expression for complex power delivered by source
Substitute
Write the expression for complex power delivered by source
Substitute
Write the expression for complex power delivered by source
Substitute
Write the expression for total complex power supplied by the source.
Substitute
Conclusion:
Thus, the total complex power supplied by the source is
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