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A balanced three-phase system has a distribution wire with impedance 2 + j6 Ω per phase. The system supplies two three-phase loads that are connected in parallel. The first is a balanced wye-connected load that absorbs 400 kVA at a power factor of 0.8 lagging. The second load is a balanced delta-connected load with impedance of 10 + j8 Ω per phase. If the magnitude of the line voltage at the loads is 2400 V rms, calculate the magnitude of the line voltage at the source and the total complex power supplied to the two loads.
Find the magnitude of the line voltage at the source and the total complex power supplied to the two loads.
Answer to Problem 82CP
The magnitude of the line voltage is
Explanation of Solution
Given data:
Three-phase distribution system has line impedance per phase is
Load 1:
The apparent power of the three phase load is
The power factor is
Load 2:
The impedance per phase for delta connected load is
The magnitude of the line voltage at loads is
Formula used:
Load 1: Wye-connected
Write the expression to find the real power
Here,
Write the expression to find the reactive power
Here,
Write the expression to find the complex power of the three-phase load.
Here,
Load 2: Delta-connected
Write the expression to find the apparent power
Here,
The phase voltage is equal to line voltage for delta connection.
Write the expression to find the total apparent power
Here,
Write the expression to find the apparent power for the wye-connected load 1.
Here,
The phase voltage and line voltage relation for wye-connection is,
Substitute
Write the expression to find the line current equivalent wye-load of the delta-connected load 2.
Here,
Write the expression to find the phase current of load 2.
Here,
Substitute
Write the expression to find the total current
Here,
Write the expression to find the source voltage
Here,
Write the expression to find the line voltage of the delta connected load.
Here,
Calculation:
Load1:
Substitute
The given leading power factor is,
Substitute
Substitute
Substitute
Thus, the line current
Load 2:
Substitute
Substitute
The current
Substitute
The line current is
Substitute
Substitute
The magnitude of the line voltage at the source is
Substitute
Conclusion:
Thus, the magnitude of the line voltage is
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