
Concept explainers
A certain store contains three balanced three-phase loads. The three loads are:
Load 1: 16kVA at 0.85 pf lagging
Load 2: 12 kVA at 0.6 pf lagging
Load 3: 8 kW at unity pf
The line voltage at the load is 208 V rms at 60 Hz, and the line impedance is

Find the line currents and the complex power delivered to the loads.
Answer to Problem 69P
The line currents
The complex power delivered to the loads is
Explanation of Solution
Given data:
The given three balanced three-phase loads are,
The reactive power of the Load 1 is
The reactive power of the Load 2 is 12 kVA and the power factor is 0.6 (lagging).
The real power of the Load 3 is
The line voltage at the load is
The line impedance is
Formula used:
Write the expression to find the complex power
Here,
Write the expression to find the average power
Here,
Write the expression to find the reactive power
Write the expression to find the complex power of the Load 2.
Here,
Write the expression to find the real power of the Load 2.
Here,
Write the expression to find the reactive power of the Load 2.
Write the expression to find the complex power of the Load 3.
Here,
Write the expression to find the real power of the Load 3.
Here,
Write the expression to find the reactive power of the Load 3.
Write the expression to find the total complex power.
Here,
Write the expression to find the phase voltage.
Here,
Write the expression to find the line to neutral voltage
Here,
Write the expression to find the complex power
Here,
Write the expression to find the line current
Here,
Write the expression to find the line current
Calculation:
The given lagging power factor of the Load 1 is,
Rewrite the above equation to find the angle
Substitute
Substitute
Substitute
The given lagging power factor of the Load 2 is,
Rearrange the above equation to find the angle
Substitute
Substitute
Substitute
The given unity power factor of the Load 3 is,
Rewrite the above equation to find the angle
Substitute
Rewrite the above equation to find
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Re-write the above equation to find the current
The complex current
The line current
Substitute
Substitute
Conclusion:
Thus,
The line currents
The complex power delivered to the loads is
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Chapter 12 Solutions
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