Need help with this problem: Power factor

[schicco]

I have a question related to power factor. I tried it and got lost on the way. If someone could help I would really appreciate it.

A feeder from a distribution transformer is 500 feet long. It consists of 3#4/0 AWG wires having a resistance of 0.052 ohms per 1000 feet and current capacity of 225 Amps. The 3 phase load is balanced and draws 120 KW at 440 Volts with 60% PF lagging. Determine the KVA Rating of capacitors capable of correcting the power factor enough to allow rated current to flow.

Thanks

Andy

 

[Flyer_PE]

I'll take a stab at the solution to the problem but you may have to better define your question as to where you got lost.

The only information you need regarding the cable is that you have a maximum current of 225 Amps. You have a 440 V load that draws 120kW with a 0.6 pf.

Given that this is a text book problem and not real-world, I'm going to assume the system voltage is 440 V 3ph.

You have to solve two power triangles. The first is for the load and the second is for the system capability.

1. Power triangle for the load: 120 kW at 0.6: P=120 kW; S=120kW/0.6=200 kVA; Q=sqrt(S2-P2)=160kVAR

2. System capability: S = sqrt3*440V*225A = 171.5 kVA

For the second triangle, we need only find the reactive power component Q. We already know S and the required value of P from the load.

Q = sqrt(171.52-1202) = 122.5 kVAR

The required reactance to get the current down is then the difference between that of the load and what the system can provide:

Q = 160kVAR - 122.5 kVAR = 37.5 kVAR

 

[schicco]

Thanks a lot Flyer PE

 

[schicco]

Thanks a lot Flyer_PE