# Power Systems Question - Power Factors

#### aedmunds

Joined May 1, 2017
11
Please can someone offer some guidance on the below question. I dont know where to begin.

An A.C. motor with power factor 0.6 draws 4200 watts of real power at 240 volts from a
10 KVA Transformer. Suppose a second motor is needed and it too draws 4200 watts.
With both motors on line, the transformer will be overloaded unless a power factor
(i) What power factor would be needed to be able to continue to use the same 10
KVA Transformer?
(ii) How many KVAr would need to be added to provide the needed power factor?
(iii) How much capacitance would be needed to provide KVAr correction?

#### WBahn

Joined Mar 31, 2012
26,398
Are you to assume that the power factor of the second motor is the same as the first?

What is the apparent power of the first motor?

How much real power do both motors combined consume?

You need to show some effort to work YOUR homework.

#### aedmunds

Joined May 1, 2017
11
I am doing exam preparation, and previously only completed examples with a single motor, but I have seen last years exam asked this question. I just want to be competent in case. I will do some calculations now of how I think should proceed. I was just after some pointers.

#### aedmunds

Joined May 1, 2017
11
Is the real power consumed of both 14000VA. I am lost now

#### WBahn

Joined Mar 31, 2012
26,398
How much real power does the first one draw?

#### WBahn

Joined Mar 31, 2012
26,398
Is the real power consumed of both 14000VA. I am lost now
Real power is measured in watts. Apparent power is measured in volt-amps.

Remember that the definition of power factor is the ratio of real power to apparent power.

• atferrari

#### aedmunds

Joined May 1, 2017
11
I am completely confusing myself.

#### crutschow

Joined Mar 14, 2008
27,753
Is the real power consumed of both 14000VA. I am lost now
The real power of both is simply twice the real power of one.
How did you arrive at 14000VA?

#### aedmunds

Joined May 1, 2017
11

#### aedmunds

Joined May 1, 2017
11
I = 10000/240 = 41.6A.

So apparent 240 x 41.6/ 1000 = 9.984VA?

#### crutschow

Joined Mar 14, 2008
27,753
Is apparent power V x I/1000?
It's just V x I.
Why did you divide it by 1000?

#### aedmunds

Joined May 1, 2017
11
I have no idea where I go next?

#### WBahn

Joined Mar 31, 2012
26,398
I have no idea where you've gotten so far.

First, be sure you understand what EACH motor is doing?

What is the REAL power of each motor?
What is the APPARENT power of each motor?
What is the REACTIVE power of each motor?

#### aedmunds

Joined May 1, 2017
11
Real = 4200 W OR Combined 4200 x 2 = 8400 W
Apparent = 240 x 41.6 = 9984 VA Where I = 10000/240 = 41.6 A
Reactive = Sqrt S^2 - P^2 = Sqrt 9984^2 - 4200^2 = 9057.60 VAR OR Combined Sqrt S^2 - P^2 = 5396.31 VAR

How does this look?

#### WBahn

Joined Mar 31, 2012
26,398
Where is this 41.6 coming from?

The transformer can deliver 10 kVA of apparent power. That does NOT mean that every load is consuming 10 kVA of apparent power.

You have a motor that consumes 4200 W of real power with a 0.6 power factor. Given nothing more than that information. What is the apparent power for this motor? What is the reactive power for this motor (keeping in mind that reactive power is a signed quantity).

#### aedmunds

Joined May 1, 2017
11
Clearly I am not grasping this topic. I need to know how to calculate the answers. Could you show me how, even if it is with different values.

#### WBahn

Joined Mar 31, 2012
26,398
For a given load, the power factor is defined as

pf = (real power) / (apparent power)

Each of your motors have a real power of 4200 W and a power factor of 0.6.

What is the apparent power?

#### WBahn

Joined Mar 31, 2012
26,398
This blog entry might help you, but it assumes you are comfortable with working with complex numbers.

#### aedmunds

Joined May 1, 2017
11
im assuming with simple transposition it is 4200/0.6 = 7000?