How to maximum apparent power through a linear transformer?

[eehelp150]

Homework Statement

given a linear transformer rated for 50kVA, 11000V/120V
How do I find the maximum apparent power? The prompt is to maximum apparent power while keeping the Load RMS voltage between 114V and 126V.
Vsource has a peak voltage of 11000*sqrt(2).
The circuit looks something like this:

Homework Equations

|S|=sqrt(P^2+Q^2)

The Attempt at a Solution

We didn't really go over maximum apparent power. Could someone give me a few hints as to what to look up?

 

[cnh1995]

Homework Statement

given a linear transformer rated for 50kVA, 11000V/120V
How do I find the maximum apparent power? The prompt is to maximum apparent power while keeping the Load RMS voltage between 114V and 126V.
Vsource has a peak voltage of 11000*sqrt(2).
The circuit looks something like this:
View attachment 109946

Homework Equations

|S|=sqrt(P^2+Q^2)

The Attempt at a Solution

We didn't really go over maximum apparent power. Could someone give me a few hints as to what to look up?

What are the values of load parameters?

 

[eehelp150]

What are the values of load parameters?

Do you mean Load 2 in the picture?
If yes:
Nominal Voltage: 120
Nominal Freq: 60
Active Power (W): 1000
Inductive Reactive Power (Q): 500
I think we were supposed to change Active/Reactive power in the parameters to see how "high" we can get while keeping in the 114<V2<126 range for load voltage but that doesn't seem very efficient.

 

[cnh1995]

Active and reactive powers will depend on the applied voltage across the load. So the maximum apparent power will be drawn at 126V. Is that what is expected?

 

[eehelp150]

Active and reactive powers will depend on the applied voltage across the load. So the maximum apparent power will be drawn at 126V. Is that what is expected?

I believe so. The instructions seem to hint that we are supposed to try random values of P and Q (real/reactive) until we find a maximum within 114<V2rms<126.
Is there a way to calculate the maximum apparent power by hand instead of trying out random values?

 

[cnh1995]

I believe so. The instructions seem to hint that we are supposed to try random values of P and Q (real/reactive) until we find a maximum within 114<V2rms<126.
Is there a way to calculate the maximum apparent power by hand instead of trying out random values?

I don't think they want you to use any random values. You are given the ratings of the load components. Use them to get the load resistance and reactance. Then calculate the real and reactive power at 126V. That should give the maximum apparent power IMO.

 

[eehelp150]

I don't think they want you to use any random values. You are given the ratings of the load components. Use them to get the load resistance and reactance. Then calculate the real and reactive power at 126V. That should give the maximum apparent power IMO.

How would I get load resistance?
This is what I am provided with:

 

[cnh1995]

How would I get load resistance?
This is what I am provided with:
View attachment 109955

The load consumes 1000W at 120V. What is the load resistance then?

 

[eehelp150]

The load consumes 1000W at 120V. What is the load resistance then?

14.4ohms
L=0.0764H
correct?

The instructions were:
Gradually increase the load from the original value. You may increase either P, or Q, or both. Monitoring the load voltage.Your objective is to maximize the apparent power (|S|=sqrt(P2 +Q2 ) of the load while ensuring that the load RMS voltage is within 114<V<126