# How to maximum apparent power through a linear transformer?

• eehelp150
In summary: Based on the given information, it seems that you would increase Q until the load voltage reached 114V and then use P2 to find the maximum apparent power.
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?

eehelp150 said:

## 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?

cnh1995 said:
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.

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?

cnh1995 said:
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?

eehelp150 said:
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.

cnh1995 said:
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:

eehelp150 said:
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?

cnh1995 said:
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

## What is a linear transformer?

A linear transformer is an electrical device that transfers energy between two or more circuits through electromagnetic induction. It consists of two or more coils of insulated wire wound around a core, and the coils are connected to different circuits.

## What is apparent power?

Apparent power is the product of voltage and current in an alternating current (AC) circuit. It represents the total power that is supplied to a circuit, including both the active (real) power and the reactive power. It is measured in volt-amperes (VA).

## How can I maximize apparent power through a linear transformer?

To maximize apparent power through a linear transformer, you can increase the voltage or the current in the circuit. This can be done by adjusting the input voltage, changing the number of turns in the transformer coils, or using a higher quality core material to reduce losses.

## Why is it important to maximize apparent power?

Maximizing apparent power is important because it ensures that the transformer is operating at its full capacity and can deliver the required amount of power to the load. This helps to prevent overloading and damage to the transformer, as well as ensuring efficient energy transfer.

## Are there any limitations to maximizing apparent power through a linear transformer?

Yes, there are limitations to maximizing apparent power through a linear transformer. Increasing the voltage or current beyond the transformer's rated capacity can cause overheating and damage to the transformer. Additionally, increasing the voltage can also lead to higher losses in the circuit and decrease the overall efficiency.

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