How do short/open-circuit tests work for step-up transformers?

[Master1022]

Homework Statement

Explain which sides each of the short/open-circuit tests are applied to on a step-up transformer and explain what circuit parameters can be deduced from them.

Relevant Equations

P = IV

Hi,

Question: I think my misunderstanding boils down to a few short questions:
1) Is the equivalent circuit for a transformer of the same topology for a step-up and step-down transformer?
I think it should be as the turns ratio is simply a constant.

2) How do the open/short-circuit tests work for a step-up transformer?

I have pasted this picture of an equivalent circuit from google. Usually I deal with problems that don't have $R_1$ and $X_1$ and all those impedances are included in $R_2$ and $X_2$ respectively. I will just refer to the '2' ones when talking about winding resistance and leakage reactance.

Attempt:

For the short circuit test, I understand that we want to achieve rated current and therefore measure the power dissipated by the winding resistance $R_2$. My lecture notes say that we want the rated current on the low voltage side and therefore apply the input voltage on the high voltage side, but only uses examples of a step-down transformer (for which the statement makes sense to me). Is this also true for step-up transformers? If it were, then that would mean that we apply the short circuit test input voltage to the 'secondary' (higher voltage end) and take measurements from the primary. However, wouldn't that mean that the primary was the side with $R_2$ and $X_2$? Unless that means that we are measuring those secondary components referenced to the primary - is this the case (i.e. we are measuring $(\frac{N_1}{N_2})^2 R_2$ and $(\frac{N_1}{N_2})^2 X_2$ ). If that isn't the case, please let me know as that would mean that I have suggested a wrong implementation of the test.

For the open circuit test, I understand that we want to use rated voltage and measure the core losses due to $R_0$ and $X_0$. We do this by applying a voltage at the lower voltage end such that rated voltage is obtained at the secondary end. Then we take measurements at the secondary. Following the above logic, does that mean that we are measuring: $(\frac{N_2}{N_1})^2 R_0$ and $(\frac{N_2}{N_1})^2 X_0$ (i.e. those 'primary' components referenced to the secondary)? Once again, please do correct me if I am wrong.

Any help is greatly appreciated as I am quite confused in this area.

 

[cnh1995]

Ideally, you can perform any test with either primary or secondary as input or output.

, I understand that we want to achieve rated current and therefore measure the power dissipated by the winding resistance R2.

.. and by R1 as well.
Short circuit test gives you the full-load copper loss in the transformer i.e. the power lost as heat in both primary and secondary windings.
Look up approximate equivalent circuit of the transformer.

 

[Master1022]

Hi,

Thank you very much for your response. Can you confirm whether the topologies for step-up and step-down transformers are the same? I believe they are.

Ideally, you can perform any test with either primary or secondary as input or output.

Okay, but are my test implementations correct? Could you provide some more explanation as to what is being measured when using different input sides?

.. and by R1 as well. Short circuit test gives you the full-load copper loss in the transformer i.e. the power lost as heat in both primary and secondary windings.

Yes that is true. However, I said in my post that the problems I face combine $R_1$ and $R_2$ into one and so I said that I would only refer to $R_2$.

Look up approximate equivalent circuit of the transformer.

Apologies, but is the picture I posted not visible? As far as I'm aware, that is an equivalent circuit for a transformer. The other images are just re-arrangements whereby all the components are referenced to either the primary or secondary.

 

[cnh1995]

Can you confirm whether the topologies for step-up and step-down transformers are the same? I believe they are.

Yes.

However, I said in my post that the problems I face combine R1 and R2 into one and so I said that I would only refer to R2.

Yes, primary and secondary impedanes are referred to one side and combined.
The purpose of the OC and SC tests is to calculate efficiency and overall transformer impedance (which is used in power flow analysis). So the individual winding resistances and reactances are not of much use in analysing a working transformer.

The other images are just re-arrangements whereby all the components are referenced to either the primary or secondary.

Yes, the "rearrangement" of the impedances allows you to separate core losses from copper losses. You move the magnetizing branch right across the primary supply and then combine primary and secondary impedances in series.
This allows you to neglect core losses in SC test and neglect copper losses in OC test.
It is a lot easier to analyse the approximate equivalent circuit and it is an excellent approximation for a practical transformer.

 

[Master1022]

Yes.

Okay, thanks.

Yes, primary and secondary impedanes are referred to one side and combined.
The purpose of the OC and SC tests is to calculate efficiency and overall transformer impedance (which is used in power flow analysis). So the individual winding resistances and reactances are not of much use in analysing a working transformer.
Yes, the "rearrangement" of the impedances allows you to separate core losses from copper losses. You move the magnetizing branch right across the primary supply and then combine primary and secondary impedances in series.
This allows you to neglect core losses in SC test and neglect copper losses in OC test.
It is a lot easier to analyse the approximate equivalent circuit and it is an excellent approximation for a practical transformer.

Sure, I already understand this. My post is more about how to interpret those test results for a step-up transformer. For example, if you apply the open circuit test to the primary (low voltage side), what do measurements from the secondary (high voltage) tell you? Is it power dissipated in the core components (technically just the resistor) referenced to the secondary?

Similarly, if I apply the short circuit test to the secondary (high voltage), then what do measurements in the primary tell me? Is it the power dissipated in the winding resistor referenced to the primary?

Thanks

 

[cnh1995]

For example, if you apply the open circuit test to the primary (low voltage side), what do measurements from the secondary (high voltage) tell you?

There are no watt-meters on the secondary in OC test. I am not sure I fully get this question.
In a 1:4 step up transformer, if you found the core loss-equivalent resistance Rc with low voltage side excitation to be 100 ohm, you will find Rc= 1600 ohm when you perform the test with high voltage side excitation.

Similarly, if I apply the short circuit test to the secondary (high voltage), then what do measurements in the primary tell me? Is it the power dissipated in the winding resistor referenced to the primary?

Are you shorting HV side and exciting LV side? The wattmeter will show the power lost in both primary and secondary winding resistances (or in the total resistance referred to the LV side).

Also, the winding which is connected to the supply is the primary winding by definition.
So it is easier to use the terms LV and HV in general.

 

[Master1022]

There are no watt-meters on the secondary in OC test. I am not sure I fully get this question. In a 1:4 step up transformer, if you found the core loss-equivalent resistance Rc with low voltage side excitation to be 100 ohm, you will find Rc= 1600 ohm when you perform the test with high voltage side excitation.

This is a theoretical example. Yes, I understand the impedance transformation. You might have implicitly answered my question. So if (for a step up transformer), you use the LV side as an input and use measurements (current, voltage, and power) from the secondary/HV then we will find the core component values relative to the HV end?

Are you shorting HV side and exciting LV side? The wattmeter will show the power lost in both primary and secondary winding resistances (or in the total resistance referred to the LV side).

Agreed regarding the power. I was thinking to short the LV side and excite the HV side. If we did this, then we can use power, current, and voltage readings to find winding component values with respect to the primary?

Thanks for taking the time to help me.

 

[cnh1995]

So if (for a step up transformer), you use the LV side as an input and use measurements (current, voltage, and power) from the secondary/HV then we will find the core component values relative to the HV end?

In both OC and SC test, you can measure power only on primary side. On the secondary side, either voltage is 0 or the current is 0. The copper and core losses are not referred to any side. They will be the same regardless of LV/HV excitation.
From these losses, you compute the relevant impedances referred to the primary (and use impedance transformation for referring that impedance to secondary).

If we did this, then we can use power, current, and voltage readings to find winding component values with respect to the primary?

Yes, but the power, voltage and current readings will also be on the primary side.

Component values can be transformed to primary/secondary sides. Copper and core losses remain fixed regardless of HV/LV excitation.