Calculating Single Phase Transformer Parameters and Performance

[dvep]

Homework Statement

Figure 1 shows the equivalent circuit of a single phase transformer and figure 2 shows the approximate equivalent circuit.

Reduce the circuit to approximate form and find:
rm, xm, R1, X1

Using the approximate equivalent circuit calculate-

With the transformer operating at no-load:

primary current , primary power factor, primary real power, secondary voltage.

I am given in the equivalent circuit:
r1, r2, rm, x1,x2,xm, turns ratio, V1

Homework Equations

R1 = r1' + r2'
X1 = x1 + x2' = x1 +x2(N2/N1)

The Attempt at a Solution

Using the equations above I have found R1 and X1
I now need to find rm and xm of the approximate equivalent circuit and primary current , primary power factor, primary real power, secondary voltage.


I am struggling with this, any help would be appreciated, thankyou.

 

[Samtheguy]

To my knowledge, rm and xm do not change when converting to the approximate equivalent circuit.
To go about finding the primary current (Io) you will have to calculate the currents Ioa (active component) and Ior (reactive component). The formulae for finding these are:
Ioa = V1 / rm
Ior = V1 / xm
Then, to find Ioa, use the formula: Io = √((Ioa)^2 + (Ior)^2)
The primary power factor is found using: Ioa / Io
Primary real power is found by: Poc (which means Open circuit power) = (V1)^2 / rm
The secondary voltage is calculated using: V2 = V1 x N2/N1

Hope this helps.

 

[dvep]

To my knowledge, rm and xm do not change when converting to the approximate equivalent circuit.
To go about finding the primary current (Io) you will have to calculate the currents Ioa (active component) and Ior (reactive component). The formulae for finding these are:
Ioa = V1 / rm
Ior = V1 / xm
Then, to find Ioa, use the formula: Io = √((Ioa)^2 + (Ior)^2)
The primary power factor is found using: Ioa / Io
Primary real power is found by: Poc (which means Open circuit power) = (V1)^2 / rm
The secondary voltage is calculated using: V2 = V1 x N2/N1

Hope this helps.

Thank you for your reply it does help.

Now with a load impedance I now need to calculate:

primary current, secondary current, secondary apparent power, secondary reactive power, the effiency, primary power factor, secondary voltage, secondary real power, secondary power factor, and voltage regulation.

I have referred the load impedance to the primary and calculated ZL', I added this impedance to R1 and X1.
So I am now left with three impedances, I took the reciprocals of these and added them together, then took the reciprocal of this again, and this gives me the input impedance.

So to calculate the primary current I used V1/ZL, however it gives me a very big number, is this the correct method?

 

[Chalex4]

To my knowledge, rm and xm do not change when converting to the approximate equivalent circuit.

I'm interested in knowing if anyone else can confirm this statement? I have a very similar problem to yours that I need to solve.

 

[DeeNos]

I would suggest first analyzing the given information and equations to understand the relationships between the parameters. From the given equations, we can see that rm and xm are related to r1 and x1, respectively, and are also affected by the turns ratio and leakage reactance. Therefore, we can use the given information to calculate rm and xm by manipulating the equations and substituting the given values.

For the primary current, we can use the relationship between primary and secondary currents, which is equal to the turns ratio. And for the primary power factor and real power, we can use the relationships between the primary and secondary voltages, currents, and power factor.

It is important to remember that these calculations are based on the approximate equivalent circuit, so there may be some degree of error. It would be beneficial to also compare these values to the exact equivalent circuit to assess the accuracy of the calculations.

In summary, as a scientist, I would approach this problem by carefully analyzing the given information and equations, manipulating them to find the desired parameters, and then comparing the results to the exact equivalent circuit to assess the accuracy.