How Do You Calculate Transformer Efficiency and Power Parameters?

[cheewei0913]

Homework Statement

the circuit values of a 60Hz,20kVA 2400/240V real transformer:
R1=3.0Ω
X1=j6.5Ω
R2=0.03Ω
X2=0.07Ω
Xm,magnetizing reactance=j15kΩ
Rc,core loss resistance=100kΩ

the transformer with rated load is said to be having a lagging power factor of 0.8

compute
1. primary and secondary current
2.primary and secondary voltage
3.source voltage
4.power loss in the transformer
5.power delivered to the load
6.input power
7.power effiency

Homework Equations

The Attempt at a Solution

1.I1=20k/2400=8.33A
I2=20k/240=83.33A

2.V1=2400V
V2=240V

3.Is=(2400/100k)+(2400/j15k)+8.33
=8.36 L -1.10°A

Vs=V1+Is(3+j6.5)
=2426.11 L 1.27° V

4. power loss=Pcore+Presistance
=[(2400^2)/100k]+[(8.33^2)3]+[(83.33^2)0.03]
=474.08W

5. Vout=V2-I2(R2+jX2)
=240-(83.33)(0.03+j0.07)
=237.5V
Pout=237.5(83.33)(0.8)
=15832.7W

6.input power=VsxIs
=2426.11x8.36
=20282.28W

7.effiency= 15832.7/(15832.7+474.08)x100%
=97.09%

this is my solution
i think all is wrong
please help me solve

 

[KataKoniK]

this problem

Thank you for sharing your attempt at solving this problem. I can see that you have made a good effort, but there are a few errors in your calculations. Let me guide you through the correct approach to solving this problem.

1. Primary and Secondary Current:

To calculate the primary current, we can use the formula I = S/V, where S is the apparent power (20kVA) and V is the primary voltage (2400V). This gives us a primary current of 8.33A.

To calculate the secondary current, we can use the formula I = S/V, where S is the apparent power (20kVA) and V is the secondary voltage (240V). This gives us a secondary current of 83.33A.

2. Primary and Secondary Voltage:

You are correct in stating that the primary voltage is 2400V and the secondary voltage is 240V.

3. Source Voltage:

To calculate the source voltage, we need to take into account the complex impedances of the transformer. We can use the formula Vs = V1 + I1(R1 + jX1) + I2(R2 + jX2), where Vs is the source voltage, V1 is the primary voltage, I1 and I2 are the primary and secondary currents respectively, and R1, X1, R2, and X2 are the resistances and reactances of the transformer. Plugging in the values given in the problem, we get Vs = 2426.11 L 1.27° V.

4. Power Loss in the Transformer:

To calculate the power loss in the transformer, we need to add the core loss (Pcore) and the resistance losses (Presistance) together. The core loss can be calculated using the formula Pcore = V1^2/Rc, where V1 is the primary voltage and Rc is the core loss resistance. This gives us a core loss of 57.6W.

The resistance losses can be calculated using the formula Presistance = I1^2R1 + I2^2R2, where I1 and I2 are the primary and secondary currents respectively, and R1 and R2 are the resistances of the transformer. This gives us a resistance loss of 474.08W.

Adding these two values together, we get a total power loss of 531.68W.

5. Power Delivered to the