Problems solved about Autotransformer

Problem 94-3 Source: Adapted Example 3-19 - page 234 - BHATTACHARYA, S. K. - Book: Electrical Machines - 4th ed. - McGraw-Hill - 2014.

The primary and secondary voltages in an autotransformer are 440 V and 200 V, respectively.

a) Calculate the current in all windings when the load current is 240 A

b) Calculate the power transformed under the conditions of the previous item.

c) Calculate the power per conduction under the conditions of the previous item.

d) Calculate the copper savings compared to a conventional transformer.

Solution fo the Problem 94-3

Item a

To calculate the currents we will use eq. 91-03a, shown below.

eq. 91-03a

So, applying the equation, we have:

I₁ = I₂ ( V₂ / V₁ ) = 240 ( 200 / 440 ) = 109.1 A

And the current flowing through the common winding is given by I₂ - I₁, that is:

I₂ - I₁ = 240 - 109.1 = 130.9 A

See Figure 94-03.1, in which we represent the autotransformer and its currents and voltages.

Item b

To calculate the transformed power, we will use eq. 94-03 presented below.

S_TR = V_AB I_AB = I₁ ( V₁ - V₂ )

eq. 94-03

Replacing the variables with their respective numerical values, we have:

S_TR = 109.1 (440 - 200 ) = 26,184 W

Item c

eq. 94-05

S_con = S_in - S_TR = V₂ I₁

eq. 94-05

Replacing the variables with their respective numerical values, we have:

S_con = 200 x 109.1 = 21,820 W

Item d

eq. 94-10

K_w

a = 440 / 200 = 2.2

K_w = ( 2.2 - 1 ) / 2.2 = 0.546

54.6%

Copper Savings = 100% - 54.6% = 45.4%

back to Top

Previous Problem

Next Problem