Problem 103-9    Source:   Example 4.1 - page 135 - SEN, P.C. -    Book: Principles of Electric Machines and Power Electronics - 3rd Edition - Ed. Wiley - 2014.

Calculate what is asked below, using the data from the previous problem (Problem 103-8) and considering the winding as wave wound. Consider that the current in the coil remains at the value calculated in the previous problem.

a) the constant, K_a of the machine.

b) the induced armature voltage, E_A, when the rotor turns at 1,000 rpm.

c) the power, P_m, developed by the machine when the armature current is 400 A .

d) the current in the coils and the electromagnetic torque developed.

Solution of the Problem 103-9   

Item a

If the winding is wave wound, the value of a changes, according to eq. 102-10, and its value is:

With these calculations we can calculate the constant K_a of the machine with wavy winding, using eq. 102-14 shown below.

So, replacing the variables by their respective values, we get:

Item b

To calculate the induced voltage in the armature, only the value of K_a changes. So, to calculate E_A, let's use eq. 102-13, shown below.

Therefore, replacing the variables by their respective values ​​in eq. 102-13, we get:

Item c

The power in the machine shaft is given by eq. 103-17, repeated below.

Therefore, replacing the variables by their respective values ​​in eq. 103-17, we get:

Note that the power developed by the machine does not change with a change in winding type.

Item d

As the coil current was calculated in the previous problem, that is, I_bob = 100 A, then the armature current is:

And to calculate the torque developed by the machine we use the eq. 103-16, shown below.

Using basic algebra in this equation, we find:

Where do we use the fact that ω = 2π x n /60 = 104.72   rad/s. Note that the torque does not change with changing the winding type.