Question

The speed of a 20 hp, 300 V, 900 rpm separately excited DC motor is controlled by a three-phase full controlled converter. The field circuit is also controlled by a three-phase full-controlled converter. The AC input to armature and field converters is three-phase, Y-connected, 208 V (line), 60 Hz. The armature resistance, R, is 0.252, the field circuit resistance, Rfis 14512, and the motor voltage constant, Ky is 1.2 V/A rad/s. The viscous friction and no-load losses can be considered negligible. The armature and field currents are continuous and ripple free. a) Prove that the average output voltage, Vo, de of the above mentioned three-phase full-controlled 313V. converter has the value of cos a (8 marks) 7

Answer 1

Vo = 120.103

Step-by-step explanation:

1. The converter takes in a three-phase AC input voltage of 208 V (line) and 60 Hz. This AC input is fed to the armature and field converters.

2. The armature and field currents are continuous and ripple-free. This means that there are no fluctuations or interruptions in the current flow.

3. The armature resistance, R, is given as 0.252, and the field circuit resistance, Rf, is given as 14512. These resistances are used in the calculations.

4. The motor voltage constant, Ky, is given as 1.2 V/A rad/s. This constant relates the armature current to the motor speed.

Now, let's consider the operation of the converter. The average output voltage, Vo, can be calculated using the formula:

Vo = (Vs / √3) * cos α

Where Vs is the AC input voltage.

Given that Vs = 208 V (line), we can substitute this value into the formula:

Vo = (208 / √3) * cos α

Simplifying further, we can calculate the value of √3:

√3 = 1.732

Substituting this value into the equation:

Vo = (208 / 1.732) * cos α

Calculating the division:

Vo = 120.103 * cos α

Therefore, we have proven that the average output voltage, Vo, of the three-phase full-controlled converter has the value of cos α. The specific value of the average output voltage will depend on the firing angle α.