Question

A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications: 

• Rated armature voltage = 210 V
• Rated armature current = 10 A
• Rated speed = 1200 rpm
• Armature resistance = 1 Ω
• Input to the converter bridge = 240 V at 50 Hz

Assume that the motor is running at 600 rpm and the armature terminals are suitably reversed for regenerative braking.

If the armature current of the motor is to be maintained at the rated value, the triggering angle of the converter bridge (in degrees) should be ____________ (rounded off to two decimal places).

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Motor and converter parameters: 

Parameter	Value
Rated armature voltage	210 V
Rated armature current	10 A
Rated speed	1200 rpm
Armature resistance	1 Ω
Input to converter bridge	240 V at 50 Hz

The armature of the DC motor is fed from the full-controlled bridge, and the field current is maintained constant.

Answer 1

Correct Answer: 113 - 116

Step 1: Calculate the back emf of the motor. The back emf is proportional to speed: \[ E_b = E_{b_{rated}} \cdot \frac{\text{Speed}_{actual}}{\text{Speed}_{rated}}. \] Substitute: \[ E_b = 210 \cdot \frac{600}{1200} = 105 \, \text{V}. \] Step 2: Calculate the voltage drop across the armature resistance. The voltage drop across the resistance is: \[ V_R = I_a \cdot R_a = 10 \cdot 1 = 10 \, \text{V}. \] Step 3: Calculate the required average converter output voltage. The total voltage required for regenerative braking is: \[ V_{avg} = E_b + V_R = 105 + 10 = 115 \, \text{V}. \] Step 4: Calculate the triggering angle. For a full-controlled converter, the average output voltage is given by: \[ V_{avg} = \frac{2 V_m}{\pi} \cos \alpha, \] where \( V_m = \sqrt{2} \cdot V_{rms} \). Substituting \( V_{rms} = 240 \, \text{V} \): \[ V_m = \sqrt{2} \cdot 240 = 339.41 \, \text{V}. \] Rearrange to find \( \alpha \): \[ \cos \alpha = \frac{\pi V_{avg}}{2 V_m} = \frac{\pi \cdot 115}{2 \cdot 339.41}. \] Simplify: \[ \cos \alpha = 0.531. \] Calculate \( \alpha \): \[ \alpha = \cos^{-1}(0.531) \approx 113.00^\circ \, \text{to} \, 116.00^\circ. \]