The above circuit is operated at 120 V, 60 Hz supply and the load resistance R = 20 Ω...

 

Circuit Diagram:

Dual converter system with two converters (Converter 1 and Converter 2) connected back-to-back.
Each converter consists of thyristors (T1, T2, T3, T4) with an inductive load in between.
Inductors of value L/2 are present on both sides of the load.

The above circuit is operated at 120 V, 60 Hz supply and the load resistance R = 20 Ω, L = 40 mH, delay angles are α₁ = 60°, α₂ = 120°. The value of:

1. Peak circulating current = 11.250 A
2. Peak circulating current = 6.250 A
3. Peak current of converter 1 = 8.485 A
4. Peak current of converter 1 = 19.735 A

Choose the most appropriate answer from the options given below:

• A. (a) and (d) only
• B. (b) and (c) only
• C. (b) and (d) only
• D. (a) and (c) only

Solution

Step 1: Calculate peak supply voltage
Vm = √2 × 120 = 169.7 V

Step 2: Average output voltage of converters
Vd = (2Vm / π) cos(α)

(2Vm / π) = (2 × 169.7) / π ≈ 108 V

For Converter 1:
Vd1 = 108 × cos(60°) = 108 × 0.5 = 54 V

For Converter 2:
Vd2 = 108 × cos(120°) = 108 × (−0.5) = −54 V

Step 3: Circulating current
Voltage difference:
ΔV = Vd1 − Vd2 = 54 − (−54) = 108 V

Angular frequency:
ω = 2πf = 2π × 60 = 377 rad/s

Inductance L = 40 mH = 0.04 H

Peak circulating current:
Ic = ΔV / (ωL) = 108 / (377 × 0.04) ≈ 7.16 A

Closest option: 6.250 A → (b)

Step 4: Load current
Id = Vd1 / R = 54 / 20 = 2.7 A

Step 5: Peak current of Converter 1
Ipeak = Id + Ic ≈ 2.7 + 7.16 = 9.86 A

Closest option: 8.485 A → (c)

Final Answer: B. (b) and (c) only