A three-phase fully controlled bridge converter is fed through a star-delta transformer. The converter is operated at a firing angle of 30 degrees. Assuming the load current (I₀) t... A three-phase fully controlled bridge converter is fed through a star-delta transformer. The converter is operated at a firing angle of 30 degrees. Assuming the load current (I₀) to be virtually constant at 1 p.u. and transformer to be an ideal one, what is the input phase current waveform?
Understand the Problem
The question presents a three-phase fully controlled bridge converter fed through a star-delta transformer. It states operational conditions: a firing angle of 30 degrees, a load current (I₀) virtually constant at 1 per unit (p.u.), and the transformer assumed to be ideal. The question asks to determine the shape of the input phase current waveform.
Answer
(B)
Answer for screen readers
(B)
Steps to Solve
- Understand the converter operation
A three-phase fully controlled bridge converter with a star-delta transformer on the input side is considered. The firing angle is $30^\circ$, and the load current $I_o$ is constant at 1 p.u. The transformer turns ratio is 1:K.
- Determine the secondary side current waveform
For a three-phase fully controlled bridge converter, each thyristor conducts for $120^\circ$. Since the load current $I_o$ is constant, the secondary side currents will be rectangular pulses of duration $120^\circ$. The conduction sequence and the corresponding secondary currents determine the primary-side current.
- Analyze the impact of the star-delta transformer
The star-delta transformer introduces a $30^\circ$ phase shift between the primary and secondary line currents. The primary line current is a stepped waveform due to the combination of two $120^\circ$ rectangular pulses that are phase-shifted, due to the delta-star transformer. Each phase in the star side injects a current on two phases on the delta side.
- Determine the primary side current waveform
Due to the star-delta connection, the primary side line current waveform will have steps. The current levels are proportional to K, the transformer turns ratio. The current in the primary side can be either $\frac{K}{3}$ or $\frac{2K}{3}$ depending on the combinations contributing to the current. Because of the $30^\circ$ firing delay, the current waveform starts $30^\circ$ late from the start of the voltage waveforms.
- Matching the waveform to the options
The primary line current waveform will exhibit the following characteristics:
- It will be a stepped waveform.
- It will have positive and negative parts.
- The steps will be proportional to the transformer turns ratio K.
- Due to the star-delta transformer and the $120^\circ$ conduction angle, the steps occur in a pattern related to multiples of $60^\circ$ or $\frac{\pi}{3}$ radians. Considering these characteristics, option (B) with values $\frac{K}{3}$ and $\frac{2K}{3}$ and a shift by $\frac{\pi}{6}$ (corresponding to $30^\circ$) is the only viable option.
(B)
More Information
The key to this problem is understanding the effect of the star-delta transformer and the conduction sequence of the thyristors in the fully controlled bridge rectifier. The transformer introduces a phase shift and affects the magnitude of the current seen on the primary side based on the turns ratio $K$.
Tips
- Forgetting the $30^\circ$ phase shift introduced by the star-delta transformer.
- Incorrectly determining the current levels on the primary side due to the transformer turns ratio.
- Not correctly analyzing the conduction sequence of the thyristors.
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