To solve this problem, we need to determine the minimum capacitance $C$ required for the given three-phase bridge rectifier.

Step 1: Key Parameters

• Line-to-line RMS voltage ($V_{LL}$) = 400V
• Load power = 1000W
• Frequency = 50Hz
• Ripple voltage requirement = 15% of the peak line-to-line input voltage

Step 2: Peak Line-to-Line Voltage ($V_{LLpeak}$)

The peak line-to-line voltage $V_{LLpeak}$ is given by:

$V_{LLpeak} = V_{LL} \times \sqrt{2}$

$V_{LLpeak} = 400V \times \sqrt{2} \approx 400V \times 1.414 \approx 565.7V$

Step 3: Output Voltage Ripple Requirement

The maximum allowable output voltage ripple is 15% of the peak line-to-line voltage:

$V_{ripple\_max} = 0.15 \times V_{LLpeak}$

$V_{ripple\_max} = 0.15 \times 565.7V \approx 84.86V$

Step 4: Load Current

The resistive load power $P$ is 1000W. The output DC voltage $V_{dc}$ can be approximated as:

$V_{dc} = V_{LLpeak} - V_{drop}$

where $V_{drop}$ represents the voltage drop across the diodes. For simplicity, we can ignore the diode drops here and assume that the output DC voltage is approximately equal to the peak of the rectified line-to-line voltage, $V_{LLpeak}$.

The load current $I_{load}$ is:

$I_{load} = \frac{P}{V_{dc}}$

Since $V_{dc} \approx V_{LLpeak}$, we have:

$I_{load} = \frac{1000W}{565.7V} \approx 1.77A$

Step 5: Capacitor Selection

The capacitor will smooth the rectified DC voltage and limit the ripple. The ripple voltage in a full-wave rectifier is given by the formula:

$V_{ripple} = \frac{I_{load}}{f_{ripple} \cdot C}$

Where:

• $I_{load}$ is the load current
• $f_{ripple}$ is the ripple frequency, which is twice the line frequency for a three-phase bridge rectifier. So $f_{ripple} = 2 \times 50Hz = 100Hz$
• $C$ is the capacitance

We can rearrange this to solve for $C$:

$C = \frac{I_{load}}{V_{ripple} \times f_{ripple}}$

Substitute the known values:

$C = \frac{1.77A}{84.86V \times 100Hz}$

$C = \frac{1.77}{8486} \approx 0.000208F = 208 \, \mu F$

Conclusion

The minimum capacitance required is 208 μF.

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Would you like more detailed steps on any part of the solution or further clarifications? Here are some related questions for further exploration:

1. How do you calculate the exact ripple voltage for different load types?
2. What impact does increasing the load resistance have on the required capacitance?
3. How would you calculate the ripple voltage in a single-phase bridge rectifier compared to a three-phase?
4. How do we account for the diode voltage drops in a real-world application?
5. What is the relationship between the capacitor value and the frequency of the AC supply in a rectifier?

Tip: When designing power supplies, it's always important to choose a capacitor with a voltage rating higher than the peak voltage to ensure reliability and prevent breakdown of the dielectric material.