13.In a single-phase Semi-converter, if output voltage has a peak and average values of 325 V and 133V respectively, then the firing angle is?

Question

Answer

To determine the firing angle in a single-phase semi-converter, we need to consider the relationship between the peak and average output voltages.

The firing angle is the delay between the time when the thyristor is triggered and when it conducts current. It is denoted by α.

Given that the peak voltage (Vp) is 325 V and the average voltage (Vavg) is 133 V, we can use the following relationship:

Vavg = (2/π) * Vp * (1 - cosα)

We can rearrange the equation to solve for the firing angle α:

α = acos(1 - (π/2) * Vavg / (Vp))

Let's calculate the firing angle using the given values.

Given:
Vp = 325 V
Vavg = 133 V

Calculations:
α = acos(1 - (π/2) * 133 / 325)
α ≈ acos(1 - 1.304)
α ≈ acos(-0.304)

Since the range of acos function is limited to 0 to π, the value of α cannot be directly calculated from the above equation. However, we can determine the approximate value using the inverse cosine function and considering the range of the firing angle.

Approximating the firing angle:
α ≈ π - acos(0.304)
α ≈ 2.836 radians

Converting to degrees:
α ≈ 162.5 degrees

Therefore, the firing angle in the single-phase semi-converter is approximately 162.5 degrees.

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