Calculation of Reactive Input Power in Single Phase Semi Converter with RL Load

Introduction:
Single phase semi converter is a power electronics device which is used to convert AC power to DC power. It is a half wave converter which means it can only convert the positive half cycle of AC waveform into DC waveform. In this question, we are given the active input power of a single phase semi converter with RL load and firing angle. Our task is to calculate the reactive input power of the converter.

Given Data:
Active input power = 200 W
Firing angle = 60 degrees

Calculation:
To calculate the reactive input power, we need to first calculate the average power delivered to the load. The average power can be calculated as follows:

Pavg = (1/2π) ∫Vsin(ωt+α)I(t)dt

Where,
V = RMS value of input voltage
ω = Angular frequency of input voltage
α = Firing angle
I(t) = Output current of converter

For a single phase semi converter with RL load, the output current can be expressed as:

I(t) = (V/R)sin(ωt+α) - (VωL/R)cos(ωt+α)

Substituting this expression into the above equation and integrating over one half cycle, we get:

Pavg = (V^2/2R) [1-cos(α)] - (V^2ωL/2R) [sin(α) - sin(π-α)]

Now, the reactive power can be calculated as:

Q = √[P^2 - Pavg^2]

Where,
P = Active power = 200 W

Substituting the values of Pavg and P, we get:

Q = √[(200)^2 - {(V^2/2R) [1-cos(α)] - (V^2ωL/2R) [sin(α) - sin(π-α)]}^2]

As we are neglecting the harmonic components of output current, we can assume that the input voltage is sinusoidal. Therefore, we can express the RMS value of input voltage as:

V = √(2) * Vm

Where,
Vm = Peak value of input voltage

Substituting this value in the above equation and simplifying, we get:

Q = √[40000 - {Vm^2/2R [1-cos(α)] - Vm^2ωL/2R [sin(α) - sin(π-α)]}^2]

Conclusion:
In this way, we can calculate the reactive input power of a single phase semi converter with RL load. The reactive power indicates the amount of energy that is stored and released by the inductor in the load circuit. It is an important parameter in power electronics as it affects the power factor and efficiency of the system.