Full bridge controlled rectifier (find average current in the load)

Hello people. In the next circuit I need to find the average current in the load (battery which it's 10[V] and the resistor it's 0.5Ω and the inductor 6.5mH) and the thyristors are shoot at \[\frac{\pi}{3}\]



there is two modes of operation, 1 where T1 and T1 drives current and the second where those drives current because the inductor's current untill T4 and T3 are shoots.

So the differential equations it's

\[v(t) = i(t) R + L \frac{d i(t)}{dt } + 10\] and \[v(t) = \sqrt{2} 120 sin (2 \pi 60 t)\]

but what I don't know it's: I must put the signal v(t) in the equation because the thyristors are shoot at \[\frac{\pi}{3}\]


\[\frac{\sqrt{2} 120}{L} sin (2 \pi 60 t) - \frac{10}{L}= \frac{R}{L}i(t) + i'(t)\]
Solving that:

\[i(t) = -20 +86.4{e}^{-76.9 t} - 66.48 cos(376.7t) + 13.56 sin(376.91)\]

and here it's the graph:

But the problem it's the voltage in the load do not start at 0s but it's star at \[(\pi /3) /(2 \pi * 60) \]

The second mode it's

i[2*0.00277]= 81[A] to two to do not use the transient



The average current is:

\[60[Hz] ({\int}_{2*0.0027}^{2*0.0027+0.00877} {i}_{t}(t)dt + {\int}_{2*0.0027+0.0087}^{2*0.0027+0.0087+0.0027}{i}_{2} (t)dt)\]



So the average current it's 6.9[A] but the rashid says that the average current by the thyristor it's 44[A]

What do you think?

Re: Full bridge controlled rectifier

I will list what I would do in order to answer that question and doing so, you will answer your questions.

1) Find if the circuit is working on continuous or discontinuous mode:

• Start by solving the differential equation for the current assuming it is its first time being powered up i.e. with i(alpha)=0.
• Calculate i(π+alpha). If it is >0 => continuous conduction mode. (probably is easier to assume this directly due to the waveform shown in your post)

2) If you are in the continous conduction mode, Fourier series is used to calculate the average current (assumes steady state)

• Calculate the voltage Fourier Series from your waveform shown earlier in this post. (or only its DC value if that is what Rashid wants)
• Calculate average current using the average voltage (remember you are in the steady state).
• OPTIONAL. You can calculate the rest of the harmonics... until the infinity :lol:

----
I have another method which I have not seen it yet in books to calculate steady state exact expression of current/voltage for simple 1st order circuits. Higher order circuits is more messy.

Re: Full bridge controlled rectifier

Thanks but here it's the doubt.

Find if the circuit is working on continuous or discontinuous mode:
Start by solving the differential equation for the current assuming it is its first time being powered up i.e. with i(alpha)=0.

Click to expand...

Why start with alpha=0 if the thyristors are shoots at alpha=Π/3?

because at alpha=Π/3 the input voltage signal at load it's difference with alpha=0. instead v(0)=0 it's \[v(\alpha)= \sqrt{2} * 120 * sin(\alpha) >0\] and if the input voltage is bigger than 0 the current magnitude will follow a difference magnitude path because

\[v(t) = i(t) R + L\frac{i(t)}{dt} + E\]

Re: Full bridge controlled rectifier

Why start with alpha=0 if the thyristors are shoots at alpha=Π/3?

Click to expand...

Where did I say alpha=0 ?

I have said, i(alpha) = 0 which is different.. current at alpha = 0 i.e. Current ( alpha ) = 0

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I have checked Rashid's book and it explains step by step and equation. Why do not you follow Rashid's steps?

I have another method which I have not seen it yet in books to calculate steady state exact expression of current/voltage for simple 1st order circuits. Higher order circuits is more messy.

Click to expand...

I have found it now in Rashid's book. That is exactly what I was doing and is the most accurate way !

Re: Full bridge controlled rectifier

Thanks!

I have checked Rashid's book and it explains step by step and equation. Why do not you follow Rashid's steps?

Click to expand...

Because I did not understand it well and wanted to reach the same solution through the method that seemed right. I will see it in detail later and comment if I have any questions.

Tanks again.
Regards