# capacitive reactance



## Omer (Jul 25, 2017)

Hi all,

just a quick one,

for a 3 phase system, we have V line and total reactive power consumed by the system Q.

then capacitive reactance Xc = V line**2/Q  or sqrt(3)*V line**2/Q ?

I am confused.


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## rg1 (Jul 25, 2017)

Omer said:


> Hi all,
> 
> just a quick one,
> 
> ...


The power consumed by any load( for the time being let us forget VARs generated or consumed) is I**2*X or V**2/X(replace I=V/X). So this gives us X=P/I**2 or V**2/P. Coming to three phase system where three phase power is given. P(3phase)=3*Vp**2/Xp . Now let me replace Vp=Vl/sqrt3 in this; it gives me P=Vl**2/Xp. I am not solving them for Xp because that is very easy from here.

Now coming to your specific question if you are taking power as 3 phase take Line Voltage. If you are taking 1/3 of given 3 phase power take Phase voltage. But formula remains same X= V**2/Q(P) and do not mix the two, it will create havoc.

If it does not make sense I will try to phrase it in a different way .


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## TNPE (Jul 25, 2017)

@rg1 you're correct.  

Thanks for saving me the typing :thumbs:


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## rg1 (Jul 25, 2017)

TNPE said:


> @rg1 you're correct.
> 
> Thanks for saving me the typing :thumbs:


But you always have a different way of explaining the concept. To be honest I get it by reading it two times but it is interesting to understand the same thing in different way. I always believed EE is more of maths but some of you guys present it in a artistic way. I appreciate that. I for that matter will simply take it to maths after the concept and understand from there. I am really skeptical about how many follows my maths here.


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## TNPE (Jul 26, 2017)

I don't approach anything with a convoluted thought process, at least not in my own mind.  I work from my strengths and how a problem makes sense to me.  Most of my explanations are due to my professional experiences, development and preparation for the PE.  I understood the material in much more detail in preparing for the PE than I did as a student.  I did well as a student, but once you're able to apply field experience with theory and analytical techniques, that's when understanding is fully achieved.

But don't misunderstand me, there's still a lot I don't know!!!


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## TNPE (Jul 26, 2017)

The "math" you speak of in EE is in the DSP and communications fields. Damn, what a nightmare.  I enjoyed Fourier and Laplace analysis.  The magic of these operations are purely genius, especially, after you're able to wrap your mind around what these operations are actually doing and how a time domain signal is decomposed into complex sines/cosines to show a complete spectral representation.  That said, I'm much happier on this side of the fence.  I could never do another Fourier transform and be as happy as a pig in mud.  Same for Laplace, convolution integrals, etc.....


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## TNPE (Jul 26, 2017)

Where are my fellow TN grads?

Dr. MJR anyone?  I know there's some of y'all around here who've experienced the total hell I did.  But I respect him and am grateful for his rigor. He made me a better student, as I'm sure the rest of you would agree.

@TNSparky


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## Omer (Jul 26, 2017)

rg1 said:


> The power consumed by any load( for the time being let us forget VARs generated or consumed) is I**2*X or V**2/X(replace I=V/X). So this gives us X=P/I**2 or V**2/P. Coming to three phase system where three phase power is given. P(3phase)=3*Vp**2/Xp . Now let me replace Vp=Vl/sqrt3 in this; it gives me P=Vl**2/Xp. I am not solving them for Xp because that is very easy from here.
> 
> Now coming to your specific question if you are taking power as 3 phase take Line Voltage. If you are taking 1/3 of given 3 phase power take Phase voltage. But formula remains same X= V**2/Q(P) and do not mix the two, it will create havoc.
> 
> If it does not make sense I will try to phrase it in a different way .


Thanks rg1,

this is what I thought, but I faced one problem where they used the sqrt(3) formula. I will post later.

Anyway, Xc we get, is it total or per phase?


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## rg1 (Jul 26, 2017)

Omer said:


> Thanks rg1,
> 
> this is what I thought, but I faced one problem where they used the sqrt(3) formula. I will post later.
> 
> Anyway, Xc we get, is it total or per phase?


Yes Xc is phase value. To make it simple to understand I started from single phase. You can read my first post again. P(3phase)=3*Vp**2/Xp. Whenever there is a confusion in understanding, imagine star grounded system. Three separate single phases. Start from there and come over to 3 phase, you will get a sense what is what? There are many ways to do a thing, if they have used sqrt3, I in absence of what exactly they have done, I can not comment, may be right. I have seen these guys sometimes using some weird thing to get an answer. If they want 15 they will simply multiply 3 with 5 and then introduce EE into that, to explain you. Lol. Post the details, we will discuss it further.


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## Omer (Jul 26, 2017)

rg1 said:


> Yes Xc is phase value. To make it simple to understand I started from single phase. You can read my first post again. P(3phase)=3*Vp**2/Xp. Whenever there is a confusion in understanding, imagine star grounded system. Three separate single phases. Start from there and come over to 3 phase, you will get a sense what is what? There are many ways to do a thing, if they have used sqrt3, I in absence of what exactly they have done, I can not comment, may be right. I have seen these guys sometimes using some weird thing to get an answer. If they want 15 they will simply multiply 3 with 5 and then introduce EE into that, to explain you. Lol. Post the details, we will discuss it further.


here we go


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## cos90 (Jul 26, 2017)

TNPE said:


> The "math" you speak of in EE is in the DSP and communications fields. Damn, what a nightmare.  I enjoyed Fourier and Laplace analysis.  The magic of these operations are purely genius, especially, after you're able to wrap your mind around what these operations are actually doing and how a time domain signal is decomposed into complex sines/cosines to show a complete spectral representation.  That said, I'm much happier on this side of the fence.  I could never do another Fourier transform and be as happy as a pig in mud.  Same for Laplace, convolution integrals, etc.....


I took a ton of classes in this area and enjoyed it even though my GPA suffered for it. I don't use any of it directly because I ended up as a Power Engineer, although it does help me to know what Protective Relays are actually doing.

I found a website that explains a lot of this DSP stuff very clearly the other day. It's very beautiful software here. http://iowahills.com/

Here's a paper specific to DSPs in protective relays by the originator of it, Edmund Schweitzer: https://cdn.selinc.com/assets/Literature/Publications/Technical Papers/6041_FilteringProtective_Web.pdf


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## rg1 (Jul 26, 2017)

Omer said:


> here we go
> 
> View attachment 9893


So as I said, to understand better, assume it to be star connected load. 150VA is 3 phase reactive power to be compensated. So single phase power is 150/3=50VA and single phase Voltage is 208/sqrt3. Now it becomes simple.

Even if you assume it to be a delta connection, answer will be same, your maths will be longer and understanding may be better after you do that. I will suggest you to do it bothways to understand the stuff. Even in delta one phase power will be 50VA, because each phase has to share it equally.


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## rg1 (Jul 26, 2017)

rg1 said:


> So as I said, to understand better, assume it to be star connected load. 150VA is 3 phase reactive power to be compensated. So single phase power is 150/3=50VA and single phase Voltage is 208/sqrt3. Now it becomes simple.
> 
> Even if you assume it to be a delta connection, answer will be same, your maths will be longer and understanding may be better after you do that. I will suggest you to do it bothways to understand the stuff. Even in delta one phase power will be 50VA, because each phase has to share it equally.


Omer it will be good idea if you post your both maths (assuming load to be star as well as delta) on the forum for benefit of many.


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## TNPE (Jul 26, 2017)

Omer said:


> here we go
> 
> View attachment 9893


Q=V^2/X=wCV^2

but

You're looking for C, which yields:

C=Q/(wV^2)

From the parameters given, and the adjustments @rg1 recommended, this is a rather easy problem.


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## Omer (Jul 26, 2017)

rg1 said:


> So as I said, to understand better, assume it to be star connected load. 150VA is 3 phase reactive power to be compensated. So single phase power is 150/3=50VA and single phase Voltage is 208/sqrt3. Now it becomes simple.
> 
> Even if you assume it to be a delta connection, answer will be same, your maths will be longer and understanding may be better after you do that. I will suggest you to do it bothways to understand the stuff. Even in delta one phase power will be 50VA, because each phase has to share it equally.


if we assumed delta connection, as you suggest power per phase is 50VA, however voltage across the capacitor is 208 V line voltage compared to 208/sqrt(3) across capacitors in wye connection. therefore, answer will be different. Is it so?


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## rg1 (Jul 26, 2017)

Omer said:


> if we assumed delta connection, as you suggest power per phase is 50VA, however voltage across the capacitor is 208 V line voltage compared to 208/sqrt(3) across capacitors in wye connection. therefore, answer will be different. Is it so?


You are absolutely right. This will help us in better understanding , what is happening there. If you get Xy in Star connection you get 3*Xy in Delta connection. Right?. If you convert this Xd again into Xy by conversion methods of delta to star of impedance you again get the same answer as you got with star calculations directly. That proves we are correct. So far we are on correct path. Is it? We will come to specific question next.


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## Omer (Jul 26, 2017)

rg1 said:


> You are absolutely right. This will help us in better understanding , what is happening there. If you get Xy in Star connection you get 3*Xy in Delta connection. Right?. If you convert this Xd again into Xy by conversion methods of delta to star of impedance you again get the same answer as you got with star calculations directly. That proves we are correct. So far we are on correct path. Is it? We will come to specific question next.


Ok, that mean capacitance required is different depending on the connection.

will assume for this specific question star as it is usually the case. this will result in capacitance of 9 micro farad per phase.

what confused me from the beginning was the solution provided. I think they are mistaken somehow.


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## rg1 (Jul 26, 2017)

Omer said:


> Ok, that mean capacitance required is different depending on the connection.
> 
> will assume for this specific question star as it is usually the case. This is what I have seen in some text books including Wildi which says if nothing is mentioned do it with star. this will result in capacitance of 9 micro farad per phase. By doing in it both ways and getting the same (lol) answer we at least are sure that we are right. I do not think we have done anything wrong.
> 
> ...


The question asks total capacitance. They seem to be attempting for that. I have check it. But that is not the way. There is nothing like total capacitance. The capacitance in star connection will have less Voltage rating and more current rating( less Xc more C); capacitance in delta will have more voltage rating and less current rating (more Xc less C).  And we say 3 capacitors of this particular ratings are required. Generally we measure total capacity in VARs and not in Farads. Because total of anything (R,L,C) will depend on how you connect them(series parallel combination). Your confusion is justified.


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## TNPE (Jul 26, 2017)

A scenario to consider:

Why do you use Vline^2/Sbase when calculating base impedance in per unit, 3-phase analysis?  Why not phase voltage, if practical and other necessary conversions are performed?


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## rg1 (Jul 26, 2017)

TNPE said:


> A scenario to consider:
> 
> Why do you use Vline^2/Sbase when calculating base impedance in per unit, 3-phase analysis?  Why not phase voltage, if practical and other necessary conversions are performed?


IMHO. Base Z= BaseV/BaseI.  In which both V and I  are the Voltage across and current through a load. There is no Z as three phase. You start from Vp and Ip for any thing star or delta. The formula given by you should be derived from here.


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## TNPE (Jul 26, 2017)

That is true, but most commonly, you're given power and voltage when doing pu analysis.  And Vline is the "base" that you use... That's my question for the board, why?  I'm askinng this since it sort of relates to the original post.


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## TNPE (Jul 26, 2017)

PU analysis can look like a sleight of hand, voodoo black magic show... But...

Z=Vline^2/Sbase is correct

But why?  It's pretty intuitive once you see it.


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## rg1 (Jul 26, 2017)

rg1 said:


> The question asks total capacitance. They seem to be attempting for that. I have check it. But that is not the way. There is nothing like total capacitance. The capacitance in star connection will have less Voltage rating and more current rating( less Xc more C); capacitance in delta will have more voltage rating and less current rating (more Xc less C).  And we say 3 capacitors of this particular ratings are required. Generally we measure total capacity in VARs and not in Farads. Because total of anything (R,L,C) will depend on how you connect them(series parallel combination). Your confusion is justified.


Yes , I studied it again,  the solution of the book is wrong, without any doubt. He too is assuming it to be star connected system and his answer that is 5 microfarad multiplied by error (sqrt3) he is making in the beginning in the formula gives your answer 8.66==9 microfarad. So there is nothing like total capacitance he is asking in the question. He should have formulated and formatted the question in a better way.


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## rg1 (Jul 26, 2017)

TNPE said:


> PU analysis can look like a sleight of hand, voodoo black magic show... But...
> 
> Z=Vline^2/Sbase is correct
> 
> But why?  It's pretty intuitive once you see it.


Zbase=Zb; Vphase base=Vpb, Vline base=Vlb, same for I ( Voltage in Volts, current in Amps)

Zb=Vpb/Ipb

=Vlb/(sqrt3*Ilb)

=Vlb**2/(sqrt3*Vlb*Ilb)

=(1000*Vlb)*(1000*Vlb)/(1000000*sqrt3*Vlb*Ilb)

=Vlb**2/Sb ( Voltage in kV and S in MVA)

Now we take can whatever is easily available to us in the question.


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## Omer (Jul 27, 2017)

Thanks @rg1 and @TNPE for elaborating on the subject.

As you mentioned rg1, the formulation of the question could have been better.


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