 This is gonna be walked through a power factor correction. We're gonna have some loads some inductive loads That's gonna give us a crappy power factor You're gonna see that we're gonna have a high current and then what we're gonna do is we're gonna throw a capacitor in there That's gonna improve a power factor and we're gonna see how our current is gonna drop like it's hot So just to get started here, we have a system that's got 480 volts. That's my supply voltage right there I got these three motor loads here. You can tell from the drawings now each of these motor loads I've given you different variables. So we're gonna go step-by-step what to do with each one of these This one's a five horsepower motor this little end here That means it has an efficiency of 79 percent a power factor of 56 percent over on this guy here It's got 13 kilowatts of true power with a phase angle of 60 degrees and over here It is got 21 k bar of inductive Power what was power being used with the power factor 71% and this little guy here. That's the power factor Capacitor that we'll be putting in there to fix it all up. So let's take a look what we're gonna be dealing with what we're gonna be looking for What we're gonna do is we're gonna go through and we're gonna figure out what our initial line current is and what our power Factor is of the entire circuit of all of this So we're gonna add all these guys up in parallel to figure out what our line is and line current and our line power factor After that, we're gonna figure out what size of this capacitor needs to be To correct the power factor to 95 percent again, we're gonna walk through every single step on the way and After we put in that power factor capacitor, we're gonna figure out what our new current is It's gonna change everything Okay, let's get started here Again, what we're gonna do is we're gonna take each one of these branches and the method I use is I create a triangle for each branch So let's get started here. We'll start with this guy over here Now before we get started, we're gonna have to figure out what the true power of this guy is we can do that using this horsepower here You add horsepower and this efficiency will give us a number we can use Again, we're always gonna be basing it off of power. We're gonna be building these power triangles now we've got to remember that for Efficiency efficiency is output over input this five horsepower that we've got here That is our output and we know that for one horsepower is 746 watts, right? We should all know that by this point. Let's take a look how this is all gonna play out There's that formula efficiency is output over input and we want the electrical input to put out that five horsepower output our first step is gonna be turning that horse power into power We're gonna take five horsepower times 746 watts and that gives us 3730 watts Now we're gonna plug in what we know so far. We know that we have an output power of 3730 watts. We know our efficiency is 79 percent or point seven nine and we are trying to figure out what our input is We do a little transposition razzle dazzle here We're gonna cross multiply point seven nine times input is equal to 3730 Then of course you want to get input alone So we have to divide the point seven nine out of there point seven nine We divide that outside as well. Whatever we do to one side we have to do the other So our input is going to be three thousand seven hundred and thirty watts divided by seventy nine percent or point seven nine and then we just Discover we've worked out that our input is actually four thousand seven hundred and twenty one point five watts Which is a number we're going to be using for the triangle. So let's go back and take a look at that circuit Okay, so I have built the triangle here What I've done is I take four point seven kilowatts and I've taken this power factor this power factor I've talked to another previous lessons power factor and angle are very closely related You can take the power factor in inverse coset to get the angle That's where I get that thirty eight or degrees from I went point five six inverse cos gave me thirty eight degrees Then from there I can use that and that and tangent to figure out my three point six k var is I'm not going to go into detail how the tangent works at this point I would expect you to know how that trigonometry works, but it's opposite over adjacent equals So we can work out these two guys here now. I've got four point seven kilowatts on the bottom three point six k var On the side. I don't really need to work out what this is at this point I could if I wanted to figure out what the current was through this branch But what we're going to be doing is we're going to be working out our kilowatts and our bars And then we're going to be adding them all up and creating one triangle to rule them all over there Let's take a look at our second branch now With our second branch. I see that I've got 13 kilowatts, which I'm going to throw on the bottom of the triangle I'm going to take again the angle using tangent and work out that I get twenty two point five k bar on the side Now let's work out this third branch right here in the third branch I put 21 k bar on the side all reactive components go on the side using this angle here I am tangent again. I can figure out that I have 21 kilowatts on the bottom Now I've worked out all three of these guys what we're going to do is we're going to take all three of these guys And add these three triangles together. I'm going to add up all my watts together to get an overall wattage on one side I'm going to add up all my bars on that side to get my overall bars together Then I'm going to work out my overall KVA Boom there you go. I went four point seven plus thirteen plus twenty one gives me thirty eight point seven kilowatts I went three point six plus twenty two point five plus twenty one gave me forty seven point one k bar Using the power of Pythagoras this squared plus this squared gives the square root of that at sixty one KVA With that now I worked out that my angle is fifty one degrees just using you can use sine cosine tangent whatever you want Okay, let's move that triangle up there now with fifty one degrees that doesn't help us out with our power factor What we need to do is figure out what our power factor is and just like I talked about over here How power factor and angle are close related the same thing is true over here You can just take the cost of fifty one Degrees is equal to point six three That's all you have to do is the cost of that angle gives you the power factor sixty three percent lagging and there you go our next steps going to be to figure out what the current is our Current is just going to be this KVA divided by this voltage 61 KVA divided by 480 volts will give us our line current of 127 amps There you have it with no power factor correction capacitor in there We are looking at 127 amps of current source current flowing there We didn't like that's what we did is I've got my two triangles here. I have a triangle that we have This is what we've already dealt with here. We got thirty eight point seven K. R. We got this We've got that now we want to improve our power factor. We were at sixty three percent We want to improve our power factor over to ninety five percent The one thing that's not going to change because the resistance in the circuit will not change is This so we're going to take this guy the thirty eight point seven kilowatts over to the triangle that we want That's the triangle we want now With this guy here and this guy here. We're going to work out this side and this side Again, I'm not going to go into the trigonometry of it because by this point I imagine you guys are all experts at trigonometry if you're not go back and watch the videos on trig now using 95% What I've done my little quick trip Trick is I take this divided by this gives me this and that works every single time your kilowatts divided by your power factor gives You a KVA then I use Pythagoras that squared minus that squared gives you the square root of that and that gives us the triangle that we want Now we have forty seven point one K bar. We want twelve point six K bar So we need a capacitor that's going to take this guy and drive it down until we get there Remember that capacitive power and inductive power opposite So all we have to do is we take the forty seven point one minus the twelve point six, which is thirty four point five K bar It's going to take a thirty four point five K bar capacitor to push this all the way down till it hits twelve point six K bar This is the size of capacitor we need to improve our power factor to ninety five percent Yeah, let's look at the circuit again here So we now know that over here this capacitor has to be sized for thirty four point five K bar This is now our triangle that we have it was the one that we let me go back a second and talk back what we had This used to be sixty three percent now. It's ninety five percent. So the triangle that we wanted is now the triangle that it becomes We have forty point seven KVA on that side Which means that if we want to work out the current same as before all we have to do is take this KVA And divide it by this voltage and we get our new line current forty point seven KVA divided by four hundred and eighty volts Gives us eighty four point eight amps, which is a significant difference. We have dropped quite a bit Just as a reminder we used to be drawing a hundred and twenty seven amps We are now drawing eighty four point eight amps That's a significant difference if you ask me well if you ask anybody really go ask your mother She'll tell you the same thing. We were running this whole system at a hundred and twenty seven amps We put in this capacitor now this capacitor has now dropped the current to eighty four point eight amps these motors They're still running. They're still doing the exact same thing You won't hear anything happen with these things They'll do the same work because a true power has not changed all we've done is we've taken this inductive power here And we've driven it down until it's hit twelve point six K bar. That's power factor correction and that's a walk-through