Chapter Four, change of base. When manufacturers specify the ratings of their various pieces of equipment that they are selling and introducing the into the system, they are usually rated at their own specific MVA rating. Such as in the case of this transformer nameplate rating the impedance is 7.51% at Sony 500 kV a at the voltage rating of the transformer or they might listed in the paperwork that comes with the components such as this generator, they would specify the generator is rated at 90 MVA At 22 kV with an internal impedance of 18% on its own base. First thing that stands out is the fact that they're specifying the impedance as a percentage rather than per unit. This is usually the case. And it's just a simple matter that percent impedance equals per unit impedance times 100%.

So if you need the, if you need to use the pure unit impedance, you just divide by 100 or move the decimal place two places to the left. Now remember, this is the manufacturer's reading of the generator in isolation. It's not connected to a system and the asset base that they manufacturer are specifying is 90 MVA, the V base is 22 kV and the previous Unit impedance is 0.18. So once the generator or the piece of equipment is connected to a more complex system and we want to do some analysis on that system, we you find it probably more convenient to have a different set of bases. And in this case, we want to set our, our VA base at 100 MVA. So we call it s n base and for the new base, and we've selected the new voltage base to be 220 kV.

Once we've selected 220 kV, the ratios of the Transformers then decide where the various zones of the equipment is and the various voltage bases that have to be used. And in this case, the Voltage base at 22 kV is where the transformer or the generator is connected. Then we also have a voltage base on line one which is 110 kV at a voltage base on the motor side of a load side which is 11 kV. So, the original manufacturer's set of bases has to be converted over to our new set of basis and that requires a bit of mathematical conversion which you will see in the next slide. So, what we need is a formula for calculating or changing per unit impedances that are calculated with one base into per unit impedances using another base within a mind going to use the letter M in referring to anything that is used in specifications by the manufacturer.

So in the case of the MVA base the manufacturer would use, I'm going to designate that as s subscript m base and the voltage base is going to be designated as the subscript m base and the impedance per unit impedance specified by the manufacturer is going to be Zed m, p you. Similarly, in in the system, new system that I want to use all my calculations in, I'm going to use the letter N as a subscript so that the new MVA base is going to be designated as subscript and base and voltages are going to be or the voltage bases are going to be designated the subscript and base. Ultimately what we want to do is we want to come up with a per unit impedance for the generator in our new system basis. We know from previous lessons that when we're calculating any type of base quiet base impedance quantity is given by the voltage base squared over the MVA base.

So, Zed m base in this case is equal to v m base squared all over s m base. Similarly, in our new system, quantity and their basis, the impedance base is designated by The formula Zed in base is equal to v n v squared all over s n base and we know from previous lessons also that the actual impedance in this case if you want to call it the impedance of the generator, the actual impedance of in ohms is equal to the per unit impedance of the of the unit times its base impedance. So, in the case of our manufacturers, quantities or manufacturer specified quantities, the actual impedance of the generator is equal to Zed MP u times said m base and the actual impedance using our new set of bass quantities is going to be designated as Zed is equal to Zed npu, time Zed and bass.

Now the impedance in ohms for both cases, the actual impedance is the same. So we can now equate the second part of those equations, and we can say that Zed MP u times said m base is equal to Zed npu Times said and base. We can now substitute Zed m base in our equation. And we can also substitute said in bass in our equation We would like to find out ultimately, what the impedance is in our new set of quantities. In other words, we would like to know what said subscript, and PDU is the rest of the terms of the equation we already know. So, we're going to do a quick mathematical manipulation and transpose the Zed npu to the left hand side of the equation, and all the other known quantities to the right hand side of the equation.

And what we have here now is the formula that is required to convert impedances per unit impedances specified at one base into the new base. So let's look at that. With our example in mind, I'm rewriting the equation here. And I'm going to go through the process of making substitutions. We know what the manufacturers per unit impedance is. And that is point one eight, we know what the base value or the MVA base is specified by the manufacturer.

And we know what the new base is that we want to convert to. We also know the voltage base of the manufacturer used is 22 kV, so we can put that in our equation. And we have to decide which voltage that we're going to use for the new voltage base. Well, we have to consider where the where the generators connected to the system and We can see that it's connected to the 22 kV b 22 kV bus. So the new voltage base that we're going to be using to convert to is 22 kV. And you can very quickly see that the fraction on the extreme right hand side of that equation, the numerator and denominator is the same, so they cancel out.

So in converting, all we have to do is convert point one eight by the ratio of 100 over 90, and that gives us a value of point two per unit, which is the value of the generator per unit impedance using our new base values. So when we're converting to one from one base value to another We can just say that we have to use this formula. This ends chapter four