Chapter three per unit analysis and the normalization process. The per unit system is a method of expressing quantities in an electrical system such as power voltage, current impedance etc as proportions of predefined base quantities. Once these quantities are expressed as a ratio of their equivalent base value, this is called a per unit value. Using per unit value simplifies the process in many ways and you'll see this as we go through some examples. This process is called normalization. There are several advantages to using a per unit system.

First of all it effectively moves the turns ratio of a transformer from circuit analysis. Manufacturers often specify their apparatus in terms of per unit quantities. For example, a generating manufacturer would express the internal impedance of a generator in terms of percent on its own base, you have to know what that means and how to use it in your system analysis. per unit values lie within a very narrow range so that as you go through your calculations, anytime type of mistakes or error, errors will show up quite readily, and it's easier to pick them out. Whereas actual values can be orders of magnitude different from one from the other. And even if you are using system computers, quantities going into that software and quantities coming out the other end are often used in terms of per unit quantity.

So you have to know what they're talking about. The main advantage in using per unit quantities is the fact that it removes the turns ratio of a transformer from circuit analysis. Okay, let's get into the normalization process. The normalization process consists of five steps for going into the process of normalization or going into the per unit system and one step to come out of it. The first step is to specify an MVA base. Now this can be completely arbitrary and It will work, you can say it'd be 100 MVA or could be a 500 MBA or could be 100 k VA or just 100 va, whatever it is, whatever volt amps it is, you can, you can specify it, but then you have to use it for the rest of the time that you're in the normalization process.

For that reason, you usually pick something that's going to be relevant to your calculations, and it'll ease your calculations. In other words, you'll pick the the MVA rating of a transformer, the MVA rating of a system, the VA rating, or the KV a rating of a generator, whatever it is, it's quite arbitrary. But once it's picked, that's what you have to use for the rest of the time. One thing that has to be mentioned here now is that that base values are magnitude only. They are not vectors, they are not phasers, they are only magnitude. And they, they don't pay have any kind of direction whatsoever.

In other words, if we were to look at a MVA quantity, it's made up of a magnitude which you see in green there, plus it's given some direction, and that's shown by the angle there. But once we pick the base value, we drop the direction, and we only maintain the magnitude. The next step we do is we determine or pick a voltage base. Again, this is quite arbitrary. You can pick any voltage you want, but it really will help if you pick one of the voltage levels that you're going to be dealing with. You could be dealing with many voltage levels in the system.

You could have 220, you could have 110, you can sub 35 but if you pick one of the system voltages, it makes the conversion to and from and the calculations much easier. So just pick any voltage level and that will be your starting point for your voltage base. And again, most voltages are from phasers are vectors, so they're made up of a quantity a magnitude and an angle. When you pick the voltage base, you're only dealing with the magnitude and that's the way it is for all basis in the normalization process. The other thing that is very important to remember that there is a once you pick a voltage base, the rat there's a voltage base a different voltage base for every voltage level in the system. transformer voltage level ratings are given usually given in line Line, those are called the transformer ratios.

So once you establish a voltage base and it is selected, the other voltage bases are determined by the transformer ratios. So I'm gonna say that again because it's really important once a voltage base is selected, the other voltage basis are determined by the transformer ratios in the system we see here, you can see that there are several voltage levels and I've tried to separate them out by using color. But if you pick a voltage base to start with, if we selected the voltage rating of the line line number one to be the base voltage, then the base of that voltage level is 220 kV. Once we say that, that is the base voltage for that voltage level, and all the rest of the voltage levels will are determined By virtue of the transformer ratios, so, the red v base is 22 kV, the orange v base is 11 kV and the blue v base is 110 kV.

This will become a little bit clearer as we start to work through examples. But as you're working with components in a system, the voltage base that you have to use is where it is connected to the system. For example, the generator on the left the 90 MVA 22 K, the generator is connected to the 22 kV bus. So you have to use when you're involved with calculations on that generator you have to use the 22 kV bus voltage as the base. Let's have another look at this. And look at the dividing lines or the boundaries of these various low voltage levels and their basis.

If we picked as I said in the beginning line one voltage rating as the voltage base, then everything inside that green box is attached to the voltage base 220 kV. So, that is the voltage base that you use for any calculations for any equipment that's going to be connected at that voltage level. The red voltage level is a 22 kV bus and all components including that generator are connected to V base two which is 22 kV. The blue line indicates the voltage base three and that is the voltage base at 110 kV So, any calculations involving the voltage base you In that area for components connected to that, that area of the system that the base you use when you have to use a voltage base is 110 kV. The last area is on the right and it is the 11 it is 11 kV bus and the components connected to the 11 kV bus.

I've designated as the base for but it is 11 kV Okay, we have gone through the first two steps of the normalization process. Firstly selecting the MVA base or the KV a base or the VA base for our normalization process and step two, we're setting a voltage base, which then sets all the basis for the various voltage levels in our system. Once these two bases are paid, or set then all of the other bases are set and are calculated from these two bases the MVA and voltage base. Now we have to determine the impedance bases and the current basis for our system. And we do that by falling back to some very basic equations in, in in electrical systems, the first one being ohms law stating that the impedance is given by the voltage over the current. And if we want to calculate a parent power for a circuit, then we have to multiply the voltage times the current and that would give you the apparent power.

If we rewrite that equation and in terms of the apparent power and voltage Then we would get is equal to s over V. And if we put that, if we substitute the the right hand side of that equation for AI in our original equation, we would get the impedance is equal to V all over s divided by V, or that would be V squared all over s. And it's important to note that we're talking about volts and volt amperes. If we were talking in terms of kilovolts, or kV, then we'd have to multiply the KV by 1000 in order to end up with the right impedance term. So, Zed is EAC. We can say Zed is equal to kV times 1000 over i in the case of putting the appearance power over the voltage in order to get the current because both of them are rated in kV a are times 1000.

If you put in multiply them times 1000, a numerator times 1000 nominator, the 2000s would cancel out. So, you can put kV a over top of kV. It However, in the case of if you're going to specify voltage in terms of kV and MVA, the numerator, if we're going to use kV would have to be the, the KV would have to be multiplied by 1000. And because we're squaring it, it would be kV times 1000 times kV times 1000. And in the denominator, because we're using MVA, we would have to multiply that times a million. Fortunately, the big this big cumbersome fraction boils down to just the KV squared, all over MVA, because all those zeros cancel out and you're just left with kV and MVA.

So if we now want to look at calculating our base values, we can use these equations to calculate our base values and the impedance base is given by the voltage base squared, all over the apparent power base or s base. You can also write that as the KV base squared all over the MVA base. As far as the current base is concerned, you can have s base all over V base or you could have kV a base all over kV base. Or you could have MVA base times 1000 All over the cavey base. Now, remember that when we're calculating these bases, it all depends on where you are in the system as to which voltage base that you're going to use the the MVA or the KV, a base is common throughout the whole system. So you don't have to worry about that changing or where you're connecting the system to use that.

But depending on where you are in the system, you have to use the voltage base associated with that point in the system. For example, for V base in the 220 kV area, the said base would be 220 squared, all over the MVA base and the current base with Be a KV a base all over 220. In the case of the V base equal to 22 kV, the Zed base would be 22 squared all over MVA base and the current would be kV a base over 22 similarily. The 11 kV base voltage would generate an impedance base of 11 squared over the MVA base, and the current would be the KV a base all over 11. And lastly, for the 110 kV base, the impedance space would be 110 squared over the MVA base and the current base would be kV a base all over 110. Now we can start to calculate the period Unit values for the system.

In Step four, the per unit quantities are calculated by dividing the actual value by its equivalent base value. Keeping in mind that the base values depend on their location in the system, whether you're in the in our example here the 22 kV, 11 kV or etc, then we must use the voltage MVA, the current the impedance bases that are associated with that location in the system. The per unit values are calculated by taking the actual value or quantity and dividing by its equivalent base quantity. Remember that we are dealing usually with With vectors or phasers, and the actual quantity is made up of a magnitude plus a direction or an angle, such as the, in this case, an MVA, and it's divided by just a magnitude. And if we put a place out equation, down, we see that the quantity MVA cancels out and you're left with a magnitude value that is usually less than one.

It's usually a decimal point. Number, the angle or the direction of the phasor and the per unit values are phasers or vectors. The actual angle or direction of that vector takes on the same direction or angle as the actual value. And these values are now designated as per unit values. So, if we look at each one of the per unit values that we're calculating in a system, keep in mind and it's worth repeating that it all depends on where you are in the system. At this point, it's assumed that all of the values of the system have been converted to per unit values.

Once you've converted everything to per unit values, you can then proceed to analyze the system in the way you want it to and come up with the the values that you've been looking for. But in this case, you're going to be doing it with per unit values and also of the formulas that you've used for analysis such as ohms law or, or kerchief swallows all of those still hold true for the per unit values, the only thing is that you're using per unit values. And that gives you a whole different look at the modeling of the system. In other words, one of the benefits of using per unit values is that you've, you're essentially removing the turns ratios of the Transformers that are in the system, which which make the analysis a whole lot easier. Once you've gone through all of your calculations using per unit values, you then would be looking for the actual values and the actual values, then, that you're looking for brings us to the fifth step of the normalization process.

Now if we want to step out of the system and go back to our original quantities, we have the fifth step that we take into consideration in the normalization process. For each component, its actual value may be found by multiplying its per unit quantity by the base value for that quantity at its connected location. So we have to take the equation that we use to calculate the per unit value and shift that around so that we can then calculate the actual quantity. And the actual quantity then is the per unit value times the base value. The normalization process has five steps. This takes you into the per unit system and the fifth step take you out of per unit system.

The first step in moving into the per unit system is to specify an MVA base. The second step is to determine the voltage base that you're going to use and then determine they've various voltage basis across the system depending on the ratios of the Transformers involved in the system, then determine the impedance basis and the current basis for each of the voltage basis. Next, you can determine what the per unit values are by taking the actual ohmic or or current or voltage value and dividing it by the base value. The last step then is to if you want to convert back out of the per unit system is step five. For each of the components, they may be calculated by taking the per unit value and then multiplying it by its base value and you will return to the actual value. This ends chapter three