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Topic 3: Change of Base Values in Per-Unit Systems, Part 3a.
In the previous topics, we introduced per-unit systems and discussed their advantages in detail.
In this Topic, we will be discussing a crucial aspect of per-unit systems that is the changes in base values.
In this video Part 3a, we will derive a formula that will come handy in complex analysis of power systems.
Until now, we have looked into examples and problems that involve a single base value for the entire power system.
But what if the different regions in a power system have varying base values?
For example, the generator side would be working on 200MVA base power,
the transmission line has base power of 50MVA and the base power of the load side is 100MVA.
Such types of power systems require the selection of one base value for the whole power system
and also require conversion of different bases to the selected one.
And same goes for the other quantities involved.
We know that when we convert a power system into its per-unit equivalent,
we find out per-unit impedances according to the selected base value.
Now, we will derive the formula for calculating a new per-unit impedance if the selected base value is different from the given one.
The general formula that is used to calculate per-unit impedance is:
Z per unit is equal to the Z actual impedance divided by the Z base impedance.
We know that the actual impedance remains the same no matter what the base is.
So, by rearranging the above equation we get:
Z actual is equal to Z per unit times Z base.
For a given base value we can write this equation as:
Z actual is equal to Z per unit given times Z base given.
If we want to calculate the per-unit impedance according to a new base value, we can then write the formula as this:
Z per unit new is equal to the Z actual divided by the Z base new
and that is equal to Z per unit given times Z base given divided by Z base new.
From our previous videos, we know that: Base impedance is equal to base voltage squared divided by the base power.
So Z base given is equal to V base given squared divided by S base given.
And Z base new is equal to V base new squared divided by S base new.
Putting these equations to find out Z per unit new, what we get is this:
Z per unit new is equal to Z per unit given multiplied by V base given squared divided by S base given.
And the whole thing divided by V base new squared over S base new.
Rearranging the above equation, we get this:
Z per unit new is equal to Z per unit given times V base given squared divided by V base new squared times S base new over S base given.
So, finally we have derived a complete formula that will aid us in tackling varying bases in a power system.
We can use this formula to calculate new per-unit impedances and hence make a per-unit equivalent model of a power system.
In the next video we will solve an example from the book that incorporates the above formula so that we can have a clear concept in our
minds. We hope, you have a continued interest in this topic and series as a student or professional.
We also hope you find this content useful and enlightening.
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