PER UNIT CALCULATIONS
A. Single Phase
Per unit system is a method of doing calculations for electric circuits that eliminates the necessity of voltage and current transformation in circuits with many voltage levels. All quantities in a circuit are expressed as a decimal fraction of chosen base quantities.
The base quantities must be chosen so that they satisfy the basic relationships as the actual quantities (i.e. the Ohm’s law and the power relationship). The per unit value of any quantity is then defined as
For example, voltage, impedance, and current are related through
If the base quantities satisfy the same relationship,
and we divide the equation with the base quantities into the equation with the actual quantities, we get
or
The same is true for other relationships between voltage, current, power, and impedance. This implies that we can do circuit analysis using the per unit equations exactly as we would do it using the actual quantities. Since the actual quantities are complex numbers and the base quantities are real numbers, the phase relationships of the per unit quantities are exactly the same as of the actual quantities.
The per unit quantities are defined
When there are transformers in the circuit, the base voltages on both sides of the transformer must be different and must be in the same ratio as the actual transformer voltages.
If
then
and
The per unit values for voltage, current and impedance are then
This eliminates the transformation. In per unit system, the equivalent circuit for a transformer is an impedance. There is no voltage and current transformation.
B. Change of Base
Manufacturers give the impedance of equipment in per unit on own base. That means that the values chosen for the base are the equipment rated values for power, voltage, and current. Power utilities choose their own values for the base for their calculations. That means that the various bases used for the equipment must be all changed to the one base that the power utility is using.
Let us assume that we want to convert from base values of system 1 to base values of system 2. The value that is constant is the ohmic value for the impedance
C. Three Phase
The three phase circuits are reduced to single phase impedance diagrams. The basic relationships between all quantities must hold, and the same is true for the base value for the three phase and the single phase quantities.
The impedances are always given per phase, so there is no change in treatment of Y connected impedances. If a load is connected in D , we define a base D impedance so that the per unit impedance is the same regardless of the connection
