Calculations are simplified because quantities expressed as per-unit do not change when they are referred from one side of a transformer to the other.
This can be a pronounced advantage in power system analysis where large numbers of transformers may be encountered.
Moreover, similar types of apparatus will have the impedances lying within a narrow numerical range when expressed as a per-unit fraction of the equipment rating, even if the unit size varies widely.
Conversion of per-unit quantities to volts, ohms, or amperes requires a knowledge of the base that the per-unit quantities were referenced to.
The per-unit system is used in power flow, short circuit evaluation, motor starting studies etc.
The main idea of a per unit system is to absorb large differences in absolute values into base relationships.
Thus, representations of elements in the system with per unit values become more uniform.
A per-unit system provides units for power, voltage, current, impedance, and admittance.
With the exception of impedance and admittance, any two units are independent and can be selected as base values; power and voltage are typically chosen.
Although power-system analysis is now done by computer, results are often expressed as per-unit values on a convenient system-wide base.
Generally base values of power and voltage are chosen.
The base power may be the rating of a single piece of apparatus such as a motor or generator.
The phase angles of complex power, voltage, current, impedance, etc., are not affected by the conversion to per unit values.
The purpose of using a per-unit system is to simplify conversion between different transformers.
Hence, it is appropriate to illustrate the steps for finding per-unit values for voltage and impedance.
First, let the base power (Sbase) of each end of a transformer become the same.
By convention, the following two rules are adopted for base quantities: With these two rules, a per-unit impedance remains unchanged when referred from one side of a transformer to the other.
As an example of how per-unit is used, consider a three-phase power transmission system that deals with powers of the order of 500 MW and uses a nominal voltage of 138 kV for transmission.
We then have: If, for example, the actual voltage at one of the buses is measured to be 136 kV, we have: The following tabulation of per-unit system formulas is adapted from Beeman's Industrial Power Systems Handbook.
It can be shown that voltages, currents, and impedances in a per-unit system will have the same values whether they are referred to primary or secondary of a transformer.
(source: Alexandra von Meier Power System Lectures, UC Berkeley) E1 and E2 are the voltages of sides 1 and 2 in volts.
(source: Alexandra von Meier Power System Lectures, UC Berkeley) where I1,pu and I2,pu are the per-unit currents of sides 1 and 2 respectively.
In this, the base currents Ibase1 and Ibase2 are related in the opposite way that Vbase1 and Vbase2 are related, in that The reason for this relation is for power conservation The full load copper loss of a transformer in per-unit form is equal to the per-unit value of its resistance:
Therefore, it may be more useful to express the resistance in per-unit form as it also represents the full-load copper loss.
By convention, a single base power (Sbase) is chosen for both sides of the transformer and its value is equal to the rated power of the transformer.
By choosing the base quantities in this manner, the transformer can be effectively removed from the circuit as described above.
For example: Take a transformer that is rated at 10 kVA and 240/100 V. The secondary side has an impedance equal to 1∠0° Ω.
The base impedance on the secondary side is equal to:
The base impedance for the primary side is calculated the same way as the secondary:
This becomes especially useful in real life applications where a transformer with a secondary side voltage of 1.2 kV might be connected to the primary side of another transformer whose rated voltage is 1 kV.