per unit system calculation method

Per unit and percentage quantities, In this article you will learn what is per unit system? Why we need to used per unit system in power system? How to convert actual values to per unit values? And formula’s of per unit system.

When a fault occurs, abnormal currents flow through the system. These currents are detected with the help of protective gear and are stopped by circuit breaker. These currents must be known in order to select the suitable rating of circuit breakers , design of the components to be used and relay settings. For easier calculations of an electrical system, the quantities are represented in their base units or per units. The formulas are given as follows:




Per unit value of voltage= Actual value of voltage/ base value of voltage

Percentage value of voltage= per unit value x 100

Base current= Base KVA/ Base Voltage   (Amperes)

Base Impedance= Base voltage(volts)/ Base current(amperes)    (ohms)




Base impedance= (Base KV)2 x 1000/ Base KVA    (ohms)

Per unit impedance= Zpu= Actual impedance/ Base impedance   (ohms)

PU current= Actual current/ Base Current

For three phase:

Base current= Base KVA/ √3 x Base voltage in KV   (amperes)

Advantages of per unit and percentage system:

  1. Simpler calculations.
  2. Manufactures usually mention pu values and comparison with other equipments also becomes easier.
  3. In a three phase system, irrespective of the connections of a transformer, the equivalent pu impedance is same.
  4. Micro machines represent the actual power system machines. This makes the research easy. These micro machines have the same pu values as the actual machines.
  5. In pu system, lines and phase values are same therefore there are less chances of error in a three phase system calculations.
  6. In a three phase transformer, whether the connections are in star or delta, the equivalent pu values are same.
  7. The transformer is represented by R+jX and magnetizing current is neglected. No pu voltage transformation occurs. By neglecting the magnetizing current, the transformer has same pu current values on both sides.

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