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# System Units | PU Definition

**P.U. = Per-Unit Quantity**

Power transmission lines are operated at voltage levels where the kilovolt is the most convenient unit to express voltage. Because of the large amount of power transmitted, kilowatts or megawatts and kilovolt-amperes or megavolt-amperes are the common terms. However, these quantities as well as amperes and ohms are often expressed as percent per unit of a base or reference value specified for each. For instance, if a base voltage of 120 kV is chosen, voltages of 108, 120 and 126 kV become 0.90, 1.00 and 1.05 PU or 90, 100, and 105% respectively.

The per-unit value of any quantity is defined as the ratio of the quantity to its base value expressed as a decimal. The quantity in percent is 100 times the value in per-unit. Both the percent and the per-unit methods of calculation are simpler than the use of the actual amperes, ohms, and volts. The per-unit method has an advantage over the percent method because the product of two quantities is expressed in per-unit itself, but the product of two quantities expressed in percent must be divided by 100 to obtain the result in percent.

Voltage, current, kilovolt-amperes and impedance are so related that selection of base values for any two of them determines the base values of the remaining two. If the base values of the current and voltage would be specified, base impedance and base kilovolt-amperes can be determined. The base impedance is that impedance which will have a voltage drop across it equal to the base voltage when the current flowing in the impedance is equal to the base value of the current.

The base kilovolt-ampere in single-phase systems is the product of base voltage in kilovolts and base current in amperes. Usually base megavolt-amperes and base voltage in kilovolts are the quantities selected to specify the base references. For single-phase systems or three-phase systems where the term current refers to line current, where the term voltage refers to voltage to neutral, and where the term kilovolt-amperes refers to kilovolt-amperes per phase, the following formulas relate the various quantities:

The conversion can be calculated as follows:

1 | Base current (A) = Base phase power [kVA] / Base voltage [kV_{LN}] |
---|---|

2 | Base impedance = Base voltage [(V_{LN}] / Base current [A] |

3 | Base impedance = (Base voltage [kV_{LN}])^{2} x 1000 / Base phase power [kVA] |

4 | Base impedance = (Base voltage [kV_{LN}])^{2} / Base phase power [MVA] |

5 | Base phase power [kW] = Base phase power [kVA] |

6 | Base phase power [mW] = Base phase power [mVA] |

7 | Per unit impedance of a circuit element = Actual impedance (Ω) / Base impedance (Ω) |

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