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In power systems, expression of system quantities as fractions

In the power systems analysis field of electrical engineering, a per unit system is the expression of system quantities as fractions of a defined base unit quantity. 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. All quantities are specified as multiples of selected base values. For example, the base power might be the rated power of a transformer, or perhaps an arbitrarily selected power which makes power quantities in the system more convenient. The base voltage might be the nominal voltage of a bus. Different types of quantities are labeled with the same symbol (pu); it should be clear whether the quantity is a voltage, current, or other unit of measurement.

The relationship between units in a per unit system depends on whether the system is single phase or three phase.

Power and voltage are specified in the same way as single phase systems. However, due to differences in what these terms usually represent in three phase systems, the relationships for the derived units are different. Specifically, power is given as total (not per phase) power, and voltage is line to line voltage. In three phase systems the equations and also hold. The apparent power now equals

The following tabulation of per unit system formulas is adapted from Beeman's Industrial Power Systems Handbook. Equation Base number selection Arbitrarily selecting from ohm's law the two base numbers: base voltage and base current 1 2 3 4 5 Alternatively, choosing base volts and base kva values, we have, in single phase systems: 6 7 8 and in three phase systems: 9 10 11 Working out for convenience per unit ohms directly, we have for single phase and three phase systems: 12 Short Circuit Calculation Formulas Ohms conversions: 13 14 15 Changing ohms from one kva base to another: 16 17 Changing incoming system reactance: a. If system reactance is given in percent, use Eq. 16 to change from one kva base to another. b. If system reactance is given in short circuit symmetrical rms kva or current, convert to per unit as follows: 18 19 Calculating approximate motor kva base: a. For induction motors and 0.8 power factor synchronous motors 20 b. For unity power factor synchronous motors 21 Converting ohms from one voltage to another: 22 Short circuit kva and current calculations Symmetrical short circuit kva: 23 24 25 26 Symmetrical short circuit current: 27 28 29 Asymmetrical short circuit current and kva: 30 31