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.
Purpose There are several reasons for using a per-unit system:
Similar apparatus (generators, transformers, lines) will have similar per-unit impedances and losses expressed on their own rating, regardless of their absolute size. Because of this, per-unit data can be checked rapidly for gross errors. A per unit value out of normal range is worth looking into for potential errors. Manufacturers usually specify the impedance of apparatus in per unit values. Use of the constant 3 {\displaystyle \textstyle {\sqrt {3}}} is reduced in three-phase calculations. Per-unit quantities are the same on either side of a transformer, independent of voltage level By normalizing quantities to a common base, both hand and automatic calculations are simplified. It improves numerical stability of automatic calculation methods. Per unit data representation yields important information about relative magnitudes. The per-unit system was developed to make manual analysis of power systems easier. Although power-system analysis is now done by computer, results are often expressed as per-unit values on a convenient system-wide base.
Base quantities 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. If a system is being studied, the base power is usually chosen as a convenient round number such as 10 MVA or 100 MVA. The base voltage is chosen as the nominal rated voltage of the system. All other base quantities are derived from these two base quantities. Once the base power and the base voltage are chosen, the base current and the base impedance are determined by the natural laws of electrical circuits. The base value should only be a magnitude, while the per-unit value is a phasor. 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. Once every S is set on the same base, the base voltage and base impedance for every transformer can easily be obtained. Then, the real numbers of impedances and voltages can be substituted into the per-unit calculation definition to get the answers for the per-unit system. If the per-unit values are known, the real values can be obtained by multiplying by the base values. By convention, the following two rules are adopted for base quantities:
The base power value is the same for the entire power system of concern. The ratio of the voltage bases on either side of a transformer is selected to be the same as the ratio of the transformer voltage ratings. With these two rules, a per-unit impedance remains unchanged when referred from one side of a transformer to the other. This allows the ideal transformer to be eliminated from a transformer model.
Relationship between units The relationship between units in a per-unit system depends on whether the system is single-phase or three-phase.
Single-phase Assuming that the independent base values are power and voltage, we have:
P base = 1 pu {\displaystyle P_{\text{base}}=1{\text{ pu}}}
V base = 1 pu {\displaystyle V_{\text{base}}=1{\text{ pu}}}
Alternatively, the base value for power may be given in terms of reactive or apparent power, in which case we have, respectively,
Q base = 1 pu {\displaystyle Q_{\text{base}}=1{\text{ pu}}}
or
S base = 1 pu {\displaystyle S_{\text{base}}=1{\text{ pu}}}
… excerpt ends here. Continue reading the full article.
