Per-unit system

The per-unit system , abbreviated pu , is an auxiliary unit of measurement related to a reference value in electrical power engineering . It is used to express electrical information as a relative and dimensionless pu value and thus enable easier comparisons of relevant electrical parameters in power grids . In contrast to the dimensionless and logarithmic level specifications , which are used in the field of communications technology and are expressed, for example, as Bel , the pu specification is linear.

The per-unit system is used for power specifications such as the specification of active and apparent powers , as well as for specifications of electrical voltages and impedances . When specifying a value, the reference value and its dimension are essential.

Applications are in the load flow calculation or in single-line diagrams . The essential parameters such as load flows or impedances of power transformers and rotating electrical machines are entered as relative pu information.

purpose

There are several reasons for using the per-unit system:

• Equipment used in a power range, such as generators , transformers or high-voltage lines, have similar parameters such as impedances, power data or loss data. Due to the relative reference in the pu system, the absolute size does not matter.
• In energy networks that are operated with three-phase alternating current , the concatenation factor is included in the reference value, which means that information such as power specifications for single-phase systems and three-phase systems can be compared directly without a conversion factor. ${\displaystyle {\sqrt {3}}}$
• With the appropriate selection, details in the per-unit system are independent of specific impedances or operating voltages and are directly comparable on both sides of a power transformer.
• The reference of the sizes to a common basis simplifies the manual rough calculation above all.

Underlyings

The base values ​​are arbitrarily chosen in the same order of magnitude as the values ​​set in relation to them. Round values ​​are common. For power specifications, such as the basis of the apparent power S _B , reference values ​​of 1 MVA , 10 MVA, 100 MVA or 1 GVA are selected depending on the application  . The nominal voltage such as 110  kV or 400 kV is usually selected for the reference voltage U _B. The reference value for the current I _B then results:

${\displaystyle I_{\text{B}}={\frac {S_{\text{B}}}{U_{\text{B}}}}}$

and for the reference value of the impedance Z _B :

${\displaystyle Z_{\text{B}}={\frac {U_{\text{B}}^{2}}{S_{\text{B}}}}}$

In three-phase systems, the values ​​of the individual strings such as string voltage and string current are generally used, which means that in three-phase systems the reference values ​​are to be divided by the concatenation factor of . Performance data are to be divided by a factor of 3. ${\displaystyle {\sqrt {3}}}$

The complex representation usual in the complex AC calculation is also possible in the per-unit system: The amounts of the complex quantities in the polar form are divided by the reference values, the angles remain unchanged.

example

An overhead line for 400 kV in a three-phase system is designed for the transmission of 1,200 MVA. The two reference values ​​are chosen as:

${\displaystyle S_{\text{B}}={\frac {1200\,\mathrm {MVA} }{3}}=400\,\mathrm {MVA} }$

${\displaystyle U_{\text{B}}={\frac {400\,\mathrm {kV} }{\sqrt {3}}}\approx 231\,\mathrm {kV} }$

With a short-term increase in output to 2,100 MVA, the voltage drops to 390 kV. In the pu system, this corresponds to:

${\displaystyle S_{\text{pu}}={\frac {2100\,\mathrm {MVA} }{3\cdot S_{\text{B}}}}=1{,}75\,\mathrm {pu} }$

${\displaystyle U_{\text{pu}}={\frac {390\,\mathrm {kV} }{{\sqrt {3}}\cdot U_{\text{B}}}}=0{,}975\,\mathrm {pu} }$

credentials

• Jr William D. Stevenson: Elements of Power System Analysis Third Edition . McGraw-Hill, New York 1975, ISBN 0-07-061285-4 .
• BM Weedy: Electric Power Systems Second Edition . John Wiley and Sons, London 1972, ISBN 0-471-92445-8 .