WOLFRAM SYSTEM MODELER

## PhaseOrientationOrientation of phases |

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`SystemModel["Modelica.Electrical.Polyphase.UsersGuide.PhaseOrientation"]`

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This information is part of the Modelica Standard Library maintained by the Modelica Association.

**In polyphase systems, the angular displacement of voltages and currents of the phases as well as the spatial displacement of machine windings have to follow the same rules, i.e., they are based on the same
orientation function.**

A symmetrical three-phases system consists of three sinusoidal sine waves with an angular displacement of 2 π / 3.

In symmetrical polyphase systems odd and even phase numbers have to be distinguished.

For a symmetrical polyphase system with m phases the displacement of the sine waves is 2 π / m.

In case of an even number of phases the aligned orientation does not add any information. Instead the m phases are divided into two or more different groups (the base systems).

The number of phases m can be divided by 2 recursively until the result is either an odd number or 2. The result of this division is called m_{Base}, the number of phases of the base system.
The number of base systems n_{Base} is defined by the number of divisions, i.e., m = n_{Base} * m_{Base}.

For a base system with m_{Base} phases the displacement of the sine waves belonging to that base system is 2 π / m_{Base}.

The displacement of the base systems is defined as π / n_{Base}.

In array or matrices, the base systems are stored one after another.

For each base system of time phasors, symmetrical components can be calculated according to the idea of Charles L. Fortescue.

The first symmetrical component is the direct component with positive sequence.

In case of m_{Base} = 2, the second component is the inverse component with negative sequence.

In case of m_{Base} > 2, the components [2..m_{Base} - 1] are components with non-positive sequence,

and the last component [m_{Base}] is the zero sequence component.

This set of symmetrical components is repeated for each of the n_{Base} base systems.

For polyphase systems, star connection of the m phases is unambiguous, i.e., each pin of the plug is connected to the starpoint pin,
whereas for polygon connection (m_{Base} - 1)/2 alternatives exist (refer to Fig. 3).

2 phase system | 2 = 2 x 2 phase system |

3 phase system | 6 = 2 x 3 phase system |

5 phase system: 2 alternative polygon connections | 7 phase system: 3 alternative polygon connections |

Therefore, using the MultiDelta component, the alternative has to be specified by the parameter kPolygon.

User's guide on polyphase winding.