Modelica.Electrical.Polyphase.UsersGuide

This library contains components for modelling of polyphase electrical circuits. The number of phases m is not restricted to three. The connector (named plug) contains an array of m single-phase pins. Most of the components use an array of single-phase components from Modelica.Electrical.Analog.

Note

For the orientation of an arbitrary number of phases m > 3, see the phase orientation concept.

Extends from Modelica.Icons.Information (Icon for general information packages).

Package Content

Name	Description
PhaseOrientation	Orientation of phases
Contact	Contact
ReleaseNotes	Release Notes
References	References

Modelica.Electrical.Polyphase.UsersGuide.PhaseOrientation

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.

Symmetrical three-phase system

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

Symmetrical polyphase system

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

Odd number of phases

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

Fig. 1: Symmetrical (a) three-phase and (b) five-phase current system

Even number of phases

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.

Fig. 2: Symmetrical (a) six and (b) ten phase current system

The displacement of the base systems is defined as π / n_Base.

Note

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

Symmetrical components

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.

Polygon connection

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).

Fig. 3: Line-to-neutral voltages and line-to-line voltages for different systems

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.

See also

User's guide on polyphase winding.

Extends from Modelica.Icons.Information (Icon for general information packages).

Modelica.Electrical.Polyphase.UsersGuide.Contact

Main authors

Dr. Christian Kral
Electric Machines, Drives and Systems
1060 Vienna, Austria
email: dr.christian.kral@gmail.com

Anton Haumer
Technical Consulting & Electrical Engineering
D-93049 Regensburg, Germany
email: a.haumer@haumer.at

Extends from Modelica.Icons.Contact (Icon for contact information).

Modelica.Electrical.Polyphase.UsersGuide.ReleaseNotes

Version 3.2.3, 2019-01-23 (Anton Haumer, Christian Kral)

• Shortened default component names, see #2301
• Removed redundant (and not identical) parameter m from MutualInductor, see #2202
• Changed epsilon from constant to parameter in MutualInductor, see #2200
• Added User's Guide
• Added blocks and functions for multiple base systems

Version 1.4.0, 2009-08-26 (Anton Haumer)

• Added conditional HeatPorts as in Electrical.Analog
• Added switches with arc as in Electrical.Analog

Version 1.3.2, 2007-08-24 (Anton Haumer)

• Removed redeclare type SignalType

Version 1.3.1, 2007-08-12 (Anton Haumer)

• Improved documentation

Version 1.3.0, 2007-01-23 (Anton Haumer)

• Improved some icons

Version 1.2, 2006-07-05 (Anton Haumer)

• Removed annotation from pin of Interfaces.Plug
• Corrected usage of resistance/conductance

Version 1.1, 2006-01-12 (Anton Haumer)

• Added Sensors.PowerSensor

Version 1.0, 2004-10-01 (Anton Haumer)

• Initial release version

Extends from Modelica.Icons.ReleaseNotes (Icon for release notes in documentation).

Modelica.Electrical.Polyphase.UsersGuide.References

Extends from Modelica.Icons.References (Icon for external references).