Library for technical 3phase transformers

Package Contents


Transformers: primary Y / secondary y


Transformers: primary Y / secondary d


Transformers: primary Y / secondary zig-zag


Transformers: primary D / secondary y


Transformers: primary D / secondary d


Transformers: primary D / secondary zig-zag


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

This package contains components to model technical three-phase transformers:
  • Transformer: transformer model to choose connection / vector group
  • Yy: Transformers with primary Y / secondary y
  • Yd: Transformers with primary Y / secondary d
  • Yz: Transformers with primary Y / secondary zig-zag
  • Dy: Transformers with primary D / secondary y
  • Dd: Transformers with primary D / secondary d
  • Dz: Transformers with primary D / secondary zig-zag

Transformers are modeled by an ideal transformer, adding primary and secondary winding resistances and stray inductances.
All transformers extend from the base model PartialTransformer, adding the primary and secondary connection.
VectorGroup defines the phase shift between primary and secondary voltages, expressed by a number phase shift/30 degree (i.e., the hour on a clock face). Therefore each transformer is identified by two characters and a two-digit number, e.g., Yd11 ... primary connection Y (star), secondary connection d (delta), vector group 11 (phase shift 330 degree)
With the "supermodel" Transformer the user may choose primary and secondary connection as well as the vector group.
It calculates winding ratio as well as primary and secondary winding resistances and stray inductances, distributing them equally to primary and secondary winding, from the following parameters:

  • nominal frequency
  • primary voltage (RMS line-to-line)
  • secondary voltage (RMS line-to-line)
  • nominal apparent power
  • impedance voltage drop
  • short-circuit copper losses
The impedance voltage drop indicates the (absolute value of the) voltage drop at nominal load (current) as well as the voltage we have to apply to the primary winding to achieve nominal current in the short-circuited secondary winding.

Please pay attention to proper grounding of the primary and secondary part of the whole circuit.
The primary and secondary starpoint are available as connectors, if the connection is not delta (D or d).
In some cases (Yy or Yz) it may be necessary to ground one of the transformer's starpoints even though the source's and/or load's starpoint are grounded; you may use a reasonable high earthing resistance.

Limitations and assumptions:
  • number of phases is limited to 3, therefore definition as a constant m=3
  • symmetry of the three phases resp. limbs
  • saturation is neglected, i.e., inductances are constant
  • magnetizing current is neglected
  • magnetizing losses are neglected
  • additional (stray) losses are neglected
Further development:
  • modeling magnetizing current, including saturation
  • temperature dependency of winding resistances
Main Authors:
Anton Haumer
Technical Consulting & Electrical Engineering
D-93049 Regensburg
email: a.haumer@haumer.at

Wolfram Language



  • v1.0.0 2006/11/19 Anton Haumer
    first stable release
  • v2.2.0 2011/02/10 Anton Haumer
    conditional ThermalPort for all machines