SIMPLORER User Manual V6.0 - FER-a

4.8 Transformers
• Single-Phase Systems
• Three-Phase Systems
SIMPLORER 6.0 — Manual 187
SIMPLORER Transformer Models According to Spiro
Transformer components, available in the Circuit folder of the «Basics» tab, are based on the
Spiro model, which is characterized by any energy flow direction, a free number of galvanically
separate windings, the exclusion of DC-current transmission and the consideration of losses.
In the Spiro model, every limb of the transformer is represented by one inductance. Each
winding, that influences the flux through the limb, contributes to the current flowing through
the inductance. Usually the ratio flux/current is different for the winding of the limb because
of different numbers of turns or, in the case of a three-phase transformers, different positions
of the windings. The current of only one winding can flow directly through the inductance.
The other windings contribute by coupling factors.
Single Phase
The circuit shows the equivalent circuit for a single phase transformer. The current through
the primary winding contributes directly to the current through the main inductance. Therefore
the main inductance is calculated with respect to the primary winding.
Because of primary and secondary side stray inductances coupling factors are introduced. The
coupling factor for the secondary side is determined by the ratio of the number of turns only.
Therefore the current through the secondary winding controls the current source at the primary
side with the control factor KTR which is the number-of-turns ratio.
The same relationships apply for the voltage induced at primary and secondary side respectively.
Since the main inductance is calculated for the primary winding and its current is calculated
with respect to the primary side, the induced voltage at the primary side equals the
voltage across the main inductance. The induced voltage at the secondary side equals the
voltage across the main inductance multiplied by the number-of-turns ratio KTR.
Model Extension for Three-Phase Systems
To model a three-phase system, the coupling between all six windings has to be considered.
The model for the single-phase transformer has to be used three times. For every phase the
influence of two more primary windings and two more secondary windings has to be modeled.
This influence is modeled as for the single-phase transformer using controlled current and
voltage sources.