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3-Winding 3-Phase Transformers

Purpose

Three-phase transformers in Ydy and Ydz connection.

Library

3-Phase Transformers

Description

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This group of components implements three-winding, three-phase transformers with a three-leg or five-leg core. The transformer core is assumed symmetrical, i.e. all phases have the same parameters. The primary winding is in star connection with an accessible neutral point and the secondary winding is in delta connection. Depending on the chosen component, the tertiary winding is wired either in star (y) or zig-zag (z) connection.

The phase angle difference between the primary and the secondary side must be an odd integer multiple of 30∘ . If the tertiary winding is in star connection the phase lag against the primary side must be an integer multiple of 60∘ . If it is in zig-zag connection, the phase lag can be chosen arbitrarily. The windings of the secondary and tertiary side are allocated to the transformer legs according to the phase lags. Please note that the phase-to-phase voltage of delta windings is by a factor of 1∕√3   lower than the voltage of star or delta windings if the number of turns are equal.

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The core saturation characteristic of the transformer legs is piece-wise linear. The magnetizing current im   and flux Ym   value pairs are referred to the primary side. To model a transformer without saturation enter 1 as the magnetizing current values and the desired magnetizing inductance Lm   as the flux values. A stiff Simulink solver is recommended if the iron losses are not negligible, i.e. Rfe   is not infinite.

Parameters and Dialog Box

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Leakage inductance
A three-element vector containing the leakage inductance of the primary side L1  , the secondary side L2   and the tertiary side L3  . The inductivity is given in henries (H).
Winding resistance
A three-element vector containing the resistance of the primary winding R1  , the secondary winding R2    and the tertiary winding R3  , in ohms (_O_  ).
No. of turns
A three-element vector containing the number of turns of the primary winding n1  , the secondary winding n2   and the tertiary winding n3  .
Magnetizing current values
A vector of positive current values in amperes (A) defining the piece-wise linear saturation characteristic of the transformer legs. The current values must be positive and strictly monotonic increasing. At least one value is required.
Magnetizing flux values
A vector of positive flux values in Vs defining the piece-wise linear saturation characteristic. The flux values must be positive and strictly monotonic increasing. The number of flux values must match the number of current values.
Core loss resistance
An equivalent resistance Rfe   representing the iron losses in the transformer core. The value in ohms (_O_  ) is referred to the primary side.
No. of core legs
The number of legs of the transformer core. This value may either be 3 or 5.
Phase lag of secondary side
The phase angle between the primary side and the secondary side, in degrees. Unless the secondary side is in zig-zag connection, the angle can only be varied in steps of 60∘ .
Initial currents wdg. 1
A vector containing the initial currents on the primary side i1,a  , i1,b   and i1,c  . The currents are given in amperes (A) and considered positive if flowing into the transformer. The default is [0 0 0].
Initial currents wdg. 2
A vector containing the initial currents on the secondary side i2,a    and i2,b  . The currents are given in amperes (A) and considered positive if flowing into the transformer. The default is [0 0 0].
Initial currents wdg. 3
A vector containing the initial currents on the tertiary side i3,a  , i3,b   and i3,c  . The currents are given in amperes (A) and considered positive if flowing into the transformer. The default is [0 0 0].