Transformers (3ph, 2 Windings)

Purpose

3-phase transformers in Yy, Yd, Yz, Dy, Dd and Dz connection

Library

Electrical / Transformers

Description

This group of components implements two-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. Depending on the chosen component, the windings are wired in star (Y) or delta (D) connection on the primary side. On the secondary side, the windings are either in star (y), delta (d) or zig-zag (z) connection. Star and zig-zag windings have an accessible neutral point.

The phase angle difference between the primary and the secondary side can be chosen. For Yy and Dd connections, the phase lag must be an integer multiple of \(60\,^\circ\). For Yd and Dy connections the phase lag must be an odd integer multiple of \(30\,^\circ\). The phase lag of zig-zag windings can be chosen arbitrarily. The windings of the secondary side are allocated to the transformer legs according to the phase lag. Please note that the phase-to-phase voltage of delta windings is by a factor of \(1/\sqrt{3}\) lower than the voltage of star or delta windings if the number of turns are equal.

Fig. 218 Transformer core saturation characteristic

The core saturation characteristic of the transformer legs (Fig. 218) is piece-wise linear and is modeled using the Saturable Inductor. The magnetizing current \(i_\mathrm{m}\) and flux \(\Psi_\mathrm{m}\) 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 \(L_\mathrm{m}\) as the flux values. A stiff Simulink solver is recommended if the iron losses are not negligible, i.e. \(R_\mathrm{fe}\) is not infinite.

Parameters

Leakage inductance

A two-element vector containing the leakage inductance of the primary side \(L_1\) and the secondary side \(L_2\). The inductivity is given in henries \((\mathrm{H})\).

Winding resistance

A two-element vector containing the resistance of the primary winding \(R_1\) and the secondary winding \(R_2\), in ohms \((\Omega)\).

No. of turns

A two-element vector containing the number of turns of the primary winding \(n_1\) and the secondary winding \(n_2\).

Magnetizing current values

A vector of positive current values in amperes \((\mathrm{A})\) 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 \((\mathrm{Vs})\) 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 \(R_\mathrm{fe}\) representing the iron losses in the transformer core. The value in ohms \((\Omega)\) 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. In a three phase transformer with 3 legs the sum of the fluxes in the three phases must add up to zero. This constraint is modeled with auxiliary windings on each core, which are connected in series. A 5-leg transformer on the other hand is similar to three uncoupled single-phase transformers. Therefore, the constraint does not apply and the auxiliary windings are deactivated.

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 \(60\,^\circ\).

Initial currents wdg. 1

A vector containing the initial currents on the primary side \(i_{1, \mathrm{a}}\), \(i_{1, \mathrm{b}}\) and, if the winding has a neutral point, \(i_{1, \mathrm{c}}\). The currents are given in amperes \((\mathrm{A})\) and considered positive if flowing into the transformer. The default is [0 0], or [0 0 0] in the presence of a neutral point.

Initial currents wdg. 2

A vector containing the initial currents on the secondary side \(i_{2, \mathrm{a}}\), \(i_{2, \mathrm{b}}\) and, if the winding has a neutral point, \(i_{2, \mathrm{c}}\). The currents are given in amperes \((\mathrm{A})\) and considered positive if flowing into the transformer. The default is [0 0], or [0 0 0] in the presence of a neutral point.