Saturable Transformers

Purpose

Single-phase transformers with two resp. three windings and core saturation

Library

Electrical / Passive Components

Description

These transformers model two or three coupled windings on the same core.

Fig. 217 Magnetizing inductance saturation characteristic

The core saturation characteristic (Fig. 217) 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.

In the transformer symbol, the primary side winding is marked with a little circle. The secondary winding is marked with a dot at the outside terminal, the tertiary winding with a dot at the inside terminal.

Parameters

Leakage inductance

A vector containing the leakage inductance of the primary side \(L_1\), the secondary side \(L_2\) and, if applicable, the tertiary side \(L_3\). The inductivity is given in henries \((\mathrm{H})\).

Winding resistance

A vector containing the resistance of the primary winding \(R_1\), the secondary winding \(R_2\) and, if applicable, the tertiary winding \(R_3\), in ohms \((\Omega)\).

No.of turns

A vector containing the number of turns of the primary winding \(n_1\), the secondary winding \(n_2\) and the tertiary winding \(n_3\), if applicable.

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.

Initial current

A vector containing the initial currents on the primary side \(i_1\), the secondary side \(i_2\) and the tertiary side \(i_3\), if applicable. The currents are given in amperes \((\mathrm{A})\) and considered positive if flowing into the transformer at the marked terminals. The default is [0 0 0].