SimPowerSystems

Linear Transformer

Implement a two-winding or three-winding linear transformer

Library

Elements

Description

The Linear Transformer block model shown consists of three coupled windings wound on the same core.

The model takes into account the winding resistances (R1 R2 R3) and the leakage inductances (L1 L2 L3), as well as the magnetizing characteristics of the core, which is modeled by a linear (Rm Lm) branch.

The Per Unit Conversion

In order to comply with industry, you must specify the resistance and inductance of the windings in per unit (p.u.). The values are based on the transformer rated power Pn, in VA, nominal frequency fn, in Hz, and nominal voltage Vn, in Vrms, of the corresponding winding. For each winding, the per unit resistance and inductance are defined as

The base resistance and base inductance used for each winding are

For the magnetization resistance Rm and inductance Lm, the p.u. values are based on the transformer rated power and on the nominal voltage of winding 1.

For example, the default parameters of winding 1 specified in the dialog box section give the following bases:

Suppose that the winding 1 parameters are R1 = 1.44 and L1 = 0.1528 H; the corresponding values to be entered in the dialog box are

To specify a magnetizing current of 0.2% (resistive and inductive) based on nominal current, you must enter per unit values of 1/0.002 = 500 p.u. for the resistance and the inductance of the magnetizing branch. Using the base values calculated previously, these per unit values correspond to Rm = 8.6e5 ohms and Lm = 995 henries.

Dialog Box and Parameters

Nominal power and frequency

The nominal power rating Pn in volt-amperes (VA) and frequency fn, in hertz (Hz), of the transformer.

Winding 1 parameters

The nominal voltage V, in volts RMS, resistance, and leakage inductance in p.u. The p.u. values are based on the nominal power Pn and on V1.

Winding 2 parameters

The nominal voltage V2 in volts RMS, resistance, and leakage inductance in p.u. The p.u. values are based on the nominal power Pn and on V2.

Three windings transformer

If selected, implements a linear transformer with three windings; otherwise, it implements a two-windings transformer.

Winding 3 parameters

The Winding 3 parameters parameter is not available if the Three windings transformer parameter is not selected.

The nominal voltage in volts RMS (Vrms), resistance, and leakage inductance in p.u. The p.u. values are based on the nominal power Pn and on V3.

Magnetization resistance and reactance

The resistance and inductance simulating the core active and reactive losses, both in p.u. The p.u. values are based on the nominal power Pn and on V1. For example, to specify 0.2% of active and reactive core losses, at nominal voltage, use Rm = 500 p.u. and Lm = 500 p.u.

Measurements

Select Winding voltages to measure the voltage across the winding terminals of the Linear Transformer block.

Select Winding currents to measure the current flowing through the windings of the Linear Transformer block.

Select Magnetization current to measure the magnetization current of the Linear Transformer block.

Select All voltages and currents to measure the winding voltages and currents plus the magnetization current.

Place a Multimeter block in your model to display the selected measurements during the simulation.

In the Available Measurements list box of the Multimeter block, the measurements are identified by a label followed by the block name.

Measurement	Label
Winding voltages	Uw1:, Uw2:, Uw3:
Winding currents	Iw1:, Iw2:, Iw3:
Magnetization current	Imag:

Note    To implement a quasi-ideal transformer model, set the winding resistances and inductances to 0, and the magnetization inductance Lm to inf. The Rm value must have a finite value. Use a large value such as 1e4 (0.01% losses).

Limitations

Windings can be left floating (that is, not connected to the rest of the circuit). However, an internal resistor is automatically added between the floating winding and the main circuit. This internal connection does not affect voltage and current measurements.

Example

The power_transformer demo shows a typical residential distribution transformer network feeding line-to-neutral and line-to-line loads.

See Also

Mutual Inductance, Saturable Transformer, Three-Phase Transformer (Two Windings), Three-Phase Transformer (Three Windings)

Impedance Measurement

Machine Measurement Demux