Linear Transformer (Power System Blockset)

Power System Blockset

Linear Transformer

Implement a two winding or three winding linear transformer.

Library

Elements

Description

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

The model takes into account the winding resistances (R1 R2 R3) 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 the industry practice, you must specify the resistance and inductance of the windings in per unit (pu). 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 nominal voltage of the winding one.

For example, the default parameters of winding one 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 above 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 (V.A) and frequency fn, in hertz (Hz), of the transformer.

Winding 1 parameters

The nominal voltage V1 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.

Winding 3 parameters

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.

Setting the Winding 3 parameters parameter to 0 implements a Linear Transformer block with two windings and a new icon will be displayed:

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 Measurement listbox of the Multimeter block, the measurements will identified by a label followed by the block name.


Measurement	Label
Winding voltages	`u w1: , u w2: , u w3:`
Winding currents	`i w1: , i w2: , i w3:`
Magnetization current	`i mag:`

Note To implement an ideal transformer model, set the winding resistances and inductances to zero, and the magnetization resistance and inductance to inf.

Inputs and Outputs

The winding 1 is connected between input one and input two of the Linear Transformer block. The winding 2 is connected between output one and output two, and the winding 3 (if defined) is connected between output three and output four.

Input one, output one and output three (if exist) are at the same instantaneous polarity.

Limitations

Windings can be left floating (i.e., not connected to the rest of the circuit). However the floating winding will be connected internally to the main circuit through a resistor. This internal connection does not affect voltage and current measurements.

Example

Typical residential distribution transformer network feeding line to neutral and line to line loads. This circuit is available in the psbtransformer.mdl file.

Impedance Measurement MOSFET