SimPowerSystems    
Saturable Transformer

Implement a two- or three-winding saturable transformer

Library

Elements

Description

The Saturable 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 resistance Rm simulating the core active losses and a saturable inductance Lsat. The saturation characteristic is specified as a piecewise linear characteristic.

The Per Unit Conversion

In order to comply with industry practice, 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, the p.u. values are based on the transformer rated power and on the nominal voltage of winding 1.

The default parameters of winding 1 specified in the dialog box section give the following bases:

For example, the winding 1 parameters are R1 = 1.44 and L1 = 0.1528 H. The corresponding values to enter in the dialog box are

Saturation Characteristic

The saturation characteristic of the Saturable Transformer block is defined by a piecewise linear relationship between the flux and the magnetization current.

Therefore, if you want to specify a residual flux phi0, the second point of the saturation characteristic should correspond to a null current, as shown in the figure (b).

The saturation characteristic is entered as (i, phi) pair values in per units, starting with pair (0, 0). Power System Blockset converts the vector of fluxes pu and the vector of currents Ipu into standard units to be used in the saturation model of the Saturable Transformer block

where the base flux (base) and base current (Ibase) are the peak values obtained at nominal voltage power and frequency:

Dialog Box and Parameters

Nominal power and frequency
The nominal power rating, Pn, in volt amperes (VA), and frequency, in hertz (Hz), of the transformer.
Winding 1 parameters
The nominal voltage in volts rms, resistance, and leakage inductance in p.u. for winding 1.
Winding 2 parameters
The nominal voltage in volts rms, resistance, and leakage inductance in p.u. for winding 2.
Winding 3 parameters
The nominal voltage in volts rms, resistance, and leakage inductance in p.u. for winding 3. Setting the Winding 3 parameters parameter to 0 implements a Saturable Transformer block with only two windings.
Saturation characteristic
Specify a series of current (p.u.) - flux (p.u.) pairs starting with (0,0).
Core loss resistance and initial flux
Specify the active power dissipated in the core by entering the equivalent resistance Rm in p.u. For example, to specify a 0.2% of active power core loss at nominal voltage, use Rm = 500 p.u. You can also specify the initial flux phi0 (p.u). This initial flux becomes particularly important when the transformer is energized. If phi0 is not specified, the initial flux is automatically adjusted so that the simulation starts in steady state.
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 Flux and magnetization current to measure the magnetization current of the Linear Transformer block.
Select All Measurements (V, I, Flux) 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:

Flux

Flux:

Inputs and Outputs

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

If you set the entry for the third winding to 0, the blockset implements a transformer with two windings and a new icon is displayed:

Limitations

Windings can be left floating (that is, not connected by an impedance to the rest of the circuit). However, the floating winding is connected internally to the main circuit through a resistor. This invisible connection does not affect voltage and current measurements.

The flux saturation model does not include hysteresis.

Example

Energization of one phase of a three-phase 450 MVA, 500/230 kV transformer on a 3000 MVA source. The transformer parameters are

Nominal power: 150e6, 60 Hz, Winding 1 parameters (primary): 500e3 Vrms/sqrt(3), R = 0.002 p.u. X = 0.08 p.u., winding 2 parameters (secondary): 230e3 Vrms/sqrt(3), R = 0.002 p.u. X = 0.08 p.u., Core loss resistance: 1000 p.u., Saturation characteristic: [0 0; 0 1.2; 1.0 1.52], residual flux = 0.8 p.u.

This circuit is available in the psbxfosaturable.mdl file.

As the source is resonant at the fourth harmonic, you can observe a high fourth harmonic content in the secondary voltage. In this circuit the flux is calculated in two ways:

Simulation of this circuit illustrates the saturation effect on the transformer current and voltage:

See Also
Linear Transformer, Mutual Inductance


  RMS Series RLC Branch