Single-phase linear transformer (Two windings)#

The Single-phase linear transformer (Two windings) block is a linear model of a single-phase double-winding transformer. The transformer equivalent circuit is shown in Fig. 1 :

This model is based on an ideal transformer the primary winding of which is connected to the magnetization branch with parameters R\(_M\), L\(_M\) and active-inductive resistance with parameters R\(_1\), L\(_1\). Secondary winding is connected to active-inductive resistance with parameters R\(_2\), L\(_2\).

Taking into account the above circuit, a two-winding single-phase transformer is described by the following system of equations (1):

\[I_1-I_{MR}-I_{ML}=K\cdot I_2\]

\[K\cdot (U_1-(I_1\cdot R_1 + L_1 \cdot \frac{dI_1}{dt}))=U_2\]

\[I_2 \cdot R_2+L_2 \cdot \frac{dI_2}{dt}=U_2\]

(1)#\[U_M=I_{MR}\cdot R_M=L_M \cdot \frac{dI_{ML}}{dt}\]

where:

\(U_1\), \(U_2\) - voltage of the primary and secondary windings, respectively, [V];

\(I_1\), \(I_2\) - currents of primary and secondary windings respectively, [A];

\(I_{ML}\) - inductive component of the magnetization branch current, [A];

\(I_{MR}\) - active component of the magnetization branch current, [A];

\(U_M\) - voltage on the magnetization branch, [V];

\(R_1\), \(R_2\) - active resistances of primary and secondary windings respectively, [Ohm];

\(L_1\), \(L_2\) - inductance of primary and secondary windings respectively, [H];

\(R_M\) - active resistance of the magnetization branch, [Ohm];

\(L_M\) - inductance of the magnetization branch, [H];

K - transformation ratio of an ideal transformer.

The model has various ways of model parameters:

Setting the parameters in SI system (then it is necessary to set only windings parameters (rated voltages, [V], active resistances, [Ohm] and spreading inductances, [H]; inductance of windings and mutual inductance are calculated inside the block));
Setting of parameters in relative units (then it is necessary to set only winding parameters (rated voltages, [V], active resistances, [r.u.] and scattering inductance, [r.u.]; winding inductance and mutual inductance are calculated inside the block, and winding parameters will be recalculated into named units));
Set catalog parameters (equivalent circuit parameters will be calculated automatically).

The procedure for calculating equivalent circuit parameters from relative units and catalog data is given in the corresponding article.

1. Properties#

Property	Default Value	Description	Units of measurement
Model parameter: SI; PU; Specification	SI	-	-
Primary winding parameters, available, when `Model parameter` - `SI`	230.0e3;4.3218;0.45856	Data structure: \(U_{1nom}\);\(R_1\);\(L_1\)	V; Ohm; H
Secondary winding parameters, available, when `Model parameter` - `SI`	115.0e3;0.7938;0.084225	Data structure: \(U_{2nom}\);\(R_2\);\(L_2\)	V; Ohm; H
Magnetizing branch parameters, available, when `Model parameter` - `SI`	1080400;2866	Data structure: \(R_M\);\(L_M\)	Ohm; H
Nominal power	250.0e6	Available, when `Model parameter` - `PU` or `Specification`	VA
Nominal frequency	50.0	Available, when `Model parameter` - `PU` or `Specification`	Hz
Primary winding parameter, available, when `Model parameter` - `PU`	230.0e3;4.3218;0.45856	Data structure: \(U_{1nom}\); \(R_1\); \(L_1\)	V; r.u.; r.u.
Secondary winding parameters, available, when `Model parameter` - `PU`	115.0e3;0.7938;0.084225	Data structure: \(U_{2nom}\);\(R_2\);\(L_2\)	V; r.u.; r.u.
Magnetizing branch parameters, available, when `Model parameter` - `PU`	500;500	Data structure: \(R_M\);\(L_M\)	r.u.; r.u.
Nominal voltage of primary winding	230.e3	Available, when `Model parameter` - `Specification`	V
Nominal voltage of secondary winding	115.e3	Available, when `Model parameter` - `Specification`	V
Nominal short-circuit loss	35.e3	Available, when `Model parameter` - `Specification`	W
Nominal impedance voltage	10.5	Available, when `Model parameter` - `Specification`	%
Nominal no load loss	10.e3	Available, when `Model parameter` - `Specification`	W
Nominal no-load current	0.5	Available, when `Model parameter` - `Specification`	%
Initial values of windings currents	0.0;0.0	Data structure: \(I_{10}\);\(I_{20}\)	А
Initial conditions for magnetizing branch	0.0;0.0	Data structure: \(I_{MO}\);\(U_{MO}\)	A; V

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
1+	Input	-	-	Electronics
1-	Output	-	-	Electronics
2+	Input	-	-	Electronics
2-	Output	-	-	Electronics

In order to see the connection capabilities of the block, you need to go to page Description of block ports