Single-phase three windings transformer#

The Single-phase three windings transformer block is a linear model of a single-phase three-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 \(R_2\), \(L_2\), and tertiary winding is connected to active-inductive resistance with parameters \(R_3\), \(L_3\).

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

\[I_1-I_{MR}-I_{ML}=K_1 \cdot I_2 + K_2 \cdot I_3\]

\[K_1 \cdot (U_1-(I_1 \cdot R_1+L_1 \cdot \frac{dI_1}{dt}))=U_2\]

\[K_2 \cdot (U_1-(I_1 \cdot R_1+L_1 \cdot \frac{dI_1}{dt}))=U_3\]

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

\[I_3 \cdot R_3+L_3 \cdot \frac{dI_3}{dt}=U_3\]

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

where:

\(U_1\), \(U_2\), \(U_3\) - voltages of primary, secondary and tertiary windings, respectively, [V];

\(I_1\), \(I_2\), \(I_3\) - currents of primary, secondary and tertiary windings respectively, [A];

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

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

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

\(R_1\), \(R_2\), \(R_3\) - active resistances of primary, secondary and tertiary windings respectively, [Ohm];

\(L_1\), \(L_2\), \(L_3\) - inductance of primary, secondary and tertiary windings respectively, [H];

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

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

\(К_1\) - transformation ratio of ideal transformer between primary and secondary windings;

\(К_2\) - transformation ratio of ideal transformer between secondary and tertiary windings.

The model has various ways of model parameters:

Setting of parameters in SI system (then it is necessary to set only the winding parameters (rated voltages, [V], active resistances, [Ohm] and inductance, [H]));
Setting of parameters in relative units (then it is necessary to set only winding parameters (rated voltages, [V], active resistances, [r.u.] and inductance, [r.u.]));
Set the catalog parameters (the parameters of the equivalent circuit will be calculated automatically).

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

1. Properties#

Property	Default value	Description	Units of measurement
Method of specifying model parameters: SI; PU; Specification	SI	-	-
Primary winding parameters, [U\(_{1ф}\); R\(_1\); L\(_1\)]	735000.0;0.3218;0.005856;	Available, when `Method of specifying model parameters` - `SI`	V; Ohm; H
Secondary winding parameters, [U\(_{2ф}\); R\(_2\); L\(_2\)]	315000.0;0.07938;0.0084225;	Available, when `Method of specifying model parameters` - `SI`	V; Ohm; H
Tertiary winding parameters, [U\(_{3ф}\); R\(_3\); L\(_3\)]	315000.0;0.07938;0.0084225;	Available, when `Method of specifying model parameters` - `SI`	V; Ohm; H
Magnetizing branch parameters, [R\(_m\); L\(_m\)]	1080400.0;2866.0;	Available, when `Method of specifying model parameters` - `SI`	Ohm; H
Nominal power	2.5e8	Available, when `Method of specifying model parameters` - `PU` or `Specification`	VA
Nominal frequency	60.0	Available, when `Method of specifying model parameters` - `PU` or `Specification`	Hz
Primary winding parameters, [U\(_{1ф}\); R\(_1\); L\(_1\)]	735000.0;0.002;0.08;	Available, when `Method of specifying model parameters` - `PU`	V; r.u.; r.u.
Secondary winding parameters, [U\(_{2ф}\); R\(_2\); L\(_2\)]	315000.0;0.002;0.08;	Available, when `Method of specifying model parameters` - `PU`	V; r.u.; r.u.
Tertiary winding parameters, [U\(_{3ф}\); R\(_3\); L\(_3\)]	315000.0;0.002;0.08;	Available, when `Method of specifying model parameters` - `PU`	V; r.u.; r.u.
Magnetizing branch parameters, [R\(_m\); L\(_m\)]	500.0;500.0;	Available, when `Method of specifying model parameters` - `PU`	r.u.; r.u.
Nominal voltage of primary winding	230000.0	Available, when `Method of specifying model parameters` - `Specification`	V
Nominal voltage of secondary winding	115000.0	Available, when `Method of specifying model parameters` - `Specification`	V
Nominal voltage of tertiary winding	115000.0	Available, when `Method of specifying model parameters` - `Specification`	V
Nominal HV - LV short-circuit losses	35000.0	Available, when `Method of specifying model parameters` - `Specification`	W
Nominal HV -MV short-circuit losses	35000.0	Available, when `Method of specifying model parameters` - `Specification`	W
Nominal MV -LV short-circuit losses	35000.00	Available, when `Method of specifying model parameters` - `Specification`	W
Nominal HV - LV impedance voltage	10.5	Available, when `Method of specifying model parameters` - `Specification`	%
Nominal HV - MV impedance voltage	10.5	Available, when `Method of specifying model parameters` - `Specification`	%
Nominal MV - LV impedance voltage	10.5	Available, when `Method of specifying model parameters` - `Specification`	%
Nominal no load losses	10000.0	Available, when `Method of specifying model parameters` - `Specification`	W
Nominal no load current	0.5	Available, when `Method of specifying model parameters` - `Specification`	%
Initial currents of windings, [I\(_1\); I\(_2\); I\(_3\)]	0.0;0.0;0.0;	-	A
Initial values of magnetizing branch current and voltage, [I\(_M\); U\(_M\)]	0.0;0.0;	-	А; V

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Primary winding, +	Input	-	-	Electronics
Primary winding, -	Output	-	-	Electronics
Secondary winding, +	Output	-	-	Electronics
Secondary winding, -	Input	-	-	Electronics
Tertiary winding, +	Output	-	-	Electronics
Tertiary winding, -	Input	-	-	Electronics

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