Three-Winding Transformer#

Note

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The Three-winding transformer block is designed for conversion of AC voltage into two other voltage systems by means of electromagnetic induction in accordance with the set transformation ratios without frequency change.

Note

The conversion is non-ideal due to natural losses in transformer steel and windings.

Equivalent circuit of the three-winding transformer shown below (see Fig. 1) is suitable for simulation of steady-state modes and electromechanical transients:

Fig. 1 Three-winding transformer equivalent circuit#

All values of the equivalent circuit parameters are calculated based on the catalog data of the transformer:

the active resistances of the windings are determined on the basis of the loss power during corresponding short-circuit experiments and brought to the higher voltage side: (1):

\[ R_{В}=\frac{∆P_{кзВ}\cdot U_{ном}^{2}}{S_{ном}^{2}}; \]

\[ R_{С}=\frac{∆P_{кзС}\cdot U_{ном}^{2}}{S_{ном}^{2}}; \]

(1)#\[ R_{Н}=\frac{∆P_{кзН}\cdot U_{ном}^{2}}{S_{ном}^{2}}. \]

where:

\[ ∆P_{кзВ}=\frac{∆P_{кзВН}+∆P_{кзВС}-∆P_{кзСН}}{2}; \]

\[ ∆P_{кзС}=\frac{∆P_{кзСН}+∆P_{кзВС}-∆P_{кзВН}}{2}; \]

\[ ∆P_{кзН}=\frac{∆P_{кзВН}+∆P_{кзСН}-∆P_{кзВС}}{2}. \]

similarly the impedance of the windings is determined (2):

\[ Z_{В}=\frac{u_{кВ}}{100}\cdot \frac{U_{ном}^{2}}{S_{ном}}; \]

\[ Z_{С}=\frac{u_{кС}}{100}\cdot \frac{U_{ном}^{2}}{S_{ном}}; \]

(2)#\[ Z_{Н}=\frac{u_{кН}}{100}\cdot \frac{U_{ном}^{2}}{S_{ном}}. \]

where:

\[ u_{кВ}=\frac{u_{кВН}+u_{кВС}-u_{кСН}}{2};\]

\[ u_{кС}=\frac{u_{кСН}+u_{кВС}-u_{кВН}}{2};\]

\[ u_{кН}=\frac{u_{кВН}+u_{кСН}-u_{кВС}}{2}.\]

the winding reactances are determined from the total and active resistances (3):

\[ X_{В}=\sqrt[]{Z_{В}^{2}-R_{В}^{2}}; \]

\[ X_{С}=\sqrt[]{Z_{С}^{2}-R_{С}^{2}}; \]

(3)#\[ X_{Н}=\sqrt[]{Z_{Н}^{2}-R_{Н}^{2}}. \]

the active and reactive shunt resistances are calculated from catalog values of the no-load operation (4):

\[ G=\frac{P_{хх}}{U_{ном}^{2}}; \]

\[ Y=\frac{I_{хх}}{100}\cdot \frac{S_{ном}}{U_{ном}^{2}}; \]

(4)#\[ B=\sqrt[]{Y_{}^{2}-G_{}^{2}}. \]

1. Properties#

Property	Default value	Description	Units of measurement
Rated power	6	Rated power of the primary winding	MVA
Rated voltage of the tertiary winding	6.3	Rated voltage of the tertiary winding	kV
Rated voltage of the secondary winding	10	Rated voltage of the secondary windin	kV
Rated voltage of the primary winding	35	Rated voltage of the primary winding	kV
Short-circuit voltage P-S	7.5	Short-circuit voltage with shorted primary and secondary windings as a percentage of the rated voltage	%
Short-circuit voltage P-T	10	Short-circuit voltage with shorted primary and tertiary windings as a percentage of the rated voltage	%
Short-circuit voltage S-T	16.5	Short-circuit voltage with shorted secondary and tertiary windings as a percentage of the rated voltage	%
Short-circuit power losses P-S	3	Short-circuit power with shorted primary and secondary windings	kW
Short-circuit power losses P-T	4	Short-circuit power with shorted primary and tertiary windings	kW
Short-circuit power losses S-T	5	Short-circuit power with shorted secondary and tertiary windings	kW
Incorporate no load power losses	Off	-	-
No load power losses	43	idle run losses (losses in steel)	kW
No-load current	0.6	idle current as a percentage of the rated current of the HV winding	%

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input voltage of the primary winding	Input	-	V	Elecrocity
Output voltage of the secondary winding	Output	-	V	Elecrocity
Output voltage of the tertiary winding	Output	-	V	Elecrocity

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