Autotransformer#

The Autotransformer block represents a mathematical modelof an autotransformer - a device for electromagnetic conversionof AC voltage into two other voltage systems in accordance with the specifiedtransformation ratios at constant frequency.

Note

The conversion isnon-ideal due tonatural losses in the steel and windings of the autotransformer.

The equivalent circuit of an autotransformer (see Fig. 1 above) is identical to the three-beamequivalent circuit of a three-winding transformer and is also suitable forsimulation of steady-state modes and electromechanical transients.

Note

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

Total winding resistances (1):

(1)#\[Z_{\mathrm{В}}=\frac{u_{\mathrm{к}\mathrm{В}}}{100}\cdot \frac{u_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}}; Z_{\mathrm{С}}=\frac{u_{\mathrm{к}\mathrm{С}}}{100}\cdot \frac{u_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}}; Z_{\mathrm{Н}}=\frac{u_{\mathrm{к}\mathrm{Н}}}{100}\cdot \frac{u_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}};\]

where (2):

(2)#\[ u_{\mathrm{к}\mathrm{В}}=\frac{u_{\mathrm{к}\mathrm{В}\mathrm{Н}}+u_{\mathrm{к}\mathrm{В}\mathrm{С}}-u_{\mathrm{к}\mathrm{С}\mathrm{Н}}}{2}; u_{\mathrm{к}{C}}=\frac{u_{\mathrm{к}\mathrm{С}\mathrm{Н}}+u_{\mathrm{к}\mathrm{В}\mathrm{С}}-u_{\mathrm{к}\mathrm{В}\mathrm{Н}}}{2}; u_{\mathrm{к}\mathrm{Н}}=\frac{u_{\mathrm{к}\mathrm{В}\mathrm{Н}}+u_{\mathrm{к}\mathrm{С}\mathrm{Н}}-u_{\mathrm{к}\mathrm{В}\mathrm{С}}}{2}.\]

The autotransformers are designed for the typical power and the LV winding is calculated for a power less than the standard power.The ratio between the rated power of the autotransformer and the LV winding power is determined by a coefficient \(\alpha\) equal to the ratio of the LV winding power to the rated power of the transformer (3):

(3)#\[ \alpha =\frac{S_{\mathrm{Н}\mathrm{Н}}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}}\]

The winding power is usually specified in the autotransformer data sheet.There may be cases when a direct ratio between LV winding power and ratedpower is given, which is equal to the value of the coefficient \(\alpha\), or when there is no data on LV winding power - in this case an average value \(\alpha\) = 0.5 is taken.

To calculate the active resistances of the AV and LV windings, the corresponding short-circuit losses shall be brought to the rated power as follows (4):

(4)#\[∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{С}}=∆P_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{С}}; ∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{Н}}=\frac{∆P_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{Н}}}{\alpha ^{2}}; \mathrm{}∆{P}_{\mathrm{к}\mathrm{э}\mathrm{С}\mathrm{Н}}=\frac{∆P_{\mathrm{к}\mathrm{э}\mathrm{С}\mathrm{Н}}}{\alpha ^{2}}; R_{\mathrm{В}}=\frac{∆P_{\mathrm{к}\mathrm{э}\mathrm{В}}U_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}; \mathrm{}R_{\mathrm{С}}=\frac{∆P_{\mathrm{к}\mathrm{э}\mathrm{С}}U_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}; \mathrm{}R_{\mathrm{Н}}=\frac{∆P_{\mathrm{к}\mathrm{э}\mathrm{Н}}U_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}};\]

where (5):

(5)#\[ ∆P_{\mathrm{к}\mathrm{э}\mathrm{В}}=\frac{∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{Н}}+∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{С}}-∆{P}_{\mathrm{к}\mathrm{э}\mathrm{С}\mathrm{Н}}}{2}; ∆P_{\mathrm{к}\mathrm{э}\mathrm{С}}=\frac{∆{P}_{\mathrm{к}\mathrm{э}\mathrm{С}\mathrm{Н}}+∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{С}}-∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{Н}}}{2}; ∆P_{\mathrm{к}\mathrm{э}\mathrm{Н}}=\frac{∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{Н}}+∆{P}_{\mathrm{к}\mathrm{э}\mathrm{С}\mathrm{Н}}-∆{P}_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{С}}}{2}.\]

In some cases, only \(∆P_{scHM}\) losses are known. In such a case, the winding resistances are calculated as follows (6):

(6)#\[ R_{\mathrm{В}}=\frac{∆P_{\mathrm{к}\mathrm{э}\mathrm{В}\mathrm{С}}U_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}; \mathrm{}R_{\mathrm{С}}=R_{\mathrm{В}}; \mathrm{}R_{\mathrm{Н}}=\frac{R_{\mathrm{В}}}{\alpha }\]

The winding reactances are determined from the total and active resistances (7):

(7)#\[ X_{\mathrm{В}}=\sqrt[]{Z_{\mathrm{В}}^{2}-R_{\mathrm{В}}^{2}}; \mathrm{}X_{C}=\sqrt[]{Z_{C}^{2}-R_{C}^{2}}; X_{\mathrm{Н}}=\sqrt[]{Z_{\mathrm{Н}}^{2}-R_{\mathrm{Н}}^{2}};\]

The active and reactance of the shunt are calculated based on the catalog values of the no-load experience (8):

(8)#\[ G=\frac{P_{\mathrm{х}\mathrm{х}}}{u_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}; \mathrm{}Y=\frac{I_{xx}}{100}\cdot \frac{S_{\mathrm{н}\mathrm{о}\mathrm{м}}}{u_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}; B=\sqrt[]{Y^{2}-G^{2}}\]

1. Properties#

Property	Default value	Description	Units of measurement
Rated power	6	Rated power of the transformer primary winding	MVA
Rated power of the tertiary winding	0	Rated power of the transformer tertiary winding	MVA
Tertiary winding rated voltage	6.3	Rated voltage of the tertiary winding	kV
Secondary winding rated voltage	10	Rated voltage of the secondary winding	kV
Primary winding rated voltage	35	Rated voltage of the primary winding	kV
Short-circuit voltage P-S	7.5	SC voltage with shorted primary and secondary windings as a percentage of the rated voltage	%
Short-circuit voltage P-T	10	SC voltage with shorted primary and tertiary windings as a percentage of the rated voltage	%
Short-circuit voltage S-T	16.5	SC voltage with shorted secondary and tertiary windings as a percentage of the rated voltage	%
Short-circuit power losses P-S	3	SC power with shorted primary and secondary windings	kW
Short-circuit power losses P-T	4	SC power with shorted primary and tertiary windings	kW
Short-circuit power losses S-T	5	SC power with shorted secondary and tertiary windings	kW
Incorporate no load power losses	Off	–	–
No load power losses	No load power losses	idle power losses (iron losses)	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	Electrocity
Output voltage of the secondary winding	Output	–	V	Electrocity
Output voltage of the tertiary winding	Output	–	V	Electrocity

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