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Single-phase center-tapped Transformer

Owned by Sylvain Ménard
Last updated: Oct 10, 2024 by Luc Marcil
5 min read

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Single-phase center-tapped (or split-phase) transformer has a single-phase input winding and a center-tapped output winding connected to a grounded neutral as seen in the figure below. This model is developed from a three winding single-phase transformer whose polarity of the tertiary winding respect to ground has been inverted to obtain twice the phase-ground voltage between secondary and tertiary. 

Single-phase 3W Transformer 

Parameters

Symbol

Description

Unit

Symbol

Description

Unit

ID

Transformer name

unique name

Status

Connect/Disconnect status

Initial value 1 (0 for disconnected)

Number of Phases

Phase count in use

for this model only 1 phase is accepted

Primary winding From

Bus1

Primary side: Bus 1

a unique name

Bus2

Primary side: Bus 2

NOT APPLICABLE

Bus3

Primary side: Bus 3

NOT APPLICABLE

V (kV)

Primary winding nominal voltage (phase-to-ground)

kV

S_base (kVA)

Nominal power in primary side

kVA

Conn. type (*)

Primary winding connection type

for this model only ‘wye’ connection is accepted

Secondary winding To

Bus1

Secondary side: Bus 1

a unique name

Bus2

Secondary side: Bus 2

NOT APPLICABLE

Bus3

Secondary side: Bus 3

NOT APPLICABLE

V (kV)

Secondary winding nominal voltage (phase-to-ground)

kV

S_base (kVA)

Nominal power in secondary side

NOT APPLICABLE

Conn. type (*)

Secondary winding connection type

for this model only ‘wye’ connection is accepted

Tertiary winding To

Bus1

Tertiary side: Bus 1

a unique name

Bus2

Tertiary side: Bus 2

NOT APPLICABLE

Bus3

Tertiary side: Bus 3

NOT APPLICABLE

V (kV)

Tertiary winding nominal voltage (phase-to-ground)

kV

S_base (kVA)

Nominal power in tertiary side

NOT APPLICABLE

Conn. type (*)

Tertiary winding connection type

for this model only ‘wye’ connection is accepted

R_12 (p.u.)

Resistance between primary and secondary windings

p.u.

Xl_12 (p.u.)

Reactance between primary and secondary windings

p.u.

R_23 (p.u.)

Resistance between secondary and tertiary windings

p.u.

Xl_23 (p.u.)

Reactance between secondary and tertiary windings

p.u.

R_31 (p.u.)

Resistance between primary and tertiary windings

p.u

Xl_31 (p.u.)

Reactance between primary and tertiary windings

p.u.

Operation

Type of operation: 0 = normal 3W trx, 1 = center-tapped trx

0 or 1 

Model Equations 

This single-phase transformer is modeled based on the primitive nodal admittance matrix Yprim [1]. 

Yprim = CT M Yw M C  matrix dimension: 3 x 3

Yw0 =A YP AT 

Yw0 is the winding admittance matrix. Matrix dimension: 4 x 4

A is the admittance-winding incidence matrix whose non-zero elements are generally either 1 and -1. Matrix dimension: 4 x 4 

YP is the primitive admittance matrix on a 1 V base. Matrix dimension: 4 x 4

Yw =Zw-1 matrix dimension: 3 x 3

Zw is the reduced impedance matrix. Calculated by inverting the matrix Yw0 and eliminating the row and column of the ficticious node. Matrix dimension: 3 x 3

C is the winding-port incidence matrix whose non-zero elements are generally either 1 and -1. Matrix dimension: 3 x 3

M is the incidence matrix whose non-zero elements are the inverse of the numbers of turns in the windings. Matrix dimension: 3 x 3

Example

1) A single-phase 3W transformer with the following data:  7.2/0.12/0.12 kV, 15 kVA, X12 = 1.44%, R12=1.95%,  X13 = 1.44%, R13=1.95%,  X23 = 0.96%, R23=2.6% will be connected like a center-tapped transformer 

 

The matrices are calculated according the diagram shown above. 

Zhl = R12 + X12i (pu) ; Zht = R13 + X13i (pu); Zlt = R23 + X23i (pu).

Calculation of Z1, Z2 and Z3.  Z123=0.5 Ztrx

Ztrx=

Zhl

-Zlt

Zht

Zhl

Zlt

-Zht

-Zhl

Zlt

Zht

from here Z1 = 0.0065+0.0096i; Z2 = 0.013+0.0048i and Z3 = 0.013+0.0048i. Transforming to a 1V base and inverting admittances Y1, Y2 and Y3 are obtained to build matrix Yp. Assuming a high value for the impedance Z0 between ficticious node and the reference (for example 500e3 ohms)  

Yw0 =A YP AT = 

A =

1

0

0

-1

0

1

0

-1

0

0

1

-1

0

0

0

1

YP =

7.5239e5 - 1.0713e6i

0

0

0

0

1.0154e6 - 3.7492e5i

0

0

0

0

1.0154e6 - 3.7492e5i

0

0

0

0

0.03

Yw0 =

7.5239e5 - 1.0713e6i

0

0

-7.5239e5 + 1.0713e6i

0

1.0154e6 - 3.7492e5i

0

-1.0154e6 + 3.7492e5i

0

0

1.0154e6 - 3.7492e5i

-1.0154e6 + 3.7492e5i

-7.5239e5 + 1.0713e6i

-1.0154e6 + 3.7492e5i

-1.0154e6 + 3.7492e5i

2.7562e6 - 1.8212e6i

Inverting this matrix and eliminating the row and column of the ficticious node, Zw is obtained

Zw =

33.3333

33.3333

33.3333

33.3333

33.3333

33.3333

33.3333

33.3333

33.3333

and Yw =Zw-1 

Yw =

6.23e5 - 5.7508e5i

-3.1150e5 + 2.8754e5i

-3.1150e5 + 2.8754e5i

-3.1150e5 + 2.8754e5i

6.6346e5 - 3.3123e5i

-3.5196e5 + 4.3691e4i

-3.1150e5 + 2.8754e5i

-3.5196e5 + 4.3691e4i

6.6346e5 - 3.3123e5i

Matrices C and M are defined as shown below. The negative sign in the matrix C allows to change the polarity of the tertiary winding to obtain the center-tapped connection,

C =

1

0

0

0

1

0

0

0

-1

M =

1/7200

0

0

0

1/120

0

0

0

1/120

which finally allows to obtain the nodal admittance matrix of the center-tapped transformer 

Yprim =

0.012 - 0.0111i 

-0.3605 + 0.3328i

0.3605 - 0.3328i

-0.3605 + 0.3328i

46.0734 - 23.0021

24.4414 - 3.0341i

0.3605 - 0.3328i

24.4414 - 3.0341i

46.0734 - 23.0021

To add this transformer in the excel file, see the next image

References

[1] Massimiliano Coppo, Fabio Bignucolo and Roberto Turri, "Generalised transformer modelling for power flow calculation in multi-phase unbalanced networks". IET Generation, Transmission and Distribution, 2017, Vol. 11, Issue: 15, pp: 3843-3852. DOI: 10.1049/iet-gtd.2016.2080

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