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Multiphase transformers can represent either a 1, 2, or 3phase transformer. In the corresponding Excel tab, there are columns for declaration of up to 6 connection points (3 for Winding From end and 3 for Winding To end).
The sending and receiving connection points must be filled in correspondingly:
 For example, if Winding From/Bus 1 is filled, Winding To/Bus 1 must be filled as well.
 The unused connection points can be left empty. However, these empty fields must be located immediately after any filled completed connection point.
For example, a data in which Winding From/Bus 2 and Winding To/Bus 2 fields are filled out but Winding From/Bus 1 and Winding To/Bus 1 are empty is not valid and it causes an error.
Finally, the sending and receiving points can be connected to different phases. For example, Winding From/Bus 1 can be connected to phase A while Winding To/Bus 1 is connected to phase B.
In summary, to represent:
To represent a ...  Fill these columns to add connection points... 

singlephase transformer 
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Only Winding From/Bus 1 
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and Winding To/Bus 1 
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columns. 
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twophase transformer 

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The Winding From/Bus1 and Winding From/Bus 2 
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as well as 
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Winding To/Bus 1 and Winding To/Bus 2 
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. 
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threephase 

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transformer  The Winding From/Bus1, Winding From/Bus 2, Winding From/Bus 3 

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as well as 
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Winding To/Bus 1, Winding To/Bus 2 and Winding To/Bus 3 
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The table below shows the parameter list for multiphase transformer.
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. 
Multiphase 2W Transformer
Symbol  Description  Unit  
ID  Transformer name 

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unique name  
Status  Connect/Disconnect status  Initial value 1 (0 for disconnected)  

Number of Phases  Phase count in use  1, 2, or 3  
Winding From 
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Bus1  Primary side: Bus 1  a unique name 

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Bus2  Primary side: Bus 2  a unique name 

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Bus3  Primary side: Bus 3  a unique name 

V (kV)  Primary winding nominal voltage (phasetophase)  kV 
S_base (kVA)  Nominal power in primary side  kVA 
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R (pu)
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Primary winding resistance
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p.u.
Conn. type ( 

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*)  Primary winding connection type  ‘wye’ and ‘delta’ 

Winding To 
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Bus1  Secondary side: Bus 1  a unique name 

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Bus2  Secondary side: Bus 2  a unique name 

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Bus3  Secondary side: Bus 3  a unique name 

V (kV)  Secondary winding nominal voltage (phasetophase)  kV 
S_base (kVA)  Nominal power in secondary side  NOT APPLICABLE 
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Conn. type (*)  Secondary winding connection type  ‘wye’ and ‘delta’  

Tap 1  Initial tap position: winding 1  Integer between Lowest and Highest Tap  
Tap 2  Initial tap position: winding 2  
Tap 3  Initial tap position: winding 3  
Lowest Tap  The lowest tap position  Integer value  
Highest Tap  The highest tap position  Integer value  
Min Range (%)  Max voltage buck  0 < value < 100  
Max Range (%)  Max voltage boost  value > 0  
X (pu)  Total reactance  p.u.  
Rw1 (p.u.)  Primary winding resistance  p.u.  
Rw2 (p.u.)  Secondary winding resistance  p.u. 
Multiphase 2W Transformer with Mutual Impedance
Symbol  Description  Unit  
ID  Transformer name  a unique name  

Status  Connect/Disconnect status  Initial value 1 (0 for disconnected)  
Number of Phases  Phase count in use  1, 2, or 3  
Winding From  Bus1  Primary side: Bus 1  a unique name 
Bus2  Primary side: Bus 2  a unique name  
Bus3  Primary side: Bus 3  a unique name  
V (kV)  Primary winding nominal voltage (phasetophase)  kV  
S_base (kVA)  Nominal power in primary side  kVA  
Conn. type ( 
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*) 

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Primary winding connection type  ‘wye’ and ‘delta’ 
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Mutual impedance (*)
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0: No mutual impedance, 1: With mutual impedance
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Winding To  Bus1  Secondary side: Bus 1  a unique name 

Bus2  Secondary side: Bus 2  a unique name  
Bus3  Secondary side: Bus 3  a unique name  
V (kV)  Secondary winding nominal voltage (phasetophase)  kV  
S_base (kVA)  Nominal power in secondary side  NOT APPLICABLE  
Conn. type (*)  Secondary winding connection type  ‘wye’ and ‘delta’  
Tap 1  Initial tap position: winding 1  Integer between Lowest and Highest Tap  
Tap 2  Initial tap position: winding 2  
Tap 3  Initial tap position: winding 3  
Lowest Tap  The lowest tap position  Integer value  
Highest Tap  The highest tap position  Integer value  
Min Range (%)  Max voltage buck  0 < value < 100  
Max Range (%)  Max voltage boost  value > 0 
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Total reactance
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p.u.
Z0 leakage (pu)  Zerosequence impedance  transformer p.u.  

Z1 leakage (pu)  Positivesequence impedance  transformer p.u.  
X0/R0  Zerosequence reactance to resistance ratio  ratio  
X1/R1  Positivesequence reactance to resistance ratio  ratio  
No Load Loss (kW)  Noload power loss  NOT APPLICABLE 
Background Color  

 
Note: (* ) For a transformer with no mutual impedance (Mutual impedance = 0) use R (pu) and X (pu) and for transformer with mutual impedance use Z0 leakage, Z1 leakage, X0/R0, X1/R1 and No load loss.(**)Four types of winding configurations are supported: 'DD0', 'YgYg0', 'DYg1', 'YgD1'. 
Available I/O
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Pins
No  Pin’s Pin Description  Pin Type  Value/Unit  Instruction 
1  Get sending end current magnitude of wire j  O  A (RMS)  transformerID/ImagFromj where j is 1, 2 or 3 
2  Get receiving end current magnitude of wire j  O  A (RMS)  transformerID/ImagToj where j is 1, 2 or 3 
3  Get sending end current angle of wire j  O  Degree  transformerID/IangFromj where j is 1, 2 or 3 
4  Get receiving end current angle of wire j  O  Degree  transformerID/IangToj where j is 1, 2 or 3 
5  Set/Get tap position  I/O  Integer between [min_tap, max_tap]  transformerID/tap_j where j is 1, 2 or 3 
Model Equations
This multiphase transformer is modeled based on the primitive nodal admittance matrix Yprim [1],[2].
Yprim = A N B Z_{B}^{1} B^{T} N^{T} A^{T} matrix dimension: np*m x np*m, np = number of phases, m= number of windings
Y_{1} = B Z_{B}^{1} B^{T} ; Y_{w} = N Y_{1} N^{T} ; Yprim = A Y_{w} A^{T}
Y_{1} is the groundreferenced nodal admittance matrix on a 1 volt base. Matrix dimension: np*m x np*m
N is the incidence matrix whose nonzero elements are the inverse of the numbers of turns in the windings. This matrix represents the effect of the ideal transformers shown to obtain actual windings voltages. Matrix dimension: 2*np*m x np*m
B is the incidence matrix whose elements are either 1,1 or 0. It relates currents in the short circuit reference frame where the first winding is assumed shorted to the currents in the nodal admittance reference frame on a 1 volt base. Matrix dimension: np*m x np
A is the incidence matrix whose nonzero elements are generally either 1 and 1, that relates the winding currents to the actual terminal currents. Matrix dimension: nc x 2*np*m, nc = number of terminal currents
Z_{B} is the short circuit impedance matrix. Matrix dimension: np*(m1) x np*(m1)
Y_{w} is the winding admittance matrix. Matrix dimension: 2*np*m x 2*np*m
Examples
1) A singlephase 2W transformer with the following data: 7.2/0.12 kV, 25 kVA, X = 20%, R=1.1%
In this case np = 1, m = 2.
Z_{B} in pu = 0.011+0.02i, ZB in 1V base = (Z_{B} in pu)*1^{2}/25 kVA = 4.4e7 + 8e7i. Z_{B}^{1}= 527.831e3  959.692e3i
Y_{1} = B Z_{B}^{1} B^{T} ; B is a matrix [np*m=2 x np=1]
B =
1 
1 
Y_{1} =
527.831e3  959.692e3i  527.831e3+959.692e3i 
527.831e3+959.692e3i  527.831e3  959.692e3i 
N is a matrix [2*np*m=4 x np*m=2]
N =
1 /7200  0 
1 /7200  0 
0  1/120 
0  1/120 
Y_{w} = N Y_{1} N^{T} =
0.01020.0185i  0.0102+0.0185i  0.6109+1.1108i  0.61091.1108i 
0.0102+0.0185i  0.01020.0185i  0.61091.1108i  0.6109+1.1108i 
0.6109+1.1108i  0.61091.1108i  36.654966.6453i  36.6549+66.6453i 
0.61091.1108i  0.6109+1.1108i  36.6549+66.6453i  36.654966.6453i 
To generate matrix A is necessary to define the number of terminal currents in the model. In this case there are 2 terminal currents (see the red currents in the figure above) so nc=2 and A matrix is [nc=2 x 2*np*m=4]
A =
1  0  0  0 
0  0  1  0 
Finally the matrix Yprim is calculated
Yprim = A Y_{w} A^{T} =
0.01010.0185i  0.6105+1.1100i 
0.6105+1.1100i  36.600766.5467i 
Below it can be seen how to add this singlephase transformer in the excel file. The total resistance was divided equally between the 2 windings (RW1 = RW2 = 0.011 pu/2 = 0.0055 pu). Note that the voltages voltages must be added as phase to phase voltages even though the model is singlephase (according to the table above)
2) A threephase 2W transformer with the following data: 12.47/0.208 kV (wye/delta), 75 kVA, X = 20%, R=1.1%
In this case np = 3, m = 2.
Z_{B} in pu = 0.011+0.02i, ZB in 1V base = (Z_{B} in pu)*1^{2}/75 kVA = 1.4667e7 + 2.6667e7i. Z_{B}^{1}= 158.349e3  287.907e3i
Y_{1} = B Z_{B}^{1} B^{T} ; B is a matrix [np*m=6 x np=3]
B =
1  0  0 
1  0  0 
0  1  0 
0  1  0 
0  0  1 
0  0  1 
Y_{1} =
158.349e3  287.907e3i  158.349e3 + 287.907e3i  0  0  0  0 
158.349e3 + 287.907e3i  158.349e3  287.907e3i  0  0  0  0 
0  0  158.349e3  287.907e3i  158.349e3 + 287.907e3i  0  0 
0  0  158.349e3 + 287.907e3i  158.349e3  287.907e3i  0  0 
0  0  0  0  158.349e3  287.907e3i  158.349e3 + 287.907e3i 
0  0  0  0  158.349e3 + 287.907e3i  158.349e3  287.907e3i 
N is a matrix [2*np*m=12 x np*m=6]
N =
1 /12470  0  0  0  0  0 
1 /12470  0  0  0  0  0 
0  1/(208*sqrt(3))  0  0  0  0 
0  1/(208*sqrt(3))  0  0  0  0 
0  0  1 /12470  0  0  0 
0  0  1 /12470  0  0  0 
0  0  0  1/(208*sqrt(3))  0  0 
0  0  0  1/(208*sqrt(3))  0  0 
0  0  0  0  1 /12470  0 
0  0  0  0  1 /12470  0 
0  0  0  0  0  1/(208*sqrt(3)) 
0  0  0  0  0  1/(208*sqrt(3 
Example
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)) 
Y_{w} = N Y_{1} N^{T} =
0.01020.0185i  0.0102+0.0185i  0.3525+0.6409i  0.35250.6409i  0  0  0  0  0  0  0  0 
0.0102+0.0185i  0.01020.0185i  0.35250.6409i  0.3525+0.6409i  0  0  0  0  0  0  0  0 
0.3525+0.6409i  0.35250.6409i  12.200222.1823i  12.2002+22.1823i  0  0  0  0  0  0  0  0 
0.35250.6409i  0.3525+0.6409i  12.2002+22.1823i  12.200222.1823i  0  0  0  0  0  0  0  0 
0  0  0  0  0.01020.0185i  0.0102+0.0185i  0.3525+0.6409i  0.35250.6409i  0  0  0  0 
0  0  0  0  0.0102+0.0185i  0.01020.0185i  0.35250.6409i  0.3525+0.6409i  0  0  0  0 
0  0  0  0  0.3525+0.6409i  0.35250.6409i  12.200222.1823i  12.2002+22.1823i  0  0  0  0 
0  0  0  0  0.35250.6409i  0.3525+0.6409i  12.2002+22.1823i  12.200222.1823i  0  0  0  0 
0  0  0  0  0  0  0  0  0.01020.0185i  0.0102+0.0185i  0.3525+0.6409i  0.35250.6409i 
0  0  0  0  0  0  0  0  0.0102+0.0185i  0.01020.0185i  0.35250.6409i  0.3525+0.6409i 
0  0  0  0  0  0  0  0  0.3525+0.6409i  0.35250.6409i  12.200222.1823i  12.2002+22.1823i 
0  0  0  0  0  0  0  0  0.35250.6409i  0.3525+0.6409i  12.2002+22.1823i  12.200222.1823i 
To generate matrix A is necessary to define the number of terminal currents in the model. In this case there are 6 terminal currents (see figure above) so nc=6 and A matrix is [nc=6 x 2*np*m=12]
A =
1  0  0  0  0  0  0  0  0  0  0  0 
0  0  0  0  1  0  0  0  0  0  0  0 
0  0  0  0  0  0  0  0  1  0  0  0 
0  0  1  0  0  0  0  0  0  0  0  1 
0  0  0  1  0  0  1  0  0  0  0  0 
0  0  0  0  0  0  0  1  0  0  1  0 
Yprim = A Y_{w} A^{T} =
0.01010.0185i  0  0  0.3524+0.6408i  0.35240.6408i  0 
0  0.01010.0185i  0  0  0.3524+0.6408i  0.35240.6408i 
0  0  0.01010.0185i  0.35240.6408i  0  0.3524+0.6408i 
0.3524+0.6408i  0  0.35240.6408i  24.400444.3645i  12.2002+22.1822i  12.2002+22.1822i 
0.35240.6408i  0.3524+0.6408i  0  12.2002+22.1822i  24.400444.3645i  12.2002+22.1822i 
0  0.35240.6408i  0.3524+0.6408i  12.2002+22.1822i  12.2002+22.1822i  24.400444.3645i 
The following image shows how to add this component in the excel file.
3) Multiple transformers in the same model
See the Transformer page in phasor08_IEEE13.xls file in demo PHASOR08.
References
[1] Roger C. Dugan, "A Perspective on Transformer Modeling for Distribution Systems Analysis". 2003 IEEE Power Engineering Society General Meeting. DOI: 10.1109/PES.2003.1267146
[2] Roger C. Dugan and Surya Santoso, "An Example of 3phase Transformer Modeling for Distribution Systems Analysis". 2003 IEEE PES Transmission and Distribution Conference and Exposition. DOI: 10.1109/TDC.2003.1335084