Mask and Parameters
General Parameters
Tertiary connection  Select whether the deltaconnected winding voltage will lead or lag the starconnected winding voltage or ground Cphase 
FluxCurrent characteristic model  Model saturation only or saturation with hysteresis 
Iteration in saturation model  Enable or disable iteration to achieve more accurate results at the expense of computation time when the saturation segment changes 
Base serial/common/tertiary winding voltage (rmsLL)  Base value for PU conversion (kV) 
Rm  Equivalent resistance of iron losses of the magnetic circuit (Ω) 
Base primary/secondary winding voltage (rmsLL)  Base value for PU conversion (kV)

Base power (total)  Base value for PU conversion (MVA) 
Base frequency  Base value for PU conversion (Hz) 
R12  Primary to secondary resistance (pu) 
R13  Primary to tertiary resistance (pu) 
R23  Secondary to tertiary resistance (pu) 
L12  Primary to secondary inductance (pu) 
L13  Primary to tertiary inductance(pu) 
L23  Secondary to tertiary inductance (pu) 
Parameter calculation method 

3limb magnetic circuit  Enables/disablesthemodelingofthethreeleggedmagneticcircuit 
Air and tank leakage inductance  Inductanceofthefictitiouswinding(pu) [uses thesamebase astertiarywinding] 
Air and tank leakage resistance  Resistanceofthefictitiouswinding(pu) [uses thesamebase astertiarywinding] 
Neutral Impedance Parameters
R1, R2, R3, R4  Neutral resistance of the winding; only applies to Y ground (Ω) 
L1, L2, L3, L4  Neutral inductance of the winding; only applies to Y ground (H) 
C1, C2, C3, C4  Neutral capacitance of the winding; only applies to Y ground (F) 
Saturation Parameters
Number of data points  Number of segments of the currentflux saturation curve; only the positive part of the curve must be specified, the negative part being completed by symmetry 
Saturation current  Current for each segment of the saturation curve; the origin (0,0) is implied (A) 
Saturation flux  Flux for each segment of the saturation curve; the origin (0.0,0.0) is implied (V.s) 
Hysteresis Parameters
Saturation data type  Determines if the saturation curve is calculated by the model or defined by a series of segments (Equation, Curve) 
Air core inductance  Value of the saturation inductance that the curve approaches asymptotically (H) 
Slope at Ic:  Flux slope at coercive current (H) 
Coercive current  Ic  Positive coercive current at null flux (A) 
Saturation current  Is  Current value of the first point in the saturation zone (A) 
Current tolerance  Special parameter limiting the generation of minor nested loops. When the magnetizing current values at the last inversion point and the preceding inversion point are closer than the specified tolerance (in % of Ic), it is assumed that there is a displacement on a trajectory represented by a straight line segment. 
Remanent flux  Φr  Positive remanent flux at null current (V.s) 
Saturation flux  Φs  Flux value of the first point in the saturation zone (V.s) 
Flux tolerance  Special parameter limiting the generation of minor nested loops. When the flux values at the last inversion point and the preceding inversion point are closer than the specified tolerance (in % of Φs), it is assumed that there is a displacement on the current loop. 
Initial flux (peak)  Initial flux determining initial trajectory which is calculated by supposing that it has an inversion point on the main cycle (V.s) 
Number of data points  Number of segments of the currentflux saturation curve; only the positive part of the curve must be specified, the negative part being completed by symmetry 
Saturation current  Current for each segment of the saturation curve; the first value must be equal to Is (A) 
Saturation flux  Flux for each segment of the saturation curve; the first value must be equal to Φs (V.s) 
Ports, Inputs, Outputs and Signals Available for Monitoring
Ports
Name  Description 

Net_1  Primary winding connection (supports only 3phase connections) 
Net_2  Secondary winding connection (supports only 3phase connections) 
Net_N1  Neutral connection for primary winding (supports only 1phase connections) 
Net_3  Tertiary winding connection (supports only 3phase connections) 
Inputs
 None
Outputs
 None
Sensors
Name  Description  Unit 

FLUX(a,b,c)  Magnetization flux for each phase  V.s 
IMAG(a,b,c)  Magnetization current for each phase  A 
IPRIM(a,b,c)  Primary current for each phase  A 
ISEC2(a,b,c)  Secondary current for each phase  A 
ISEC3(a,b,c)  Tertiary current for each phase  A 
ISEC4(a,b,c)  Fictitious winding current for each phase ( onlyavailablewhenthe"3limbmagneticcircuit"settingis"yes."  A 
SEG(a,b,c)  Segment number of the saturation curve

Internal Connection and Parameters
The internal connection of the autotransformer is shown below. Note that it is the phase C's terminal of tertiary and fictitious windings which are grounded. The neutral point of the autotransformer is accessible via the singlephase "N" terminal.
The main parameters (R_{12}, R_{13}, R_{23}, X_{12}, X_{13}, X_{23}) are entered in "per unit" only. They are then used to determine the parameters of windings (R_{1}, R_{2}, R_{3}, X_{1}, X_{2} and X_{3}) as a function of the nominal voltages of the windings (N_{1} and N_{2}) according to the expressions below, N_{1} and N_{2 }corresponds to the series winding and common winding, respectively.
Latex formatting 

\begin{equation} k=\frac{N_{2}}{N_{1}+N_{2}} \end{equation} \begin{equation} X_{1}=\frac{\frac{1+k}{1k} X_{12}+X_{13}X_{23}}{2(1k)} \end{equation} \begin{equation} X_{2}=\frac{X_{12}X_{13}+X_{23}}{2(1k)} \end{equation} \begin{equation} X_{3}=\frac{X_{12}+X_{13}+(12 k) X_{23}}{2(1k)} \end{equation} If "Parameter calculation method" = Equal R1 R2 \begin{equation} R_{1}=R_{2}=\frac{R_{12}}{2(1k)^{2}} \end{equation} \begin{equation} R_{3}=R_{13}R_{1}{(1k)^{2}}  R_{2}{(k)^{2}} \end{equation} If "Parameter calculation method" = Classic \begin{equation} R_{1}=\frac{\frac{1+k}{1k} R_{12}+R_{13}R_{23}}{2(1k)} \end{equation} \begin{equation} R_{2}=\frac{R_{12}R_{13}+R_{23}}{2(1k)} \end{equation} \begin{equation} R_{3}=\frac{R_{12}+R_{13}+(12 k) R_{23}}{2(1k)} \end{equation} 
The values obtained are referenced to the primary nominal voltages (VbasePrimary = VnomSeries + VnomCommon), secondary (VbaseSecondary = VnomCommon) and tertiary (VbaseTertiary = VnomTertiary).
V base primary  Base primary winding voltage of the autotransformer in kV rms LL 
V base secondary  Base secondary winding voltage of the autotransformer in kV rms LL 
V base tertiary  Base tertiary winding voltage of the autotransformer in kV rms LL 
V nom  Rated voltage of winding (kV rms) as defined in General Parameters 
All other parameters are entered in the same way as for other HYPERSIM transformer models. The saturation is placed at the series winding and uses the nominal voltage of this winding for the "per unit" conversion.
Load Flow and Initialization
The autotransformer sends the parameters of a standard equivalent transformer to the power flow algorithm.
Latex formatting 

\begin{equation} R_{1}=R_{2}=\frac{R_{12}}{2} \end{equation} \begin{equation} X_{1}=\frac{X_{12}+X_{13}X_{23}}{2} \end{equation} \begin{equation} X_{2}=\frac{X_{12}X_{13}+X_{23}}{2} \end{equation} 
Tertiary winding is considered for power flow whereas the fourth winding (if activated) does not participate in the power flow.
Once the power flow calculation is performed, the values obtained are used to calculate the internal voltages and currents of the autotransformer taking into account the true topology.