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Description

In three-limb transformers, the magnetic flux associatedwith quasi DC Geomagnetic Induced Currents (GICs) passesthroughthe high reluctance path of the transformertankand air. Therefore.  three-limb transformers are  less sensitive to GICs. To consider the impact of the core structure in GIC studies, a fictitious winding (delta grounded) is added to the basic autotransformer model.  


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Mask and Parameters

General Parameters

Tertiary connectionSelect whether the delta-connected winding voltage will lead or lag the star-connected winding voltage or ground C-phase
Flux-Current characteristic modelModel saturation only or saturation with hysteresis
Iteration in saturation modelEnable 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)
RmEquivalent resistance of iron losses of the magnetic circuit (Ω)
Base primary/secondary winding voltage (rmsLL)

Base value for PU conversion (kV)

  • Voltage expressed in kV rms LL
  • This base voltage and nominal voltage will change, if the corresponding winding connection switches between delta and Y.
Base power (total)Base value for PU conversion (MVA)
Base frequencyBase value for PU conversion (Hz)
R12Primary to secondary resistance (pu)
R13Primary to tertiary resistance (pu)
R23Secondary to tertiary resistance (pu)
L12Primary to secondary inductance (pu)
L13Primary to tertiary inductance(pu)
L23Secondary to tertiary inductance (pu)
Parameter calculation method
  • EqualR1 R2: Resistance oftheseries winding is set equalto thecommonwinding
  • Classic: R1, R2, and R3 are calculated using between winding resistances R12,R13andR23 
3-limb magnetic circuit

Enables/disablesthemodelingofthethree-leggedmagneticcircuit 

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, R4Neutral resistance of the winding; only applies to Y ground (Ω)
L1, L2, L3, L4Neutral inductance of the winding; only applies to Y ground (H)
C1, C2, C3, C4Neutral capacitance of the winding; only applies to Y ground (F)

Saturation Parameters

Number of data pointsNumber of segments of the current-flux saturation curve; only the positive part of the curve must be specified, the negative part being completed by symmetry
Saturation currentCurrent for each segment of the saturation curve; the origin (0,0) is implied (A)
Saturation fluxFlux for each segment of the saturation curve; the origin (0.0,0.0) is implied (V.s)

Hysteresis Parameters

Saturation data typeDetermines if the saturation curve is calculated by the model or defined by a series of segments (Equation, Curve)
Air core inductanceValue of the saturation inductance that the curve approaches asymptotically (H)
Slope at Ic:Flux slope at coercive current (H)
Coercive current - IcPositive coercive current at null flux (A)
Saturation current - IsCurrent value of the first point in the saturation zone (A)
Current toleranceSpecial 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 - ΦrPositive remanent flux at null current (V.s)
Saturation flux - ΦsFlux value of the first point in the saturation zone (V.s)
Flux toleranceSpecial 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 pointsNumber of segments of the current-flux saturation curve; only the positive part of the curve must be specified, the negative part being completed by symmetry
Saturation currentCurrent for each segment of the saturation curve; the first value must be equal to Is (A)
Saturation fluxFlux 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


NameDescription
Net_1Primary winding connection (supports only 3-phase connections)
Net_2Secondary winding connection (supports only 3-phase connections)
Net_N1

Neutral connection for primary winding (supports only 1-phase connections)

Net_3Tertiary winding connection (supports only 3-phase connections)


Inputs

  • None

Outputs

  • None

Sensors


NameDescriptionUnit
FLUX(a,b,c)Magnetization flux for each phaseV.s
IMAG(a,b,c)Magnetization current for each phaseA
IPRIM(a,b,c)Primary current for each phaseA
ISEC2(a,b,c)Secondary current for each phaseA
ISEC3(a,b,c)Tertiary current for each phaseA
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

  • In the saturation model, the numbering is always positive starting at 1 for the last segment in the negative saturation zone.
  • In the hysteresis model, the numbering is positive/negative starting at 1/-1 in the positive/negative saturation zone. In the hysteresis zone, it takes a null value.



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 single-phase "N" terminal.

The main parameters (R12, R13, R23, X12, X13, X23) are entered in "per unit" only. They are then used to determine the parameters of windings (R1, R2, R3, X1, X2 and X3) as a function of the nominal voltages of the windings (N1 and N2) according to the expressions below, N1 and Ncorresponds 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}{1-k} X_{12}+X_{13}-X_{23}}{2(1-k)}
\end{equation}
\begin{equation}
X_{2}=\frac{X_{12}-X_{13}+X_{23}}{2(1-k)}
\end{equation}
\begin{equation}
X_{3}=\frac{-X_{12}+X_{13}+(1-2 k) X_{23}}{2(1-k)}
\end{equation}
If "Parameter calculation method" = Equal R1 R2

\begin{equation}
R_{1}=R_{2}=\frac{R_{12}}{2(1-k)^{2}}
\end{equation}
\begin{equation} 
R_{3}=R_{13}-R_{1}{(1-k)^{2}} - R_{2}{(k)^{2}} 
\end{equation}

If "Parameter calculation method" = Classic
\begin{equation}
R_{1}=\frac{\frac{1+k}{1-k} R_{12}+R_{13}-R_{23}}{2(1-k)}
\end{equation}
\begin{equation} R_{2}=\frac{R_{12}-R_{13}+R_{23}}{2(1-k)} 
\end{equation} 
\begin{equation} R_{3}=\frac{-R_{12}+R_{13}+(1-2 k) R_{23}}{2(1-k)}
\end{equation}

The values obtained are referenced to the primary nominal voltages (VbasePrimary = VnomSeries + VnomCommon), secondary (VbaseSecondary = VnomCommon) and tertiary (VbaseTertiary = VnomTertiary).

V base primaryBase primary winding voltage of the auto-transformer in kV rms LL
V base secondaryBase secondary winding voltage of the auto-transformer in kV rms LL
V base tertiaryBase tertiary winding voltage of the auto-transformer in kV rms LL
V nomRated 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.