Mask and Parameters
General Parameters
Tertiary connection | Select whether the delta-connected winding voltage will lead or lag the star-connected winding voltage or ground C-phase |
Flux-Current 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)
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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 |
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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, 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 current-flux 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 current-flux 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 3-phase connections) |
Net_2 | Secondary winding connection (supports only 3-phase connections) |
Net_N1 | Neutral connection for primary winding (supports only 1-phase connections) |
Net_3 | Tertiary winding connection (supports only 3-phase 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
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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 N2 corresponds to the series winding and common winding, respectively.
Latex formatting |
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\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 primary | Base primary winding voltage of the auto-transformer in kV rms LL |
V base secondary | Base secondary winding voltage of the auto-transformer in kV rms LL |
V base tertiary | Base tertiary winding voltage of the auto-transformer 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 |
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\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.