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3-Winding 3-Phase Saturable Transformer with Internal Tertiary
- Sylvain Ménard
Description
The 3-winding saturable transformer with internal tertiary adds modelling of saturation and hysteresis to the linear transformer at the expense of some computation time. It still spares some computation time in comparison to the saturable model with three flexible winding types.
Mask and Parameters
General Parameters
| Description | Use this field to add all kinds of information about the component |
| Flux-Current 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 primary/secondary/tertiary 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 frequency | Base value for PU conversion (Hz) |
Magnetization Impedance Parameters
- Rm: Equivalent resistance of iron losses of the magnetic circuit (Ω)
Winding Parameters
| Primary/secondary connection | Winding type
|
| Tertiary connection | Forced to Delta |
| Voltage (rmsLL) | Rated voltage of the winding (kV)
|
| R1, R2, R3 | Leakage resistance of the winding (Ω) |
| L1, L2, L3 | Leakage inductance of the winding (H) |
Neutral Impedance Parameters
| R1, R2 | Neutral resistance of the winding; only applies to Y ground (Ω) |
| L1, L2 | Neutral inductance of the winding; only applies to Y ground (H) |
| C1, C2 | Neutral capacitance of the winding; only applies to Y ground (F) |
Saturation Parameters
The saturation is characteristic of the core, thus of the winding and not the type of 3-phase connection (Y, Delta or Zigzag). It is represented only for the magnetization branch (schematically using line segments).
| 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
The main hysteresis cycle is characterized by four parameters. It is measured in DC so as not to include the Foucault losses, which are considered by the parallel resistance (Rm). The initial trajectory is characterized by only one parameter, the initial flux. Two other special parameters serve to minimize the generation of internal nested loops, and their corresponding trajectories, saved in memory (e.g. the loops that are too small will be ignored and their trajectories modelized by a straight line segment).
This is useful since their number must be limited (100 which suffices in most simulated cases). Above this cycle (limited to ±Is), the saturation zone is entered. The saturation is then characterized either by a series of points on the curve or by an inductance that the curve approaches asymptotically. In this last case, the model generates automatically segments (in the positive and negative saturation zone) of equal length (Is).
| 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) |
| Coercitive 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. |
| Remnant flux - Φr | Positive remnant 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 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
| 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_N2 | Neutral connection for secondary winding (supports only 1-phase connections) |
Inputs
- None
Outputs
- None
Sensors
| FLUX(a,b,c) | Magnetization flux for each phase (V.s) |
| ILMAG(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) |
| SEG(a,b,c) | Segment number of the saturation curve
|
References
«Hysteresis Modeling in the Matlab/Power System Blockset», Silvano Casoria, Patrice Brunelle, Gilbert Sybille, Mathematics and Computers in Simulation, Volume 63, Issues 3-5, Pages 237-248
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