Induction Machine with Saturation
Purpose
Induction machine with slip-ring rotor and main-flux saturation
Description
The Induction Machine with Saturation models main flux saturation by means of a continuous function.
The machine operates as a motor or generator; if the mechanical torque has the same sign as the rotational speed the machine is operating in motor mode, otherwise in generator mode. All electrical variables and parameters are viewed from the stator side. In the component icon, phase a of the stator and rotor winding is marked with a dot.
Electrical System:
The machine model offers two different implementations of the electrical system: a traditional stationary reference frame and a voltage-behind-reactance formulation.
Stationary Reference Frame This implementation is based on machine equations in the stationary reference frame (Clarke transformation). Constant coefficients in the stator and rotor equations make the model numerically efficient. However, interfacing the reference frame with the external 3-phase network may be difficult. Since the coordinate transformations are based on voltage-controlled current sources inductors and naturally commutated devices such as diode rectifiers may not be directly connected to the stator terminals. In these cases, fictitious RC snubbers are required to create the necessary voltages across the terminals. The implementation can be used with both the continuous and the discrete state-space method.
Voltage behind Reactance This formulation allows for direct interfacing of arbitrary external networks with the 3-phase stator terminals. The rotor dynamics are expressed using explicit state-variable equations while the stator branch equations are described in circuit form. However, due to the resulting time-varying inductance matrices, this implementation is numerically less efficient than the traditional reference frame.
In both implementations, the value of the main flux inductances and
are not constant but depend on the main flux linkage
as illustrated in
the
diagram.






plsaturation(Lm0, Lmsat, PsiT, fT)
plots the main flux vs. current curve and the magnetizing inductance vs. current curve for the parameters specified.
The model accounts for steady-state cross-saturation, i.e. the steady-state magnetizing inductances along the d-axis and q-axis are functions of the currents in both axes. In the implementation, the stator currents and the main flux linkage are chosen as state variables. With this type of model, the representation of dynamic cross-saturation can be neglected without affecting the machine's performance. The computation of the time derivative of the main flux inductance is not required.
In order to inspect the implementation, please select the component in your circuit and choose Look under mask from the Subsystem submenu of the Edit menu. If you want to make changes, you must first choose Break library link and then Unprotect, both from the same menu.
Electro-Mechanical System
Electromagnetic torque:
Mechanical System
Mechanical rotor speed :
Mechanical rotor angle :
Parameters
- Model
- Implementation in the stationary reference frame or as a voltage behind reactance.
- Stator resistance
- Stator winding resistance
in ohms (
).
- Stator leakage inductance
- Stator leakage inductance
in henries (H).
- Rotor resistance
- Rotor winding resistance
in ohms (
), referred to the stator side.
- Rotor leakage inductance
- Rotor leakage inductance
in henries (H), referred to the stator side.
- Unsaturated magnetizing inductance
- Unsaturated main flux inductance
, in henries (H), referred to the stator side.
- Saturated magnetizing inductance
- Saturated main flux inductance
in henries (H), referred to the stator side. If you do not want to model saturation, set
.
- Magnetizing flux at saturation transition
- Transition flux linkage
, in Vs, defining the knee between unsaturated and saturated main flux inductance.
- Tightness of saturation transition
- Form factor
defining the tightness of the transition between unsaturated and saturated main flux inductance. The default is 1.
- Inertia
- Combined rotor and load inertia
in
.
- Friction coefficient
- Viscous friction
in Nms.
- Number of pole pairs
- Number of pole pairs
.
- Initial rotor speed
- Initial mechanical rotor speed
in
.
- Initial rotor position
- Initial mechanical rotor angle
in radians. If
is an integer multiple of
the stator windings are aligned with the rotor windings at simulation start.
- Initial stator currents
- A two-element vector containing the initial stator currents
and
of phases a and b in amperes (A).
- Initial stator flux
- A two-element vector containing the initial stator flux
and
in the stationary reference frame in Vs.
Probe Signals
- Stator phase currents
- The three-phase stator winding currents
,
and
, in A. Currents flowing into the machine are considered positive.
- Rotor phase currents
- The three-phase rotor winding currents
,
and
in A, referred to the stator side. Currents flowing into the machine are considered positive.
- Stator flux (dq)
- The stator flux linkages
and
in the stationary reference frame in Vs.
- Magnetizing flux (dq)
- The magnetizing flux linkages
and
in the stationary reference frame in Vs.
- Rotor flux (dq)
- The rotor flux linkages
and
in the stationary reference frame in Vs, referred to the stator side.
- Rotational speed
- The rotational speed
of the rotor in radians per second (
).
- Rotor position
- The mechanical rotor angle
in radians.
- Electrical torque
- The electrical torque
of the machine in Nm.
References
- D. C. Aliprantis, O. Wasynczuk, C. D. Rodriguez Valdez, "A voltage-behind-reactance synchronous machine model with saturation and arbitrary rotor network representation", IEEE Transactions on Energy Conversion, Vol. 23, No. 2, June 2008.
- K. A. Corzine, B. T. Kuhn, S. D. Sudhoff, H. J. Hegner, "An improved method for incorporating magnetic saturation in the Q-D synchronous machine model", IEEE Transactions on Energy Conversion, Vol. 13, No. 3, Sept. 1998.
- E. Levi, "A unified approach to main flux saturation modelling in D-Q axis models of induction machines", IEEE Transactions on Energy Conversion, Vol. 10, No. 3, Sept. 1995.
- E. Levi, "Impact of cross-saturation on accuracy of saturated induction machine models", IEEE Transactions on Energy Conversion, Vol. 12, No. 3, Sept. 1997.