Switched Reluctance Machine
Purpose
Detailed model of switched reluctance machine with open windings
Library
Electrical / Machines
Description
These components represent analytical models of three common switched reluctance machine types: three-phase 6/4 SRM, four-phase 8/6 SRM and five-phase 10/8 SRM.
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. In the component icon, the positive terminals of the stator windings are marked with a dot.
Note The Switched Reluctance Machine models can only be simulated with the Continuous State-Space Method.
The machine flux linkage is modeled as a non-linear function of the stator current
and rotor angle accounting for both the magnetization characteristic of the
iron and the variable air gap.
In the aligned rotor position the flux linkage is a non-linear function of the stator current:
where
For intermediate rotor positions the flux linkage is written as a weighted sum of these two extremes
using the weighting function
where is the number of rotor poles,
is the number of stator poles, and
is the index of the stator phase.
Electrical System
The electromagnetic torque produced by one phase is the derivative of the coenergy with respect to the rotor angle:
The total torque of the machine is given by the sum of the individual phase
torques.
Mechanical System
Rotor speed:
Rotor angle:
Parameters
- Stator resistance
- Stator resistance
in ohms (
).
- Unaligned stator inductance
- Stator inductance
in the unaligned rotor position, in henries (H).
- Initial aligned stator inductance
- Initial stator inductance
in the aligned rotor position, in henries (H).
- Saturated aligned stator inductance
- Saturated stator inductance
in the aligned rotor position, in henries (H).
- Aligned saturation flux linkage
- Flux linkage
at which the stator saturates in the aligned position, in Vs.
- Inertia
- Combined rotor and load inertia
in
.
- Friction coefficient
- Viscous friction
in Nms.
- Initial rotor speed
- Initial mechanical speed
in radians per second (
).
- Initial rotor angle
- Initial mechanical rotor angle
in radians.
- Initial stator currents
- A three-element vector containing the initial stator
currents
,
and
of phases a, b and c in amperes (A).
Probe Signals
- Stator phase currents
- The three-phase stator winding currents
,
and
, in A. Currents flowing into the machine are considered positive.
- Back EMF
- The back EMF voltages
,
,
in volts (V).
- Stator flux linkage
- The flux linkages in the individual phases of the machine in Vs.
- 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.A. Torrey, J.A. Lang, "Modelling a nonlinear variable-reluctance motor drive", IEE Proceedings, Vol. 137, Pt. B, No. 5, Sept. 1990.
- D.A. Torrey, X.-M. Niu, E.J. Unkauf, "Analytical modelling of variable-reluctance machine magnetisation characteristic", IEE Proceedings Electric Power Applications, Vol. 142, No. 1, Jan. 1995.