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Switched Reluctance Machine

Purpose

Detailed model of a switched reluctance machine with open windings.

Library

Machines

Description

[Picture]

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 machines operate as motor or generator; the sign of the mechanical torque determines the mode of operation (positive for motoring, negative for generating). 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 nonlinear function of the stator current and rotor angle Y(i;) accounting for both the magnetization characteristic of the iron and the variable air gap.

pict

In the unaligned rotor position the flux linkage is approximated as a linear function:

Yu(i) = Lu  i

In the aligned rotor position the flux linkage is a nonlinear function of the stator current:


Ya(i) = Ysat  1   e  K  i + Lsat  i

where

K  = La---Lsat-
       Ysat

For intermediate rotor positions the flux linkage is written as a weighted sum of these two extremes

Y(i;  ) = Y (i)+ f(  )  (Y (i)   Y (i))
          u           a      u

using the weighting function


f(  ) = 1 + 1cos N     + 2    -x-
      2   2      r        Ns

where Nr is the number of rotor poles, Ns is the number of stator poles, and x = 0(Ns=2 1) is the index of the stator phase.

Electrical System

pict

The terminal voltage of a stator phase is determined by the equation

v = R   i+ dY-= R   i+ @Y-   di+ @Y-   d--
          dt          @i  dt  @     dt

The electromagnetic torque produced by one phase is the derivative of the coenergy with respect to the rotor angle:

         @ Z i
T(i;  ) =---  Y(i0;  )di0
        @    0

The total torque Te of the machine is given by the sum of the individual phase torques.

Mechanical System

Rotor speed:

 d    1
dt! = J-(Te   F!    Tm)

Rotor angle:

-d   = !
dt

Parameters and Dialog Box

[Picture]

Stator resistance
Stator resistance R in ohms (_O_).
Unaligned stator inductance
Stator inductance Lu in the unaligned rotor position, in henries (H).
Initial aligned stator inductance
Initial stator inductance La in the aligned rotor position, in henries (H).
Saturated aligned stator inductance
Saturated stator inductance Lsat in the aligned rotor position, in henries (H).
Aligned saturation flux linkage
Flux linkage Ysat at which the stator saturates in the aligned position, in Vs.
Inertia
Combined rotor and load inertia J in Nms2.
Friction coefficient
Viscous friction F in Nms.
Initial rotor speed
Initial mechanical speed !m;0 in radians per second (s1).
Initial rotor angle
Initial mechanical rotor angle m;0 in radians.
Initial stator currents
A three-element vector containing the initial stator currents ia;0, ib;0 and ic;0 of phases a, b and c in amperes (A).

Inputs and Outputs

Mechanical torque
The input signal Tm represents the mechanical torque at the rotor shaft, in Nm.

The output vector "m" contains the following 7 signals:

(1) Rotor speed
The rotational speed !m of the rotor in radians per second (s1).
(2) Rotor position
The mechanical rotor angle m in radians.
(3) Electrical torque
The electrical torque Te of the machine in Nm.
(4-6) Flux linkages
The flux linkages in the individual phases of the machine in Vs.

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 Characteristics", IEE Proceedings Electric Power Applications, Vol. 142, No. 1, Jan. 1995.