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MULTILEVEL MODELING

AND SIMULATION OF A

SWITCHED RELUCTANCE MACHINE

P.J. van Duijsen

Simulation Research,

P.O. Box 397

2400 AJ Alphen aan den Rijn

The Netherlands

Tel/Fax +31172092353

ABSTRACT

In this paper
the modeling and simulation of a Switched Reluctance Machine is described.
Modeling and simulation is an already accepted method in the design
of drive systems. The entire drive, including power converter, SRM,
mechanical load and control are modeled in one multilevel model. In
the paper it is explained why use is made of a multilevel package for
modeling and simulation of a complete drive system.

The application
of mechatronic systems requires more modeling effort compared to modeling
of regular electronic systems. This is caused by the difference in models
for the electrical machine, the power converter and the control of the
drive. A multilevel model is applied, which combines the circuit model,
a block-diagram and programming language and thereby eases the modeling
process.

Because of the
required small time step in the simulation of the power converter the
total simulation time is large. Therefore a simulation program has to
be used, which has special ideal models for the semiconductor switches
and thus reducing the total simulation time.

Results from
the simulation show the internal waveforms of the converter, such as
the rotor angle dependent inductance of the stator, angular frequency
of the rotor and the torque produced by the SRM.

INTRODUCTION

The design of an electrical drive system is a cumbersome task. Modeling
and simulation can help the designer to meet his goals. The number of
modeling and simulation programs is large and the application of the
simulation programs is diverse.

An electromechanical
system combines the electrical machine and power converter in one system.
This so called mechatronics system therefore contains various techniques,
like power electronics, electrical machine, mechanical load and control.

A main problem
with the simulation of mechatronic systems is the simulation time. The
simulation for the power converter requires a time step in the order
of microseconds. The dynamics of the drive are mostly in the order of
seconds. Therefore a large number of time steps is required to simulate
the entire behavior of the total SRM drive. A requirement for the simulation
program is therefore that the simulation has to be very fast. This is
achieved by applying special ideal models for semiconductor models.
The used simulation package CASPOC [Duijsen, 1994] provides these ideal
models.

In this paper
a model of Switched Reluctance Machine: (SRM) is described [Buja, 1991],
[Buja, 1993]. The modeling is described and the results from the simulation
are discussed. The main interest is the way in which a model is build
for mechatronic systems.

Figure 1: Multilevel model of the SRM drive.Modeling and
simulation programs are mainly devoted towards one type of technique.
It is either a circuit simulation for power electronics, a block-diagram
oriented program for the electrical machine or mechanical load or a
high level programming language for the control. The modeling and simulation
of the entire system, the power converters, electrical machine, mechanical
load and control, is found only rarely. The reason for this is the lack
of simulation programs able to handle the modeling and simulation of
such an entire system.

The available
modeling and simulation programs are in many cases not satisfactory
for the modeling of the different used techniques.

Circuit simulation   Difficult or impossible to model the electric machine
and no modeling of the control.

Block-diagram  Difficult to model the power converter. Semiconductor
switches are state event depending and thereby changing the topology
of the block-diagram model.

Programming language Impossible to model a dynamic system including
integrators, unless a complete new simulation program is written.

The solution
for this problem is a multilevel modeling and simulation program. A
multilevel model has to incorporate at least a:

1 circuit model,

2 block-diagram model,

3 modeling language ( Pascal, C ).

The combination
of the circuit model, block-diagram model and programming language is
called the multilevel model. Interconnections exist between the circuit
model, block-diagram model and the programming language. Figure 1 shows
the multilevel model and the interconnections between the different
models of a Switched Reluctance Drive.

Figure 2 : Value of inductance per phase of a SRM.The simulation
of the multilevel model includes the simulation with all the models
in the multilevel model. As result a simulation of the entire system,
which is modeled by the different models, is possible. The simulation
will show the behavior of the entire system. The dynamics of the different
subsystems are connected via the multilevel model and therefore the
simulation shows the dynamic behavior of the total system. Influences
in, for example, the mechanical load which lead to different waveforms
in the power converter are directly visible.

EXAMPLE SRM

The modeling
of a SRM is chosen because of the various techniques which are used
to build a SRM drive system. The model contains a description of the
electrical machine, the power converter which drives the electrical
machine, the dynamics of the mechanics in the drive and the applied
control, which is dependent on the position of the rotor of the SRM.

The construction
of the SRM which is examined in this paper is given in figure 2. The
SRM,  is modeled by non-linear mathematical relations describing
the value of an inductance [Buja, 1991], [Buja, 1993]. The value of
the inductance per phase is depending on the position of the rotor in
the SRM: