Permanent Magnet Synchronous Machine Model for Real- Time Simulation

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INTRODUCTION
IN recent years, Permanent Magnet Synchronous Motors
(PMSMs) are increasing applied in several areas such as
traction, automobiles, robotics and aerospace technology [1].
Accurate digital simulation tools are necessary to evaluate
their field performance particularly when they are driven with
solid-state drives connected to larger electrical networks. One
of the areas of interest is the design of controllers for these
motor drives. In many applications the physical controls have
to be designed and tuned for best performance. If the
simulation of the motor and drive can be implemented in realtime,
it becomes possible to interface the physical
manufacturer-built controller (not its model) and protection
equipment to the simulation using appropriate digital-analog
and analog-digital converters. The real time digital simulator
is a combination of specialized computer hardware and
software designed specifically for the solution of power
system electromagnetically transients in real-time.



III. INTERFACE MODEL OF THE PMSM IN RTDS
Equations (1) and (2) can be used in the diagram of Fig.5
to interface the machine to the network. In every time step the
program reads the voltage from the previous time step and
applies the Park transform to get the dq0 components of the
voltage, then using (1) it calculates the derivatives of the
fluxes. Predictor corrector integration calculates the new
values of the fluxes and by multiplying the inverse of
inductance matrix to the fluxes, dq0 component of the currents
can be obtained.



IV. EMBEDDED MODEL OF THE PMSM IN RTDS
The machine can be modeled as set of mutual inductances
that change in value with time. In this case the model doesn’t
have the problem of interface that may cause numerical
instabilities. This model doesn’t use the Park transform and
directly solves the machine equations in phase domain. For a
machine, or in general, a set of time-varying mutual
inductances can be written:


V. COMPARING DIFFERENT MODELS OF THE PMSM IN RTDS
The dq0 and embedded model of the PM machine have
been implemented in RTDS in addition to the normal RTDS
synchronous machine model. Both of the machine models are
running at rated speed. It is possible to add a mechanical load
to the machine and project ω from the previous time step [6].



C. Numerical Stability of the Machines
Numerical stability of the different types of the permanent
magnet synchronous machine was studied by running the case
with different time steps. The embedded model of the machine
has the best performance among these models and is stable
even for very large time steps. This model is accurate and the
results are the same in different time steps. The RTDS
synchronous machine is unstable with the time-steps larger
than169μ S , the same thing happens with the interface model
with the time-steps larger than167μ S .Typical time-steps are
50μ S . Similar results obtained when an inductive source
supplied the machines.