Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Modeling and control modes of PM synchronous motor drives
Chapter 2
MODELING AND CONTROL MODES OF PM SYNCHRONOUS DRIVES
2.1 Mathematical model of PM synchronous motor
Development of the machine model through the understanding of physics of the
machine is the key requirement for any type of electrical machine control. Since in this
project a Surface type Permanent Magnet Synchronous Motor (SPMSM) is used for the
investigation [9,13,14,15,16]. The development of those models is under bellow
assumptions as [3]:
• three-phase motor is symmetrical,
• only a fundamental harmonic of the magneto motive force (MMF) is taking in to
account,
• the spatially distributed stator and rotor winding are replaced by a concentrated
coil,
• an anisotropy effects, magnetic saturation, iron loses and eddy currents are not
taking into considerations,
• the coil resistances and reactances are taking to be constant,
• in many cases, especially when is considered steady state, the currents and
voltages are assumed to be sinusoidal,
• thermal effect for permanent magnets is omitted.
The synchronous motor model will be presented in space vector notation. Space vector
form of the machine equations has many advantages such as compact notation, easy
algebraic manipulation, and very simple graphical interpretation. Specially, this notation
is very useful when analyzing the vector control based technique of the AC machines.
The space vector representation of AC machine equations has been discussed in detail
in number of text books ([3,4,12]).
The instantaneous value of a three-phase system KA, KB,
K
C
(such as currents, voltages
and flux linkages) can be replaced by one resultant vector called the space vector,
2
K = ⎡ 1 ⋅ K + a⋅ K + a K
3 ⎣
2
A B C
⎤
⎦
(2.1)
8