Performance analysis and control of permanent magnet synchronous motor drive over a wide speed range

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Performance Analysis and Control of Permanent
Magnet Synchronous Motor Drive over a wide speed
range
Poonam Jayal and G. Bhuvaneswari
Department of Electrical Engineering, IIT Delhi, India.
poonam.jayal@gmail.com bhuvan@ee.iitd.ac.in
Abstract— This paper presents the state of the art closed-loop
control technique namely the Field Oriented Control (FOC) for a
Permanent Magnet Synchronous Motor (PMSM) drive. An
effective model implementing FOC with field-weakening control
is presented to analyze and control the performance of a PMSM
drive over a wide range of speeds including the constant torque
and constant power regions of operation. A sinusoidal pulse
width modulated (SPWM) three-phase voltage source inverter
(VSI) fed low-power surface-mounted PMSM (SMPMSM) drive
system is modeled and simulated in MATLAB/Simulink
environment. It is analyzed for various dynamic operating
conditions for speeds ranging from as low as 100 rpm to 3500
rpm. The maximum speed attainable in field-weakening region is
found to be dependent on the machine parameters . This is
further validated by the simulation results of the drive under
investigation.
Keywords— FOC, PMSM, SMPMSM,field-weakening, SPWM
I. INTRODUCTION
Variable speed drives have gained huge popularity lately
especially in the low power applications (<10kW) like fans,
blowers, centrifugal pumps etc. Various high performance
applications like robots, hybrid vehicles, machine tools also
prefer adjustable speed drives to fixed speed drives to promote
energy conservation. Permanent Magnet Synchronous Motors
are gradually replacing the DC and induction motors in the
domain of variable speed drives owing to some of their
excellent properties like higher torque and flux density, higher
efficiency and superior dynamic performance, high power
factor, spark-less operation, low noise, longer life and most
importantly a smaller volume and size. Therefore, PMSM and
its control techniques have been researched heavily all over
the world lately.
Field Oriented Control (FOC) is one of the most popular
closed-loop control techniques employed to obtain an
excellent dynamic performance for the PMSM. It enables the
separation of the torque-producing and flux-producing
components of stator current, thereby providing a decoupled
control for the PMSM drive emulating the control structure of
a separately-excited DC machine [1]. Thus, FOC transforms
the control of an alternating current machine into that of a DC
machine by allowing independent torque and flux control.
FOC imparts complete motor torque capability to the PMSM
at speed ranges below rated speed and an efficient
performance over a wider speed range.
Servo drives require constant torque operation whereas
traction applications require an extended range of operation of
the PMSM i.e. both the constant torque and constant power
regions [2]. Speeds beyond base speed can be achieved with
an appropriate control of the permanent magnet flux.
In the literature, several papers [3-5] have dealt with the
field-weakening control of PMSM. Dongyun Lu and Kar
present comprehensive classification and overview of the
state-of-the art of flux weakening strategies for the PMSM [6].
It classifies the flux weakening methods broadly into two
types- one is by improving the magnetic design of the motor,
while the other is the electronic control approach which is
based on the control of the d and q-axis current components of
the stator current to manipulate the constant air gap flux
generated by the permanent magnet rotor. A further
classification of the electronic control approach as Model-
based and Model-free approaches is presented in [7]. Model-
based control gives precise control as long as not hindered by
parameter sensitivity. Model-free flux weakening control
strategies give better steady state and dynamic performance as
they are insensitive to parameter variations.
This paper presents the modeling and simulation of a
surface-mounted PMSM drive over a wide range of operating
speed using FOC and field-weakening control to obtain speeds
above base speed.
Another popular technique which is extensively explored
by researchers for control of a PMSM is Direct Torque
Control (DTC) which selects a suitable voltage vector based
on a predefined switching table to obtain the desired torque.
DTC has a simpler structure and better dynamic performance,
but its starting performance and low speed operation are
known to have several problems related to torque pulsations.
Since this paper analyses the operation of a PMSM over a
wide speed range, starting from a very low speed to beyond
base speed, FOC was the preferred choice. Also DTC has a
direct control over voltages while FOC has a direct control
over d and q axis currents, which can be manipulated to obtain
the desired speed and torque.
II. MODELING AND CONTROL ASPECTS OF A PMSM DRIVE
A PMSM has a constant flux in the air gap as long as no
current is supplied from the stator side along the direct axis.
Any modification in the air gap flux value is normally effected
by the direct axis stator current.
2017 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC)

A. Dynamic model of the PMSM
The dynamic model of the PMSM is developed based on
the following mathematical equations[8].The voltage
equations for a surface mounted PMSM in the synchronously
rotating reference frame, with the d-axis aligned with the rotor
field axis are given by (1) and (2),
sd
sd sd s s s e sq
di
i R L L i
dt
v

  
(1)
sq
sq sq s s s e sd m e
di
v i R L L i
dt
  
   
(2)
The electromechanical torque is given by (3).
3
22
d m sq T sq
P
M i K i


(3)
The mechanical equation for the drive is given by (4).
d L m m
d
M M J B
dt

  
(4)
The mechanical speed and rotor position are related as
m
d
dt


(5)
Vsd, vsq, isd and isq are the d-q axis stator voltages and currents
respectively. Rs and Ls are the stator per phase resistance and
inductance respectively. ωe and ωm are the electrical and
mechanical rotor speeds respectively. P is the number of poles,
J is the motor inertia, B is the viscous friction coefficient, Md
is the electromechanical torque, ML is the load torque, ε is the
rotor position w.r.t the stator R phase, λm is the flux linkage of
the permanent magnet and KT is the torque constant.
B. Principle of Field-oriented control (FOC)
Determining the rotor field-flux position is the core of
FOC (thus called field-oriented control). Figure 1. shows the
vector diagram for the FOC of a PMSM [9].The permanent
magnet rotor flux is aligned along the rotor d axis. Thus it is
fixed with respect to the rotor axis and is determined by an
encoder or resolver . The rotor position information (ε), in
turn, is used in the current transformations. The space vector
of stator currents are first transformed into a two coordinate
time variant system (α-β reference frame) as per (6) and then
into the synchronously rotating two coordinate time invariant
system (d-q reference frame) as per (7) using the rotor
position information.
For a balanced three phase system with phase currents ia, ib
and ic ,
0
abc
i i i  
11
122
33
022
a
b
c
i
ii
ii






 


 


 



(6)
where iα and iβ are the two orthogonal components of stator
current in the α-β two coordinate time-variant system.
cos sin
sin cos
sd
sq
ii
ii




 


 





(7)
α
β
d
i s
i sd
i sq ε
m

Figure 1. Vector diagram of FOC for PMSM
Thus the stator current is decomposed into two
orthogonal components, isd and isq, in the d-q two coordinate
time invariant system, thereby simplifying the control and
analysis of a PMSM similar to a separately excited DC motor.
C. Principle of Field-weakening control (FWC)
The speed of operation of PMSM below base speed is
controlled by adjusting the motor terminal voltage by varying
the width of the PWM pulses as long as the inverter output
voltage does not reach its maximum limit. After the machine
attains its rated speed, the output torque will decrease due to
the limitation on the maximum voltage that could be supplied
by the inverter. Therefore, to ensure a constant power region
above base speed, the machine has to be operated in the field-
weakening region. In this region, a negative d-axis current
i.e., a demagnetizing current is injected into the stator to
weaken the permanent magnet rotor flux. This invariably
reduces the q-axis component of stator current and hence the
electromagnetic torque, as there is a limitation on the
maximum current drawn by the machine. An extra d-axis
current, which was maintained zero in the below base speed
operation, leads to additional copper losses and increased
stator winding temperature.
The DC link voltage and the PWM strategy decide the
maximum voltage that an inverter can supply to the motor.
The maximum current also depends on inverter device current
ratings and the machine thermal rating. Let Vmax and Imax be
the maximum inverter voltage and maximum inverter current
per phase respectively. Thus the voltage and current limits of
the PMSM are given by (8) and (9) which would pose
limitations on the maximum attainable speed and the
electromagnetic torque respectively [8].
22
maxs sd sq
i i i I  
(8)
22
maxs sd sq
v v v V  
(9)
Here, Vmax = 0.5 Vdc for Sine Pulse Width Modulation
(SPWM) fed inverter and Vmax = 0.577 Vdc for Space Vector
Pulse Width Modulation (SVPWM) fed voltage source
inverter.

The maximum speed that can be achieved by the PMSM
under no load, in the field weakening region, as obtained from
the steady state voltage equations (1) and (2) is given by (10)
[10].
22
()
(max) (1 )
sn sn sn
mn
sn sn
v i R
Li



(10)
where ωmn is the normalized speed, Vsn is the normalized
stator phase voltage, Rsn and Lsn are the normalized stator
resistance and stator inductance per phase respectively. In this
paper the PMSM drive performance has been found to be
satisfactory up to a maximum speed of 3500 rpm in field
weakening region, which is found to be in accordance with
(10).
III. SYSTEM DESCRIPTION
The complete schematic showing the basic building blocks
of a PMSM closed-loop drive system, functioning over the
complete range of operating speed, including the constant
torque and constant power regions of operation, is depicted in
figure 2.
The instantaneous position of the rotor (and hence rotor
flux) ε is measured using an encoder. The three phase currents
are transformed into the synchronously rotating d-q reference
frame using the rotor position information and thus stator
current is decomposed into its flux producing component (isd)
and torque producing component (isq). The rotor speed is
compared with the reference speed. The field weakening
controller continuously estimates the phase voltage and
compares it with the maximum available phase voltage as
shown in figure 3 [11]. The resulting error signal is processed
by a PI controller, the output of which becomes the reference
for the d axis current controller (isd
*). This is with negative
polarity. The PI speed controller saturation is calculated from
isd
* to limit the stator current to its rated value.
Wm
SPWM
Or
SVPWM
Voltage
source
Inverter PMSM
Speed
PI
+
+
-
-
q-axis
current
PI
controller
Isd
Vsq
Vsd
abc
dq
Field
Weakening
Controller
d-axis
current
PI
controller
dq
abc
isq
+
-
E
N
C
O
D
E
R
d
dt
+
-
Isd*
Isq*

Vdc
Figure 2. Vector controlled PMSM drive system with field weakening
In this cascaded type of closed loop control, the system
time constants are so designed that the inner current loops
respond faster than the outer speed loop. The output of PI
controllers is saturated to limit the voltages and currents to
rated values.
SPWM
Voltage
Source
Inverter
PI
-
+
+
-
-
PI
PI
dq
-
abc
Wm * Vsq
Vsd
Isq*
Isd*
isq
isd
Vsmax
PMSM
dq
abc
isq
isd
PI +
-
22
sd sq
VV
22
m ax sd
II
Figure 3. Field weakening controller
The output voltage of an inverter has been controlled to
obtain variable voltage and frequency for driving the PMSM
using sine PWM (SPWM). In SPWM the reference is
compared with a high frequency carrier wave to generate the
gating signals for the inverter.
IV. MAXIMUM SPEED IN FIELD WEAKENING REGION
The maximum speed of the PMSM drive system with field
weakening can be analytically verified according to (10). The
parameters of the PMSM used for simulation are specified in
Table- I and also used for analytical calculations.
TABLE I
PARAMETERS OF PMSM USED FOR SIMULATION
Rated output power (Pbase)
3485 Watts
Poles
2
Rated speed
3000 RPM
Rated torque (Tbase)
11.1 Nm
Rated current (Ibase)
6.94 A rms
Stator per phase resistance(Rs)
1.3 ohms
Stator per phase inductance (Ls)
0.0069 H
Inertia (J)
0.0027 Kg-m2
Torque constant (KT)
1.13 Nm/ARMS
Back emf constant (Ke)
96.7 VRMS(LL)/KRPM
The base values of power , torque and current are Pbase,
Tbase and Ibase respectively as tabulated above. From these
values we can calculate the following :
Base voltage ,
V ( / 3* ) 167.39
base base base
P I V
Base speed
/ 313.96 / sec
base base base
P T rad


Base impedance
/ 24.12
base base base
Z V I  
Base inductance
/ 0.0768
base base base
L Z H


Nominal phase resistance
/ 0.054
sn s base
R R Z
Nominal phase inductance
/ 0.0898
sn s base
L L L
Stator phase voltage
(0.5* ) /1.414 176.8
s dc
V V V
Nominal stator voltage
/ 1.056
sn s base
V V V
From (10),
Maximum speed attainable in field weakening region
max 1.159


p.u

Hence for a rated speed of 3000 rpm, the maximum speed
possible for the motor under investigation, whose parameters
are specified in Table 1, is 1.159*3000= 3476 RPM. From the
simulation results it is verified that the maximum speed that is
attained with field weakening has been limited to 3500 RPM.
V. SIMULATION AND RESULTS
Figure 4. shows the MATLAB/Simulink model of the
complete PMSM drive system . The dynamic and steady state
response of the drive have been analyzed for various operating
conditions. Table I lists the parameters of the PMSM drive
which is being investigated in this paper.
Figure 4. MATLAB/Simulink model of the PMSM drive functional for a
wide range of speed operation
A. Dynamic response of the PMSM drive
The responses of the PMSM drive during starting, load
perturbation and reference speed change are investigated for
below and above the base speed regions.
(i) Below base speed
In Figure 5. the PMSM drives attains a speed of 2000 rpm
from standstill in 0.12 sec, without any overshoot. The motor
is started with a load torque of 0.2 p.u. which is further
increased to 0.9 p.u. at 0.18 sec, due to which there is a slight
dip seen in the motor speed; however the speed control loop
retrieves the motor speed back to the original value. At 0.25
sec, the load torque is again reduced to 0.2 p.u. At 0.35 sec,
the motor reference speed is changed to 2500 rpm keeping the
load torque unaffected, which is tracked precisely by the drive
in about 0.385 sec. The stator currents and the torque response
have been shown along with the variations in speed.
Figure 5. Dynamic response of the PMSM drive below base speed
(ii) Above base speed
Figure 6. shows the response of the drive for above base
speed operation. The drive initially ramps up to a speed of
1000 rpm in 0.05 sec with a load torque of 0.2 p.u. At 0.14
sec, the reference speed is changed to 3500 rpm. The motor
attains 3500 rpm in 0.21sec at no load, with a slight overshoot.
Thereafter, a load torque of 0.3 p.u. is applied at 0.4 sec. As
this is field weakening zone, the torque capability of the
machine comes down; but it retains constant power
deliverability.
Figure 6. Dynamic response of the PMSM drive above base speed
B. Steady state response of the PMSM drive
Figure 7(a) and Figure 7(b) show the steady state response
of the PMSM drive below base speed for one cycle of steady
state condition as obtained from Fig. 5.
(a)

(b)
Figure 7. (a) Steady state response of the PMSM drive below base
speed (b) THD of stator current
The THD in the motor currents is found to be 5.94%. The low
current THD indicates that the torque pulsations are well
within limits.
C. Speed tracking over a wide range
Figure 8. shows the speed tracking of the PMSM over a
wide speed range, from 100 rpm to 3500 rpm. The drive
attains a speed of 100 rpm within 0.01 sec with a load torque
of 0.2 p.u. Thereafter the speed is increased from 100 rpm to
500 rpm, then to 2500 rpm and finally to 3500 rpm. The drive
is capable of delivering the desired load torques and follow the
speed trajectory without any significant overshoots or
undershoots.
Figure 8. Dynamic response of the PMSM drive over a wide speed range
Figure 9. shows the output phase voltage of the SPWM
two-level inverter after elimination of the common mode
voltage from the pole voltage and its magnitude is 2/3*Vdc.
Figure 9. Simulated waveforms for a two-level inverter operating at unity
modulation index and switching frequency of 5KHz.
VI CONCLUSIONS
Permanent magnet synchronous motor drives have been
gaining importance in the variable speed arena due to their
increased controllability, better dynamic response and higher
torque to inertia ratio. This paper is yet another attempt to
bring out the superior performance of a PMSM drive while
being controlled by FOC technique using Sine PWM
technique over a wide speed range. The PMSM drive has been
investigated under various dynamic operating conditions such
as starting, load perturbation and reference speed change for a
wide range of operating speeds ranging from a few hundred
rpm to 3500 rpm. The drive is able to start and attain a steady
state speed of 2000 rpm within a couple of cycles. The
electromagnetic torque and speed changes are also tracked
effectively without much overshoot or undershoot, thereby
validating the appropriate tuning of the PI controllers. The
stator current THD is well below 10% thereby indicating
nominal torque pulsations. Thus it can be concluded that the
PMSM drive investigated in this paper can be used for specific
applications like in traction, which requires a wide range of
speed operation with constant power output and also a
nominal power output (one-third of rated power) at low
speeds. This paper thus presents an effective method of
controlling the PMSM drive to obtain excellent dynamic
performance over a wide range of speed ranging from 100 rpm
to 3500 rpm and also emphasizes the fact that the maximum
speed attainable in the field-weakening region is limited by the
machine parameters.
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