DESIGNING SPACE VECTOR CURRENT CONTROLLERS FOR PMSM DRIVES

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JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH

IN
ELECTRONICS AND COMMUNICATION ENGINEERING

ISSN: 0975


6779|
NOV 11 TO OCT 12
|
VO
LUME


02, ISSUE
-

01


Page
246

DESIGN
ING

SPACE VECTOR
CURRENT
CONTROLLERS FOR PMSM

DRIVES


1
PROF.
VINOD J. RUPAPARA.
2

PROF.
M.V.MAKWANA


1
Assistant
Professor &
P
.
G
.
Student
,
Power
Electronics Dep
t,
L
.
E
.
College
,
Morbi

2
Assistant
Professor,
Power
Electronics
Dep
t
,
Om
Shanti Engineer
ing College,
Rajkot


drivecon@yahoo.co.in,
shafimakwana@indiatimes.com










Keywords

PMSM, hysteresis, delta, space vector, PSIM


I.

INTRODUCTION

Permanent magnet ac motors have the advantage of
not
requiring any magnetizing current, and hence can
operate at a higher power factor and efficiency than
an induction motor in the fractional to 30
kW
regions. Inverter
-
fed PM machines do not need slip
rings or brushes; hence the reliability of the motor is
h
igher than that of a wound rotor synchronous motor.
The use of the permanent magnets tends to reduce the
weight compared to other motors of equivalent power
output. This leads to an increased torque to inertia
ratio and power density [
1
], which make PM ac
motors suitable for a variety of applications including
robotics and aerospace [
1
]


Figure
1
basic block diagram of vector controlled
PMSM drive.


A current controlled inverter is required to provide
the dc machine servo characteri
stics, however the
different current control strategies available require
investigation as their performance differs over a
range of operating conditions. An

analytical study of
hysteresis controllers has been performed
[
5
]

While the space vector controll
er is described in
[
6
].

The ramp comparison controller is modeled on a
computer in [
3
] and the delta controller discussed in
[
4
].

This paper uses two criteria of current controllers
to evaluate them as a function of operating
conditions. The inverter trans
istor average switching
frequency and the rms current error have been chosen
as readily accessible parameters by which the current

controllers can be evaluated and compared. To
compare the controllers with each other, the motor is
run at a constant speed
and the controller parameters
adjusted to produce the same rms current error. Due
to the complexity of the controllers, only the constant
torque operating condition is considered in this paper
.

II.


VECTOR CONTROL OF A PMSM

Vector control enables ac motors to

obtain
performance characteristics similar to dc machines.
This control technique uses the instantaneous rotor
position to calculate the required stator currents
which are oriented at some specified angle with
respect to the rotor. Current controllers are

used to
force the actual current to follow the commanded
current.

Under usual operating conditions, the magnetic
flux
of the permanent magnets remains

constant.

Therefore by

controlling only the stator currents, the
magnet flux in the air

gap and stator
can be

controlled. The rotor position is used to orientate the
stator currents at any required phase angle with

respect to the rotor flux, and hence with respect to the
back
-
emf
[9].
For a non
-
salient motor (as used in

this
paper), the most efficient opera
tion occurs when the
stator flux is perpendicular to the rotor flux, that is
when it is in phase with the back
-
emf.


ABSTRACT

:
AC induction motor has lower efficiency and poor performance.
PM
synchronous motors (PMSMs) can achieve the servo performance characteristics of dc
machines. This requires the PMSM to be vector controlled with additional tight current
control.

An experimental evaluation of hysteresis, delta,
and ramp

comparison and s
pace
vector current controllers is made, or which circuits are given.


JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH

IN
ELECTRONICS AND COMMUNICATION ENGINEERING

ISSN: 0975


6779|
NOV 11 TO OCT 12
|
VO
LUME


02, ISSUE
-

01


Page
247

III.

TYPES OF CURRENT CONTROLLERS

A permanent magnet synchronous machine has a
sinusoidal back
-
emf, and hence for smooth torque
generation, th
e stator currents must also be
sinusoidal. Of the various methods of non
-
linear
current control, the hysteresis method is one of the
simplest Conceptually. It also has the advantage of a
fast transient response compared to other methods
such as delta or ra
mp comparison. In the discussion
to follow, the current error is defined as:

AI
-

I
-

I*, where I
-

actual current

I* = commanded current

III.I
HYSTERESIS CURRENT C
ONTROL


The hysteresis controller compares the actual phase
current with the commanded, and

if the magnitude of
the error is greater than a preset level, the inverter leg
is switched appropriately [10], although the actual
current also depends on the currents in the other
phases. This is shown for a single phase in figure
2
.



Figure
2

single phase commanded current with
hysteresis band.


For a given phase, the transistor that requires to be
switched is dependent on both the error sign and the
sign of the commanded current (I*). For a hysteresis
bandwidth of h, the algor
ithm used for the inverter
(figure
3
) leg of T1/T4 and individual current control
in each phase is:

if I*>=O and I>(I* + h/2) then turn off T1

if I*bO and I<(I*
-

h/2) then turn on T1

if I*<O and I>(I* + h/2) then turn on T4

if I*<O and I<(I*
-

h/2) th
en turn off T4

This is non
-
complementary switching, which has
been used for all the controllers. The disadvantage of
the hysteresis current controller is that the switching
frequency is dependent on the motor parameters,
speed and dc bus voltage.


Figure

3

inverter circuit

III.II

DELTA CURRENT CONTRO
L

The delta controller [6] uses a fixed frequency
sampling of the current with zero hysteresis
bandw
idth logic, as shown in figure 4
, and control is
only applied at those sampling time
s. This has the
advantage of limiting the inverter switching
frequency, but the disadvantage of a poorer transient
response and current error when compared to the
hysteresis controller.



Figure
4

delta current controller

III.III
SPACE VECTOR CURRENT

CONTROL


The space vector [4] is defined as:

I = 2/3(Ia+aIb+a21c), a=e(j2n/3)
……………
(1)

The two axes used are the real axis, which is
coincident with the phase a
-
axis, and an axis
orthogonal to the a
-
axis. The effect is the same as
vec
tor ally

adding the
phases
. The resultant can be
used to determine the inverter gating signals, taking
into account all

the current errors simultaneously.
The space vector current error is defined as:

-

AI = 1.
-
I*
……………

…………………..

(2)

A space vector curre
nt controller compares the space
vector current error with hysteresis boundaries, as
shown in figure 5, and then applies the voltage vector
nearest to the current error vector. It is shown in the
appendix that due to the absence of a neutral, the
dependenc
y between the phases causes the space
current error vector to exceed the hysteresis boundary
whenever the largest individual phase error

exceeds
2/3 of the hysteresis boundary.


Figure
5

space vector diagram of the current error,
showing the vector hysteresis bands

III.
DESIGN AND IMPLEMENTATION OF
THE PMSM VECTOR CURRENT
CONTROLLERS

III.I
SPACE VECTOR CONTROL
LER
IMPLEMENTATION

Implementing space vector control is a matter of
using the standard hysteresis controller (for zero
hyst
eresis bandwidth) with a comparator to select the
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH

IN
ELECTRONICS AND COMMUNICATION ENGINEERING

ISSN: 0975


6779|
NOV 11 TO OCT 12
|
VO
LUME


02, ISSUE
-

01


Page
248

largest error and compare it to the hysteresis
bandwidth. This can then operate a latch. The circuit
used is given in figure 7. The voltage drops across the
diodes are taken into account by the provision of

biasing voltages.



Figure
6

space vector current controller

The diodes are used to compare the current errors,
such that the most positive error will appear at F and
the most negative error at G. The negative error is
inverted a
nd is then compared to the positive error by
another pair of diodes. The larger of the two is now
compared to the hysteresis band. Should either of the
two exceed the hysteresis band, the latch is enabled
to update the inverter gating signals from three ot
her
phase current error comparators with zero hysteresis.
The advantage of the space vector controller over the
hysteresis is that no zero voltage vectors can be
applied.


IV.

CURRENT CONTROLLER R
ESULTS

To
find the result of

current controller, a single spee
d
and commanded current was chosen. The controller
parameters were adjusted to produce the same rms
current error. The speed of the motor affects the
controller characteristics due to the back
-
emf.

The average inverter transistor switching frequency
was t
hen measured. This is relevant to inverter
efficiency and also to rating the transistors
adequately. The overall ability of the current
controller to track the current can be described by the
rms current error, which is defined 2s the rms of the
difference

between the actual and commanded
currents


IV.I
SPACE VECTOR CURRENT

CONTROL

The commanded current was set at 1.10 A (rms), with
the bandwidth set at 0.58 A. The bandwidth is
defined from zero.


Motor speed

avg. switching
frequency
(kHz)

rms ∆i

(A)


㔰5

0.726

0.486

3.32

0.652

ㄵ〰

2.80

0.609

5.00

0.750


IV.II
CONSTANT SPEED WITH
VARIABLE
COMMANDED CURRENT

Motor speed of 1500 rpm was chosen, which was
maintained for different commanded currents by
adjusting the load on the motor. The commanded
cu
rrent was increased in all cases from approximately
1.4 A (rms) to 4.3 A (rms).

Both the hysteresis and the space vector controller
showed no clear trend in the average switching
frequency and the current error as a function of the
commanded current, both
remaining approximately
constant.

The delta controller shows a pronounced effect as the
commanded current increases, with the
-
switching
frequency decreasing and the current error increasing.
The reason for this can be seen in figures
7 & 8.


Figure
7


Commanded and actual delta controlled
current with I* = 1.73 A (rms), 1490 rpm

Figure 6 shows that the current often reaches zero
before increasing. At larger current amplitudes
(figure 7, note the change in scale), there is further

for the current to fall and therefore the current error
will increase.

As the commanded phase current increases from 0.9
A (rms) to 4.24 A (rms), the ramp comparison
controller average switching frequency decreases
from

6.5 kHz to 4.5 kHz and the rms cur
rent error
increases from 0.25 A to 0.33 A
.


Figure
8

Commanded and actual delta controlled
current with I* = 4.28 A (rms), 1500 rpm
.


JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH

IN
ELECTRONICS AND COMMUNICATION ENGINEERING

ISSN: 0975


6779|
NOV 11 TO OCT 12
|
VO
LUME


02, ISSUE
-

01


Page
249

V.

CONCLUSION

This paper has presented the study of three different
current controllers suitable
for vector controlled
drives. They include the hysteresis, delta and space
vector controllers. An evaluation based on average
switching frequency and rms current error for space
vector type has also been included.

The hysteresis controller has a reduced av
erage
switching frequency near the waveform peaks due to
the increase in the magnitude of the back
-
emf, and
for the same reason, as the motor speed increases, the
average switching frequency over the entire
waveform decreases. Negotiable effect is produced

by changes in the magnitude of the commanded
current waveform. The space vector controller is
similar, but produces no zero voltage vectors.

At a
motor speed of 1500 rpm, with an rms current error
of 0.49 A, the vector control controller demands the
suita
ble

switching frequency from the inverter.

REFERENCES


[1] M. A. Jabbar, T. S. Low and M.A. Rahman,
"Permanent magnet motors for brushless operation",
1988 IAS Annual Meeting

[
2
] P. Pillay and R. Krishnan, "Application
characteristics of permanent magnet
synchronous and
brushless dc motors for servo drives.", 1987 IAS
Annual Meeting, pp 380
-

390.

[3]
P. Pillay and R. Krishnan, "Modeling, simulation,
and analysis of permanent
-
magnet motor drives, part
1: the permanent
-
magnet synchronous motor drive",
IEEE

Trans. Industry Applications, vol. 25, no. 2,
March/April 1989

[4]
R. D. Lorenz and D. M. Divan, "Dynamic
analysis & experimental evaluation of delta
modulators for field oriented ac machine current
regulators", 1987 IAS Annual Meeting,

[5]
W. McMurray,

"Modulation of the chopping
frequency in DC choppers and PWM inverters having
current hysteresis controllers", IEEE PESC
Conference Record


[6]
G. Pfaff, A. Wick, "Direct current control of AC
drives with pulsed frequency converters", Process
Automation,
1983


[7] B. K. Bose, "A high performance inverter
-
fed
drive system of an interior permanent magnet
synchronous

machine", 1987 IAS Annual Meeting, pp 269
-

276.

(81 P. Freere and P. Pillay, "Systematic
designs of a
permanent magnet synchronous motor driv
e
", IAS
Annual Meeting, 1990.

[9] R. Dhaouadi and N. Mohan, "Analysis of current
-

regulated voltage
-
source inverters for permanent
magnet synchronous motor drives in normal and
extended

speed ranges", PES 1989 Summer Meeting, pp 1
-

8.

[
10
] R. G. Palani
appan and J. Vithayathil, "A control
strategy for reference wave adaptive current
generation", IEEE trans. on Industrial Electronics and
Control Instrumentation, vol., IECI
-
27, no.2, May
1980.

[11] Shenzhen
-

sunfar electric technology company
Ltd, PMSM d
rives manual