Research Journal of Applied Sciences, Engineering and Technology 4(14): 2259-2264, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: March 23, 2012
Accepted: April 08, 2012
Published: July 15, 2012
Dynamic Dead-Time Effect Compensation Scheme for Pmsm Drive
Xianqing Cao and Liping Fan
Shenyang University of Chemical Technology, Shenyang 110142, China
Abstract: In general, Voltage distortion is existed between the reference and the actual output voltages in a
pulse-width-modulated voltage-source inverter. This distortion is dead-time effects, which caused by the deadtime setting and the trailing effect of non-ideal switching characteristics of the optical coupler and power
devices. To improve the performance of the drive system effectively, this study presents a novel dynamic deadtime compensation, which is based on the device characteristics and the running conditions of the motor.
Finally, the results of experiment verify its validity.
Key words: Dead-time effect, dynamic compensation, the trailing effect
INTRODUCTION
ANALYSIS OF DEAD-TIME EFFECTS
One of the key technology for the electric vehicle
inustry is reducing the interference to other vehicle
electrical appliance, which can be realized by the
harmonic suppression for the permanent magnet
synchronous motor drive system. In general, there exists
voltage distortion between the reference and the actual
output voltage in a pulse-width-modulated voltage-source
inverter. This distortion is dead-time effect which caused
by the dead-time setting and non-ideal switching
characteristics of power devices (Wang et al., 2008;
Hyun-Soo et al., 2003; Kim et al., 2004).
To compensate the dead-time effects, several
approaches are presented. All the methods can be
classified into two categories: the PWM gate signals
mdification and the feed forward method. Choi and Sul,
(1996) and Munoz and Lipo (1999) present a
implementation to modify the PWM gate signals using
hardware circuits such as the current polarity detection
and logic combination circuit. But it is difficult to sense
the switching delay, transition time and on-drop of power
devices. Wu et al. (2005), fixed error voltage vectors
generated by dead-time, switching devices turn-on and
turn-off time are introduced. Actually, the running
condition of the motor affects the compensating voltages.
Hyun-Soo et al. (2003) and Kim et al. (2004) present an
online disturbance observer, in this method, the
compensating voltages are calculated using the dead time,
switching period, current command and dc link voltage.
However, it ignores the parameter variations of the motor.
In order to improve the compensation effect, a
dynamic compensation method is proposed in this study,
which is based on the characteristics of the power devices
and the actual motor running state.
One leg of the three-phase inverter which employs
the space vector PWM technique is shown in Fig.1. Under
ideal conditions, the state of the two power switches is
complementary. But in practical application, the switch
signals outputted by the controller (DSP) are delivered to
power switches of the main circuit by the driving circuit
which contains optical couplers. Considering the switch
delay and tailing effect (the turn-off time is greater than
the opening time) of optical couplers and power switches,
the switch signals of the same bridge leg are shown as
Fig. 2.
Where, t1 is the turn-on time of optical coupler; t2 is
the turn-on time of power switch; t3 is the turn-off time of
optical coupler; t4 is the turn-off time of power switch.
To prevent the simultaneous conduction of two
switching devices in each leg of the inverter, it is
necessary to set dead time tdead. In fact, the actual deadtime Tdead should also includes turn-on time and turn-off
time of the optical couple and the power switch, which is
shown as:
Tdead = tdead + ( t1 + t2 ) − ( t3 + t4 )
(1)
In addition, the direction of current ia will also affect
the voltage applied to the motor. Considering the direction
of current ia and the conduction voltage drop of the power
switch and anti-parallel diode, the terminal ua0 is given in
Table 1.
As can be seen from Table 1, the general voltage can
be represented as (Kim et al., 2004):
ua 0 = (U dc − U ce + U d )( Sa − 0.5) − 0.5(U ce + U d ) sgn ( ia )
Corresponding Author: Xianqing Cao, Shenyang University of Chemical Technology, Shenyang 110142, China
2259
(2)
Res. J. Appl. Sci. Eng. Technol., 4(14): 2259-2264, 2012
where, Ts is the sampling period. Ta(n) = Ta*(n)sgn(ia)Tdead, Ta*(n) is the on-time reference value of the
upper power switch of phase a at the nth PWM period.
According to the theory of electrical engineering, the
relationship between the phase voltage and the neural
voltage can be expressed as follows (Kim et al., 2004):
uao + ubo + uco
=
3
U dc − U ce + U d ⎛ Ta (n) + Tb (n) + Tc (n)
⎞
×⎜
− 15
.⎟
⎝
⎠
3
Ts
uno (n) =
−
(4)
( sgn(ia ) + sgn(ib ) + sgn(ic ))(U ce + U d )
6
From (3) and (4), it can be derived as:
Fig. 1: One leg of three phase inverter
uan (n) =
U dc − U ce + U d ⎛ 2Ta (n) − Tb (n) − Tc (n) ⎞
×⎜
⎟
Ts
3
⎠
⎝
(2 sgn(ia ) − sgn(ib ) − sgn(ic ))(Uce + Ud )
−
(5)
6
From the above analysis, phase a voltage distortion
caused by the dead-time effect can be represented as:
*
∆ uan (n) = uan
(n) − uan (n) =
(U ce − U d )
3
⎛ 2Ta* (n) − Tb* (n) − Tc* (n) ⎞
U + Ud
⎟⎟ + Sgn( A) ce
× ⎜⎜
Ts
6
⎝
⎠
+ Sgn( A)
(6)
U dc − U ce + U d Tdead
×
Ts
3
where Sgn(A) = (2sgn(ia)-sgn(ib)-sgn(ic)).
Considering the actual selection of the power switch
and anti-parallel diode (Uce and Ud is 2.3V and 2.5V
respectively), the maximum value of the first part
⎛ U −U
⎛ 2T * (n) − Tb* (n) − Tc* (n) ⎞
ce
d
⎟
× ⎜⎜ a
max⎜
⎟
⎜
Ts
3
⎠
⎝
⎝
it can be ignored relative to the remaining parts. Thus (6)
can be simplified as:
Fig. 2: Ideal and practical switching pattern
Table 1: Relationship between ua0 and ia
Sa=1
ua0=Udc/2-Uce
ia$0
ia<0
ua0=Udc/2+Ud
Sa=0
ua0= -Udc/2-Ud
ua0= -Udc/2+Uce
*
∆ uan (n) = uan
(n) − uan (n) = Sgn( A)
+ Sgn( A)
where, Udc represents the DC bus voltage, Uce and Ud
represents the saturation voltage of the power switch and
the anti-parallel diode respectively, sgn(is a sign function.
Thus, the voltage during the nth PWM step can be derived
from (2) and shown as (Kim et al., 2004):
uao (n) = (U dc − U ce
⎞ 0.2
⎟≤
× 2 = 013
. V
⎟
3
⎠
⎛ T ( n)
⎞
+ Ud ) ⎜ a
− 0.5⎟ − 0.5(U ce + U d ) sgn(ia )
⎝ Ts
⎠
U dc − U ce + U d Tdead
×
Ts
3
U ce + U d
6
(7)
Similarly, voltage distortion of phase b and phase c can be
expressed as follows:
(3)
2260
U ce + U d
6
U dc − U ce + U d Tdead
+ Sgn( B)
×
3
Ts
∆ubn (n) = Sgn( B)
(8)
Res. J. Appl. Sci. Eng. Technol., 4(14): 2259-2264, 2012
U ce + U d
6
U − U ce + U d Tdead
+ Sgn(C) dc
×
3
Ts
∆ ucn (n) = Sgn(C)
o
5
(9)
Tj = 25 C
o
Tj = 125 C
UCE /V
4
where, Sgn(B) = (2sgn(ib)-sgn(ia)-sgn(ic)) Sgn(C) = (2sgn
(ia)-sgn(ib)).
3
2
1
ALGORITHM OF DEAD TIME EFFECT
DYNAMIC COMPENSATION
0
0
⎧U ce = 0.5 + 0.025ic 0 A < ic < 20 A
⎨
20 A ≤ ic ≤ 280 A
⎩U ce = 1 + 0.006ic
320
1
10
Vcc = 600V
Tj = 25 oC
o
T j = 125 C
toff
t on
0
10
-1
10
1
2
10
10
ic /A
3
10
Fig. 4: The relation curve between switch time and ic
(10)
Determination of Tdead: In this study, the optical couplers
for driving circuit are 6n137, its turn-on and turn-off time
are almost unchanged at constant ambient temperatures,
so t1 and t3 can be chosen as its typical values 0.05 and
0.13 µs, respectively. If the power switches of the main
circuit are IGBT, the turn-on and turn-off time of the
driving chip will be bigger.
The value of the turn-on time and turn-on time of
power switch is also related with the conduction current
ic. The relation curve is shown in Fig. 4, their value can be
derived by (11):
. + 0.001ic
⎪⎧ ton = t2 = 16
⎨ t = t = 2.5 − 0.0006i
c
⎩⎪ off 4
240
Fig. 3: The relation curve between Uce and ic
ton and toff /µs
Determination of Uce: The dead time dynamic
compensation scheme proposed in this study is valid
when the entire system studies in steady state, that is, the
temperature rising is constant.
The power switch selected in this study is Intelligent
Power Module (IPM) PM200DSA120, its stable junction
temperature is 125 according to the product manual.
When the temperature keeping constant, the saturation
voltage of the power switch Uce will change with the
conduction current ic. The relation curve of Uce and ic is
given in Fig. 3, using the partition linearization means, Uce
can calculated by (10):
160
ic /A
80
(11)
Because they all have little changes during the whole
operating range, for simplicity,t2 and t4 can be chosen as
1.7 and 2.45µs, respectively in the practical application.
Determination of Sgn(C): Sgn(C) depends on the current
direction. According to SVPWM theory, the current
direction determined by the sector of the current vector.
The relationship between Sgn(C) and the sector is given in
Table 2.
Table 2: Relationship between sign function and the sector
Sgn(A)
Sgn(B)
sector
Sgn(ia) Sgn(ib) Sgn(ic)
1
+
4
-2
2
+
+
2
2
3
+
-2
4
4
+
+
-4
2
5
+
-2
-2
6
+
+
2
-4
Sgn(C)
-2
-4
-2
2
4
2
Determination of voltage distortion: The voltage
distortion in two-phase stationary frame can be derived
from (7), (8) and (9), shown as follows:
1
⎡
⎡ ∆ usα ⎤ 2 ⎢ 1 − 2
⎥= ⎢
⎢
3
⎢⎣ ∆ usβ ⎥⎦ 3 ⎢ 0
⎢⎣
2
1 ⎤ ⎡∆u ⎤
an
⎥
2 ⎥⎢
⎥ ∆u
3 ⎥ ⎢ bn ⎥
⎢∆u ⎥
−
2 ⎥⎦ ⎣ cn ⎦
−
(12)
Once )ua" and )us$ is determined, the suitable
voltage vector can be calculated by the SVPWM
algorithm.
RESULTS OF SIMULATION AND EXPERIMENT
A block diagram of the PMSM drive based on
dynamic dead-time compensation is shown in Fig. 5. The
parameters of PMSM used in this study are shown in
Table 3.
Because the dead-time effects phenomena are
obvious when the motor runs at low speed and light load,
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Res. J. Appl. Sci. Eng. Technol., 4(14): 2259-2264, 2012
Fig 5: Block diagram of PMSM drive based on the proposed dynamic dead-time effects compensation
55
440
3
1800
90
0.061
2.53
3.29
0.65
iA /20A
Table 3: Relationship between sign function and the sector
Rated power PN (kW)
Rated voltage UN (V)
Magnetic pole pairs p
Rated speed (r/min)
Rated current (A)
Stator resistance Rs S
d-axis stator inductance Ld mH
q-axis stator inductance Lq mH
Rotor flux linkageQf Wb
20
uddead
uqdead
10
Harmonic magnitude/
fundamental amplitude (%)
uddead , uqdead
50 ms
0.0210
0.0208
0.0206
0.0204
0.0202
0.0200
0
t/S
2
(a) q- and d-axis voltage distortion
20
iA , i B , iC /A
18.0
16.2
14.4
12.6
10.8
9.0
7.2
5.4
3.6
1.8
0
5
8
11
14 17 20
Harmonic order
23
26
29
Fig. 7: a-phase current and harmonious analysis without
compensation at case 1
therefore, the effectiveness of the proposed approach is
verified only in this case.
0
Simulation results: Results of simulation are shown in
Fig. 6 in the condition: TZ = 30 N.m , n* = 200 r/min, It
can be seen: In the steady state, the q- and d-axis error
voltage caused by dead-time effects are periodic
functions, whose cycle is same as the cycle of the PWM;
there exists zero clamp, at the same time, the shoulder of
the current wave will became flat. These phenomena will
have adverse effects on the motor system, therefore, it is
necessary for dead-time compensation.
-20
0.05
0.10
0.15
t/S
(b) dead-time effects
Fig. 6: Current difference caused by dead-time effects
2262
iA /35 A
iA /20A
Res. J. Appl. Sci. Eng. Technol., 4(14): 2259-2264, 2012
50 ms
Harmonic magnitude/
fundamental amplitude (%)
Harmonic magnitude/
fundamental amplitude
50 ms
11.3%
10.17%
9.04%
7.91%
6.78%
5.65%
4.52%
3.39%
2.26%
1.13%
0
2
5
8
11
14 17
20
Harmonic order
23
26
29
2
Fig. 8: a-phase current wave and harmonious analysis of the
proposed compensation scheme at case 1
5
8
11
14 17
20
Harmonic order
23
26
29
Fig.10: a-phase current wave and harmonious analysis of the
proposed compensation scheme at case
iA /35A
without compensation and it reduced to 12.83% with the
proposed compensation method.
At case2, the THD of the current is 11.52% when
without compensation and it reduced to 7.81% with the
proposed compensation method.
From these Figures, we can see that the proposed
scheme can improve the response performance and give
an ideal current wave at different load torque and different
reference speed. It is especially apparent at the low speed
and light load.
50 ms
Harmonic magnitude/
fundamental amplitude (%)
6.70
6.03
5.36
4.69
4.02
3.35
2.68
2.01
1.34
0.67
0
9.90
8.91
7.92
6.93
5.94
4.95
3.96
2.97
1.98
0.99
0
CONCLUSION
2
5
8
11
14 17 20
Harmonic order
23
26
A practical dead-time effects compensation method
for PMSM drive based on the device characteristics and
the running conditions of the motor is proposed. Results
of experiments are provided to demonstrate the
effectiveness of the proposed method at different load
torque and different reference speed, at the low speed and
light load, the compensation effect is especially apparent.
29
Fig. 9: a-phase current and harmonious analysis without
compensation at case 2
ACKNOWLEDGMENT
Experimental results: The experimental conditions are
considered here:
This study is supported by the national science
foundation of china (No.61143007) and Scientific
Research Project of Liaoning province education
department (No.L2010443).
Case 1: TZ = 30 N.m, n* = 200 r/min
Case 2: TZ = 70 N.m, n* = 200 r/min
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