1. A Variable-Speed, Sensorless, Induction Motor Drive
Using DC Link Measurements
S. B. Bodkhe M. V. Aware
Department of Electrical Engineering Department of Electrical Engineering
G. H. Raisoni College of Engineering Visvesvarya National Institute of Technology
Nagpur, India Nagpur, India
s_b_bodkhe@yahoo.co.in mva_win@yahoo.com
Abstract— This paper presents a new control strategy for on applying speed sensorless FOC to high performance
three-phase induction motor which includes independent speed & applications that is based on estimation of rotor speed by using
torque control loops and the current regulation thereby the machine parameters, instantaneous stator currents and
overcoming the limitation (i.e. sluggish response) of volts per voltages [1]-[6]. The benefits of speed sensorless control are
hertz controlled industrial drives. For close-loop control, the
the increased reliability of overall system with the removal of
feedback signals including the rotor speed, flux and torque are
not measured directly but are estimated by means of an mechanical sensors, thereby reducing sensor noise and drift
algorithm. The inputs to this algorithm are the reconstructed effects as well as cost and size. However to exploit the
waveforms of stator currents and voltages obtained from the dc benefits of sensorless control, the speed estimation methods
link and not measured directly on stator side. The proposed drive must achieve robustness against model and parameter
thus requires only one sensor in the dc link to implement the uncertainties over a wide speed range. To address this issue, a
close-loop speed and torque control of a three-phase induction variety of approaches have been proposed.
motor. The simulation results on a 2.2 kW induction motor drive The adaptive observers (AO) like Luenberger observer or the
in Matlab/Simulink software show fast dynamic response and extended Kalman filter [1], [5] gets accurate estimates under
good agreement between the actual values and the estimated
detuned operating conditions but these solutions are
values of torque and speed. Replacement of the open-loop control
strategy of existing v/f drive by the proposed close-loop strategy computationally intensive, require more memory space and are
appears to be possible without requiring any additional power difficult to tune because the initial values of three covariance
components and sensors. matrices have to be assumed and selected after much trial and
error. So their application in low cost drives is limited. The
Index Terms— Speed-sensorless, estimation, dc link, band-pass model reference adaptive system is also an AO technique [7],
filter, reconstruction, three-phase induction motor, space-vector. where the same quantity is calculated by two different ways.
One of them is independent of variable to be estimated while
NOMENCLATURE the other one is dependent on it. The two computed quantities
Rs Rr ' Stator and rotor resistances ( Ω ) are used to formulate the error signal. The error signal is then
Magnetizing and rotor inductances (Henry) fed to an adaptation mechanism which in most cases is a PI
Lm Lr '
controller. The output of the adaptation mechanism is the
I. INTRODUCTION estimated quantity.
While all the speed sensorless techniques eliminate the use
The widespread industrial use of induction motor (IM) has of mechanical speed sensor, they require the stator current and
been stimulated over the years by their relative cheapness, low stator voltage signals as input. This requires at-least two
maintenance and high reliability. The control of IM variable current sensors and two voltage sensors on the stator side. It is
speed drives [1] often requires control of machine currents, difficult to get current sensors with equal gains over the wide
which is normally achieved by using a voltage source inverter. range of frequencies, voltages and currents used in a practical
A large number of control strategies have been registered so inverter. The problem is exacerbated if the motor windings are
far [2]-[4]. The volts per hertz (v/f) IM drives with inverters not perfectly balanced or if the current sensors have some dc
are widely used in a number of industrial applications offset. Over last few years, techniques of stator current
promising not only energy saving, but also improvement in reconstruction from the dc link current have been suggested in
productivity and quality. The low cost applications usually literature [8]-[9].
adopt v/f scalar control when no particular performance is In this paper, a new speed sensorless control strategy for IM
required. Variable-speed pumps, fans are the examples. is proposed that includes the speed control, torque control and
For those applications which require higher dynamic current regulation. Unlike conventional close loop estimators,
performance than v/f control, the dc motor like control of IM it involves less computation and is less dependent on machine
that is called, the field oriented control (FOC) is preferred. parameters. The stator currents and stator voltages are
During the last few years, a particular interest has been noted
978-1-4244-2800-7/09/$25.00 ©2009 IEEE 3591 ICIEA 2009

2. reconstructed from dc link quantities and the inverter recovery effect of diode, this leg is in fact shorted through at
switching signals. For faithful reconstruction of currents, use this moment such that a positive current spike will appear at
of adaptable gain band-pass filter is proposed in the scheme. the dc link side. To establish the basic relationship between dc
The simulation results of proposed scheme shows fast link current, winding currents and inverter switching pattern,
performance as compared to v/f control and therefore can be the switches shown in Fig. 2 are considered as ideal; the diode
regarded as an improvement. For the close loop speed control, recovery effect and the snubber action are not considered.
a single current sensor in the dc link is sufficient. Thus it is
suitable for low-cost, moderate performance, sensorless IM
drive applications. The proposed drive is modeled in
Matlab/Simulink software for a 2.2 kW IM. The simulation
results are presented to verify the workability of proposed
strategy.
II. PROPOSED SCHEME
Fig. 1 shows the block diagram of the proposed scheme. It
consists of a speed (frequency loop), a torque loop, and a Figure 2. Voltage source inverter fed induction motor drive
current regulator. The output of speed/frequency regulator
represents the torque reference for the torque loop. The torque A. Space-Vectors
regulator generates the q-axis current command iqe∗ . The d- During normal state, there are eight switching states of inverter
which can be expressed as space voltage vector (SA,SB,SC) such
axis current command i ∗ is directly generated from the as (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0) and
de
reference rotor flux ψ r * as given by (1) [1]. This eliminates (1,1,1). SA =1 means upper switch of leg A is on while the
lower one is off, and vice versa. The same logic is applicable to
an additional PI controller and reduces the computational
SB and SC also. Amongst above eight voltage vectors, (0,0,0)
burden. These dc commands expressed in synchronously and (1,1,1) are termed as zero vectors while the other six as
rotating reference after transformation to the three phase active vectors. The switching vectors describe the inverter
current commands are than compared with the actual three- output voltages.
phase currents (reconstructed waveforms) to generate the
switching signals for the inverter. In the proposed scheme, all B. Basic Principle of Phase Voltage & Line Current
the feedback signals including the stator currents and stator Reconstruction
voltages are estimated/reconstructed from the dc link For different voltage vectors, the phase voltage that will
quantities. appear across stator winding can be determined by circuit
* ψ * (1) observation. This is summarized in Table 1. It is assumed that
i = r
de Lm the stator winding is star connected. From this table, the
expressions for the reconstruction of three phase voltages are
III. RECONSTRUCTION OF STATOR VOLTAGES & CURRENTS as follows (assuming no dwelling time):
FROM DC LINK
~ V
v = dc (2S − S − S ) (2)
a A B C
As indicated in [1], [6], the stator flux, torque and speed can 3
be derived from the stator voltages and currents expressed in ~ Vdc (3)
vb = (−S A + 2SB − SC )
d-q reference frame. The phase currents and voltages are 3
Vdc (4)
related to the dc link current and voltage by inverter switching ~
vc = (−S A − SB + 2SC )
states. A voltage source inverter-IM drive is shown in Fig. 2 3
where Vdc is the dc link voltage, Idc is the instantaneous dc link The stator voltages as expressed in stationary d-q frame are:
~ s ~ V (5)
current and ia, ib, ic are the instantaneous three-phase winding vqs = va = dc ( 2 S A − S B − SC )
currents. Generally, IGBTs associated with snubber protection 3
and feedback diode are used as switch in inverters. When a ~ s 1 ~ ~ V
vds = (vb − vc ) = dc (SB − SC ) (6)
switch is being turned-on and the conducting diode at the same 3 3
leg is being blocked off by this turn-on, because of the reverse
TABLE I. DC LINK CURRENT & PHASE VOLTAGES
Voltage Vector va (V) vb (V) vc (V) Idc (A)
(SA,SB,SC)
(0,0,0) 0 0 0 0
(0,0,1) -Vdc/3 -Vdc/3 2Vdc/3 + ic
(0,1,0) -Vdc/3 2Vdc/3 -Vdc/3 + ib
(0,1,1) -2Vdc/3 Vdc/3 Vdc/3 - ia
(1,0,0) 2Vdc/3 -Vdc/3 -Vdc/3 + ia
(1,0,1) Vdc/3 -2Vdc/3 Vdc/3 - ib
(1,1,0) Vdc/3 Vdc/3 -2Vdc/3 - ic
Figure 1. Block diagram of the proposed scheme. (1,1,1) 0 0 0 0
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3. The relationship between the applied active vectors and the can be obtained on integration of the phase voltage minus
phase currents measured from the dc link is also shown in voltage drop in the stator resistance Rs [1]:
Table 1. It is clear that at-most, one phase current can be ψ = (v
~
ds
~ s − R ~ s ) dt
∫ ds si ds
(15)
related to the dc.-link current at every instant. The
qs = ∫ (v qs
~
ψ ~ s − R ~ s ) dt (16)
reconstruction of phase currents from the dc-link current can s iqs
be achieved easily only if two active vectors are present for at ~ ~ ~
ψ s = ψ ds 2 + ψ qs 2 (17)
least enough time to be sampled. Fortunately, as indicated in ~ ~
~ ψ ~ ψ
cos θ e = ~ ; sin θ e = ~ (18)
[10], for most PWM strategies, two phase currents can be ds qs
sampled by looking at the dc link current over every PWM ψ s ψ s
period. If the PWM frequency is high enough, the phase ~
where θ e is the stator flux angle with respect to the q-axis of
current does not change much over one PWM period. Hence, a the stationary d-q frame.
reconstructed current derived from the dc link current gives a
reasonable approximation of the actual current. In terms of B. Estimation of Torque
switching states and Idc, the three ac line currents can be The electromagnetic torque can be expressed in terms of stator
derived as follows: currents and stator flux as follows [1]:
S
~
a
S
i = I (S − B − C )
dc A 2 2
(7) T =
e (ψ i −ψ i )
~ 3P ~ ~ s ~ ~ s
4 ds qs qs ds
(19)
~ S SC (8)
ib = I dc (− A + SB − ) C. Estimation of Synchronous Speed &Rotor Speed
2 2
S A SB ~
The synchronous speed ωe can be calculated from the
~
ic = Idc (− − + SC ) (9)
2 2 expression of the angle of stator flux as:
The stator currents as expressed in stationary d-q frame are: ~
~
ψ
θe = tan−1 ~ds (20)
~ s ~ ~ s 1 ~ ~ (10)
i =i ;
qs i =
a (2 i + i )
ds b a ψ qs
3
~
~ s ~ ~ s −1 ~ ~ (11) ~ dθ e (21)
or iqs = ia ; ids = ( 2 ic + ia ) ωe =
3 dt
~
To obtain the rotor speed ωr , simple slip compensation can be
~ s ~ ~
or iqs = −( ib − ic );
~ s
ids =
1 ~ ~
( i + ic )
(12)
3 b derived using the steady-state torque speed curve for the
machine being used:
C. Filter Stage ~
~
ω = KsTe (22)
The dc link current Idc consists of a train of short duration sl
pulses and has information about the stator currents of all the where Ks is the rated slip frequency/rated torque and it can be
three phases. By using (7)-(9), these pulses can be segregated derived from the name plate of the machine. Alternately, if the
into three ac line currents. Generally, an active or passive-type rotor flux ψ r is assumed as constant, the slip speed can also
low-pass filter (LPF) with narrow bandwidth is used to filter be calculated as:
out the high frequency components in the ac current waveform ~ s
~ R ' iqs (23)
thus obtained from Idc. This filter actually works as an ω = r ~
sl Lr ' ids s
integrator. However, a LPF causes phase lag and amplitude
attenuation that vary with fundamental frequency [11]. In this The rotor speed is than given by,
~ ~ ~
ωr = ωe − ωsl (24)
paper, we propose the use of band-pass filter with adaptable
gain to overcome this problem. The transfer function of the
filter is given below: V. PROPOSED CONTROL STRATEGY
⎡⎛ sT ⎞⎛ T ⎞⎤ (13) Majority of IM drives are of open-loop, constant-v/f, voltage-
y= ⎢⎜ 1 + sT ⎟⎜ 1 + sT ⎟⎥
x
⎣⎝ ⎠⎝ ⎠⎦ source-inverter type. These drives are cost effective but they
offer sluggish response. Due to high current transients during
where x, y and T are input, output and time constant of the the torque changes, they are subject to undesirable trips. To
band-pass filter. For sT >>1; (1+sT) ≅ 1. Therefore, avoid the un-necessary trips, the control parameters like
1 (14) acceleration/deceleration rate has to be adjusted (reduced)
y= x
s according to the load. This results in underutilization of torque
capability of the motor. Thus the drawback of v/f drive can be
IV. ESTIMATION OF FEEDBACK SIGNALS FROM attributed to lack of torque control. This is the reason why
RECONSTRUCTED QUANTITIES open-loop, constant-v/f drives are mostly used in low
The feedback signals required to simulate the proposed performance fan and pump type loads. In this paper, we
scheme i.e., flux, torque and rotor speed are estimated as: propose a modified control scheme that includes the torque
control and a current regulated PWM inverter to avoid the
A. Estimation of Flux undesirable trips due to transient currents.
The stator flux in stationary d-q frame ψ s ,ψ qs s and thus ψ s As shown in Fig.1, the feedback signals i.e. torque and rotor
ds
speed are obtained from the dc link quantities and hence from
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4. the reconstructed line currents and phase voltages. The 500
accuracy of reconstructed waveforms depends upon the
a )
v (V
0
sampling rate [8], [9]. Higher the sampling rate less is the error
-500
between the actual and reconstructed waveforms. In a hard- 0.05 0.06 0.07 0.08 0.09 0.1
switching inverter, the switching frequency is limited to a 500
typical value of a few kHz. This limits the sampling rate of dc
b )
v (V
0
current and hence the update rate of torque and rotor speed.
Consequently, closing the loop directly on the instantaneous -500
0.05 0.06 0.07 0.08 0.09 0.1
value of the estimated torque now becomes difficult because 500
estimation error during a PWM cycle could become
c )
v (V
significantly high. In order to use the estimated torque in a 0
more robust manner, a control strategy should use the -500
averaged torque instead of the instantaneous value. This leads 0.05 0.06 0.07 0.08
Tim e (s )
0.09 0.1
to the control strategy depicted in Fig.1. In this system, two P- (a)
I controllers are used to regulate the average value of torque
iAind lin ( )
c kA
5
and speed. The output of the P-I regulators forms the q-axis 0
reference in a synchronously rotating reference frame. -5
1.78 1.8 1.82 1.84
VI. SIMULATION STUDIES
iBind lin ( )
c kA
5
In order to predict the behavior of the drive during steady-state 0
and transient conditions, detailed simulation studies of the -5
scheme shown in Fig.1 are carried out on a 2.2kW IM by
1.78 1.8 1.82 1.84
iC d lin ( )
in c k A
5
using Simulink software. Fig. 3. shows the internal structure of
the controller that consists of the speed loop, torque loop and
0
the current regulation loop in synchronously rotating frame of -5
1.78 1.8 1.82 1.84
reference. The switching signals for inverter are generated by Time (A)
(b)
comparing the command ac currents with reconstructed ac
Figure 4. Reconstructed waveforms of (a) three phase voltages and (b) three
currents. For the reconstruction of stator voltages and ac line
line currents separated from the dc link current.
currents, the dc link quantities with Vdc = 600V are sampled
with a sampling time of 2e-6 seconds and than segregated into values of time constants T for the band-pass filter are selected
the three-phase voltages and three ac currents as per (2)-(4) by trial and error. The simulation output of band-pass filter
and (7)-(9) respectively. The simulation was carried out for which represents the reconstructed ac line currents is shown in
five different operating conditions as is presented ahead. A Fig.5(a). For the sake of comparison, the actual ac line
variable- step ode23tb(stiff/TR-BDF2) solver was used. The currents are illustrated in Fig.5(b). The reconstructed and
waveforms of reconstructed phase voltages and the three ac actual waveforms of ac line currents during 100% speed
line currents as reflected in the dc current, are presented in reversal at no-load are presented in Fig.6(a) & (b). The
Fig.4. From these waveforms, it is clear that the samples of response of speed sensorless drive during different
phase currents available in the dc link current are not evenly
)
econstructed line
currents 'a,b,c',(A
5
spread and being discontinuous, the set of resulting points do
0
not constitute an acceptable reconstruction. Therefore a zero-
order hold is employed followed by a band-pass filter. The -5
R
1.78 1.8 1.82 1.84
Tim e (s )
(a)
c re ts'ab ' ( )
ur n , ,c A
5
c a e
Atu l lin
0
-5
1.78 1.8 1.82 1.84
Time (s)
(b)
Figure 5. Stator currents at rated load (a) reconstructed (b) actual waveforms
R c n tr c d
10
e o s u te
c r e ts ( )
ur n A
0
-10
1.1 1.2 1.3
Time (s)
Figure 3. Simulink model of control strategy (a)
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5. outer speed loop and is very similar to open-loop v/f drive in
A tu l c r e ts( )
c a ur n A
10
0
terms of power components and sensors required. Due to the
-10
inclusion of torque control loop, the drive response is fast and
1.1 1.2 1.3 stable. Simulation results confirm the effectiveness of the
Time (A)
proposed scheme. The technique uses only dc link voltage and
(b) dc link current measurements to generate the estimates of
Figure 6. Stator currents during reversal at no-load (a) reconstructed
E tim te toq e( .u E t a ds e d( .u)
s a d r u p ) sim te p e p .
waveform (b) actual waveform 1
0.5
dynamic conditions was studied in detail. To check the
accuracy of estimated variables, these variables were obtained 0
0 0.1 0.2 0.3 0.4 0.5
by two different methods. In the first one, the machine 15
10
variables which include the flux, torque, synchronous-speed, 5
slip-speed and rotor-speed are estimated by using (15)-(24) 0
and in the second method, these variables are calculated with -5
0 0.1 0.2 0.3 0.4 0.5
the help of dynamic model of IM [1] by using the stator Tim e (s )
(a)
currents and voltages measured directly. The simulation
cu l p e pu)
At a s e d( . .
results of the first method were treated as estimated values 1
while those of the latter method as actual values. 0.5
Case 1: Free acceleration characteristics: 0
The machine was allowed to accelerate from zero speed to
0 0.1 0.2 0.3 0.4 0.5
cu l oq e pu)
15
At a t r u ( . .
rated speed at no-load. The steady-state was reached at 0.3 10
seconds. The waveform of estimated speed show faster 5
0
response (less damped) as compared to its actual counterpart. -5
This is shown in Fig. 7(a) & (b). 0 0.1 0.2 0.3
Tim e (s )
0.4 0.5
Case 2: Step change in speed reference: (b)
Step change in speed reference was applied two times. At 0.5 Figure 7. Free-acceleration characteristics (a) estimated & (b) actual values
sec., from +100% to +60% and vice-versa at 1 sec. was
Et a dt r u ( .u Et ae s e d p .)
simt oq e p .) simt d pe ( .u
applied. The response is shown in Fig.8. The torque becomes 1
negative during the first change to decelerate the motor. Upon 0.5
reaching steady state, the torque becomes equal to the load 0
torque. The response time of the drive for this step change is 10
0.4 0.6 0.8 1 1.2
100ms. The estimated values of torque and speed vary in 0
accordance with their corresponding actual values.
e
-10
Case 3: Speed reversal: 0.4 0.6 0.8 1 1.2
A step change in speed reference from +100% to -100% is Time (s)
(a)
applied at 1.5 seconds. This step change is equivalent to 100%
A tu l s e d(p .)
c a p e .u
1
speed change. The response is shown in Fig. 9. The phase
sequence reverses to rotate the motor in reverse direction. The 0.5
drive reaches steady state after the change in reference speed 0
0.4 0.6 0.8 1 1.2
in 700 ms. this proves that the speed estimation is stable even
A tu l to u (p .)
10
c a rq e .u
at very low speeds.
Case 4: Step change in load:
0
A step change in load is applied at 0.5 seconds. The response -10
of the drive is shown in Fig.10. The electromagnetic torque 0.4 0.6 0.8
Tim e (s )
1 1.2
increases to correct the speed error. Upon reaching the steady (b)
state, the torque becomes equal to the load torque. The rotor Figure 8. Variation in rotor speed and electromagnetic torque for step
speed, after an initial droop attains back its earlier speed . The changes in reference speed (a) estimated values, (b) actual values
motor reaches the steady state in 300ms.
s a d oq e p . s a d p e p .)
E timte t r u ( .u)E timte s e d( .u
Case 5: Low speed operation: 1
The response of the drive at 40% and 20% of rated speed is 0
shown in Fig.11. For the machine under consideration, 20% -1
corresponds to 3.14 rad/sec angular mechanical speed. The 1.4 1.6 1.8 2 2.2
speed estimation is very stable even at this low speed range. 5
0
VII. CONCLUSION -5
-10
In this paper, a new control strategy for induction motor drive 1.4 1.6 1.8
Time (s)
2 2.2
is proposed. The drive is operated under torque control with an (a)
3595

6. A tu l s e d(p .)
phase voltages, line currents, flux, torque and rotor speed. If
c a p e .u
1
0 the dc link voltage is assumed as constant, only one current
-1
sensor in the dc link is sufficient to give the estimates of all
1.4 1.6 1.8 2 2.2
required feedback variables. Moreover, the same current
sensor that is already available in the dc link of an open-loop
A a to u (p .)
5
ctu l rq e .u
0 v/f drive for protection purpose can be used. Thus the open-
-5 loop control strategy in an existing v/f drive can be replaced
-10 by the proposed close-loop control strategy without requiring
1.4 1.6 1.8
Time (s)
2 2.2
any additional power components or the physical sensors. The
(b) proposed strategy appears to be a good compromise between
Figure 9. Variation in rotor speed and electromagnetic torque during reversal the high-cost, high-performance field-oriented drives and the
(a) estimated values, (b) actual values low-cost, low-performance v/f drives.
Practical implementation of the proposed scheme on a 16
E tim te toq e( .u E tim te s e d(p .)
s a d r u p .) s a d p e .u
1 bits floating point arithmetic Texas Instrument TMS320C31
processor are the subject of future follow-up research work.
0.5
APPENDIX
0
0 0.2 0.4 0.6 0.8 1
MACHINE PARAMETERS
15
10 Rs = 11.1Ω; R’r = 2.2605Ω
5 Ls = 0.7329H; L’r = 0.7329H
0
Lm = 0.71469H; P = 4
-5
0 0.2 0.4 0.6 0.8 1
Time (s)
(a) REFERENCES
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c a p e p .)
A tu l s e d( .u
1
India, Pearson Education, Inc., 2003.
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0 0.2 0.4 0.6 0.8 1 Electron., vol. 49, no. 1, pp. 87-95, Feb. 2002.
c a r u p .)
15
[3] L. Harnefors, M. Jansson, R. Ottersten, and K. Pietilainen,
A tu l toq e( .u
10
5
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0
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s a d r u p .) s a d p e p .)
E timte toq e( .u E timte s e d( .u
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1
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