Dtc (1)

DIRECT TORQUE CONTROL FOR INDUCTION
MOTOR DRIVES
MAIN FEATURES OF DTC
• Decoupled control of torque and flux
• Absence of mechanical transducers
• Current regulator, PWM pulse generation, PI control
of flux and torque and co-ordinate transformation
are not required
• Very simple control scheme and low computational
time
• Reduced parameter sensitivity

BLOCK DIAGRAM OF DTC SCHEME
ϕ s
s*
+ _
Induction
Motor
Selection
Voltage
T*
ϕ s
s
s
vs
i
s
s
Estimator
Stator
Flux
Estimator
Torque
+
_
s
∆ϕs
+
_
Vector
T∆ϕ s
s
T
2
3
2
3
aS Sb Sc
E
ia
ib
In principle the DTC method selects one of the six
nonzero and two zero voltage vectors of the inverter on
the basis of the instantaneous errors in torque and stator
flux magnitude.

MAIN TOPICS
⇒ Space vector representation
⇒ Fundamental concept of DTC
⇒ Rotor flux reference
⇒ Voltage vector selection criteria
⇒ Amplitude of flux and torque hysteresis band
⇒ Direct self control (DSC)
⇒ SVM applied to DTC
⇒ Flux estimation at low speed
⇒ Sensitivity to parameter variations and current
sensor offsets
⇒ Conclusions

INVERTER OUTPUT VOLTAGE VECTORS
a b cE
I
1 3 5
2 4 6
Sw Sw Sw
Sw Sw Sw
Voltage-source inverter (VSI)
For each possible switching configuration, the output
voltages can be represented in terms of space vectors,
according to the following equation
v v v e v es
s
a b
j
c
j
= + +








2
3
2
3
4
3
π π
where va, vb and vc are phase voltages.

Sw1 Sw2 Sw3 Sw4 Sw5 Sw6 Sa(t) Sb(t) Sc(t) vk
OFF ON OFF ON OFF ON 0 0 0 v0
ON OFF OFF ON OFF ON 1 0 0 v1
ON OFF ON OFF OFF ON 1 1 0 v2
OFF ON ON OFF OFF ON 0 1 0 v3
OFF ON ON OFF ON OFF 0 1 1 v4
OFF ON OFF ON ON OFF 0 0 1 v5
ON OFF OFF ON ON OFF 1 0 1 v6
ON OFF ON OFF ON OFF 1 1 1 v7
I
i s
s
Im (q)
Re (d)
E=
_
V3 V
_
2
V
_
1
V
_
4
V
_
5 V
_
6
V
_
0
_
V7
_
k
1_
k
V
Inverter output voltage vectors

GENERAL REPRESENTATION OF THE
INVERTER OUTPUT VOLTAGE VECTORS
The inverter switching configuration defines the line-
to-line voltages by
( ) ( )[ ]v E S t S tab a b= −
( ) ( )[ ]v E S t S tbc b c= −
( ) ( )[ ]v E S t S tca c a= −
In the absence of omopolar generators and assuming a
symmetrical machine yields
v v va b c+ + = 0
and the line-to-neutral voltages can be expressed as a
function of two line-to-line voltages
v
v v
a
ab bc
=
+2
3
v
v v
b
bc ab
=
−
3
v
v v
c
ab bc
=
− −2
3

Then, by substitution we obtain
( ) ( ) ( )
v E
S t S t S t
a
a b c
=
− −2
3
( ) ( ) ( )
v E
S t S t S t
b
b a c
=
− −2
3
( ) ( ) ( )
v E
S t S t S t
c
c a b
=
− −2
3
Using these equations the space vector of the phase
voltages becomes
( ) ( ) ( )v S t S t e S t es
s
a b
j
c
j
= + +








2
3
2
3
4
3E
π π
The power balance equation, neglecting the inverter
losses, leads to
( ) ( ) ( )I S t S t e S t e ia b
j
c
j
s
s
= + +








•
2
3
2
3
4
3
π π

FUNDAMENTAL CONCEPT OF DTC
STATOR FLUX VECTOR VARIATION
Assuming the voltage drop R is s
s
small, the stator flux is
driven in the direction of the stator voltage vs
s
∆ϕ ∆s
s
s
s
v T≅ , where ∆T is the sampling period
k+3
k+2
k-2 k-1
ϕs
k-th sector
∆ϕs
_
kv
_
v k+1
v
_
v
_
v
_
v
_
v
_
o
ωs
s
The flux variation is proportional to E, ∆T and has the same direction of
the voltage vector applied.

VOLTAGE SPACE VECTOR NAMES
k+3
k+2
k-2 k-1
ϕs
k-th sector
∆ϕs
_
kv
_
v k+1
v
_
v
_
v
_
v
_
v
_
o
ωs
s
vk ⇒ radial positive voltage vector
vk+1 ⇒ forward positive “
vk+2 ⇒ forward negative “
vk+3 ⇒ radial negative “
vk-1 ⇒ backward positive “
vk-2 ⇒ backward negative “
v0 e v7 ⇒ zero “

ROTOR FLUX AND TORQUE VARIATION
From the general equations written in the rotor
reference frame, we can derive
ϕ
στ
ϕr
r m
s r
s
rL
L s
=
+
1
1
with σ = −1
2
L
L L
m
s r
This equation shows the nature of rotor flux
dynamic response for changes in stator flux
T p
L
L L
j p
L
L L
m
s r
s
r
r
r m
s r
s r sr= =•
3
2
3
2σ
ϕ ϕ
σ
sinϕ ϕ ϑ
Any stator flux vector variation determines a torque
variation on the basis of two contributions
I) The variation of the stator flux magnitude
II) The variation of the stator flux phase angle with
respect to rotor flux
Any command which causes the flux angle ϑsr to
change will determine a quick torque variation.

EXPERIMENTAL SET-UP
ADC
DAC
DSP
Personal
Computer
Main
Driver &
Protection
LOAD
Torque & Flux
Command
E
i c
S
S
S
a
b
c
torque meter
i a
l IGBT inverter, 1000 V, 50 A
l DSP TMS320E15, 20 MHz.
l 1 MHz, 8-channel, 12-bit A/D
converter
l 2-channel, 16-bit D/A converter

EXPERIMENTAL RESULTS
Stator flux locus, steady state, ωm = 100 rad/s
Rotor flux locus, steady state, ωm = 100 rad/s

EXPERIMENTAL RESULTS
Estimated d and q components of stator flux during the
response to a torque command alternating between
50% and 200% of the rated torque
These results show that the decoupling between the
stator flux components can be achieved controlling
directly the magnitude of the stator flux

Dtc (1)

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