Download direct torque control of induction motors

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 ss*
+
_
ϕ ss
T* +
_
∆ϕ ss
∆T
T
Torque
Estimator
s
ϕs
Stator
s
Flux vs
Estimator
i ss
Voltage
Vector
Selection
Sa Sb Sc
E
2
3
2
3
ib
ia
Induction
Motor
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
I
Sw 1
Sw 3
a
b
E
Sw 2
Sw 4
Sw 5
c
Sw 6
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
2π
4π 

j
j
2
s
vs =
v a + vb e 3 + v c e 3 

3 

where va, vb and vc are phase voltages.
Sw1 Sw2 Sw3 Sw4
Sw5
Sw6
OFF ON OFF ON
OFF
ON
0
0
0
ON OFF OFF ON
OFF
ON
1
0
0
ON OFF
ON OFF OFF
ON
1
1
0
OFF ON
ON OFF OFF
ON
0
1
0
OFF ON
ON OFF
ON
OFF
0
1
1
OFF ON OFF ON
ON
OFF
0
0
1
ON OFF OFF ON
ON
OFF
1
0
1
ON OFF
ON
OFF
1
1
1
ON OFF
Im (q)
_
V3
Sa(t) Sb(t) Sc(t)
_
V2
_
V4
_
_
V 0 V7
_
_1 I
k
V1
Re (d)
Vs = k E
_
is
_
V5
_
V6
Inverter output voltage vectors
vk
v0
v1
v2
v3
v4
v5
v6
v7
GENERAL REPRESENTATION OF THE
INVERTER OUTPUT VOLTAGE VECTORS
The inverter switching configuration defines the lineto-line voltages by
vab = E [ S a (t ) − Sb (t )]
vbc = E [ Sb (t ) − S c (t )]
vca = E [ S c (t ) − S a (t )]
In the absence of omopolar generators and assuming a
symmetrical machine yields
va + vb + vc = 0
and the line-to-neutral voltages can be expressed as a
function of two line-to-line voltages
va =
vb =
vc =
2vab + vbc
3
vbc − vab
3
− vab − 2vbc
3
Then, by substitution we obtain
va = E
vb = E
vc = E
2 S a ( t ) − Sb ( t ) − S c ( t )
3
2 Sb ( t ) − S a ( t ) − S c ( t )
3
2 S c ( t ) − S a ( t ) − Sb ( t )
3
Using these equations the space vector of the phase
voltages becomes
2π
4π 

j
j
2
s
v s = E  S a (t ) + Sb (t )e 3 + S c (t )e 3 
3 



The power balance equation, neglecting the inverter
losses, leads to
2π
4π 

j
j
2
3
I =  S a (t ) + Sb (t )e
+ S c (t )e 3  • i ss
3 



FUNDAMENTAL CONCEPT OF DTC
STATOR FLUX VECTOR VARIATION
Assuming the voltage drop R s i ss small, the stator flux is
driven in the direction of the stator voltage v ss
s
∆ϕ s
s
≅ vs
∆T ,
where ∆T is the sampling period
_
_
v k+2
v k+1
_
_
v k+3
_
vo
k-th sector
vk
ωs
ϕ ss
∆ϕs
_
v k-2
The flux variation is proportional to E,
the voltage vector applied.
_
v k-1
∆T and has the same direction of
VOLTAGE SPACE VECTOR NAMES
_
_
v k+2
v k+1
_
_
v k+3
_
vo
k-th sector
vk
ϕ ss
∆ϕs
_
_
v k-2
vk
vk+1
vk+2
vk+3
vk-1
vk-2
v0 e v7
v k-1
⇒
⇒
⇒
⇒
⇒
⇒
⇒
radial positive voltage vector
forward positive
“
forward negative
“
radial negative
“
backward positive
“
backward negative “
zero
“
ωs
ROTOR FLUX AND TORQUE VARIATION
From the general equations written in the rotor
reference frame, we can derive
ϕ rr =
Lm
1
Ls 1 + sστ r
ϕ sr
with
σ = 1−
Lm2
L s Lr
This equation shows the nature of rotor flux
dynamic response for changes in stator flux
3
Lm
T= p
2 σLs Lr
ϕ sr •
j ϕ rr
3
Lm
ϕ s ϕ r sin ϑ sr
= p
2 σLs Lr
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 ϑ sr to
change will determine a quick torque variation.
EXPERIMENTAL SET-UP
Main
Driver &
Protection
Personal
Computer
Sa
Sb
Sc
E
DSP
DAC
ADC
ia
ic
torque meter
Torque & Flux
Command
l
l
l
l
LOAD
IGBT inverter, 1000 V, 50 A
DSP TMS320E15, 20 MHz.
1 MHz, 8-channel, 12-bit A/D
converter
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