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
+ _
s* s j s + Djs _ Voltage Vector s * T + j s DT Selection _ T S S S s Stator a b c Torque j s s E Flux vs 2 Estimator Estimator 3 s is 2 i b i a 3
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
Þ Space vector representation Þ Fundamental concept of DTC Þ Rotor flux reference Þ Voltage vector selection criteria Þ Amplitude of flux and torque hysteresis band Þ Direct self control (DSC) Þ SVM applied to DTC Þ Flux estimation at low speed Þ Sensitivity to parameter variations and current sensor offsets Þ Conclusions
INVERTER OUTPUT VOLTAGE VECTORS
I Sw1 Sw3 Sw5
E a b c
Sw2 Sw4 Sw6
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
æ 2p 4p ö s 2 j j v = ç v + v e 3 + v e 3 ÷ s ç a b c ÷ 3 è ø 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
_ Im (q) _ V 3 V2
_ _ V _ _ 4 _1 I V1 V0 V7 k Re (d)
Vs = kE _ i s
_ _ V 5 V6
Inverter output voltage vectors GENERAL REPRESENTATION OF THE INVERTER OUTPUT VOLTAGE VECTORS
The inverter switching configuration defines the line- to-line voltages by
vab = E [Sa (t)- Sb (t)]
vbc = E [Sb (t)- Sc(t)]
vca = E [Sc(t) - Sa (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 2v + v v = ab bc a 3 v -v v = bc ab b 3 -v -2v v = ab bc c 3 Then, by substitution we obtain
2S (t)- S (t)- S (t) v = E a b c a 3 2S (t)- S (t)- S (t) v = E b a c b 3 2S (t)- S (t)- S (t) v = E c a b c 3 Using these equations the space vector of the phase voltages becomes
é 2p 4p ù s 2 j j 3 3 v s = E êSa (t) + Sb (t)e + Sc (t)e ú 3 ê ú ë û The power balance equation, neglecting the inverter losses, leads to 2p 4p 2 é j j ù 3 3 s I = êSa (t)+ Sb (t)e + Sc (t)e ú· is 3 ê ú ë û
FUNDAMENTAL CONCEPT OF DTC
STATOR FLUX VECTOR VARIATION
s Assuming the voltage drop Rsis small, the stator flux is s driven in the direction of the stator voltage vs s s Dj s @ v s DT , where DT is the sampling period _ v _ k+2 v k+1
_ _ v v k+3 _ k w vo k-th sector s
j s s
Djs _ _ v k-2 vk-1
The flux variation is proportional to E, DT and has the same direction of the voltage vector applied. VOLTAGE SPACE VECTOR NAMES _ v _ k+2 v k+1
_ _ v v k+3 _ k w vo k-th sector s
j s s
Djs _ _ v k-2 vk-1
vk Þ radial positive voltage vector
vk+1 Þ forward positive “
vk+2 Þ forward negative “
vk+3 Þ radial negative “
vk-1 Þ backward positive “
vk-2 Þ backward negative “
v0 e v7 Þ zero “ ROTOR FLUX AND TORQUE VARIATION
From the general equations written in the rotor reference frame, we can derive 2 r Lm 1 r Lm jr = js with s = 1- Ls 1+ sstr Ls Lr
This equation shows the nature of rotor flux dynamic response for changes in stator flux
3 Lm r r 3 Lm T = p js · j jr = p j s jr sin J sr 2 sLs Lr 2 sLs 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 Jsr to change will determine a quick torque variation.
EXPERIMENTAL SET-UP
Main
Driver & Personal Protection Computer
Sa Sb Sc
E
DSP DAC i a
ADC i c torque meter
LOAD Torque & Flux Command
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, wm = 100 rad/s
Rotor flux locus, steady state, wm = 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