![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](https://image.slidesharecdn.com/dtc1-170110064102/85/Dtc-1-6-320.jpg)
Dtc (1)
- 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
- 2. 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.
- 3. 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
- 4. 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.
- 5. 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
- 6. 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
- 7. 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
- 8. 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.
- 9. 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 “
- 10. 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.
- 11. 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
- 12. EXPERIMENTAL RESULTS Stator flux locus, steady state, ωm = 100 rad/s Rotor flux locus, steady state, ωm = 100 rad/s
- 13. 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