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Unformatted text preview: 131 Chapter 13
Vector Control of InductionMotor Drives: A Qualitative
Examination Exit 2001 by N. Mohan Print TOC " ! 132 DC Motor Drive Sa + N S
Tem Na ia ia
φf P
P va
U
− φa La 0 Ra + ea t
Tem = kT ia Tem − 0 t Tem = kT ia Exit 2001 by N. Mohan TOC " ! 133 Brushless DC Motor Drive
!"
is (t ) ˆ
Is
!!"
Br (t )
90 o S N 0 θm
a − axis t
ˆ
Tem = kT I s Tem
0 t ˆ
Tem = kT I S Exit 2001 by N. Mohan TOC " ! 134 VectorControlled Induction
Motor Drive
!!
"
Fr (t ) !!
"
vs (t ) θr θr !!"
Br (t )
!!!
"
Blr (t ) !!
"
ir '(t ) a − axis
!!!
"
Fr '(t ) !!!!
"
Bms (t ) IM P
P
U Tacho current
feedback speed feedback "
"
"
Br (t ) perpendicuar to Fr′(t ) and Fr (t )
ˆ
Tem = kT I r'
Exit 2001 by N. Mohan ˆ
(keeping Br constant)
TOC " ! 135 Analogy to a CurrentExcited
Transformer With a Shorted
Secondary
φm,i1 φm,i2 i2
i1 0 φl 2 i1 t R2 shown explicitly R2 v2 = 0 short net = 0
N:N λ2 (0+ ) = λ2 (0 ) = 0
φm,i (0+ ) = φm,i (0 + ) + φ# 2 (0+ )
Lm
+
i 2 (0 ) =
i1 (0+ )
L2
1 Exit 2001 by N. Mohan 2 TOC " ! 136 d and q Axis Winding
Representation
isd = "
2
the projection of is (t) vector along the daxis
3 isq = "
2
the projection of is (t) vector along the qaxis
3 b − axis at t ib b − axis isq !
"
is
ia a − axis Exit 2001 by N. Mohan at t !
"
is b − axis c − axis q − axis at t
!
"
is d − axis
isd a − axis
isq ic c − axis q − axis projection
2
= projection ×
3 d − axis
a − axis
projection
isd = projection × 2
3 c − axis TOC " ! 137 Initial Flux Buildup Prior to t = 0  q − axis
isq = 0 t = 0− φm,isd
!"
is
!!"
Br d − axis isd isd
−∞ 0 t 1ˆ
ˆ
i a (0 ) = I m,rated and i b (0 ) = i c (0 ) =  I m,rated
2
2ˆ
2 3ˆ
3ˆ
isd (0 ) =
Ims,rated =
( I m,rated ) =
Im,rated
3
3 2
2
 isq = 0
Exit 2001 by N. Mohan TOC " ! 138 Step Change in Torque at t = 0  ω slip
isq isq ωm = 0 t = 0+
φm,isq
φm,ir φlr
!!"
Br ω slip
a − axis isd isd net = 0 −∞ 0 t ! ωm = 0
! Isd unchanged
! Stepchange in isq
" Φq,net = 0
+
+
+
" φm,i (0 ) = φm,i (0 ) + φ#r (0 )
sq Exit 2001 by N. Mohan r ˆ , Lm i
" Tem α Br
sq
Lr TOC " ! 139 Flux Densities at t = 0 !!!!
"
Bms θ Exit 2001 by N. Mohan !!!
"
Blr
!!"
Br + t = 0+
a − axis TOC " ! Transformer Analogy – Voltage
Needed to Prevent the Decay of
Secondary Current
R1 Ll′2 Ll1 ′
R2 ′
i2 t >0
− i1 ⋅ u (t ) Lm 1310 im ′
′ ′
v2 = R2 i2 (0 + ) u (t ) + Exit 2001 by N. Mohan TOC " ! Currents and Fluxes at Sometime
Later t > 0, Blocked Rotor
q − axis ωm = 0 ω slip
isq 1311 t >0 φm,isq isq φm,ir
φlr !!"
Br ω slip d − axis isd
a − axis net = 0 ω slip R ′ , (L m /L r )isq
α r
ˆ
B
r Exit 2001 by N. Mohan TOC " ! VectorControlled Condition
With a Rotor Speed ωm 1312 q − axis ω syn t >0 isq isq φm,isq φ
m,ir φlr ωm !!"
Br ω syn d − axis isd
a − axis net = 0 ωsyn = ωm + ωslip
Exit 2001 by N. Mohan TOC " ! 1313 Similarity Between VoltageFed
and VectorControlled Induction
Machines in Steady State
!!
"
vs θr
!!"
isd !!!
"
ims θr
!!"
Br Exit 2001 by N. Mohan !!!
"
Blr !!!!
"
Bms !"
is at t !!
"
ir '
!!"
isq TOC " ! 1314 Torque, Speed, and Position
Control
ω m (measured)
motor mathematical model ˆ
Br (calculated) Tem ˆ
Br
θ Br − ˆ
Br
ωm
(measured) ωm ˆ*
Br
∑
+ PI calculations *
isd *
θm + ∑
− θm
(measured) P *
ωm
+ ∑
− PI *
Tem + ωm
(measured) *
isq ∑ dq to
abc *
ia
*
ib
*
ic isd
isq abc
to dq current
regulated
PPU ia
ib
ic Motor PI − ωm
d / dt
(measured) Tem
(calculated) θm
encoder ωsyn (t) = ωm (t) + ωslip (t)
t θ B (t) = 0 + 0∫ ωsyn (τ) ⋅ dτ
r Exit 2001 by N. Mohan TOC " ! 1315 SensorLess Drives
! DTC
Reference 4: M. Depenbrock, “Direct Self Control
(DSC) of InverterFed Induction Machines,” IEEE
Transactions on Power Electronics, Vol. 3, 1988, pp.
420429
Reference 5: I. Takahashi and Y. Ohmori, “High
Performance Direct Torque Control of an Induction
Motor,” IEEE/IAS Annual Meeting, 1987, pp. 163169
Exit 2001 by N. Mohan TOC " ! 1316 Summary/Review
! How is torque controlled in brushtype dc drives and
brushlessdc drives?
! In a sentence, describe the vector control of inductionmotor
drives that emulates the performance of dc drives. Why is it
more challenging?
! What does the Theorem of Constant Flux Linkage state?
! In words, what does the analogy of a transformer with the
shortcircuited secondary, and excited by a stepcurrent
conclude?
! What is the reason for introducing the daxis and the qaxis
windings?
! Without the details, state the reason for choosing 3/2 N s 2
as the number of turns in the daxis and qaxis windings.
Exit 2001 by N. Mohan TOC " ! 1317 Summary/Review
"
! How are isd and isq obtained from the is space vector?
! At the end of the initial flux buildup process at t = 0, are
there any currents in the rotor bar?
! How are the currents induced in the rotor bars at t = 0+ ?
! What needs to be done to maintain the torque produced at t =
0+ ?
! Why does the slip speed at which the daxis and qaxis
windings need to be rotated, to maintain the torque produced
beyond t = 0+, depend on various quantities as given in Eq.
1312?
! Describe the similarity between voltagefed induction
machines and vectorcontrolled induction machines.
! Describe the control block diagram of vector control.
! Describe DTC and its objectives.
Exit
TOC
" !
2001 by N. Mohan ...
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 Fall '06
 Scalzo

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