1@2modeling asaof an electric machine
Post on 06-Jul-2018
214 Views
Preview:
TRANSCRIPT
-
8/17/2019 1@2modeling asaof an Electric Machine
1/24
Modeling and Operation ofan Electric Machine
Dr S.P. Singh
Professor
Department of Electrical Engineering
IIT Roorkke
-
8/17/2019 1@2modeling asaof an Electric Machine
2/24
-
8/17/2019 1@2modeling asaof an Electric Machine
3/24
-
8/17/2019 1@2modeling asaof an Electric Machine
4/24
-
8/17/2019 1@2modeling asaof an Electric Machine
5/24
TORQUE AND VOLTAGE IN NONSALIENT – POLE MACHINES
• The machine is regarded as a circuit elementwhose inductances depend on the angular positionof the rotor.
• – lu! linkages "λ # and magnetic $eld energ% are
e!pressed in terms of currents and inductances.
–
– Tor&ue can 'e found from the partial deri(ati(e of
magnetic $eld energ% or co)energ%. –
• The result is a set of non)linear di*erentiale&uations
-
8/17/2019 1@2modeling asaof an Electric Machine
6/24
VIEW POINTS :
• Parallel de(elopment of following two (iewpoints help in o'taining an appro!imatee!pression for inductance parameters. The% are+
• To&ue is e!pressed e!plicitl% as the tendenc%for two magnetic $elds to line up in the samewa% as permanent magnets tend to alignthemsel(es.
• ,enerated (oltage is e!pressed as the result ofthe relati(e motion 'etween a $eld and awinding
-
8/17/2019 1@2modeling asaof an Electric Machine
7/24
Assumptions
• Stator and rotor are concentric c%linders and the slot openings are neglected.
• Therefore- the stator and rotor self +inductances ss and rr respecting areconsidered to 'e constant.
• ut
•
• Stator)rotor mutual inductance depends on the angle /θ0 'etween themagnetic a!es of stator and rotor winding.
• • Mutu!" In#u$t!n$%
•
• The ma!imum positi(e (alue when θ12 or 3π
• is 4ero when θ 1 ± π53.
• The ma!imum negati(e (alue when θ1±π
• • 6ence 7
•
• sr "θ# 1 sr.8osθ "i#
•
-
8/17/2019 1@2modeling asaof an Electric Machine
8/24
Mathematical Model of the Machine
• lu! linkages of rotor and the stator in terms of
inductances- are 7• λs 1 ss.is 9 sr"θ#.ir 1 ss.is 9 sr.8osθ. i r
• λr 1 sr"θ#.is9 rr.Ir 1 rr 8osθ .is9 rr.ir
• Terminal (oltages :s and :r are +
• (s 1 rs .is9pλs
• (r 1 rr .ir9pλr
• p 1 d5dt 1 time)deri(ati(e operator
-
8/17/2019 1@2modeling asaof an Electric Machine
9/24
T%&min!" 'o"t!(% E)u!tions *o&Dou+", E-$it%# m!$.in%
• The d%namics and statics of Electromechanicalenerg% con(ersion- tor&ue and (oltagee&uations in non salient pole machine
forrotor pSini L piCos L pi Lir v forstator pSini L piCos L pi Lir v
sr sr s sr r rr r r r
r sr r sr s ss s s s
−−−−−−++=
−−−−−++=
)()()()(θ θ θ
θ θ θ
pθ - instantaneous speed in electrical radians per second.
In a P-pole machineθ = P/2 θ
m
• The d%namics and statics of Electromechanicalenerg% con(ersion- tor&ue and (oltagee&uations in non salient pole machine
The a'o(e e&uations are the fundamental e&uations of themachine and (alid for dou'l% e!cited ac as well as dcmachines. ;ith a little modi$cations in the a'o(e e&uationsare (alid for di*erent t%pes of ac and dc machines
-
8/17/2019 1@2modeling asaof an Electric Machine
10/24
θ Cosii Li Li LW r s sr r rr s ss fld ...21.
21 22
++=
m
r sr sm
m
fld
ed
d ii
d
dWfLd ii
W T
θ
θ θ
θ θ
θ )..,(),,(
+=
∂
∂+=
Therefore Te for a P-pole machine is :-
mr s sr r s sr e
P Sinii L
P Sinii L
P T θ θ
2..
2...
2−=−=
-
8/17/2019 1@2modeling asaof an Electric Machine
11/24
(s 1 rs< is 9ss."p is#9sr 8osθ "p ir # + sr ir Sinθ "pθ# ====">#
(r 1 rr< ir 9rr."p ir#9sr 8osθ "p is# + sr is Sinθ "pθ# ===="3#
Basic Equations
mr s sr r s sr e P Sinii L P Sinii L P T θ θ 2
..2
..2
−=−=
)(1
Lr me
r T BT J dt
d −−= ω
ω
And usin torsional – mechanical equation:
Electric tor&ue is 9 (e for motor and + (e in case of generator.
or a an% dc machine ?rd term of the (oltage e&uations is alwa%sa'sent as $eld and armature mmf in case of dc machine are at&uadrature.
The fourth term - speed (oltage which is due to relati(e motion incoils is there for stator (oltage e&uation 'ut a'sent in rotor(oltage e&uations. is
On the 'asis of a'o(e assumption the d%namic e&uations forseparatel% e!cited dc motor can deri(ed as follows
-
8/17/2019 1@2modeling asaof an Electric Machine
12/24
Model of D8 Shunt Motor
a
a
r f
a
af
a
aaa v L
i L
L
L
ir
dt
di.
1..
.+−
−= ω
f
f f
f f f v
L L
ir
dt
di.
1.+
−
=
Lr m
f a
af r T J J
Bii
J
L
dt
d .
1.. −−= ω
ω
-
8/17/2019 1@2modeling asaof an Electric Machine
13/24
-
8/17/2019 1@2modeling asaof an Electric Machine
14/24
Out put
0 0.2 0.4
-100
0
100
200
300
Time (second)
Armature currnt ia [A]
0 0.2 0.4
0
2
4
6
Time (second)
Field currnt if [A]
0 0.2 0.4
0
100
200
300
Time (second)
Angular velocity, wr rad/sec
-
8/17/2019 1@2modeling asaof an Electric Machine
15/24
SIMNI MODE
-
8/17/2019 1@2modeling asaof an Electric Machine
16/24
Separatel% E!cited dc Motor
a
a
r f
a
af
a
aaa v L
i L
L
L
ir
dt
di.
1..
.+−
−= ω
f
f f
f f f v
L L
ir
dt
di.
1.+
−
=
Lr m
f a
af r T
J J
Bii
J
L
dt
d .
1.. −−= ω
ω
-
8/17/2019 1@2modeling asaof an Electric Machine
17/24
Separatel% E!cited D8 ,enerator
• θ1K22
• T 1) T
• :a1 ):a
Separatel% E!cited D8 ,enerator
• θ1K2 2
• T 1) T
• :a1 ):a
-
8/17/2019 1@2modeling asaof an Electric Machine
18/24
Shunt connected dc motor
f a vv =
ff a f r vi /=
ar f af aa r wi Lvi /)( −=
)/(*)/1( 2 f aa f r af af e r ivr w L LT −=
θ=" 0
-
8/17/2019 1@2modeling asaof an Electric Machine
19/24
To&)u%/sp%%# )u!#&!nt o* op%&!tion
ω
T01
2 3
T 4'%ω 4'%Pm 4'%
T /'%ω 4'%Pm /'%
T /'%ω /'%
Pm 4'%
T 4'%ω /'%
Pm /'%
-
8/17/2019 1@2modeling asaof an Electric Machine
20/24
ITRODN8TIO TO EE8TRI8 DRI:ES ) MODNE >
3/)u!#&!nt op%&!tion
ωm
Te
Te
ωm
Teωm
Te
ωm
ω
T
• Direction of positi(e"forward# speed is ar'itrar%chosen
• Direction of positi(e tor&uewill produce positi(e"forward# speed
Quadrant 1
Forward motoringQuadrant 2
Forward braking
Quadrant 3
Reverse motoringQuadrant 4
Reverse braking
-
8/17/2019 1@2modeling asaof an Electric Machine
21/24
our Quadrant dc motorcharacteristic
5un$tion Qu!#&!nt
Sp%%# To&)u% Po6%&output
orwardMotoring"M#
I 9 9 9
orwardRegeneration"R#
I: 9 )
Re(erse
Motoring"RM#
III 9
Re(erseRegeneration "RR#
II 9
-
8/17/2019 1@2modeling asaof an Electric Machine
22/24
Grmature and (oltage and currentre&uirement of four &uadrant dc dri(e
5un$tion Sp%%# To&)u% 'o"t!(% $u&&%nt Po6%&output
orwardMotoring
"M#
9 9 9 9 9
orwardRegeneration"R#
9 ) 9 ) )
Re(erseMotoring"RM#
) 9
Re(erseRegeneration "RR#
9 9 )
-
8/17/2019 1@2modeling asaof an Electric Machine
23/24
ITRODN8TIO TO EE8TRI8 DRI:ES ) MODNE >
R!tin(s o* $on'%&t%&s !n# moto&s
Torque
Speed
Power limit for
continuous torque
Continuous
torque limit
Maximum
speed limit
Power limit for
transient torque
Transient
torque limit
-
8/17/2019 1@2modeling asaof an Electric Machine
24/24
ITRODN8TIO TO EE8TRI8 DRI:ES ) MODNE >
C"!ssi7$!tion o* IM #&i'%s (Buja, Kamierkowski, “Direct torque control of PWM inerter!fed "# motors ! asure$%, &''' Transactions on &ndustrial 'lectronics, ))*+
top related