actionari electrice cu turatia variabila - users.utcluj.rousers.utcluj.ro/~birok/sa/curs 4_actionari...
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Actionari electrice cu turatiavariabila
Consumuri energetice
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Consumul de energie electrica in sistemele de actionare
M3 ~
Mecanism
Transformator
Convertor
Motor
Pierderielectrice
Posibilitatea econimisiriiPierderi in mecanism
Energia mecanica utila
scazuta
ridicata
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Avantajele sistemelor cu turatie variabila
Reducerea pierderilor in transmisie (mecanice)
M 3 ~ transmisiacontrol,mecanic
retea
control
electric
mecanic
proces
M 3 ~ transmisia
retea
electric
mecanic proces
control
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Consumul de energie la un elevator
Flender-Loher,Systemtechnic
0 20 40 60 80 100
Motor cu poli schimbabil
Control conventional (mecanic)
Invertor conventional
Invertor special
Invertor special cmd.dupa camp
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Pierderile in invertoare
D1
T1
D4
T4
D3
T3
D6
T6
D5
T5
D2
T2
Schema de principiu a unui inverter trifazat cu tranzistoare.
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Tipuri de invertoare
RFiltruR
etea M
3 ~
Inv.
RFiltru
Ret
ea M3 ~
Inv.
Tensiune
Curent
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Pierderile in invertoare
10 20 30 40 50 60 70 804
5
6
7
8
9
10
11
f [Hz]
pt [%]
Inv. de curent
Inv.de tensiune
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Randamentul invertoarelor
0 10 20 30 40 50 60 70 8085
86
87
88
89
90
91
92
93
94
95ηηηη [%]
curent
tensiune
f [Hz]
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Influienta frecventei de comutatie
Pn = 37 [kW]
0 5 10 151
2
3
4
5
6
7
8
9
invertor
motor
totalpt [%]
fcom [kHz]
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Schema de principiu a unui sistem de actionare cuconvertor static si motor de inductie
RFiltru
Ret
ea M3 ~
Inv.ir
uduc
L
C
idTr
Circuit intermediar de curent continuu format din L si C
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Legatura dintre retea si convertorul static
( ) ( )tUtu ⋅⋅⋅= ωsin2
( ) ( )∑ −⋅⋅⋅⋅=ν
νν ϕων tIti sin2
11 sinϕ⋅⋅= IUP
Se presupune reteaua de putere infinita.
Tensiunea este sinusoidala
Curentul este nesinusoidal
Puterea activa se transmite numai prin fundamentala
Puterea aparenta este2
1
2
11
2 11 iTHDIUIIIUIUIUS +⋅⋅=
+⋅⋅=⋅=⋅= ∑∑
∞∞
ν
ν
νν
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Puterea aparenta si reactiva
2
11
cos iTHDPS +=ϕ
21
1cos
iTHDSPPF
+== ϕ
1ϕtgPQB ⋅=
Tinind seama ca puterea activa este data de fundamentala curentului
THDi factorul total de distorsiune a curentului
Puterea aparenta se poate scrie
Factorul de putere global
Puterea reactiva se poate defini in mai multe moduri (Budeanu,Czarnecki, )
Budeanu ( )∑∞
=⋅=
1
2sinν
νν ϕIUQC
∑∞
=
+=
2
2
11 sinsin1
ν
νν
ϕϕ
II
QQB
C
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Puterea deformanta
ii
iBB THDP
THDTHDSQPSD
12
222
cos1 ϕ=
+=−−=
∑∞
=
−=−−=
2
2
1
2
1
222 sincos ν
νν ϕ
ϕ IITHDPQPSD iCC
Diferenta dintre cele doua relatii
La puterea activa impusa
Se poate minimiza puterea aparenta daca:cosϕ1=1 si THDi =0 deci in regim sinusoidal
Deoarece cosϕ1 si THDi depind de componentele filtrului,factorul de putere global este deasemenea dependent de filtru.
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Expresia puterilor la motorul de inductie
( ) ( )
( ) ( )∑
∑
∞
=
∞
=
−⋅⋅⋅=
−⋅⋅⋅=
1
1
sin2
sin2
ννν
ννν
ϕων
ϕων
i
u
tIti
tUtu
∑∞
==
1cos
νννν ϕIUP
Tensiunea si curentul sunt nesinusoidali
Puterea activa
Puterea aparenta
2211
1
2
1
2 11 iu THDTHDIUIUS ++== ∑∑∞
=
∞
= νν
νν
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Minimizarea puterii aparente
22
212
111cos
cos1
cos iu THDTHDIUPS ++
−−=
∂∂
∑∞
=νννν ϕ
ϕϕ
22
12 11
cos1
cos iu THDTHDIUS ++−=∂
∂νν
ν ϕϕ
Se calculeaza derivatele partiale ale puterii aparente dacaputerea activa totala este constanta
21
2
2
21
22
1
1
1cos
cos1
11coscos
II
YHD
THDIUP
THDTHDUIS
i
u
iu
ν
µµµµ
νν
ν
ϕϕ
ϕϕ
+
+
−+
+++−=∂∂
∑∞
=
Expresia este negativa si diferita de zero, deci valoarea minima se obtine pentrucosϕ1=1.
Similar si pentru derivatele in raport cu cosϕν
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Minimizarea puterii aparente
( ) 212
2 coscos1IIIUPTHDU iν
µµµµνν ϕϕ
−=+ ∑
∞
=
νµϕϕ
µ
µµ
ν
νν ≠=I
UI
U coscos
Derivatele puterii aparente in raport cu curenti armonici se anuleaza pentru
Se observa ca ecuatia are solutii nenule.
Dupa simplificari pentru doua armonici ν > µ
Cu conditia de extrem rezulta ecuatia
( )( )
01coscos
cos
cos
1
112
12
2
2
=+−
∑∞
=
II
UU
II
U
Uν
νν
ν
νν
µµµ
ϕϕ
ϕ
ϕ
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Minimizarea puterii aparente
( )( ) ( )
−±= ∑
∑
∞
=∞
=
2
221111
2
21cos4coscos
cos2
cosµ
µµ
µµµ
ννν ϕϕϕϕ
ϕ UUUU
UII
Solutia generala a ecuatiei
Expresia puterii aparente optime rezulta
( )( ) ( )
( ) ( )
−±±−⋅
⋅−±+
⋅=
∑
∑∑
∞
=
∞
=∞
=
2
22111111
1
2
221111
2
2
2
1
1
cos4coscoscos2
cos4coscoscos
1cos2
ννν
ννν
ννν
ϕϕϕϕ
ϕϕϕϕϕ
UUUUIP
UUUU
THDUS uo
Pentru semnul “-” rezulta puterea minima, iar pentru “ + “ puterea maxima.
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Particularizare pentru un motor asincron
νµϕϕ
µ
µµ
ν
νν ≠=I
UI
U coscos
{ } { } µνµµν ≠≥ℜ=ℜ 2ZeZePentru doua impedante Zν si Zµ corespunzatoare armonicilor rezulta
Considerand schema echivalenta in T si neglijand pierderile in fier pentruarmonica ν
( )
( )
( )
++
++
++
+
++
+=
22
2
22
2
νσνν
νσνσνν
νσν
νσνν
ν
νν
mRR
mRRR
mS
mRR
mRS
XXsR
XXXsR
XXj
XXsR
XsRRZ
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Particularizare pentru un motor asincron
νν
νν
νrn
nnns −=
⋅−⋅=1
1
{ } ( )( ) ( )222
2
mRrR
mRrS XXnR
XRnRZe+−+
−+=ℜσ
ν ννν
Tinand seama de expresia alunecarii fata de armonica ν si de viteza relativa n/n1
Partea reala a impedantei devine
Punand conditia de egalitate a partilor reale
( )( ) ( )
( )( ) ( )222
2
222
2
mRrR
mRr
mRrR
mRr
XXnRXRn
XXnRXRn
+−+−=
+−+−
σσ µµµ
ννν
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Particularizare pentru un motor asincronRezulta
( ) ( ) ( ) 02222232 =+−+++− µννµµν RrRRrRrR RnXRnXnX
Se poate calcula viteza relativa la care are loc egalitatea partilor reale.
Se obtine totdeauna o solutie reala subunitara- apropiata de nr =0
Concluzie :
Este necesar realizarea unor filtre astfel ca cosϕ sa fie apropiat de unitate
Sa poate realiza comanda corespunzatoare a redresorului.
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Dependenta partii reale ale impedantelor motorului deinductie in functie de alunecare