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Experimentalverificationofafield-circuitsquirrelcagemotormodel
J
(
α
n
+
1
−
2
α
n
+
α
n
-
1
)()
/
∆
t
2
=
T
−
T
0
9
(4)
where
T
=
T
()
t
α
n
,
isanangularpositionoftherotor,
T
0
isaloadtorque,
T
0
=
T
0
()
t
n
,
J
isamomentofinertia.
T
isanelectromagnetictorque,
Theelectromagnetictorqueiscalculatedonthebasisofthemagneticfield
components.Themovementoftherotorissimulatedbymeansofthemovingband
method[4].
Themethodofsolvingthefield-circuitequationsincludestimeandspacedis-
cretisationsandperformssearchingforthevaluesoffunctionsthatdeterminethe
distributionofmagneticvectorpotentialoverasetofdiscretepoints.Inthepaper
thefiniteelement(FE)methodisused[6],todeterminethemagneticfielddistri-
bution.Thespatialdiscretisationmethodutilizestriangularelementstorepresent
themagneticcircuitgeometry.Thesetofthealgebraicequationsdescribingthe
electromagneticfieldandcurrentsinthemotorwindingcanbeexpressedas
f
|
|
L
ϑ
S
β
∆
m
t
−
+
1
k
∆
T
t
−
1
G
ϑ
R
−
+
ϑ
∆
k
t
−
1
L
c
1
|
|
J
f
|
L
ϕ
i
n
n
1
|
J
=
=
f
|
|
L
−
(
1
−
ϑ
∆
)
S
t
−
β
1
m
k
T
+
∆
t
−
1
G
−
(
1
−
(
ϑ
1
)
−
R
ϑ
+
)
k
∆
t
−
1
L
c
1
|
|
J
f
|
|
L
ϕ
i
n
n
−
−
1
1
1
|
|
J
+
+
f
|
L
ϑ
u
n
+
0
(
1
−
ϑ
)
u
n
−1
1
|
J
(5)
Intheaboveequationthe
n
indexisusedtoshowquantitiesfor
t
=,time
t
n
stepsandthe
n-1
indexappliestoquantitiesfor
t
=
t
n
−
1
timesteps,
ϑ
isaweight-
ingcoefficient,
∆
tisthetimesteplength.Thestiffnessmatrix
S
β
m
includessubma-
tricesresultedfromskewdiscretisation,thereforesubscriptβdenotestheskew
angle,and
m
thenumberofsubmatrices.Themethodofsliceswasusedforskew
approximationwhichisexplainedgraphicallyinFig.1.Symbol
ϕ
isavectorof
modifiednodalpotential
(
φ
=
A
z
l,
l
−
lenght
of
the
disc
)
,Gisamatrixofelemen-
taryconductancesassociatedwiththeelementnodes,
L
c
isamatrixofselfinduct-
ancesandmutualinductanceduetoend-winding,
k
isamatrixthattransforms
modifiednodalmagneticpotentialsintolinkagefluxesofthewinding.
Thesetofequationspresentedaboveappliestomachineswithstraightslots.In
ordertodecreasetheimpactofparasiticalphenomenacausedbyhigherharmonics
ofthemagneticfield,particularlyelectromagneticturningtorques,skewedslots
areutilizedinsidethemagneticcoreofelectricmachines.Morepreciseanalysisof
electromagneticfielddistributioninsystemswithskewedslotsrequiresathree-
