Page - 249 - in Emerging Technologies for Electric and Hybrid Vehicles
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Energies 2017,10, 616
Whenthevoltagevector isat itsmaximumusmax,wecanget thechangerateofaxisq’s current
fromEquation(13):
diq
dt = √
u2smax−(ωrLqiq)2−ωrψf−Rsiq
Lq . (13)
InEquation(13),becauseof themechanical inertiabeinggreater thantheelectronic inertia,wecan
assumethatωr is constantduringtorque integration time tint, butduringthis time iq increases from0
tothemaximumofstatorcurrentvectoramplitude, ismax. Inorder tosimplify the torquefollowing
process into a linearprocess, diq/dtmustbea constant. Bymaximizing iq to ismax,we canget the
minimumofdiq/dt foran increasedintegrationtimeandthusahigher torquesaturationthreshold.
Ifweneglect statorelectric resistanceRs, thenwegetdiq/dtas:
diq
dt = √
u2smax− (
ωrLqismax ) 2−ωrψf
Lq . (14)
It isobvious thatwithmotorrotaryvelocityωr increasing, thepartialvoltageofelectromotive
force increases, voltageof stator gets almost saturated, and thevoltage allowanceused to control
motorcuttentdecreases,which in turnresults indiminishingdiq/dt.Whenωr approaches theright
boundaryof thenon-flux-weakeningregion’sexternal characteristics incurrentwindingmode,diq/dt
slips to0, implying that thedrivesystemis losingcontrolof themotor’s current. Inorder toguarantee
acertainamountofvoltagemarginusedtocontrol themotor’scurrent,we, inaccordancewithbase
speedratio, canget themotorangularvelocityωrsusedtocalculatediq/dt ineachwindingmodeby
Equation(15):
ωrs= ksωrb. (15)
InEquation(15),ωrb is therotator’sbaseangularvelocityof themotor incurrentwindingmode.
WhenignoringRs in id=0control strategy,wecanget:
ωrb= usmax
ψs = usmax√
ψ2f+(Lqismax) 2 . (16)
Because theapproximationofdiq/dt is constant, the integrationtime tint of thisprocess is:
tint= Δiq
diq/dt = Lqismax√
u2smax−(ωrsLqismax)2−ωrsψf = Lqismax√
u2smax−(ksωrbLqismax)2−ksωrbψf . (17)
InEquation (17), ks is the rotator speed sensitivity coefficient and ks ∈ (0,1); thebigger ks is,
thecloser themotor’sangularvelocity ksωrbused tocalculate integration time tint is to thecurrent
windingmode’sbaseangularvelocity,andthesmallervoltagemarginanddiq/dtare,which leads to
bigger tint andviceversa. ks reflects toleranceof torquefollowingspeed.Thebiggerks is, the lower
therequirements for torque followingspeed,which leads toaslowerresponseof the torquesaturation
judgmentalalgorithm. In theabove twoexpressions, ismax is themaximumof thestatorcurrentvector
in thepresentwindingmodeandusmax is themaximumofanyanglevoltagevector in thepresent
windingmode.
Because theapproximationof diq/dt is constant, the torque followingprocess is simplified to
a linearprocess. The integrationof torqueerrorof thisprocess is:
Ilim= ∫ tint
0 |ΔTdt|= ∫ tint
0 |Tl−T∗e |dt= 1
2 Temaxtint. (18)
249
Emerging Technologies for Electric and Hybrid Vehicles
- Title
- Emerging Technologies for Electric and Hybrid Vehicles
- Editor
- MDPI
- Location
- Basel
- Date
- 2017
- Language
- English
- License
- CC BY-NC-ND 4.0
- ISBN
- 978-3-03897-191-7
- Size
- 17.0 x 24.4 cm
- Pages
- 376
- Keywords
- electric vehicle, plug-in hybrid electric vehicle (PHEV), energy sources, energy management strategy, energy-storage system, charging technologies, control algorithms, battery, operating scenario, wireless power transfer (WPT)
- Category
- Technik