POLITECHNIKA WARSZAWSKA

2. Mathematical description of induction motor
d
u
sK
sK = rs
isK
+ TN
+ jωKψ
dt
sK
dψ
u
rK
rK = rr
irK
+ TN
+ j(
ωK
−ωm
)
dt
= x
sK s isK
+ xM
irK
= x
rK r irK
+ xM
isK
dωm
1 *
= [ Im( ψ isK
) − mL
]
dt T sK
M
ψ
ψ
ψ
ψ
rK
(2.10)
Note, that:
• time t, T M and T N are expressed in absolute units,
• l = x, the inductances in the flux-current equation are replaced by the reactances
corresponding to them,
• the rotor quantities recalculated to the stator side are referred to the same base
units - for that reason the prime index is omitted.
2.2.4. Orientation of the model
When resolving vector equations, one can adopt an arbitrary coordinate reference
frame. The main applied coordinate systems are chosen as follows:
• stator-fixed system of coordinates (α-β) (ω K = 0),
• rotor-fixed system of coordinates (d-q) (ω K = ω m ),
• synchronous-rotating system of coordinates (x-y);
In the last case the coordinate system is oriented along one of the space vectors in the
motor. This vector could be:
• the space vector for the stator currents
• the space vector for the stator voltages
• the space vector for the rotor currents
• the space vector for the rotor flux linkages
Some of these possibilities will be presented.
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