Latvian Maritime academy

u U
n
0
U i max
* sin( i t i
)
i1
; (6)
i I I *sin( i t
) . (7)
0 i max
i i
The basic task of the investigation of the processes in air gap is the determination of the currents in
the machine windings at a changing operation mode (space oscillation of the rotor) that requires the
solution of the system of equations of emf balance in the electrical circuits of the machine. The
complexity and accuracy of the investigation and the mathematical model as well usually increase with
the increasing of the number of factors taken into account and depend on the types of these factors and
methods of the investigation. All the equations in the system are in the relative units or p.u. system with
equal resistances of the mutual inductance and magnetization forces [7, 10].
The mathematical model of induction motor in d, q, 0 - axes.
(10)
dcd
ucd
rci
cd
cq;
dt
dcq
ucq
rci
cq
cd ;
dt
dpd
u
pd
rpi
pd
pq
k
;
dt
dpq
u
pq
rpi
pq
pd
k
(11)
dt
The flux linkages for all the loops of the machine in d, q 0 - axes contain only the constant
inductivities not depending on time:
x i x i ;
cd
cq
c cd
x i
c cq
x
ad
ad
i
pd
pq;
x i x i ;
(12)
pd
pq
x
ad
i
cd
ad cq
x
p pd
. pipq The equation of motion is shown by Formula 13.
d
J M out
M c
dt
. (13)
where: J- is the moment of inertia of the rotor and load mechanism;
M out – rotating torque on the shaft;
M c – resistive torque.
When the rotor is oscillating the kinetic energy is converted into the energy of electromagnetic field
and vice versa. In this case along with the constant component M out 0 the rotating torque of the motor
contains also the torques of the harmonic components M out ν .
M
M M cos( t
)
out out 0
out m
. (14)
The electromagnetic torque of the motor is related to the magnetic flux with the equation
M CI
2s
cos
2s
;
(15)
where: С- is a constructive constant of electric motor;
13