POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 | NUMBER: 1 | 2016 | MARCH
i
r
qs
i
r
ds
i
0
=
cos θ
r
cos
θ
r
−
2π
3
cos
θ
r
+
2π
3
sin θ
r
sin
θ
r
−
2π
3
sin
θ
r
+
2π
3
1
2
1
2
1
2
·
i
as
i
bs
i
cs
. (3)
p
i
r
qs
i
r
ds
ω
r
θ
r
=
−
R
s
L
q
−
L
d
L
q
ω
r
−
λaf
L
q
0
L
d
L
q
ω
r
−
R
s
L
d
0 0
λ
af
2H
−
(L
d
−L
q
)i
r
qs
2H
−
B
2H
0
0 0 1 0
·
i
r
qs
i
r
ds
ω
r
θ
r
+
1
L
q
0 0
0
1
L
d
0
0 0 −1
0 0 0
·
ν
r
qs
ν
r
ds
T
1
. (5)
Transforming the voltages into q- and d-axes in the
same reference frame as:
ν
qsi
ν
dsi
= V
i
sin θ
i
cos θ
i
. (8)
The injected flux linkage vector in estimated rotor
reference frame can be given by:
λ
qsi
λ
dsi
= V
si
sin θ
i
cos θ
re
− sin θ
re
. (9)
The injected frequency component of the stator cur-
rents can be obtained as:
i
qsi
i
dsi
= sin θ
i
I
1
cos θ
re
− I
2
cos {2 (θ
r
− θ
re
)}
−I
1
sin θ
re
+ I
2
sin {2 (θ
r
− θ
re
)}
,
(10)
where:
I
1
=
V
i
ω
i
L
q
+L
d
2
L
q
+L
d
2
2
−
L
q
−L
d
2
2
, (11)
I
2
=
V
i
ω
i
L
q
−L
d
2
L
q
+L
d
2
2
−
L
q
−L
d
2
2
. (12)
Transforming the d-axis current to the estimated ro-
tor position reference frames yields [9].
i
e
dsi
= i
qsi
sin (θ
re
) + i
dsi
cos (θ
re
) . (13)
Equation 13 can be rewritten as:
i
e
dsi
= I
2
sin θ
i
[sin {2 (θ
r
− θ
re
)}] . (14)
From Eq. 14 it can be seen that it contains the in-
formation related to rotor position error. This useful
signal can be extracted using a bandpass filter (BPF)
which separates the fundamental component from the
HF component followed by an observer. This posi-
tion error can be demodulated by any demodulation
schemebut in this model heterodyning process is used-
for the estimation of position and speed [5].
4. Implementation of
Speed-Controlled Sensorless
PMSM Drive by Estimating
Rotor Position Using Signal
Injection
The proposed model developed for sensorless vector
control of PMSM drive using signal injection, as pre-
sented in Fig. 2, is implemented using the software
Matlab/Simulink. It consists of a speed loop, current
and torque angle calculator, stator current synthesizer,
inverter with SPWM current control, PMSM model,
HF signal injection, demodulation process, controller
and observer for rotor position and speed estimation.
Each functional block is elaborated in detail in the fol-
lowing sections. The principle for this speed control
strategy is based on comparing the reference speed and
the estimated speed [10]. The speed error thus ob-
tained is then processed through the speed controller
and the output of this block represents the reference
torque (T
∗
e
) for the current and torque angle calcula-
tor. The stator current synthesizer generates the phase
reference current commands. The three phase reference
currents are compared with their respective actual cur-
rents resulting in the current errors in a PWM current
controller which is then used to generate the switching
signals for the inverter. In the proposed scheme the
feedback signal i.e. rotor position (θ
re
) is estimated
using external signal injection scheme. Once the rotor
position is estimated, the rotor speed (ω
re
) can be es-
timated by using Eq. (6) [11]. The inability with most
of the methods to provide accurate rotor position esti-
mation at low speeds, which directly affects the control
performance, would not be a problem with this tech-
nique [12].
4.1. Speed Controller
The speed error between command and estimated val-
ues of speed is processed in the proportional and inte-
c
2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 31