JWW"ffl'N\-
I
----- � -----+----- - - - - t-
--
I 1 ______ I
- - - t+---�"'4------___j_--Il:::-____ :l ____l
---t --
-----r-----
'--____---"-______--'---______'---__ -- __---"-____-----.l 0.1
.-------,--,---�--�
- - - - - � - - - - - � - ----
--
0.05
J1 --
-0.15 '------�--'--" 0.2 5 0.05 0.1 0.15 02 o .
25.------,------,-------,-�--_,--�__.
�: I �
----
I ______1_
-----+-----
0.1
�1
Modified FOe
I
0.24
0.05
SIMULATION RESULTS
The proposed approach with the modified FOC has been verified on a simulation model employing a BLDC motor with an almost ideal trapezoidal shape of back EMF. The normalized functions of the back-EMF have been determined by (8). Harmonics higher than 19th have been neglected.
o
�
-;= 3i---:---T-----:I --=====;l
0.2
.0'"
-10
I
0.23
L-____---'-__ - ____"---__ -- __---"-______-"---____---.J o 0.05 0.1 0.15 0.2 0.25 Time [51
02 . 5
(21)
-5
0.22
Fig. 6 compares the dq feedback currents on the output of the BLDC model (with significant perturbation of the magnitude) and on the output of extended transfonnation (modified currents) with unalterable magnitude. As can be seen, the extended transfonnation provides current feedback significantly smoother than the standard FOC. This behavior can also be clearly observed in the current error signal entering the PI controllers, Fig. 7.
Fig. 4 Modified field oriented control strategy
VI.
I O�.-......r-
Fig. 6 Feedback currents in dq reference frame
eqn.14,15
A.
-----
Time [5]
0.15
0.2
0.4
0.25
0.2
Fig. 5 Voltages in the dq reference frame after decoupling
Fig. 5 represents the decoupled voltages in the dq frame which supply the model of the motor. Inverter nonlinearities are not taken into account because space
o
-
- - - r -
---0.23
'--------cL =�.:-' ---------:-L :------ :"- :------� O .05 0. 15 0. 1 0.25 0 0.2
lime [sl
Fig. 8 Electromagnetic and load torque
183
To express the power requirements for each control strategy, it is appropriate to evaluate the root mean square (RMS) value of currents with the following equation:
Fig. 8 shows the produced electromagnetic torque and applied load torque, including a detail of the torque behavior in the steady state. As can be seen, a very smooth torque behavior with minimized torque ripple is achieved.
IIOO
...j IRMS
Comparison of control stategies
B.
Keeping the same simulation conditions, such as the same commands for the desired angular velocity, same load torque commands and the same parameters of the BLDe motor, the six-step commutation strategy, the standard Foe and proposed modified Foe (MFOC) focusing on produced torque, the total harmonic distortion of the current, and the power rating can all be compared. One period of the current waveforms of all the control strategies is shown in Fig.9. 3
Tripple
D-
--Foe --MFoe -- SIX-S TEP
� 0.95
f-
- - - - - - - r- ------- r --
-2
- - - - - - - � - - - - - - - � - --
Q
_3L0.225
0.23
0.235
Time
[s]
Their harmonic spectrum is analyzed using a fast Fourier transformation and the graphical interpretation is shown in Fig. 10.
.
2 5 2
� :;
15
"
--
.
u
o
7 9 11 Harmonic order
. 13
• 15
17
--------------
0.23
19
The amount of distortion in a phase current in the machine is quantified by the total harmonic distortion (THO), which is defined by: THD%
·2 h=2,3 ,4 .... 1h
=
.
11
100%
--Foe --MFoe --SIX-STEP
I --------------
0.235
Time
[s]
0.24
--
0.245
TABLE 1. STMULAnON RESULTS
•
Fig. 10 Harmonic contents of the phase currents
JIOO
---I I
0.5
_.
-
As seen in Fig. 11, produced torque with the Six-step control strategy has a significant torque ripple due to the phase current commutation which occurs six-times per one electrical revolution. Electromagnetic torque produced during the Foe control has also some ripple in the torque caused by the rippled back-EMF (Fig. 3). Significantly reduced ripple in produced electromagnetic torque has been achieved by the proposed modified Foe by injecting the right current harmonics (Fig.6 - detail). The results achieved are summarized in Table 1.
3
�
---
Fig. 11 Produced electromagnetic torque of three different control strategies
Fig. 9 Current waveforms of three different control strategies
�
-
0.225
0.245
0.24
9
Q�
�________�______�_________L�
______
(24)
Te_avg
1.05
'" .... Q) :0
-1
Te max - Te min
1.1 ,------�--,____--�__,
� 0
.c
_
-
where Te max and Te min are the maximum and minimum instantaneous values, -and Te_avg is the average value of produced torque.
c :0 " Q)