Drive methods for a three-phase motor
A method of driving a three-phase motor includes, while a first phase is energized, driving a second phase using a first drive function which is sinusoidal. The first phase is switched to a non-energized state and a back electromotive force (BEMF) voltage of the first phase is detected. For at least a portion of a time when the first phase is non-energized the driving of the second phase depends on the output of a second drive function different from the first drive function. The second drive function may be non-sinusoidal and may be a cosine function. The second drive function may drive the second phase when the output of the second drive function is a modulation ratio less than 1. When the output of the second drive function is a modulation ratio greater than or equal to 1 the second phase may be driven to a modulation ratio of 1.
1. A method of driving a star-connected three-phase motor, comprising:
driving a first phase of the star-connected three-phase motor using a first sinusoidal drive function when all three phases are energized;
driving the first phase using a first non-sinusoidal drive function for at least a portion of a time when one phase other than the first phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio less than 1; and
driving the first phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the first phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio greater than or equal to 1.
2. The method of claim 1 , wherein the first non-sinusoidal drive function is a first cosine drive function.
3. The method of claim 2 , wherein the modulation ratios are low torque ripple modulation ratios, wherein the first cosine drive function is
❘
"\[LeftBracketingBar]"
M
cos
(
θ
-
θ
wc
)
❘
"\[RightBracketingBar]"
,
wherein M is a modulation ratio ranging from 0 to 1, wherein θ is an angle of rotation of the three-phase motor, and wherein θ wc has a value of 0 degrees when θ is less than 30 degrees and greater than or equal to 0 degrees, a value of 60 degrees when θ is less than 90 degrees and greater than or equal to 30 degrees, a value of 120 degrees when θ is less than 150 degrees and greater than or equal to 90 degrees, a value of 180 degrees when θ is less than 210 degrees and greater than or equal to 150 degrees, a value of 240 degrees when θ is less than 270 degrees and greater than or equal to 210 degrees, a value of 300 degrees when θ is less than 330 degrees and greater than or equal to 270 degrees, and a value of 0 degrees when θ is less than 360 degrees and greater than or equal to 330 degrees.
4. The method of claim 1 , wherein the modulation ratios are low torque ripple modulation ratios, wherein the first sinusoidal drive function is
U
2
pm
=
2
3
M
*
{
U
3
pm
-
min
(
U
3
pm
,
V
3
pm
,
W
3
pm
)
}
,
wherein U 3pm ½sinθ, V 3pm =½sin(θ−⅔π), W 3pm =½sin(θ− 4/3π), wherein M is a modulation ratio ranging from 0 to 1, and wherein θ is an angle of rotation of the three-phase motor.
5. The method of claim 1 , further comprising: driving a second phase of the three-phase motor using a second sinusoidal drive function when all three phases are energized; driving the second phase using the first non-sinusoidal drive function for at least a portion of a time when one phase other than the second phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio less than 1; and driving the second phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the second phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio greater than or equal to 1.
6. The method of claim 5 , wherein the modulation ratios are low torque ripple modulation ratios, wherein the second sinusoidal drive function is
V
2
pm
=
2
3
M
*
{
V
3
pm
-
min
(
U
3
pm
,
V
3
pm
,
W
3
pm
)
}
,
wherein U 3pm ½sinθ, V 3pm =½sin(θ−⅔π), W 3pm =½sin(θ− 4/3π), wherein M is a modulation ratio ranging from 0 to 1, and wherein θ is an angle of rotation of the three-phase motor.
7. The method of claim 5 , further comprising: driving a third phase of the three-phase motor using a third sinusoidal drive function when all three phases are energized; driving the third phase using the first non-sinusoidal drive function for at least a portion of a time when one phase other than the third phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio less than 1; and driving the third phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the third phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio greater than or equal to 1.
8. The method of claim 7 , wherein the modulation ratios are low torque ripple modulation ratios, wherein the third sinusoidal drive function is
W
2
p
m
=
2
3
M
*
{
W
3
p
m
-
min
(
U
3
pm
,
V
3
pm
,
W
3
p
m
)
}
,
wherein U 3pm ½sinθ, V 3pm =½sin(θ−⅔π), W 3pm =½sin(θ− 4/3π), wherein M is a modulation ratio ranging from 0 to 1, and wherein θ is an angle of rotation of the three-phase motor.
9. A method of driving a star-connected three-phase motor, comprising:
driving a first phase of the star-connected three-phase motor using a first sinusoidal drive function when all three phases are energized;
driving the first phase using a first cosine drive function for at least a portion of a time when one phase other than the first phase is not energized and when the first cosine drive function results in a low torque ripple modulation ratio less than 1; and
driving the first phase to a low torque ripple modulation ratio of 1 for at least a portion of a time when one phase other than the first phase is not energized and when the first cosine drive function results in a low torque ripple modulation ratio greater than or equal to 1.
10. The method of claim 9 , wherein the first cosine drive function is
❘
"\[LeftBracketingBar]"
M
cos
(
θ
-
θ
w
c
)
❘
"\[RightBracketingBar]"
,
wherein M is a modulation ratio ranging from 0 to 1, wherein θ is an angle of rotation of the three-phase motor, and wherein θ wc has a value of 0 degrees when θ is less than 30 degrees and greater than or equal to 0 degrees, a value of 60 degrees when θ is less than 90 degrees and greater than or equal to 30 degrees, a value of 120 degrees when θ is less than 150 degrees and greater than or equal to 90 degrees, a value of 180 degrees when θ is less than 210 degrees and greater than or equal to 150 degrees, a value of 240 degrees when θ is less than 270 degrees and greater than or equal to 210 degrees, a value of 300 degrees when θ is less than 330 degrees and greater than or equal to 270 degrees, and a value of 0 degrees when θ is less than 360 degrees and greater than or equal to 330 degrees.
11. The method of claim 9 , wherein the first sinusoidal drive function is
U
2
p
m
=
2
3
M
*
{
U
3
p
m
-
min
(
U
3
pm
,
V
3
pm
,
W
3
p
m
)
}
,
wherein U 3pm ½sinθ, V 3pm =½sin(θ−⅔π), W 3pm =½sin(θ− 4/3π), wherein M is a modulation ratio ranging from 0 to 1, and wherein θ is an angle of rotation of the three-phase motor.
12. The method of claim 9 , further comprising: driving a second phase of the three-phase motor using a second sinusoidal drive function when all three phases are energized; driving the second phase using the first cosine drive function for at least a portion of a time when one phase other than the second phase is not energized and when the first cosine drive function results in a modulation ratio less than 1; and driving the second phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the second phase is not energized and when the first cosine drive function results in a modulation ratio greater than or equal to 1.
13. The method of claim 12 , wherein the second sinusoidal drive function is
V
2
p
m
=
2
3
M
*
{
V
3
p
m
-
min
(
U
3
p
m
,
V
3
p
m
,
W
3
p
m
)
}
,
wherein U 3pm ½sinθ, V 3pm =½sin(θ−⅔π), W 3pm =½sin(θ− 4/3π), wherein M is a modulation ratio ranging from 0 to 1, and wherein θ is an angle of rotation of the three-phase motor.
14. The method of claim 12 , further comprising: driving a third phase of the three-phase motor using a third sinusoidal drive function when all three phases are energized; driving the third phase using the first cosine drive function for at least a portion of a time when one phase other than the third phase is not energized and when the first cosine drive function results in a modulation ratio less than 1; and driving the third phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the third phase is not energized and when the first cosine drive function results in a modulation ratio greater than or equal to 1.
15. The method of claim 14 , wherein the third sinusoidal drive function is
W
2
p
m
=
2
3
M
*
{
W
3
p
m
-
min
(
U
3
pm
,
V
3
pm
,
W
3
p
m
)
}
,
wherein U 3pm ½sinθ, V 3pm =½sin(θ−⅔π), W 3pm =½sin(θ− 4/3π), wherein M is a modulation ratio ranging from 0 to 1, and wherein θ is an angle of rotation of the three-phase motor.
16. A method of driving a star-connected three-phase motor, comprising:
driving a first phase of the star-connected three-phase motor using a first sinusoidal drive function when all three phases are energized;
driving the first phase using a first non-sinusoidal drive function for at least a portion of a time when one phase other than the first phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio less than 1; and
driving the first phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the first phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio greater than or equal to 1;
wherein the method is configured to decrease torque ripple.
17. The method of claim 16 , wherein the first non-sinusoidal drive function is a first cosine drive function.
18. The method of claim 16 , wherein the modulation ratios are low torque ripple modulation ratios.
19. The method of claim 16 , further comprising: driving a second phase of the three-phase motor using a second sinusoidal drive function when all three phases are energized; driving the second phase using the first non-sinusoidal drive function for at least a portion of a time when one phase other than the second phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio less than 1; and driving the second phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the second phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio greater than or equal to 1.
20. The method of claim 19 , further comprising: driving a third phase of the three-phase motor using a third sinusoidal drive function when all three phases are energized; driving the third phase using the first non-sinusoidal drive function for at least a portion of a time when one phase other than the third phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio less than 1; and driving the third phase to a modulation ratio of 1 for at least a portion of a time when one phase other than the third phase is not energized and when the first non-sinusoidal drive function results in a modulation ratio greater than or equal to 1.