Space vector modulation for matrix converter and current source converter
A converter includes a transformer including primary windings and secondary windings, switches connected to the primary windings, an output inductor connected to the secondary windings, and a controller connected to the switches. The controller turns the switches on and off based on dwell times calculated using space vector modulation with a reference current ref whose magnitude changes with time.
1. A converter comprising:
a transformer including primary windings and secondary windings;
switches connected to the primary windings;
an output inductor connected to the secondary windings; and
a controller connected to the switches; wherein
the controller turns the switches on and off based on dwell times calculated using space vector modulation with a reference current ref whose magnitude changes with time.
2. A converter of claim 1 , wherein:
the switches include six switches;
the space vector modulation includes using six active switching states and three zero switching states;
a current space is divided into six sectors by the six active switching states such that a vector with θ=0 is located halfway between two of the active switching states; and
magnitudes of the six active switching states change with time.
3. A converter of claim 2 , wherein:
the controller turns the six switches on and off based on dwell times that are calculated based on an ampere-second balance equation:
ref T s =∫ 0 T α α dt+∫ 0 T β β dt+∫ 0 T 0 0 dt
where {right arrow over (I)} ref =I ref e jθ , θ is an angle between the reference current ref and the vector with θ=0, T s is a sampling period, α , β , 0 , are three nearest adjacent active vectors to ref , and T α , T β , T 0 are dwell times of α , β , 0 .
4. A converter of claim 3 , wherein the controller turns the six switches on and off based on a vector sequence α , 0 , − β , 0 , β , 0 , − α , 0 , during the sampling period T s .
5. A converter of claim 4 , wherein the controller turns the six switches on and off based on a timing sequence T α /2, T 0 /4, T β /2, T 0 /4, T β /2, T 0 /4, T α /2, T 0 /4, during the sampling period T s .
6. A converter of claim 4 , wherein:
the controller calculates the dwell times using:
T
α
=
-
B
+
B
2
+
AC
sin
(
π
/
6
-
θ
)
A
T
β
=
-
B
+
B
2
+
AC
sin
(
π
/
6
-
θ
)
A
·
sin
(
π
/
6
+
θ
)
sin
(
π
/
6
-
θ
)
T
0
=
T
s
-
T
α
-
T
β
where
A
=
(
4
u
1
α
/
k
-
u
o
)
+
(
4
u
1
β
/
k
-
u
o
)
sin
(
π
/
6
+
θ
)
sin
(
π
/
6
-
θ
)
B
=
4
L
o
I
L
0
-
3
u
o
T
s
/
2
C
=
8
kL
o
I
ref
T
s
u 1α is a line-to-line voltage depending on the active switching state {right arrow over (I)} a , u 1β is a line-to-line voltage depending on the active switching state Î β , k is a transformer turns ratio, u o is an output voltage of the converter, θ is the angle between the reference current ref and the vector with θ=0, L o is an inductance of the output inductor, I L0 is the current through inductor L o at a beginning of the sampling period T s , T s is the sampling period, and I ref is a magnitude of the vector {right arrow over (I)} ref .
7. A converter of claim 4 , wherein:
the controller calculates the dwell times using:
T
α
=
2
kI
ref
L
o
T
s
sin
(
π
/
6
-
θ
)
u
1
α
/
k
-
u
o
T
β
=
2
kL
o
I
ref
T
s
sin
(
π
/
6
-
θ
)
u
1
β
/
k
-
u
o
where k is a transformer turns ratio, L o is an inductance of the output inductor, I ref is the magnitude of the vector {right arrow over (I)} ref , T s is the sampling period, θ is an angle between the reference current ref and the vector with θ=0, u 1α is a line-to-line voltage depending on the active switching state {right arrow over (I)} α , u 1β is a line-to-line voltage depending on the active switching state {right arrow over (I)} β , and u o is an output voltage of the converter.
8. A converter of claim 1 , wherein the converter is one of a matrix rectifier, a current-source rectifier, and a current-source inverter.
9. A converter of claim 1 , wherein the converter is operated in a continuous-conduction mode.
10. A converter of claim 1 , wherein the converter is operated in a discontinuous-conduction mode.
11. A space-vector-modulation method for a converter including a transformer with primary windings and secondary windings, switches connected to the primary windings, and an output inductor connected to the secondary windings, the space-vector-modulation method comprising:
turning the switches on and off based on dwell times calculated using space vector modulation with a reference current {right arrow over (I)} ref whose magnitude changes with time.
12. A method of claim 11 , wherein:
the switches include six switches;
calculating the dwell times uses:
six active switching states and three zero switching states; and
a current space that is divided into six sectors by the six active switching states such that a vector with θ=0 is located halfway between two of the active switching states; and
magnitudes of the six active switching states change with time.
13. A method of claim 12 , wherein:
turning the six switches on and off is based on dwell times that are calculated based on an ampere-second balance equation:
ref T s =∫ 0 T α α dt+∫ 0 T β β dt+∫ 0 T 0 0 dt
where {right arrow over (I)} ref =I ref e jθ , θ is an angle between the reference current ref and the vector with θ=0, T s is a sampling period, α , β , 0 , are three nearest adjacent active vectors to ref , and T α , T β , T 0 are dwell times of α , β , 0 .
14. A method of claim 13 , wherein turning the six switches on and off is based on a vector sequence α , 0 , − β , 0 , β , 0 , − α , 0 , during the sampling period T s .
15. A method of claim 14 , wherein turning the six switches on and off is based on a timing sequence T α /2, T 0 /4, T β /2, T 0 /4, T β /2, T 0 /4, T α /2, T 0 /4, during the period T s .
16. A method of claim 14 , wherein:
the dwell times are calculated using:
T
α
=
-
B
+
B
2
+
AC
sin
(
π
/
6
-
θ
)
A
T
β
=
-
B
+
B
2
+
AC
sin
(
π
/
6
-
θ
)
A
·
sin
(
π
/
6
+
θ
)
sin
(
π
/
6
-
θ
)
T
0
=
T
s
-
T
α
-
T
β
where
A
=
(
4
u
1
α
/
k
-
u
o
)
+
(
4
u
1
β
/
k
-
u
o
)
sin
(
π
/
6
+
θ
)
sin
(
π
/
6
-
θ
)
B
=
4
L
o
I
L
0
-
3
u
o
T
s
/
2
C
=
8
kL
o
I
ref
T
s
u 1α is a line-to-line voltage depending on the active switching state {right arrow over (I)} a , u 1β is a line-to-line voltage depending on the active switching state Î β , k is a transformer turns ratio, u o is an output voltage of the converter, θ is the angle between the reference current ref and the vector with θ=0, L o is an inductance of the output inductor, I L0 is the current through inductor L o at a beginning of the sampling period T s , T s is the sampling period, and I ref is a magnitude of the vector {right arrow over (I)} ref .
17. A method of claim 14 , wherein:
the controller calculates the dwell times using:
T
α
=
2
kI
ref
L
o
T
s
sin
(
π
/
6
-
θ
)
u
1
α
/
k
-
u
o
T
β
=
2
kL
o
I
ref
T
s
sin
(
π
/
6
+
θ
)
u
1
β
/
k
-
u
o
where k is a transformer turns ratio, L o is an inductance of the output inductor, I ref is the magnitude of the vector {right arrow over (I)} ref , T s is the sampling period, θ is an angle between the reference current ref and the vector with θ=0, u 1α is a line-to-line voltage depending on the active switching state {right arrow over (I)} α , u 1β is a line-to-line voltage depending on the active switching state {right arrow over (I)} β , and u o is an output voltage of the converter.
18. A method of claim 11 , wherein the converter is one of a matrix rectifier, a current-source rectifier, and a current-source inverter.
19. A method of claim 11 , further comprising operating the converter in a continuous-conduction mode.
20. A method of claim 11 , further comprising operating the converter in a discontinuous-conduction mode.