Methods and apparatuses for elimination of torque pulsation in doubly fed induction generators using the field reconstruction method
Methods and apparatuses for substantially eliminating torque pulsation in a doubly fed induction machine are disclosed. An example method comprises: measuring a stator current of the doubly fed induction machine, measuring a rotor current of the doubly fed induction machine, calculating a total magnetic flux density in an airgap of the doubly fed induction machine, calculating a tangential force density, calculating an electromagnetic torque, repeating the calculation of the electromagnetic torque over one electrical cycle to estimate a torque pulsation, determining a new rotor current that substantially eliminates the torque pulsation by referencing a set of optimal rotor currents in a look-up table, and changing the rotor current in response to the determination. Other embodiments are described and claimed.
1. A method for substantially eliminating torque pulsation in a doubly fed induction machine, the method comprising:
measuring a stator current of the doubly fed induction machine;
measuring a rotor current of the doubly fed induction machine;
calculating a total magnetic flux density in an airgap of the doubly fed induction machine;
calculating a tangential force density;
calculating an electromagnetic torque;
repeating the calculation of the electromagnetic torque over one electrical cycle to estimate a torque pulsation;
determining a new rotor current that substantially eliminates the torque pulsation by referencing a set of optimal rotor currents in a look-up table; and
changing the rotor current in response to the determination.
2. The method of claim 1 , further comprising calculating the set of optimal rotor currents, wherein calculating the set of optimal rotor currents comprises:
determining an optimal rotor current, wherein determining the optimal rotor current comprises:
applying a known stator current to the doubly fed induction machine;
calculating a field reconstruction model of the doubly fed induction machine;
computing an electromagnetic torque resulting from applying the known stator current; and
computing an optimal rotor current which substantially eliminates the electromagnetic torque.
3. The method of claim 2 , wherein calculating the set of optimal rotor currents further comprises repeating the steps of determining the optimal rotor current.
4. The method of claim 2 , wherein calculating the set of optimal rotor currents further comprises storing the set of optimal rotor currents in the look-up table.
5. The method of claim 2 , wherein computing the optimal rotor current is completed within two electrical cycles.
6. The method of claim 1 , wherein the doubly fed induction machine comprises a doubly fed induction generator.
7. The method of claim 1 , wherein changing the rotor current comprises feeding the new rotor current into a rotor current controller.
8. The method of claim 1 , wherein calculating the total magnetic flux density in the airgap of the doubly fed induction machine is calculated according to the equations of:
B
t
(
ϕ
g
)
=
∑
j
=
1
M
i
rj
·
h
tr
(
ϕ
g
-
ϕ
rj
)
+
∑
k
=
1
N
i
sk
·
h
ts
(
ϕ
g
-
ϕ
sk
)
B
n
(
ϕ
g
)
=
∑
j
=
1
M
i
rj
·
h
nr
(
ϕ
g
-
ϕ
rj
)
+
∑
k
=
1
N
i
sk
·
h
n
s
(
ϕ
g
-
ϕ
sk
)
,
where N denotes the number of stator conductors, M denotes the number of rotor conductors, φ g denotes the airgap displacement, φ s denotes the displacement in the stator, φ r denotes the displacement in the rotor, φ sk denotes the location of the k-th conductor in the stator, φ rj denotes the location of the j-th conductor in the rotor, h ts denotes the tangential basis function for the stator, h tr denotes the tangential basis function for the rotor, h ns denotes the normal basis function for the stator, h nr denotes the normal basis function for the rotor, i sk denotes the magnitude of the current in the k-th stator conductor, and i rj denotes the magnitude of the current in the j-th conductor of the rotor.
9. The method of claim 1 , wherein calculating the tangential force density is calculated according to the equation of:
f
t
(
ϕ
g
)
=
1
μ
0
B
n
(
ϕ
g
)
B
t
(
ϕ
g
)
,
where μ 0 denotes permeability of the air, B n (φ g ) denotes the total normal magnetic flux density, and B t (φ g ) denotes the total tangential magnetic flux density.
10. The method of claim 1 , wherein calculating the electromagnetic torque is calculated according to the equation of:
T
=
LR
∫
0
2
π
f
t
(
ϕ
g
)
ⅆ
ϕ
g
,
where L denotes the length of the stator, R denotes the radius of the rotor, f t (φ g ) denotes the tangential force density, and φ g denotes the airgap displacement.
11. An apparatus for substantially eliminating torque pulsation in a doubly fed induction machine, the apparatus comprising:
one or more processors; and
one or more memory units coupled to the processors,
the apparatus being configured to:
measure a stator current of the doubly fed induction machine;
measure a rotor current of the doubly fed induction machine;
calculate a total magnetic flux density in an airgap of the doubly fed induction machine;
calculate a tangential force density;
calculate an electromagnetic torque;
repeat the calculation of the electromagnetic torque over one electrical cycle to estimate a torque pulsation;
determine a new rotor current that substantially eliminates the torque pulsation by referencing a set of optimal rotor currents in a look-up table; and
change the rotor current in response to the determination.
12. The apparatus of claim 11 , wherein the apparatus is further configured to calculate the set of optimal rotor currents, wherein calculating the set of optimal rotor currents comprises the apparatus being further configured to determine an optimal rotor current, wherein determining the optimal rotor current comprises:
applying a known stator current to the doubly fed induction machine;
calculating a field reconstruction model of the doubly fed induction machine;
computing an electromagnetic torque resulting from applying the known stator current; and
computing an optimal rotor current which substantially eliminates the electromagnetic torque.
13. The apparatus of claim 12 , wherein calculating the set of optimal rotor currents further comprises the apparatus being further configured to repeat the steps of determining the optimal rotor current.
14. The apparatus of claim 12 , wherein calculating the set of optimal rotor currents further comprises the apparatus being further configured to store the set of optimal rotor currents in the look-up table.
15. The apparatus of claim 12 , wherein computing the optimal rotor current is completed within two electrical cycles.
16. The apparatus of claim 11 , wherein the doubly fed induction machine comprises a doubly fed induction generator.
17. The apparatus of claim 11 , wherein the apparatus being configured to change the rotor current comprises feeding the new rotor current into a rotor current controller.
18. The apparatus of claim 11 , wherein the apparatus being configured to calculate the total magnetic flux density in the airgap of the doubly fed induction machine is calculated according to the equations of:
B
t
(
ϕ
g
)
=
∑
j
=
1
M
i
rj
·
h
tr
(
ϕ
g
-
ϕ
rj
)
+
∑
k
=
1
N
i
sk
·
h
ts
(
ϕ
g
-
ϕ
sk
)
B
n
(
ϕ
g
)
=
∑
j
=
1
M
i
rj
·
h
nr
(
ϕ
g
-
ϕ
rj
)
+
∑
k
=
1
N
i
sk
·
h
n
s
(
ϕ
g
-
ϕ
sk
)
,
where N denotes the number of stator conductors, M denotes the number of rotor conductors, φ g denotes the airgap displacement, φ s denotes the displacement in the stator, φ r denotes the displacement in the rotor, φ sk denotes the location of the k-th conductor in the stator, φ rj denotes the location of the j-th conductor in the rotor, h ts denotes the tangential basis function for the stator, h tr denotes the tangential basis function for the rotor, h ns denotes the normal basis function for the stator, h nr denotes the normal basis function for the rotor, i sk denotes the magnitude of the current in the k-th stator conductor, and i rj denotes the magnitude of the current in the j-th conductor of the rotor.
19. The apparatus of claim 11 , wherein the apparatus being configured to calculate the tangential force density is calculated according to the equation of:
f
t
(
ϕ
g
)
=
1
μ
0
B
n
(
ϕ
g
)
B
t
(
ϕ
g
)
,
where μ 0 denotes permeability of the air, B n (φ g ) denotes the total normal magnetic flux density, and B t (φ g ) denotes the total tangential magnetic flux density.
20. The apparatus of claim 11 , wherein the apparatus being configured to calculate the electromagnetic torque is calculated according to the equation of:
T
=
LR
∫
0
2
π
f
t
(
ϕ
g
)
ⅆ
ϕ
g
,
where L denotes the length of the stator, R denotes the radius of the rotor, f t (φ g ) denotes the tangential force density, and φ g denotes the airgap displacement.