Current reference based selective harmonic current mitigation pulsed width modulation
Methods and apparatuses for selective harmonic current mitigation pulse width modulation (SHCM-PWM) are provided. Low switching frequencies can be utilized for grid connected cascaded H-bridge multilevel rectifiers to meet harmonic requirements within an extended harmonic spectrum. Instead of using voltage references to calculate switching angles for rectifiers as in conventional selective harmonic elimination-PWM (SHE-PWM) and selective harmonic mitigation-PWM (SHM-PWM), current references can be used to compensate for current harmonics and meet current harmonic requirements and total demand distortion (TDD) within the entire harmonic spectrum.
1. A method of selective harmonic current mitigation pulse width modulation (SHCM-PWM), the method comprising:
determining parameters including RMS grid voltage (V ac-Grid-1 ), converter maximum demand load current (I L ), and grid voltage frequency (ω), initial values for converter switching transitions in each quarter period (K), and converter inductance (L T ″);
determining the dc link voltage of each cell (V dc ) and the number of CHB converter cells (i) using the V ac-Grid-1 and I L and equation
4
V
d
c
×
i
π
>
Max
(
V
a
c
-
Grid
-
1
)
;
determining the required inductance based on equation (19) (L T ) from
L
T
≥
V
a
c
-
Grid
-
35
35
ω
C
35
I
L
;
determining the number of harmonics that can be eliminated using the number of converter switching transitions in each quarter period (K);
using SHE-PWM equations to obtain an initial number harmonics that need to be controlled;
having values for K, V ac-Grid-1 , I L , V dc , ω, and h, obtaining the required inductance (L T ′) using equation
L
T
′
≥
V
a
c
-
CHB
-
h
max
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
=
4
V
d
c
K
ω
h
2
C
h
I
L
π
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
;
ensuring that the designed inductance is greater than or equal to L T and L T ′ in both of equation
L
T
≥
V
a
c
-
Grid
-
35
35
ω
C
35
I
L
and equation
L
T
′
≥
V
a
c
-
CHB
-
h
max
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
=
4
V
d
c
K
ω
h
2
C
h
I
L
π
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
;
determining the minimum inductance using equation (19)
L
T
≥
V
a
c
-
Grid
-
35
35
ω
C
35
I
L
;
determining the required inductance (L T ′) using K, h, and equation
L
T
′
≥
V
a
c
-
CHB
-
h
max
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
=
4
V
d
c
K
ω
h
2
C
h
I
L
π
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
;
using L T ′ and the other parameters, determining the solutions of SHCM-PWM using equation set
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
i
n
-
3
I
1
)
2
+
(
I
i
n
-
5
I
1
)
2
+
…
+
(
I
i
n
-
h
I
1
)
2
+
…
≤
C
TDD
V
a
c
-
Grid
-
h
+
V
a
c
-
CHB
-
h
ω
hL
T
I
L
≤
C
h
,
h
=
3
,
5
,
7
,
…
;
wherein, if there are solutions for the SHCM-PWM with a highest number of controlled harmonics h, then increase h by 2 (h=h+2) and, with the new h, determining a new L T ′ using equation (23)
L
T
′
≥
V
a
c
-
CHB
-
h
max
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
=
4
V
d
c
K
ω
h
2
C
h
I
L
π
+
V
a
c
-
Grid
-
h
ω
hC
h
I
L
and solving equation set (25)
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
i
n
-
3
I
1
)
2
+
(
I
i
n
-
5
I
1
)
2
+
…
+
(
I
i
n
-
h
I
1
)
2
+
…
≤
C
TDD
V
a
c
-
Grid
-
h
+
V
a
c
-
CHB
-
h
ω
hL
T
I
L
≤
C
h
,
h
=
3
,
5
,
7
,
…
using the new parameters;
wherein, if there are no solutions for equation set (25) of SHCM-PWM with the highest number of harmonics h that must be controlled, reducing h by two (h=h−2) and recalculating L T ′ using equation (23);
comparing the obtained inductance L T ′ with L T in equation (19) and determining if the L T ′ is lower than L T in equation (19);
obtaining all of the required parameters including switching transitions of SHCM-PWM (K) and the maximum number of harmonics that should be met (h);
wherein, if the L T ′ is greater than L T , the method further comprises determining whether the value of
L
T
″
-
L
T
′
L
T
″
is higher or lower than a predefined threshold δ and, if the value of
L
T
″
-
L
T
′
L
T
″
is lower than δ, then determining the designed inductance as L T ′ (and the other parameters can be determined); and
wherein if
L
T
″
-
L
T
′
L
T
″
is greater than δ, the method further comprises increasing the switching transitions K by one (to K+1) and substituting L T ″ for L T ′ and iterating again the steps of: determining the number of harmonics that can be eliminated using the number of converter switching transitions in each quarter period (K), and using SHE-PWM equations to again obtain the number harmonics that need to be controlled.
2. A method of selective harmonic current mitigation pulse width modulation (SHCM-PWM), the method comprising:
determining parameters including RMS grid voltage (V ac-Grid-1 ), converter maximum demand load current (I L ), and grid voltage frequency (ω), initial values for converter switching transitions in each quarter period (K), and converter inductance (L T ″);
determining the dc link voltage of each cell (V dc ) and the number of CHB converter cells (i) using the V ac-Grid-1 and I L and equation
4
V
dc
×
i
π
>
Max
(
V
ac
-
Grid
-
1
)
;
determining the required inductance based on equation (19) (L T ) from
L
T
≥
V
ac
-
Grid
-
35
35
ω
C
35
I
L
;
determining the number of harmonics that can be eliminated using the number of converter switching transitions in each quarter period (K);
using SHE-PWM equations to obtain an initial number harmonics that need to be controlled;
having values for K, V ac-Grid-1 , I L , V dc , ω, and h, obtaining the required inductance (L T ′) using equation
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
;
ensuring that the designed inductance is greater than or equal to L T and L T ′ in both of equation
L
T
≥
V
ac
-
Grid
-
35
35
ω
C
35
I
L
and equation
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
;
determining the minimum inductance using equation (19)
L
T
≥
V
ac
-
Grid
-
35
35
ω
C
35
I
L
;
determining the required inductance (L T ′) using K, h, and equation
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
;
using L T ′ and the other parameters, determining the solutions of SHCM-PWM using equation set
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
in
-
3
I
1
)
2
+
(
I
in
-
5
I
1
)
2
+
…
+
(
I
in
-
h
I
1
)
2
+
…
≤
C
TDD
V
ac
-
Grid
-
h
+
V
ac
-
CHB
-
h
ω
h
L
T
I
L
≤
C
h
,
h
=
3
,
5
,
7
,
…
;
wherein, if there are solutions for the SHCM-PWM with a highest number of controlled harmonics h, then increase h by 2 (h=h+2) and, with the new h, determine a new L T ′ using equation (23)
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
and solve equation set (25)
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
in
-
3
I
1
)
2
+
(
I
in
-
5
I
1
)
2
+
…
+
(
I
in
-
h
I
1
)
2
+
…
≤
C
TDD
V
ac
-
Grid
-
h
+
V
ac
-
CHB
-
h
ω
h
L
T
I
L
≤
C
h
,
h
=
3
,
5
,
7
,
…
using the new parameters;
comparing the obtained inductance L T ′ with L T in equation (19) and determining if the L T ′ is lower than L T in equation (19); and
obtaining all of the required parameters including switching transitions of SHCM-PWM (K) and the maximum number of harmonics that should be met (h).
3. The method according to claim 2 , wherein
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
in
-
3
I
1
)
2
+
(
I
in
-
5
I
1
)
2
+
…
+
(
I
in
-
h
I
1
)
2
+
…
≤
C
TDD
V
ac
-
Grid
-
h
+
V
ac
-
CHB
-
h
ω
h
L
T
I
L
≤
C
h
,
h
=
3
,
5
,
7
,
…
is solved using multi-objective particle swarm optimization.
4. The method according to claim 3 , wherein the method is applied to a cascaded H-bridge multilevel active rectifier.
5. The method according to claim 2 , wherein the method is applied to a cascaded H-bridge multilevel active rectifier.
6. The method according to claim 5 , wherein, if there are no solutions for equation set (25) of SHCM-PWM with the highest number of harmonics h that must be controlled, then reduce h by two (h=h−2) and recalculate L T ′ using equation (23).
7. The method according to claim 6 , further comprising comparing the obtained inductance L T ′ with L T in equation (19) and determining if the L T ′ is lower than L T in equation (19).
8. The method according to claim 7 , wherein if the L T ′ is higher than L T , determining whether the value of
L
T
″
-
L
T
′
L
T
″
is higher or lower than a predefined threshold δ and, if the value of
L
T
″
-
L
T
′
L
T
″
is lower than δ, determining the inductance L T ′.
9. The method according to claim 8 , wherein if
L
T
″
-
L
T
′
L
T
″
is greater than δ, the method further comprises increasing the switching transitions K by one (to K+1) and substituting L T ″ for L T ′ and iterating again the steps of: determining the number of harmonics that can be eliminated using the number of converter switching transitions in each quarter period (K); and using SHE-PWM equations to obtain an initial number harmonics that need to be controlled.
10. A method of selective harmonic current mitigation pulse width modulation (SHCM-PWM), the method comprising:
determining parameters including RMS grid voltage (V ac-Grid-1 ), converter maximum demand load current (I L ), and grid voltage frequency (ω), initial values for converter switching transitions in each quarter period (K), and converter inductance (L T ″);
determining the dc link voltage of each cell (V dc ) and the number of CHB converter cells (i) using the V ac-Grid-1 and I L and equation
4
V
dc
×
i
π
>
Max
(
V
ac
-
Grid
-
1
)
;
determining the required inductance based on equation (19) (L T ) from
L
T
≥
V
ac
-
Grid
-
35
35
ω
C
35
I
L
;
determining the number of harmonics that can be eliminated using the number of converter switching transitions in each quarter period (K);
using SHE-PWM equations to obtain an initial number harmonics that need to be controlled;
having values for K, V ac-Grid-1 , I L , V dc , ω, and h, obtaining the required inductance (L T ′) using equation
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
;
ensuring that the designed inductance is greater than or equal to L T and L T ′ in both of equation
L
T
≥
V
ac
-
Grid
-
35
35
ω
C
35
I
L
and equation
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
;
determining the minimum inductance using equation (19)
L
T
≥
V
ac
-
Grid
-
35
35
ω
C
35
I
L
;
determining the required inductance (L T ′) using K, h, and equation
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
;
using L T ′ and the other parameters, determining the solutions of SHCM-PWM using equation set
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
in
-
3
I
1
)
2
+
(
I
in
-
5
I
1
)
2
+
…
+
(
I
in
-
h
I
1
)
2
+
…
≤
C
TDD
V
ac
-
Grid
-
h
+
V
ac
-
CHB
-
h
ω
h
L
T
I
L
⌉
≤
C
h
,
h
=
3
,
5
,
7
,
…
;
wherein, if there are solutions for the SHCM-PWM with a highest number of controlled harmonics h, then increase h by 2 (h=h+2) and, with the new h, determine a new L T ′ using equation (23)
L
T
′
≥
V
ac
-
CHB
-
h
max
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
=
4
V
dc
K
ω
h
2
C
h
I
L
π
+
V
ac
-
Grid
-
h
ω
h
C
h
I
L
and solve equation set (25)
{
M
a
=
cos
θ
1
-
cos
θ
2
+
cos
θ
3
…
+
cos
θ
k
(
I
in
-
3
I
1
)
2
+
(
I
in
-
5
I
1
)
2
+
…
+
(
I
in
-
h
I
1
)
2
+
…
≤
C
TDD
V
ac
-
Grid
-
h
+
V
ac
-
CHB
-
h
ω
h
L
T
I
L
⌉
≤
C
h
,
h
=
3
,
5
,
7
,
…
using the new parameters;
comparing the obtained inductance L T ′ with L T in equation (19) and determining if the L T ′ is lower than L T in equation (19);
obtaining all of the required parameters including switching transitions of SHCM-PWM (K) and the maximum number of harmonics that should be met (h);
storing the all of the required parameters into a lookup table;
providing a control signal from the lookup table to a gate signal driver; and
providing a gate signal from the gate signal driver to a cascaded H-bridge multilevel active rectifier.
11. The method according to claim 10 , the cascaded H-bridge multilevel active rectifier being connected a grid through an inductor.
12. The method according to claim 11 , the grid being at least one of a neutral point clamped (NPC) and a flying capacitor (FC).
13. The method according to claim 10 , the cascaded H-bridge multilevel active rectifier being connected to a motor.
14. The method according to claim 13 , the motor being at least one of a three-phase asynchronous motor and a single phase asynchronous motor.
15. The method according to claim 10 , the cascaded H-bridge multilevel active rectifier being connected to a filter.
16. The method according to claim 15 , the filter being at least one of an L filter, an LC filter, and an LCL filter.
17. The method according to claim 10 , wherein, if there are no solutions for equation set (25) of SHCM-PWM with the highest number of harmonics h that must be controlled, then reduce h by two (h=h−2) and recalculate L T ′ using equation (23).
18. The method according to claim 17 , further comprising comparing the obtained inductance L T ′ with L T in equation (19) and determining if the L T ′ is lower than L T in equation (19).
19. The method according to claim 18 , wherein if the L T ′ is higher than L T , determining whether the value of
L
T
″
-
L
T
′
L
T
″
is higher or lower than a predefined threshold δ and, if the value of
L
T
″
-
L
T
′
L
T
″
is lower than δ, determining the inductance L T ′.
20. The method according to claim 19 , wherein if
L
T
″
-
L
T
′
L
T
″
is greater than δ, the method further comprises increasing the switching transitions K by one (to K+1) and substituting L T ″ for L T ′ and iterating again the steps of: determining the number of harmonics that can be eliminated using the number of converter switching transitions in each quarter period (K); and using SHE-PWM equations to obtain an initial number harmonics that need to be controlled.