METHOD FOR BALANCING CAPACITORS IN AN INVERTER
The PWM modulating method comprises the following steps: detecting actual voltage values (Vc1, Vc1, Vc2, Vc3 . . . ) across bulk capacitors (C 1 , C 2 , C 3 ) provided across input terminals of said inverter; calculating a duty cycle vector (D) based on electric parameters defining a rotating vector (V0) representing an output electric quantity required from the inverter; and modifying said duty cycle vector (D) as a function of said actual voltage values to re-balance said bulk capacitors.
1 - 32 . (canceled)
33 . A method of pulse width modulating (PWM) a multiphase inverter comprising:
in an inverter control and drive system, calculating a duty cycle vector based on electric parameters defining a rotating vector representing an output electric quantity required from the inverter;
detecting actual voltage values across bulk capacitors provided across input terminals of the inverter; and
modifying the duty cycle vector as a function of the actual voltage values to re-balance the bulk capacitors.
34 . The method of claim 33 , wherein the duty cycle vector is modified by altering a conduction time of inverter switches during a PWM cycle, such as to modify the voltage across bulk capacitors, which are in an unbalanced condition, towards a balanced condition.
35 . The method of claim 33 , wherein:
the duty cycle vector is calculated as a function of the electric parameters defining the rotating vector;
the duty cycle vector is multiplied by a scale factors matrix, containing elements which are a function of the actual voltage values across the bulk capacitors of the inverter, to generate a modified duty cycle vector.
36 . The method of claim 35 , wherein the elements of the scale factors matrix are calculated based on the voltage values across the bulk capacitors and a balancing matrix, the balancing matrix containing information on a power flux through each bulk capacitor in each inverter state.
37 . The method of claim 36 , wherein the balancing matrix is formed by “0” and “1” digits, and wherein:
the digit is “0” for each bulk capacitor through which, in the corresponding inverter state, no power flows; and
the digit is “1” for each bulk capacitor through which, in the corresponding inverter state, power flows.
38 . The method of claim 36 , wherein a balancing matrix is defined for each point along an axis of a state vectors diagram, each balancing matrix having (L−i) rows and (L−1) columns, wherein:
L is the number of levels of the inverter; and
0<i<L−1 is the position of the point along the axis.
39 . The method of claim 34 , wherein the modified duty cycle vector is multiplied by at least one stored modulation matrix to obtain a plurality of modified duty cycle signals for driving a plurality of electronic switches of the inverter.
40 . The method of claim 34 , wherein the duty cycle vector is defined as:
D
=
[
δ
1
δ
1
…
δ
1
L
L
-
1
2
elements
δ
2
δ
2
…
δ
2
L
L
-
1
2
elements
δ
3
δ
3
…
δ
3
L
elements
]
δ
1
=
M
2
*
(
L
-
1
)
*
(
3
cos
α
_
-
sin
α
_
)
δ
2
=
M
L
-
1
*
sin
α
_
δ
3
=
1
L
(
1
-
M
2
*
(
L
-
1
)
(
3
cos
α
_
+
sin
α
_
)
)
in which L is the number of voltage levels of the inverter and
α
_
=
α
-
π
3
(
P
-
1
)
wherein:
α is the electric angle of the rotating vector;
M is the modulation index of the rotating vector; and
P is the sector of the complex plane in which the rotating vector is located at the PWM cycle considered.
41 . The method of claim 34 , wherein the modified duty cycle vector is multiplied by a number of modulation matrices determined by the number of voltage levels of the inverter.
42 . The method of claim 33 , wherein, for each PWM cycle, the following steps are performed:
calculating a duty cycle vector containing a plurality of duty cycle values;
detecting the voltage values across the bulk capacitors;
when the capacitors are un-balanced, calculating scale factors for rebalancing the capacitors;
correcting the duty cycle values with scale factors to obtain a corrected duty cycle vector; and
applying the corrected duty cycle vector to drive switches of the inverter.
43 . The method of claim 33 , further comprising:
storing in a memory unit data defining a plurality of modulation matrices;
for each PWM cycle, determining a modulation index and a phase angle of the rotating vector;
determining in which sector of a complex plane the rotating vector is located;
calculating the duty cycle vector based on the phase angle and on the modulation index of the rotating vector;
detecting the actual voltage values across the bulk capacitors of the inverter;
calculating the modified duty cycle vector based on the actual voltage values;
executing a matrix multiplication between the modified duty cycle vector and at least one modulation matrix corresponding to the sector to obtain a plurality of modified duty cycles for a plurality of electronic switches of the inverter; and
loading the modified duty cycles into a PWM modulator of the inverter and generating, by means of the PWM modulator, physical signals for driving the switches on the basis of the duty cycles.
44 . The method of claim 33 , wherein the electric quantity is one of either an output voltage from the inverter or an output current from the inverter.
45 . The method of claim 33 , wherein the inverter is a three-phase inverter.
46 . The method of claim 33 , wherein the inverter is a multi-level inverter.
47 . The method of claim 33 , wherein for each sector into which the complex plane is subdivided, data are stored for the determination of a number of modulation matrices that depends on the number of levels of the inverter, and wherein each modulation matrix comprises a number of rows equal to a number of state vectors lying on the edges of each sector into which the complex plane is subdivided and a number of columns equal to the number of branches of the inverter.
48 . The method of claim 47 , wherein for each sector into which the complex plane is subdivided, data are stored for the determination of L−1 matrices, where L is the number of levels of the inverter.
49 . The method of claim 48 , wherein the inverter is a three-phase, two-level inverter and wherein the modulation matrices, one for each one of six 60-electric degrees sectors in which the complex plane is divided, are defined as follows:
Sector no.
Matrix S 0 _M
1
[
1
0
0
1
1
0
0
0
0
1
1
1
]
2
[
1
1
0
0
1
0
0
0
0
1
1
1
]
3
[
0
1
0
0
1
1
0
0
0
1
1
1
]
4
[
0
1
1
0
0
1
0
0
0
1
1
1
]
5
[
0
0
1
1
0
1
0
0
0
1
1
1
]
6
[
1
0
1
1
0
0
0
0
0
1
1
1
]
50 . The method of claim 48 , wherein the inverter is a three-phase, three-level inverter and wherein the modulation matrices, one for each one of six 60-electric degrees sectors in which the complex plane is divided, are defined as follows:
Sector no.
Matrix S 0 _M
1
[
1
0
0
1
1
0
0
0
0
1
1
1
]
2
[
1
1
0
0
1
0
0
0
0
1
1
1
]
3
[
0
1
0
0
1
1
0
0
0
1
1
1
]
4
[
0
1
1
0
0
1
0
0
0
1
1
1
]
5
[
0
0
1
1
0
1
0
0
0
1
1
1
]
6
[
1
0
1
1
0
0
0
0
0
1
1
1
]
51 . The method of claim 33 , wherein the modulation matrices are calculated by means of rotation and shift operations from a series of compressed modulation matrices.
52 . The method of claim 51 , wherein the inverter is a three-phase two-level inverter and wherein the compressed modulation matrices comprise:
Matrix R 0 — M
[13 5 1]
[9 13 1]
expressed in decimal notation, each decimal number in the matrices converted to binary notation defining a column of a corresponding compressed matrix in binary notation.
53 . The method of claim 51 , wherein the inverter is a three-phase, three-level inverter and wherein the compressed modulation matrices
vector no. (X)
matrix R x — M (1)
matrix R x — M (2)
0
[361 41 1]
[507 123 75]
1
[321 361 1]
[459 507 75]
expressed in decimal notation, each decimal number in the matrices converted into binary notation defining a column of a corresponding compressed matrix in binary notation.
54 . The method of claim 34 , wherein the inverter is a three-level, three-phase inverter, and the scale factors matrix is defined as:
A
_
=
[
1
1
+
K
*
(
Vb
2
-
Vc
2
)
1
+
K
*
(
Vb
2
-
Vc
1
)
1
1
+
K
*
(
Vb
2
-
Vc
2
)
1
+
K
*
(
Vb
2
-
Vc
1
)
1
1
1
]
and wherein
Vb is the bulk voltage across the input terminals of the inverter, VCI, VC2 are actual voltage values across the two bulk capacitors of the inverter; and
K is a gain factor.
55 . The method of claim 54 , wherein the duty cycle vector is defined as:
D=[δ 1 δ 1 δ 1 δ 2 δ 2 δ 2 δ 3 δ 3 δ 3 ]
in which
δ
1
=
M
4
(
3
cos
α
_
-
sin
α
_
)
δ
2
=
M
2
sin
α
δ
3
=
1
3
-
M
6
(
3
cos
α
_
+
sin
α
_
)
and the modified duty cycle vector is defined as:
D
_
=
[
δ
1
δ
1
δ
1
δ
2
δ
2
δ
2
δ
3
δ
3
δ
3
]
⊗
[
1
1
+
K
*
(
Vb
2
-
Vc
2
)
1
+
K
*
(
Vb
2
-
Vc
1
)
1
1
+
K
*
(
Vb
2
-
Vc
2
)
1
+
K
*
(
Vb
2
-
Vc
1
)
1
1
1
]
56 . The method of claim 34 , wherein the inverter is a four-level, three-phase inverter, and the scale factors matrix is defined as:
A
_
=
[
1
1
+
K
*
(
Vb
-
(
2
*
Vc
2
+
Vc
3
)
)
1
+
K
*
(
Vb
-
(
2
*
Vc
2
+
Vc
1
)
)
1
+
K
*
(
Vb
3
-
Vc
3
)
1
+
K
*
(
Vb
3
-
Vc
2
)
1
+
K
*
(
Vb
3
-
Vc
1
)
1
1
+
K
*
(
Vb
-
(
2
*
Vc
2
+
Vc
3
)
)
1
+
K
*
(
Vb
-
(
2
*
Vc
2
+
Vc
1
)
)
1
+
K
*
(
Vb
3
-
Vc
3
)
1
+
K
*
(
Vb
3
-
Vc
2
)
1
+
K
*
(
Vb
3
-
Vc
1
)
1
1
1
1
]
57 . The method of claim 33 , further comprising:
identifying a rotating vector representing of the multi-phase voltage output from the inverter, the rotating vector being defined by a modulation index and by an electric angle in a complex plane;
at each PWM cycle, determining the sector of the complex plane in which the rotating vector is located;
determining a modified phase angle offsetting the phase of the rotating vector until bringing back the rotating vector and the sector in which it lies in a geometric condition coinciding with that of the first sector of the complex plane;
calculating the duty cycle vector (±)1 as a function of the modified phase angle and of the modulation index of the rotating vector;
detecting the voltages across the bulk capacitors of the inverter; calculating a scale factors matrix based on the detected voltages;
calculating a modified duty cycle vector as a matrix product between the duty cycle vector and the scale factors matrix;
executing a row by column product of the modified duty cycle vector by the modulation matrices;
loading the values obtained from the product between the modified duty cycle vector and the modulation matrices into a PWM modulator; and
driving the switches of the inverter as a function of the output PWM signals from the modulator.
58 . The method of claim 33 , wherein the modified duty cycle vector and the modulation matrix are multiplied by means of a multiply and accumulate operator.