US 2015/0318807 A1 · DIRECT TORQUE CONTROL METHOD FOR INHIBITING TORQUE RIPPLES

Abstract

The present invention relates to a direct torque control method for inhibiting torque ripples, mainly comprising the following steps: establishing an MC voltage vector switching table visually displaying degrees of change in torque and flux, and, proposing, on the basis of the MC voltage vector switching table visually displaying the degrees of change in torque and flux, an MC-DTC mark-to-space ratio computing policy for torque quantification control. The MC-DTC mark-to-space ratio computing policy allows for inhibition of torque ripples of a PMSM speed control system and for a constant switching frequency, uses the MC voltage vector switching table visually displaying the degrees of change in torque and flux, has a simple algorithm, does not reply on motor parameters, and obviates the need for rotational coordinate transformation.

A direct torque control method for inhibiting torque ripples, comprising the following steps:

step 1:
establishing an MC voltage vector switching table visually displaying degrees of change in torque and flux
a spatially rotational coordinate system x-y is established and a stator flux ψs is positioned on the x-axis, with a relationship between the torque and stator flux amplitude of a permanent magnet synchronous motor and a stator voltage as follows:
d
dt
|
Ψ
s
|
=
v
x
(
1
)
d
dt

T
e
∝
v
y
-
ω
r
|
Ψ
s
|
(
2
)
in formulae (1) and (2), vx and vy denote components of the stator voltage on the x-axis and the y-axis, ωr denotes an electrical angular speed of a rotor;
|ψs| denotes the stator flux amplitude, Te denotes the electromagnetic torque, and t denotes the time;
a voltage vector V+1 of a +1 switching combination is decomposed on the x-y coordinates to obtain:
V+1y=2/3νab sin(−θs)=−2/√{square root over (3)}Vm cos(αi+π/6)sin θs (3)
V+1x=2/3νab cos(−θs)=2/√{square root over (3)}Vm cos(αi+π/6)cos θs (4)
in formulae (3) and (4), V+1x denotes a projection of V+1 on the x-axis, V+1y denotes a projection of V+1 on the y-axis, Vm denotes the maximum value of an MC input phase voltage, θs denotes an included angle between the x-axis and an A phase winding of a motor, and αi denotes a vector angle of the MC input phase voltage;
Vab is the ab line voltage of MC input side;
a torque evaluation function τ, a flux evaluation function λ and a counter electromagnetic force evaluation function e are defined as below:
τ
=
v
y
2

/

3

V
m
(
5
)
λ
=
v
x
2

/

3

V
m
(
6
)
e
=
ω
r
|
Ψ
s
|
2

/

3

V
m
;
(
7
)
formula (3) and formula (4) are substituted into formula (5) and formula (6) respectively, to obtain torque and flux evaluation functions τ+1 and λ+1 of the +1 switching combination:
τ+1=cos(αi+π/6)sin θs (8)
λ+1=cos(αi+π/6)cos θs (9)
similarly, torque and flux evaluation functions of all voltage vectors of the MC are obtained;
both the torque evaluation function τ and the flux evaluation function λ are binary periodic functions;
within one of θsε[0,2π] and αiε[0,2π], θs and αi are divided into intervals every π/6 from 0 and then represented as a stator flux sector I74ε[1,12] and a stator voltage sector Iαε[1,12], so that the whole plane is divided into 12×12 regions;
the average value of each of the regions is used to represent the value of the torque evaluation function τ and the value of the flux evaluation function λ of this region, and thus functions for calculating the average value of the torque evaluation function τ and the average value of the flux evaluation function λ are defined as:
p
τ
=
round

[
k
(
π

/

6
)
2

∫
π
6

(
l
α
-
1
)
π
6

l
α

∫
π
6

(
l
θ
-
1
)
π
6

l
θ

τ



θ
s



α
i
]
(
10
)
p
λ
=
round

[
k
(
π

/

6
)
2

∫
π
6

(
l
α
-
1
)
π
6

l
α

∫
π
6

(
l
θ
-
1
)
π
6

l
θ

λ



θ
s



α
i
]
(
11
)
in formulae (10) and (11), Iα={1, 2, 3 . . . 12}, Iθ={1, 2, 3 . . . 12};
and round( ) denotes proximity rounding function, ρτ denotes a torque evaluation value, and ρλ denotes a flux evaluation value;
if k=10, the torque evaluation value ρτ and the flux evaluation value ρλ are integers between −9 and +9;
formula (5), formula (6) and formula (7) are substituted into formula (1) and formula (2) to obtain a function relational expression between the torque evaluation function τ, the flux evaluation function λ, the counter electromagnetic force evaluation function e, and a rate of change in torque and a rate of change in flux of the motor:
d
dt

T
e
∝
τ
-
e
(
12
)
d
dt
|
Ψ
s
|
∝
λ
;
(
13
)
from formula (10), formula (11), formula (12) and formula (13), a function relational expression between the MC torque evaluation value ρτ, the MC flux evaluation value ρλ and the rate of change in torque and the rate of change in flux of the motor may be obtained:
d
dt

T
e
≈
d
dt

T
e
_
∝
p
τ
-
p
e
(
14
)
d
dt
|
Ψ
s
|
≈
d
dt
|
Ψ
s
|
_
∝
p
λ
(
15
)
in formulae (14) and (15), the left part of symbol ∝ denotes an average value of the rate of change in torque and the rate of change in flux of the motor within a region, wherein the average value of the counter electromagnetic force evaluation function is:
ρe=round(10e) (16);
it can be seen from formula (14) and formula (15) that the torque evaluation value ρτ and flux evaluation value ρλ after discretization and averaging are approximately in direct proportion to the rates of change in torque and flux of the motor;
the ρτ values of the vector V+1 within all regions may be calculated by substituting formula (8) into formula (10), these values are gathered in form of a table to obtain a switching table showing the effect of the vector V+1 to the change in torque, where a horizontal header of the switching table showing the effect of the vector V+1 to the change in torque is a stator flux sector while a vertical header thereof is a stator voltage sector;
the torque evaluation function τ and the flux evaluation function λ are products of the two functions, wherein the term containing αi is related to time and called herein as a temporal expression, and the term containing θs is related to the stator flux and the spatial position of the voltage vector and called herein as a spatial expression;
the torque evaluation functions τ and flux evaluation functions λ of 18 effective vectors of the MC have the following situations:
situation 1:
τ and λ of a same vector have a same temporal expression, and the spatial expression of λ is π/2 lagged behind the spatial expression of τ;
situation 2:
τ+1, τ+2 and τ+3 have a same spatial expression, but each has a temporal expression 2π/3 lagged behind another in this order;
situation 3:
τ+1, τ+4 and τ+7 have a same temporal expression, but each has a spatial expression 2π/3 lagged behind another in this order;
and
τ+2, τ+5 and τ+8 have a same temporal expression, but each has a spatial expression 2π/3 lagged behind another in this order;
and
τ+3, τ+6 and τ+9 have a same temporal expression, but each has a spatial expression 2π/3 lagged behind another in this order;
situation 4:
the values of negative vectors τ−1, τ−2 to τ−9, λ+1, λ−2 to λ−9 are negative numbers of the values of corresponding positive vectors τ+1, τ+2 to τ+9, λ+1, λ+2 to λ−9;
In the situation 1-4, τ+1 to τ+9 and λ+1 to λ+9 respectively represent torque and flux evaluation functions of the +1 to +9 switching combination, τ−1 to τ−9 and λ−1 to λ−9 respectively represent torque and flux evaluation functions of the −1 to −9 switching combination;
according to situation 2 and situation 3, the vertical header, i.e., the stator voltage sector, and the horizontal header, i.e., the stator flux sector, of the switching table showing the effect of the vector V+1 to the change in torque may be translated to obtain a switching table showing the effect of all positive vectors of the MC to the change in torque;
then, according to situation 1, the horizontal header, i.e., the stator flux sector, of the switching table showing the effect of the vector V+1 to the change in torque may be translated to obtain a switching table showing the effect of all positive vectors of the MC to the change in flux;
finally, according to situation 4, ρτ and ρλ values corresponding to all negative vectors of the MC are calculated;
and
after translating the vertical header, i.e., the stator voltage sector, and the horizontal header, i.e., the stator flux sector, an MC voltage vector switching table visually displaying degrees of change in torque and flux is formed;
and
step 2:
inquiring the torque evaluation value ρτ from the MC voltage vector switching table visually displaying degrees of change in torque and flux, and optimization calculating the mark-to-space ratio of the voltage vector
according to a conventional MC-DTC control method, a voltage vector of a matrix converter is selected from the MC voltage vector switching table;
the number of a sector of the stator flux vector is calculated;
the number of a sector of the input voltage vector is calculated;
the torque evaluation value ρτ of the MC vector is obtained through the MC voltage vector switching table visually displaying degrees of change in torque and flux;
a counter electromagnetic force evaluation value ρe is calculated;
a torque coefficient is set offline;
and, the flux torque evaluation value ρτ, the counter electromagnetic force evaluation value ρe and the torque coefficient are substituted into a mark-to-space ratio calculation formula to calculate the mark-to-space ratio for optimization;
the calculation formula of mark-to-space ratio d is as follows:
d
=
T
e
*
-
T
e
K
T

p
τ
+
p
e
p
τ
(
17
)
In formulae (17), Te* is electromagnetic torque reference value Te is electromagnetic torque and KT is torque coefficient.

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Direct torque control method for inhibiting torque ripples

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Direct torque control method for inhibiting torque ripples

Life of this patent

Abstract

Claims1