High-performance control method for carrier- based modulation t-type three-level converters
The invention relates to a high-performance control method for carrier-based modulation T-type three-level converters. The method includes: S 1, representing the mathematical model of the converter using the switching function; S 2, representing the three-phase modulation signal using the sine function, and representing upper and lower carrier signals using the piecewise function; S 3, determining the time distribution of the converter switching state and obtaining the critical phase shift angle of the lower carrier under the switching state without maximum common-mode voltage; S 4, sampling voltage values of two DC-side capacitors and using the voltage difference as the basis for left or right shifts of the lower carrier; S 5, comparing the three-phase modulation wave with the upper and lower carriers to output the switching pulse signal. This method addresses neutral-point potential balance, common-mode voltage suppression, and reduces digital processor resource usage during PWM modulation.
1 . A high-performance control method for carrier-based modulation T-type three-level converters, comprising a neutral-point potential balance and a common-mode voltage suppression, the specific steps are as follows:
S 1 , representing a mathematical model of T-type three-level converter by using a switching function;
S 2 , representing a three-phase modulation signal by using a sine function expression, and representing upper and lower carrier signals by using a piecewise function expression;
S 3 , using ideas of a sector partition and a regular sampling method, determining a time distribution of a converter switching state, and obtaining a critical phase shift angle of a lower carrier under the switching state without a maximum common-mode voltage;
S 4 , sampling voltage values of two DC-side capacitors, and using a voltage difference as a basis for left or right shifts of a lower carrier;
S 5 , comparing a three-phase modulation wave with the upper and lower carriers to realize a PWM control and output a switching pulse signal.
2 . The high-performance control method for the carrier-based modulation T-type three-level converters, according to claim 1 , in S 1 , a working principle of the T-type three-level converter is described by a switching function, and switching function expressions of an output voltage and a load voltage are obtained, and the switching function expressions of the common-mode voltage are derived by using the switching function and switching function expressions according to an output level state of the T-type three-level converter, the switching function values of each phase representing the output level states are 1, 0 or −1, and values are substituted into a common-mode voltage expression, under a carrier-based sinusoidal pulse width modulation, there are 25 combinations of the converter switching state, excluding [1, 1, 1] and [−1, −1, −1], and a final common-mode voltage will only have three cases, if DC-side voltage is expressed as V dc , then amplitudes of the three common-mode voltages are V dc/3, V dc /6 and 0 respectively, and the maximum common-mode voltage is V dc /3.
3 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 2 , the common-mode voltage switching function of the three-level converters are expressed as:
V
CMV
=
V
dc
6
·
(
S
A
+
S
B
+
S
C
)
.
wherein S A , S B and S C are the switching state functions of the T-type three-level converters.
4 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 1 , in S 2 , output information of the converter is collected by a voltage sensor or a resistance divider, and a fundamental amplitude of the load voltage is obtained by Fourier decomposition method, then compared with maximum amplitude value for a normalized processing to obtain modulation information, and the sinusoidal function expression of the three-phase modulation wave is provide, the piecewise function is used to represent an the upper carrier and a phase-shifted of the lower carrier by using a switching period as a piecewise interval.
5 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 4 , the expression of the three-phase modulation wave:
{
u
ra
=
m
·
sin
(
ω
r
t
+
π
/
6
)
u
rb
=
m
·
sin
(
ω
r
t
-
π
/
2
)
u
rc
=
m
·
sin
(
ω
r
t
+
5
π
/
6
)
.
the expressions of the upper carrier and the phase-shifted of the lower carrier:
u
c
1
=
{
-
2
ω
c
t
+
(
2
k
+
1
)
,
k
=
0
,
1
,
2
…
n
-
1
t
∈
[
kT
c
,
kT
c
+
T
c
/
2
]
-
2
ω
c
t
-
(
2
k
+
1
)
,
k
=
0
,
1
,
2
…
n
-
1
t
∈
[
kT
c
+
T
c
/
2
,
(
k
+
1
)
T
c
]
u
c
2
=
{
-
2
ω
c
(
t
+
T
c
·
θ
/
2
π
)
+
2
k
,
k
=
0
,
1
,
2
…
n
-
1
t
∈
[
kT
c
,
kT
c
+
T
c
/
2
]
2
ω
c
(
t
+
T
c
·
θ
/
2
π
)
-
(
2
k
+
2
)
,
k
=
0
,
1
,
2
…
n
-
1
t
∈
[
kT
c
+
T
c
/
2
,
(
k
+
1
)
T
c
]
.
wherein m is a modulation index, ω r is an angular frequency of the modulation wave, ω c is an angular frequency of a carrier wave, and T c is the switching period, θ is the phase shift angle of the lower carrier.
6 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 1 , in S 3 , periodicity and symmetry are used to conduct the sector partition on carrier and modulation waveforms in an unit power frequency period, to obtain twelve similar sectors, then, at a peak or a trough of the carrier wave in a single sector, a time function of the converter switching state is determined according to a regular sampling principle and a geometric relationship, and the time function is used to determine the critical phase shift angle of the lower carrier.
7 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 6 , the time functions of the converter switching state and the critical phase shift angle of the lower carrier of twelve sectors are as follows:
the time function of sector 1 is:
{
δ
a
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
π
/
6
]
δ
b
=
T
c
+
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
-
π
/
2
]
δ
c
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
5
π
/
6
]
the critical phase shift angle of the lower carrier of sector 1 is:
θ
*
=
1
2
·
ω
c
(
δ
b
+
δ
c
)
the time function of sector 2 is:
{
T
c
-
δ
a
=
T
c
-
mT
c
sin
(
ω
r
·
kT
c
+
π
/
6
)
T
c
-
δ
b
=
-
mT
c
sin
(
ω
r
·
kT
c
-
π
/
2
)
T
c
-
δ
c
=
-
mT
c
sin
(
ω
r
·
kT
c
+
5
π
/
6
)
the critical phase shift angle of the lower carrier of sector 2 is:
θ
*
=
1
2
·
ω
c
[
(
T
c
-
δ
a
)
+
(
T
c
-
δ
c
)
]
the time function of sector 3 is:
{
T
c
-
δ
a
=
T
c
-
mT
c
sin
(
ω
r
·
kT
c
+
π
/
6
)
T
c
-
δ
b
=
-
mT
c
sin
(
ω
r
·
kT
c
-
π
/
2
)
T
c
-
δ
c
=
-
mT
c
sin
(
ω
r
·
kT
c
+
5
π
/
6
)
the critical phase shift angle of the lower carrier of sector 3 is:
θ
*
=
1
2
·
ω
c
[
(
T
c
-
δ
a
)
+
(
T
c
-
δ
b
)
]
the time function of sector 4 is:
{
δ
a
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
π
/
6
]
δ
b
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
-
π
/
2
]
δ
c
=
T
c
+
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
5
π
/
6
]
the critical phase shift angle of the lower carrier of sector 4 is:
θ
*
=
1
2
·
ω
c
(
δ
b
+
δ
c
)
the time function of sector 5 is:
{
δ
a
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
π
/
6
]
δ
b
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
-
π
/
2
]
δ
c
=
T
c
+
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
5
π
/
6
]
the critical phase shift angle of the lower carrier of sector 5 is:
θ
*
=
1
2
·
ω
c
(
δ
a
+
δ
c
)
the time function of sector 6 is:
{
T
c
-
δ
a
=
-
m
T
c
sin
(
ω
r
·
kT
c
+
π
/
6
)
T
c
-
δ
b
=
T
c
-
m
T
c
sin
(
ω
r
·
kT
c
-
π
/
2
)
T
c
-
δ
c
=
-
m
T
c
sin
(
ω
r
·
kT
c
+
5
π
/
6
)
the critical phase shift angle of the lower carrier of sector 6 is:
θ
*
=
1
2
·
ω
c
[
(
T
c
-
δ
a
)
+
(
T
c
-
δ
b
)
]
the time function of sector 7 is:
{
T
c
-
δ
a
=
-
m
T
c
sin
(
ω
r
·
kT
c
+
π
/
6
)
T
c
-
δ
b
=
T
c
-
m
T
c
sin
(
ω
r
·
kT
c
-
π
/
2
)
T
c
-
δ
c
=
-
m
T
c
sin
(
ω
r
·
kT
c
+
5
π
/
6
)
the critical phase shift angle of the lower carrier of sector 7 is:
θ
*
=
1
2
·
ω
c
[
(
T
c
-
δ
b
)
+
(
T
c
-
δ
c
)
]
the time function of sector 8 is:
{
δ
a
=
T
c
+
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
π
/
6
]
δ
b
=
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
-
π
/
2
]
δ
c
=
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
5
π
/
6
]
the critical phase shift angle of the lower carrier in sector 8 is:
θ
*
=
1
2
·
ω
c
(
δ
a
+
δ
c
)
the time function of sector 9 is:
{
δ
a
=
T
c
+
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
π
/
6
]
δ
b
=
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
-
π
/
2
]
δ
c
=
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
5
π
/
6
]
the critical phase shift angle of the lower carrier of sector 9 is:
θ
*
=
1
2
·
ω
c
(
δ
a
+
δ
b
)
the time function of sector 10 is:
{
T
c
-
δ
a
=
-
m
T
c
sin
(
ω
r
·
kT
c
+
π
/
6
)
T
c
-
δ
b
=
-
mT
c
sin
(
ω
r
·
kT
c
-
π
/
2
)
T
c
-
δ
c
=
T
c
-
mT
c
sin
(
ω
r
·
kT
c
+
5
π
/
6
)
the critical phase shift angle of the lower carrier of sector 10 is:
θ
*
=
1
2
·
ω
c
[
(
T
c
-
δ
b
)
+
(
T
c
-
δ
c
)
]
the time function of sector 11 is:
{
T
c
-
δ
a
=
-
m
T
c
sin
(
ω
r
·
kT
c
+
π
/
6
)
T
c
-
δ
b
=
-
mT
c
sin
(
ω
r
·
kT
c
-
π
/
2
)
T
c
-
δ
c
=
T
c
-
mT
c
sin
(
ω
r
·
kT
c
+
5
π
/
6
)
the critical phase shift angle of the lower carrier of sector 11 is:
θ
*
=
1
2
·
ω
c
[
(
T
c
-
δ
a
)
+
(
T
c
-
δ
c
)
]
the time function of sector 12 is:
{
δ
a
=
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
π
/
6
]
δ
b
=
T
c
+
mT
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
-
π
/
2
]
δ
c
=
m
T
c
sin
[
ω
r
·
(
k
+
1
/
2
)
T
c
+
5
π
/
6
]
the critical phase shift angle of the lower carrier of sector 12 is:
θ
*
=
1
2
·
ω
c
(
δ
a
+
δ
b
)
.
8 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 7 , a phase shift angle range of the lower carrier is:
π
≥
❘
"\[LeftBracketingBar]"
θ
❘
"\[RightBracketingBar]"
≥
θ
*
.
9 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 1 , in S 4 , a voltage sensor or a resistance divider are used to sample the voltage values of two DC-side capacitors, and a phase shift direction of the lower carrier is determined according to a voltage difference between the two DC-side capacitors when an upper capacitor voltage is greater than a lower capacitor voltage, that is, ΔV C >0, then the lower carrier is selected to move to right within a phase shift angle range to lift aneutral-point potential; when the upper capacitor voltage is less than the lower capacitor voltage, that is, ΔV C <0, then the phase shift angle range of the lower carrier is selected to move left to reduce the neutral-point potential, a voltage difference limit is set.
10 . The high-performance control method for the carrier-based modulation T-type three-level converters according to claim 1 , in S 5 , an upper carrier and a phase-shifted lower carrier are compared with a normalized modulation signal respectively to obtain two sets of PWM pulse signals, and the two signals are complementary assigned to four power switches of each phase bridge arm.