CN114785101B - Harmonic group on-line suppression method and system for single-phase cascade H-bridge converter - Google Patents

Harmonic group on-line suppression method and system for single-phase cascade H-bridge converter Download PDF

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CN114785101B
CN114785101B CN202210453616.9A CN202210453616A CN114785101B CN 114785101 B CN114785101 B CN 114785101B CN 202210453616 A CN202210453616 A CN 202210453616A CN 114785101 B CN114785101 B CN 114785101B
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harmonic
module
bridge
group
phi
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CN114785101A (en
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马俊鹏
焦宁
王顺亮
刘天琪
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Sichuan University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current

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Abstract

The invention relates to the technical fields of harmonic analysis, harmonic suppression and modulation of converters, and particularly discloses a harmonic group on-line suppression method and system of a single-phase cascade H-bridge converter. The invention mainly aims at a single-phase cascade H-bridge converter, reveals the characteristics of harmonic groups at the low frequency multiplication position of a carrier wave, establishes a harmonic group suppression strategy based on a harmonic vector relation diagram among modules, and further designs a control method for harmonic group suppression based on a static coordinate system. The harmonic wave group suppression system comprises a harmonic wave voltage acquisition module, a harmonic wave phase angle difference acquisition module and a carrier wave phase angle adjustment module. The on-line suppression strategy for the harmonic groups formulated by the invention can effectively suppress the AC side voltage harmonic groups of the single-phase cascade H-bridge converter, and can be applied to analysis and solving of the problem of harmonic instability of the single-phase cascade H-bridge converter.

Description

Harmonic group on-line suppression method and system for single-phase cascade H-bridge converter
Technical Field
The invention relates to the technical fields of harmonic analysis, harmonic suppression and modulation of converters, in particular to a harmonic group on-line suppression method of a single-phase cascade H-bridge converter based on a harmonic domain mathematical model.
Background
The single-phase cascade H-bridge converter (CHBC) has the advantages of good output waveform, low harmonic content, easy expansion and capacity increase due to modularized design, access to multiple paths of different loads, flexible control and the like. In recent years, the system has been applied to many engineering applications in the fields of new energy grid connection, electric locomotive traction systems, static synchronous compensators (Static Synchronous Compensator, STATCOM) and the like. The carrier phase shift modulation strategy (Carrier Phase Shifting Pulse Width Modulation, CPS-PWM) is the most widely applied modulation mode of the cascaded H-bridge converter and is also the key of high-quality output voltage and current. CPS-PWM effectively reduces the harmonic distortion of the CHBC output voltage and current, and ensures that the harmonic is mainly concentrated at the high frequency multiplication of the carrier frequency. In the actual operation process, the cascade H-bridge converter cannot reach a complete ideal operation state due to unbalanced modulation signals and direct-current side capacitor voltage caused by power difference among modules, and low frequency multiplication harmonic waves of carrier frequency can be caused. Harmonic resonance is extremely easy to be caused when the higher harmonic frequency is the same as the resonance frequency of the system, and the phenomenon is particularly obvious in a train traction transmission system. The interaction of the train as an excitation source of high-frequency resonance with the CHBC-based power electronic transformer can generate a resonance band consisting of a main resonance point and a plurality of resonance points in the traction power supply system. Harmonic resonance can cause resonance overvoltage, increase loss, accelerate equipment aging, cause equipment failure, and endanger safe and stable operation of the system. Therefore, the safe and stable operation of the system is ensured, and the suppression of the harmonic group at the carrier frequency multiplication is very necessary.
At present, research on harmonic group suppression at the carrier low frequency multiplication of CHBC at home and abroad is mainly focused on a carrier phase shift modulation strategy (Variable Displacement Angle Carrier Phase Shifting Pulse Width Modulation, VA.PS-PWM) based on a variable phase shift angle. The method is to perform off-line adjustment on the phase shift angle of the module carrier wave, the acquisition of the new phase shift angle depends on the solution of a large number of inverse trigonometric functions, and the method is not applicable to cascaded H-bridge converters of a large number of module units and is not applicable to all operation conditions. Therefore, the suppression of the ac side harmonic group of the single-phase cascaded H-bridge converter still needs further intensive research.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a harmonic group on-line suppression strategy and a harmonic group suppression control system for a single-phase cascade H-bridge converter.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
the harmonic group on-line suppression method of the single-phase cascade H-bridge converter comprises the following steps of:
step 1: extracting center frequency to be suppressed from total voltage of single-phase cascade H-bridge converter as 2 momega c Harmonic group h m And the center frequency of each H bridge module is 2 momega c Harmonic groups of (2)
Figure BDA0003617920420000021
Where m is the index variable, ω, of the carrier c Is the carrier angular frequency;
step 2: solving for harmonicsGroup of
Figure BDA0003617920420000022
Sum of the corresponding remaining harmonic groups +.>
Figure BDA0003617920420000023
Phase angle difference>
Figure BDA0003617920420000024
Figure BDA0003617920420000025
N is the total module number;
step 3: according to the harmonic amplitude and the phase angle difference
Figure BDA0003617920420000026
Based on the static coordinate system, the carrier phase shift angle of each module is adjusted to obtain a new phase shift angle phi' i Harmonic suppression is realized.
Further, in the step 1, specifically:
definition of the ith H-bridge module ac outlet voltage u abi In 2mω c The harmonic group of the central angular frequency is
Figure BDA0003617920420000027
It is expressed in dual fourier form as:
Figure BDA0003617920420000028
Figure BDA0003617920420000029
Figure BDA00036179204200000210
Figure BDA00036179204200000211
where m is the index variable of the carrier, ω 0 Is the fundamental angular frequency;
Figure BDA00036179204200000212
and phi is equal to i The initial phase angle of the modulation wave and the carrier phase shift angle are respectively;
Figure BDA00036179204200000213
Is a harmonic group->
Figure BDA00036179204200000214
Is set, the initial phase angle of (a);
Figure BDA00036179204200000215
Is a disturbance variable;
Figure BDA00036179204200000216
Is a harmonic envelope, namely a disturbance variable +.>
Figure BDA00036179204200000217
Absolute value of (2); u (u) dci And M is as follows i The direct-current capacitor voltage and the modulation degree of the ith H bridge module are respectively;
Figure BDA00036179204200000218
As to disturbance variables
Figure BDA00036179204200000219
Function of>
Figure BDA00036179204200000220
When (I)>
Figure BDA00036179204200000221
Otherwise->
Figure BDA00036179204200000222
According to cascade H-bridge variationThe serial connection of the H bridge modules in the current transformer leads the current transformer to output the total voltage u ab In 2mω c The whole set of harmonics h being the center frequency m Amplitude H of the same m Expressed as:
Figure BDA00036179204200000223
Figure BDA00036179204200000224
further, the step 2 specifically includes:
for N-module cascade H-bridge converters, the ith module is taken as a reference to define
Figure BDA00036179204200000225
The sum of the harmonics of the other modules, except the ith H-bridge module:
Figure BDA0003617920420000031
wherein k is the kth H bridge module, k=1, 2, …, N, k+.i;
Figure BDA0003617920420000032
and->
Figure BDA0003617920420000033
Harmonic wave->
Figure BDA0003617920420000034
Amplitude and phase angle of (a):
Figure BDA0003617920420000035
in the method, in the process of the invention,
Figure BDA0003617920420000036
is the kthDisturbance variables of harmonic groups in the module;
Figure BDA0003617920420000037
And->
Figure BDA0003617920420000038
The disturbance variables x, y epsilon k and x not equal to y of harmonic groups in the x and y th modules respectively; phi (phi) x And phi is equal to y Carrier phase shift angles for the x and y th modules, respectively;
then a harmonic group h is obtained m Amplitude H of (2) m The expression of (2) is:
Figure BDA0003617920420000039
when formulae (5) to (9) are combined, formula (9) is rewritten as:
Figure BDA00036179204200000310
in the method, in the process of the invention,
Figure BDA00036179204200000311
is a harmonic group->
Figure BDA00036179204200000312
Phase angle difference between>
Figure BDA00036179204200000313
Further, in the step 3, a new phase shift angle phi 'is obtained' i The method comprises the following steps:
harmonic group of H bridge module
Figure BDA00036179204200000314
Expressed in a stationary coordinate system as:
Figure BDA00036179204200000315
Figure BDA00036179204200000316
in the method, in the process of the invention,
Figure BDA00036179204200000317
and->
Figure BDA00036179204200000318
Harmonic groups respectively representing the ith H bridge module +.>
Figure BDA00036179204200000319
Alpha and beta components of (a);
the total voltage harmonic H of the cascaded H-bridge converter m Expressed in a stationary coordinate system as:
Figure BDA00036179204200000320
in the method, in the process of the invention,
Figure BDA00036179204200000321
and->
Figure BDA00036179204200000322
Respectively represents the total AC output voltage u of the cascade H-bridge converter ab Middle harmonic group h m Alpha and beta components of (a);
Figure BDA00036179204200000323
And->
Figure BDA00036179204200000324
Respectively represent harmonic groups->
Figure BDA00036179204200000325
Alpha and beta components of (a);
definition f αβ (φ i ) To be related to phase shift angle phi i Is a function of:
Figure BDA00036179204200000326
when the phase angle is different
Figure BDA00036179204200000327
Approaching pi, we can get:
f αβ (φ i )→0 (15)
from equation (15), by making the function f αβ (φ i ) Approaching 0, i.e. effecting a phase angle difference
Figure BDA0003617920420000041
Approaching pi and further suppressing harmonic group h m ；
For function f αβ (φ i ) With respect to phase shift angle phi i Is the derivative of:
Figure BDA0003617920420000042
from the derivative (16), in
Figure BDA0003617920420000043
And->
Figure BDA0003617920420000044
Within the region, the function f αβ (φ i ) And phase shift angle phi i Respectively in a direct-proportion and inverse-proportion relation;
thus, a phase shift angle adjustment expression for each H-bridge module is obtained:
Figure BDA0003617920420000045
Figure BDA0003617920420000046
in phi' i The phase shift angle after being adjusted for the ith H bridge module; k (k) pV And k is equal to rV Respectively the proportional resonance parameters; omega cV And omega rV Cut-off frequency and resonant frequency, respectively, omega rV Is the even angular frequency; k (K) PR An expression for a PR controller; s=jω, ω is the angular frequency of the waveform entering the PR controller; g αβ (φ i ) As a function of the derivative formula (16):
Figure BDA0003617920420000047
Figure BDA0003617920420000048
a harmonic group on-line suppression system of a single-phase cascade H-bridge converter comprises the following analysis modules:
the harmonic voltage acquisition module is used for extracting that the center frequency to be suppressed in the total voltage of the single-phase cascade H-bridge converter is 2momega c Harmonic group h m And the center frequency of each H bridge module is 2 momega c Harmonic groups of (2)
Figure BDA0003617920420000049
Harmonic phase angle difference acquisition module for extracting harmonic wave group of each module
Figure BDA00036179204200000410
Sum of the corresponding remaining harmonic groups +.>
Figure BDA00036179204200000411
Included angle->
Figure BDA00036179204200000412
The carrier phase shift angle adjusting module is used for adjusting the carrier phase shift angle of each module to obtain a new phase shift angle phi' i Achieving harmonic suppression
Compared with the prior art, the invention has the beneficial effects that: the invention establishes an on-line inhibition strategy of the alternating-current side carrier low frequency multiplication harmonic group of the single-phase cascade H-bridge converter, designs a harmonic inhibition control system, can effectively inhibit the harmonic near the carrier low frequency multiplication caused by unbalanced operation of the module, and can be applied to analysis and solve the problem of harmonic instability of the single-phase cascade H-bridge converter.
Drawings
FIG. 1 is a flow chart of the CHBC AC side harmonic group suppression strategy of the present invention;
FIG. 2 is a CHBC topology of the present invention;
FIG. 3 is a block diagram of harmonic group suppression control according to an embodiment of the present invention;
fig. 4 shows the results of harmonic analysis before and after suppression based on harmonic groups.
Detailed Description
The present invention will be described in further detail with reference to the drawings and detailed description.
Examples:
step 1: extracting harmonic group voltage h to be suppressed of CHBC m And the corresponding harmonic group voltages of each H bridge module
Figure BDA0003617920420000051
In step 1, the harmonic group voltage h to be suppressed of the CHBC is obtained by a dual Fourier analysis method m And the corresponding harmonic group voltages of each H bridge module
Figure BDA0003617920420000052
Figure BDA0003617920420000053
Wherein m and n are index variables of the carrier and the baseband respectively; phi (phi) i Phase shifting angle for carrier wave of the ith module; omega c Is the carrier angular frequency;
Figure BDA0003617920420000054
respectively is harmonic group->
Figure BDA0003617920420000055
The initial phase angle, disturbance variable, envelope curve of (2), can be expressed as +.>
Figure BDA0003617920420000056
Figure BDA0003617920420000057
Figure BDA0003617920420000058
Wherein u is dci And M is as follows i The direct-current capacitor voltage and the modulation degree of the ith module are respectively;
Figure BDA0003617920420000059
an initial phase angle for the modulated wave; omega 0 Is the fundamental angular frequency;
Figure BDA00036179204200000510
For->
Figure BDA00036179204200000511
Function of>
Figure BDA00036179204200000512
When (I)>
Figure BDA00036179204200000513
Otherwise->
Figure BDA00036179204200000514
Step 2: solving a total voltage harmonic group h which needs to be suppressed by CHBC m Amplitude H of (2) m ExtractingHarmonic wave group of each module
Figure BDA00036179204200000515
Sum of the corresponding remaining harmonic groups +.>
Figure BDA00036179204200000516
Included angle->
Figure BDA00036179204200000517
According to the serial connection relation of all H bridge modules in the cascade H bridge converter, the converter outputs total alternating current voltage u ab In 2mω c The whole set of harmonics h being the center frequency m Amplitude H of the same m Can be expressed as:
Figure BDA0003617920420000061
Figure BDA0003617920420000062
in step 2: for N-module cascade H-bridge converters, the ith module is taken as a reference to define
Figure BDA0003617920420000063
The sum of the harmonics of the other modules, except for the ith module, is:
Figure BDA0003617920420000064
wherein k is the kth-bridge module, (k=1, 2, …, N, k+.i);
Figure BDA0003617920420000065
and->
Figure BDA0003617920420000066
Harmonic wave->
Figure BDA0003617920420000067
Amplitude and phase angle of (a):
Figure BDA0003617920420000068
the available harmonic h m Amplitude H of (2) m Is represented by the expression:
Figure BDA0003617920420000069
when formulae (25) to (29) are combined, formula (29) can be rewritten as:
Figure BDA00036179204200000610
in the method, in the process of the invention,
Figure BDA00036179204200000611
is +.>
Figure BDA00036179204200000612
Phase angle difference between>
Figure BDA00036179204200000613
From the formula (30), h m Harmonic amplitude H of (2) m Dependent on phase angle difference
Figure BDA00036179204200000614
According to the expression of the harmonic phase angle, the harmonic suppression can be realized by adjusting the phase shift angle of each module. With phase angle difference->
Figure BDA00036179204200000615
Approaching pi, harmonic h m Continuously decreasing, the harmonic reaches a minimum when the phase angle difference is equal to pi. />
Step 3: the carrier phase shift angle of each module is adjusted to obtain new phase shiftPhase angle phi' i 。
In step 3, the adjusted carrier phase shift angle phi is obtained based on the stationary coordinate system i ′。
The phase angle difference acquisition method based on the static coordinate system comprises the following steps:
harmonics of H-bridge module
Figure BDA00036179204200000616
Expressed in a stationary coordinate system as:
Figure BDA00036179204200000617
Figure BDA0003617920420000071
Figure BDA0003617920420000072
the total voltage harmonic H of the cascaded H-bridge converter m Within the stationary coordinate system can be expressed as:
Figure BDA0003617920420000073
definition f αβ (φ i ) To be related to phase shift angle phi i Is a function of:
Figure BDA0003617920420000074
when the phase angle is different
Figure BDA0003617920420000075
Approaching pi, we can get:
f αβ (φ i )→0 (36)
from equation (36), by making the function f αβ (φ i ) Approaching 0, can realize the phase angle difference
Figure BDA0003617920420000076
Approaching pi, thereby suppressing harmonic h m 。
Combining phase angles
Figure BDA0003617920420000077
Expression, for function f αβ (φ i ) With respect to phase shift angle phi i Is the derivative of:
Figure BDA0003617920420000078
from the derivative formula (37), in
Figure BDA0003617920420000079
And->
Figure BDA00036179204200000710
Within the region, the function f αβ (φ i ) And phase shift angle phi i Respectively, in a proportional and inverse relationship.
Thus, the phase shift angle adjustment expression for each H-bridge module can be obtained:
Figure BDA00036179204200000711
Figure BDA00036179204200000712
in phi' i The phase shift angle after being adjusted for the ith H bridge module; k (k) pV And k is equal to rV Respectively the proportional resonance parameters; omega cV And omega rV Cut-off frequency and resonant frequency, ω rV Is the even angular frequency; g αβ (φ i ) As a function of the derivative formula (38):
Figure BDA00036179204200000713
Figure BDA00036179204200000714
in phi' i The phase shift angle after being adjusted for the ith H bridge module; the method comprises the steps of carrying out a first treatment on the surface of the k (k) pV And k is equal to rV Respectively the proportional resonance parameters; omega cV And omega rV Cut-off frequency and resonant frequency, ω rV Is the even angular frequency.
The harmonic wave group on-line inhibition method of the single-phase cascade H-bridge converter further comprises the step of adjusting the carrier wave phase shift angle phi 'of each module' i The method is applied to carrier phase shift modulation, and can realize the suppression of a harmonic group at the low frequency multiplication position of the carrier.
Fig. 3 shows a harmonic group suppression control block diagram based on a stationary coordinate system.
The harmonic group on-line suppression system of the single-phase cascade H-bridge converter comprises the following analysis modules:
the harmonic voltage acquisition module is used for extracting that the center frequency to be suppressed in the total voltage of the single-phase cascade H-bridge converter is 2momega c Harmonic group h m And the center frequency of each H bridge module is 2 momega c Harmonic groups of (2)
Figure BDA0003617920420000081
Harmonic phase angle difference acquisition module for extracting harmonic wave group of each module
Figure BDA0003617920420000082
Sum of the corresponding remaining harmonic groups +.>
Figure BDA0003617920420000083
Included angle->
Figure BDA0003617920420000084
Carrier phase shift angle modulationThe whole module is used for adjusting the carrier phase shift angle of each module to obtain a new phase shift angle phi' i 。
Examples
Simulation verification is carried out by taking a six-module cascade H-bridge inverter as an example, the carrier frequency is 500Hz, and a harmonic group taking 1000Hz as a central frequency in the CHBC alternating-current side voltage is restrained. And comparing and analyzing the CHBC alternating-current side voltage harmonic spectrums obtained before and after the harmonic group inhibition respectively to prove that the harmonic group inhibition strategy can effectively inhibit the harmonic group at the low frequency multiplication position of the CHBC carrier. By comparing the harmonic groups taking 1000Hz as the center frequency in the voltage harmonic spectrum of fig. 4, the harmonic group suppression method can prove that the harmonic group at the carrier low frequency multiplication position of the CHBC alternating-current side voltage can be effectively suppressed.

Claims (2)

1. The harmonic group on-line suppression method of the single-phase cascade H-bridge converter is characterized by comprising the following steps of:
step 1: extracting center frequency to be suppressed from total voltage of single-phase cascade H-bridge converter as 2 momega c Harmonic group h m And the center frequency of each H bridge module is 2 momega c Harmonic groups of (2)
Figure FDA0004214545750000011
Where m is the index variable, ω, of the carrier c Is the carrier angular frequency;
step 2: find harmonic set
Figure FDA0004214545750000012
Sum of the corresponding remaining harmonic groups +.>
Figure FDA0004214545750000013
Phase angle difference>
Figure FDA0004214545750000014
Figure FDA0004214545750000015
N is the total module number;
step 3: according to the harmonic amplitude and the phase angle difference
Figure FDA0004214545750000016
Based on the static coordinate system, the carrier phase shift angle of each module is adjusted to obtain a new phase shift angle phi' i Harmonic suppression is realized;
the step 1 specifically comprises the following steps:
definition of the ith H-bridge module ac outlet voltage u abi In 2mω c The harmonic group of the central angular frequency is
Figure FDA0004214545750000017
It is expressed in dual fourier form as:
Figure FDA0004214545750000018
Figure FDA0004214545750000019
Figure FDA00042145457500000110
Figure FDA00042145457500000111
where m is the index variable of the carrier, ω 0 Is the fundamental angular frequency;
Figure FDA00042145457500000112
and phi is equal to i The initial phase angle of the modulation wave and the carrier phase shift angle are respectively;
Figure FDA00042145457500000113
Is a harmonic group->
Figure FDA00042145457500000114
Is set, the initial phase angle of (a);
Figure FDA00042145457500000115
Is a disturbance variable;
Figure FDA00042145457500000116
Is a harmonic envelope, namely a disturbance variable +.>
Figure FDA00042145457500000117
Absolute value of (2); u (u) dci And M is as follows i The direct-current capacitor voltage and the modulation degree of the ith H bridge module are respectively;
Figure FDA00042145457500000118
For->
Figure FDA00042145457500000119
Function of>
Figure FDA00042145457500000120
When (I)>
Figure FDA00042145457500000121
Otherwise->
Figure FDA00042145457500000122
According to the serial connection relation of all H bridge modules in the cascade H bridge converter, the converter outputs total alternating current voltage u ab In 2mω c The whole set of harmonics h being the center frequency m Amplitude H of the same m Expressed as:
Figure FDA00042145457500000123
Figure FDA00042145457500000124
the step 2 specifically comprises the following steps:
for N-module cascade H-bridge converters, the ith module is taken as a reference to define
Figure FDA00042145457500000125
The sum of the harmonics of the other modules, except the ith H-bridge module:
Figure FDA0004214545750000021
wherein k is the kth H bridge module, k=1, 2, …, N, k+.i;
Figure FDA0004214545750000022
and->
Figure FDA0004214545750000023
Harmonic wave->
Figure FDA0004214545750000024
Amplitude and phase angle of (a):
Figure FDA0004214545750000025
in the method, in the process of the invention,
Figure FDA0004214545750000026
the disturbance variable of the harmonic group in the kth module;
Figure FDA0004214545750000027
And->
Figure FDA0004214545750000028
The disturbance variables x, y epsilon k and x not equal to y of harmonic groups in the x and y th modules respectively; phi (phi) x And phi is equal to y Carrier phase shift angles for the x and y th modules, respectively;
then a harmonic group h is obtained m Amplitude H of (2) m The expression of (2) is:
Figure FDA0004214545750000029
when formulae (5) to (9) are combined, formula (9) is rewritten as:
Figure FDA00042145457500000210
in the method, in the process of the invention,
Figure FDA00042145457500000211
is a harmonic group->
Figure FDA00042145457500000212
Phase angle difference between>
Figure FDA00042145457500000213
Obtaining a new phase shift angle phi' i The method comprises the following steps:
harmonic group of H bridge module
Figure FDA00042145457500000214
Expressed in a stationary coordinate system as:
Figure FDA00042145457500000215
Figure FDA00042145457500000216
in the method, in the process of the invention,
Figure FDA00042145457500000217
and->
Figure FDA00042145457500000218
Harmonic groups respectively representing the ith H bridge module +.>
Figure FDA00042145457500000219
Alpha and beta components of (a);
the total voltage harmonic H of the cascaded H-bridge converter m Expressed in a stationary coordinate system as:
Figure FDA00042145457500000220
in the method, in the process of the invention,
Figure FDA00042145457500000221
and->
Figure FDA00042145457500000222
Respectively represents the total AC output voltage u of the cascade H-bridge converter ab Middle harmonic group h m Alpha and beta components of (a);
Figure FDA00042145457500000223
and->
Figure FDA00042145457500000224
Respectively represent harmonic groups->
Figure FDA00042145457500000225
Alpha and beta components of (a);
definition f αβ (φ i ) To be related to phase shift angle phi i Is a function of:
Figure FDA0004214545750000031
when the phase angle is different
Figure FDA0004214545750000032
Approaching pi, we can get:
Figure FDA0004214545750000033
from equation (15), by making the function f αβ (φ i ) Approaching 0, i.e. effecting a phase angle difference
Figure FDA0004214545750000034
Approaching pi and further suppressing harmonic group h m ；
For function f αβ (φ i ) With respect to phase shift angle phi i Is the derivative of:
Figure FDA0004214545750000035
from the derivative (16), in
Figure FDA0004214545750000036
And->
Figure FDA0004214545750000037
Within the region, the function f αβ (φ i ) And phase shift angle phi i Respectively in a direct-proportion and inverse-proportion relation; />
Thus, a phase shift angle adjustment expression for each H-bridge module is obtained:
Figure FDA0004214545750000038
Figure FDA0004214545750000039
in phi' i The phase shift angle after being adjusted for the ith H bridge module; k (k) pV And k is equal to rV Respectively the proportional resonance parameters; omega cV And omega rV Cut-off frequency and resonant frequency, respectively, omega rV Is the even angular frequency; k (K) PR An expression for a PR controller; s=jω, ω is the angular frequency of the waveform entering the PR controller; g αβ (φ i ) As a function of the derivative formula (16):
Figure FDA00042145457500000310
Figure FDA00042145457500000311
2. the harmonic group on-line suppression system of the single-phase cascade H-bridge converter is characterized by comprising the following analysis modules:
the harmonic voltage acquisition module is used for extracting that the center frequency to be suppressed in the total voltage of the single-phase cascade H-bridge converter is 2momega c Harmonic group h m And the center frequency of each H bridge module is 2 momega c Harmonic groups of (2)
Figure FDA00042145457500000312
Harmonic phase angle difference acquisition module for extracting harmonic wave group of each module
Figure FDA00042145457500000313
Sum of the corresponding remaining harmonic groups +.>
Figure FDA00042145457500000314
Included angle of (2)
Figure FDA0004214545750000041
The carrier phase shift angle adjusting module is used for adjusting the carrier phase shift angle of each module to obtain a new phase shift angle phi' i Harmonic suppression is realized;
the harmonic voltage is obtained specifically as follows:
definition of the ith H-bridge module ac outlet voltage u abi In 2mω c The harmonic group of the central angular frequency is
Figure FDA0004214545750000042
It is expressed in dual fourier form as:
Figure FDA0004214545750000043
Figure FDA0004214545750000044
Figure FDA0004214545750000045
Figure FDA0004214545750000046
where m is the index variable of the carrier, ω 0 Is the fundamental angular frequency;
Figure FDA0004214545750000047
and phi is equal to i The initial phase angle of the modulation wave and the carrier phase shift angle are respectively;
Figure FDA0004214545750000048
Is a harmonic group->
Figure FDA0004214545750000049
Is set, the initial phase angle of (a);
Figure FDA00042145457500000410
Is a disturbance variable;
Figure FDA00042145457500000411
Is a harmonic envelope, namely a disturbance variable +.>
Figure FDA00042145457500000412
Absolute value of (2); u (u) dci And M is as follows i The direct-current capacitor voltage and the modulation degree of the ith H bridge module are respectively;
Figure FDA00042145457500000413
For->
Figure FDA00042145457500000414
Function of>
Figure FDA00042145457500000415
When (I)>
Figure FDA00042145457500000416
Otherwise->
Figure FDA00042145457500000417
According to the serial connection relation of all H bridge modules in the cascade H bridge converter, the converter outputs total alternating current voltage u ab In 2mω c The whole set of harmonics h being the center frequency m Amplitude H of the same m Expressed as:
Figure FDA00042145457500000418
Figure FDA00042145457500000419
the harmonic phase angle difference is obtained specifically as follows:
for N-module cascade H-bridge converters, the ith module is taken as a reference to define
Figure FDA00042145457500000420
The sum of the harmonics of the other modules, except the ith H-bridge module:
Figure FDA00042145457500000421
wherein k is the kth H bridge module, k=1, 2, …, N, k+.i;
Figure FDA00042145457500000422
and->
Figure FDA00042145457500000423
Harmonic wave->
Figure FDA00042145457500000424
Amplitude and phase angle of (a):
Figure FDA0004214545750000051
in the method, in the process of the invention,
Figure FDA0004214545750000052
the disturbance variable of the harmonic group in the kth module;
Figure FDA0004214545750000053
And->
Figure FDA0004214545750000054
Respectively the firstThe harmonic group disturbance variables x, y epsilon k in the x and y modules are x not equal to y; phi (phi) x And phi is equal to y Carrier phase shift angles for the x and y th modules, respectively;
then a harmonic group h is obtained m Amplitude H of (2) m The expression of (2) is:
Figure FDA0004214545750000055
when formulae (5) to (9) are combined, formula (9) is rewritten as:
Figure FDA0004214545750000056
in the method, in the process of the invention,
Figure FDA0004214545750000057
is a harmonic group->
Figure FDA0004214545750000058
Phase angle difference between>
Figure FDA0004214545750000059
Obtaining a new phase shift angle phi' i The method comprises the following steps:
harmonic group of H bridge module
Figure FDA00042145457500000510
Expressed in a stationary coordinate system as:
Figure FDA00042145457500000511
Figure FDA00042145457500000512
in the method, in the process of the invention,
Figure FDA00042145457500000513
and->
Figure FDA00042145457500000514
Harmonic groups respectively representing the ith H bridge module +.>
Figure FDA00042145457500000515
Alpha and beta components of (a);
the total voltage harmonic H of the cascaded H-bridge converter m Expressed in a stationary coordinate system as:
Figure FDA00042145457500000516
in the method, in the process of the invention,
Figure FDA00042145457500000517
and->
Figure FDA00042145457500000518
Respectively represents the total AC output voltage u of the cascade H-bridge converter ab Middle harmonic group h m Alpha and beta components of (a);
Figure FDA00042145457500000519
and->
Figure FDA00042145457500000520
Respectively represent harmonic groups->
Figure FDA00042145457500000521
Alpha and beta components of (a);
definition f αβ (φ i ) To be related to phase shift angle phi i Is a function of:
Figure FDA00042145457500000522
when the phase angle is different
Figure FDA00042145457500000523
Approaching pi, we can get:
f αβ (φ i )→0 (35)
from equation (35), by making the function f αβ (φ i ) Approaching 0, i.e. effecting a phase angle difference
Figure FDA00042145457500000524
Approaching pi and further suppressing harmonic group h m ；
For function f αβ (φ i ) With respect to phase shift angle phi i Is the derivative of:
Figure FDA0004214545750000061
from the derivative formula (36), in
Figure FDA0004214545750000062
And->
Figure FDA0004214545750000063
Within the region, the function f αβ (φ i ) And phase shift angle phi i Respectively in a direct-proportion and inverse-proportion relation;
thus, a phase shift angle adjustment expression for each H-bridge module is obtained:
Figure FDA0004214545750000064
Figure FDA0004214545750000065
in phi' i Is the ithPhase shift angle after H bridge module adjustment; k (k) pV And k is equal to rV Respectively the proportional resonance parameters; omega cV And omega rV Cut-off frequency and resonant frequency, respectively, omega rV Is the even angular frequency; k (K) PR An expression for a PR controller; s=jω, ω is the angular frequency of the waveform entering the PR controller; g αβ (φ i ) As a function of the derivative formula (36):
Figure FDA0004214545750000066
Figure FDA0004214545750000067
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