CN117955322A - Method and system for inhibiting output voltage harmonic waves of three-phase inverter - Google Patents
Method and system for inhibiting output voltage harmonic waves of three-phase inverter Download PDFInfo
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- 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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- H02M7/53876—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 with analogue control of three-phase output based on synthesising a desired voltage vector via the selection of appropriate fundamental voltage vectors, and corresponding dwelling times
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Abstract
The invention discloses a method and a system for inhibiting output voltage harmonic waves of a three-phase inverter power supply. The method comprises the following steps: constructing a three-phase inverter model and a circuit topology, and obtaining a mathematical model of the three-phase inverter under a two-phase static coordinate system by Clark transformation; based on the mathematical model, a composite control method combining proportional resonance control and state feedback control is adopted to obtain an optimal control law equation and a feedback gain matrix; based on the feedback gain matrix, solving to obtain an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm; and utilizing the state feedback coefficient and the resonance controller parameter to combine the generalized integral extended state observer, realizing the static-difference-free tracking of the output voltage, reducing the output voltage harmonic wave and obtaining the integral control block diagram of the inverter. The invention integrates the PR controller, the optimal controller and the extended state observer, and improves the output power quality and the capacity of nonlinear load of the three-phase inverter.
Description
Technical Field
The invention belongs to the technical field of three-phase inverter power supplies, and particularly relates to a method and a system for inhibiting output voltage harmonic waves of a three-phase inverter power supply.
Background
When a normal nonlinear load is put into use, the output voltage of the inverter power supply will have waveform distortion to a certain extent, so that the harmonic content in the power system exceeds standard, and the existence of the harmonic will have different adverse effects on various electrical equipment such as motors, transformers, capacitors and the like. The motor and the transformer are easily affected by harmonic waves to generate heat, vibrate and aggravate, the running efficiency is reduced, and when the harmonic content is high, even the motor is caused to vibrate to cause mechanical damage; the capacitor is influenced by the electric, thermal and mechanical effects of harmonic waves, and the internal dielectric medium of the capacitor is easy to have problems of partial discharge, mechanical damage and the like, so that the damage is large; the relay protection device is influenced by harmonic waves, so that misoperation is easy to occur, the power system is stopped by mistake, and normal operation is difficult to realize; precision instruments such as sensors are easily misaligned due to harmonic interference; communication and control systems are also prone to system failure due to interference and even loss of information from high frequency harmonics.
The general method for inhibiting the three-phase voltage harmonic wave in the prior art comprises the following steps: improved PWM technology, filter technology, multilevel inverter technology. Among other things, improved PWM techniques reduce the Total Harmonic Distortion (THD) or torque ripple of the current in the high modulation ratio region, mainly by optimizing PWM (pulse width modulation) strategies, using random or periodic PWM spread spectrum techniques, and improved Space Vector Pulse Width Modulation (SVPWM) techniques. The PWM harmonics of certain specific frequencies are shifted to the vicinity of other frequencies so that the harmonic distribution characteristics of the PWM are changed, thereby suppressing the PWM harmonics. And in the filter technology, a filter is added at the output end of the inverter, so that the harmonic content can be further reduced. The sine wave filter is mainly used for filtering PWM harmonic waves and enabling fundamental wave components to pass through unimpeded, so that the voltage output by the inverter can be close to a sine wave. The sine wave filter can reduce the iron loss of a motor stator, inhibit high-frequency PWM noise and avoid overvoltage of a motor input end caused by long-line transmission. In addition, other types of filters such as LCL type filters may be used to filter out harmonic components in the output voltage. In the multi-level inverter technology, phase voltages which are more similar to sine waves are output by utilizing a plurality of series switching tubes and bus voltages with a plurality of levels on each phase bridge arm. As the number of levels increases, PWM harmonics in the multilevel inverter voltage decrease accordingly.
However, in the improved PWM technology, the switching frequency may be increased by adopting a more complex PWM strategy, so that switching loss may be increased, and inverter efficiency may be reduced; the use of complex components increases the complexity and cost of the system and may introduce new harmonics. In the filter technology, the filter is an additional hardware component, requires additional investment and space, causes efficiency reduction on voltage drop of current, and may cause resonance due to improper design, thereby causing instability and performance reduction. In the technology of the multilevel inverter, more switching tubes and more complex control circuits are needed, so that the complexity and the cost of the system are increased; as the number of levels increases, the control strategy becomes more complex, requiring higher levels of control algorithms and processors. Therefore, the invention is needed to better improve the output power quality and the capacity with nonlinear load of the three-phase inverter.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a method and a system for inhibiting the output voltage harmonic waves of a three-phase inverter power supply, which are used for providing high gain at a specific frequency by integrating the application of a PR controller, an optimal controller and an extended state observer so as to accurately track and inhibit the harmonic waves of specific times; searching optimal control parameters through an optimization algorithm to ensure that the system performance reaches the optimal; on the basis of considering uncertainty and interference of a system, robustness on system parameter change and external interference can be provided, so that complementary advantages are formed, and the capacity of the three-phase inverter power supply with nonlinear load is improved.
According to a first aspect of the present invention, there is provided a method of suppressing harmonics of an output voltage of a three-phase inverter, comprising the steps of:
S100, constructing a three-phase inverter model and circuit topology, and obtaining a mathematical model of the three-phase inverter under a two-phase static coordinate system by using Clark transformation based on the model;
S200, based on the mathematical model, adopting a composite control method combining proportional resonance control (PR control) and state feedback control to obtain an optimal control law equation and a feedback gain matrix;
s300, solving to obtain an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm based on the feedback gain matrix;
S400, utilizing the state feedback coefficient and the resonance controller parameter to combine the generalized integral extended state observer, realizing the static-difference-free tracking of the output voltage and reducing the output voltage harmonic wave.
Specifically, step S100 includes:
S101, constructing a three-phase inverter model and a structure topology, and setting model parameters;
the three-phase inverter adopts a three-phase three-wire system H-bridge inversion structure, la, lb and Lc are output filter inductors, ca, cb and Cc are filter capacitors, R is filter equivalent resistance, and the direct-current input voltage is The midpoint output voltage of the H bridge arm is/>、、/>The currents flowing through the filter inductance are respectively/>、/>、/>The filter capacitor terminal voltages are respectively/>、、/>Three-phase inverter output currents are/>, respectively、/>、/>; The filter adopts an LC filtering structure; the filter capacitors are connected in a star shape;
S102, based on the model in S101, constructing a mathematical equation of the three-phase inverter under a three-phase stationary coordinate system by adopting a kirchhoff voltage law and a kirchhoff voltage law:
（1），
（2），
wherein C is a filter capacitor, R is a filter equivalent resistor, and the DC input voltage is The midpoint output voltage of the H bridge arm is/>、/>、/>The currents flowing through the filter inductance are respectively/>、/>、/>The filter capacitor terminal voltages are respectively/>、/>、/>Three-phase inverter output currents are/>, respectively、/>、/>。
S103, based on a mathematical equation of the three-phase inverter under a three-phase static coordinate system, acquiring a state space equation and a model of the three-phase inverter under the three-phase static coordinate system;
arranging the formula (1) and the formula (2) to obtain a state space equation of the three-phase inverter under a three-phase static coordinate system;
（3），
The simplification of formula (3) can be obtained:
（4），
Wherein, ，/>，/>，/>，/>；
Setting output filter capacitor voltage and inductor current as state variables to obtain a state space model of the inverter:
（5），
Wherein, ，/>，/>，/>，/>，/>，。
S104, converting a three-phase inverter state space equation into a state space equation under a two-phase static coordinate system by Clark conversion;
Establishing a coordinate system, and making The axis coincides with the a-axis, the resultant vector/>, under a three-phase stationary coordinate systemAt angular velocity/>Rotating counterclockwise; at any time/> ，/>Is projected to/>, by vector decomposition, for the included angle between the rotating voltage vector and the a-axis of the three-phase static coordinate systemOn the coordinate system, clark conversion is carried out to obtain the three-phase inverter at/>Mathematical model under coordinate system:
（6），
Wherein, ，/>，/>，/>，/>。
Specifically, step S200 includes:
S201, constructing a resonant controller expression function and a state space model thereof;
Constructing a resonance controller expression:
（7），
Wherein, For the transfer function of the resonant controller,/>And/>For the control parameters to be solved,/>Is a Laplace transform factor,/>Is angular frequency;
writing equation (7) into a state space model:
（8），
Wherein, Is a state variable of the resonance controller,/>For the output of the resonant controller,For system output/>And reference input/>Error of (2); /(I)，/>，，/>；/>Is 50Hz;
S202, constructing a state space equation of an inverter under an external interference signal based on the state space model;
under the condition of an external interference signal, the state space equation of the inverter is converted into:
（9），
Wherein, Representing external interference vectors,/>；
Control signal of inverterThe method comprises the following steps:
（10），
Wherein, And/>Is a state feedback coefficient.
S203, combining output feedback and state feedback in the system, establishing an augmented state space equation of the inverter, and obtaining an optimal control law equation and a feedback gain matrix;
and establishing an augmented state space equation of the inverter by combining output feedback and state feedback in the system:
（11），
Wherein, ,/>,/>,/>, ,
,/>；
Establishing a performance index J function:
（12），
Obtaining an optimal control law by using an LQR optimal control method Equation:
（13），
where P is the semi-positive symmetric solution of the following Riccati equation:
（14），
Thus, the obtained feedback gain matrix is:
（15），
k is the obtained state feedback and resonance controller parameter.
Specifically, in step S300,
The LQR optimal control algorithm comprises the following specific steps:
for a linear steady system, the time interval is the whole In the process, three dimensions of voltage fluctuation in the operation process, energy loss of a control system and steady-state error of inverter output are comprehensively considered to obtain the optimal control law/>So that the performance index J reaches the minimum:
（16），
in the method, in the process of the invention, AndIs thatA weight matrix of a constant value of the dimension semi-positive definite symmetry,Is thatMaintaining a normal symmetric constant weight matrix;、 the start time and the end time of the control process are respectively realized;
Performance index J comprises three parts:
the method is used for limiting the output voltage fluctuation in the operation process of the inverter, namely, the requirement on the dynamic performance of the output voltage of the inverter is met;
representing the limitation of the control energy of the inverter system, namely reflecting the requirement on energy consumption;
the method represents the limitation of steady-state deviation and meets the requirement of the steady-state control precision of the output voltage of the inverter.
Specifically, in step S400, the following steps are included:
s401, adding a state observer, taking the input quantity and the output quantity of a controlled object as the input quantity of the observer, observing harmonic output signals of the controlled object, and establishing a controller structural block diagram;
S402, a structure diagram of the GI-ESO is established, and a state equation of the quasi-resonance controller and the GI-ESO is obtained;
Introducing a generalized integral extended state observer GI-ESO, establishing a structure diagram of the GI-ESO, and adopting a quasi-resonance controller:
（17），
Wherein, As a quasi-resonant controller transfer function,/>Is a proportional gain,/>Is the bandwidth of the i times quasi-resonant controller,/>Is the resonant frequency of the i-order quasi-resonant controller;
Obtaining a state equation of the GI-ESO according to the structure diagram of the GI-ESO:
（18），
Wherein, And/>Is a state variable, u is an input,/>，/>For the gain factor of the GI-ESO,Is the estimated total interference,/>For the ith interference to be present,; Gain coefficient of observer/>。
S403, combining the quasi-resonance controller type and the state equation of the GI-ESO to obtain an estimated error and a transfer function thereof;
Combining equation (17) with equation (18) to obtain an estimated error:
（19），
the transfer functions of the disturbance estimation errors e2 and X2 are obtained through the state equation and the estimation errors of the quasi-resonant controller:
（20），
S404, selecting fundamental wave frequency, constructing The GI-ESO state equation of the shaft current is obtained, and an overall control block diagram of the inverter is obtained;
selecting fundamental wave frequency, selecting fifth harmonic frequency and seventh harmonic frequency as selection frequency of quasi-resonance controller, and constructing GI-ESO equation of state for shaft current:
（21），
Wherein, And/>To augment state variables,/>And/>Is a variable in the augmented state variable; taking observer bandwidth as/>The gain factor of the observer is: /(I); Wherein/> 、/>Gain factor for GI-ESO;
In the case of the GI-ESO, 、/>And/>The method comprises the following steps of:
（22），
and establishes an inverter overall control block diagram.
According to a second aspect of the present invention, there is also provided a system for suppressing harmonics of an output voltage of a three-phase inverter,
Comprising the following steps: the system comprises a coordinate system model module, a control module, an LQR algorithm module and an observer module;
the coordinate system model module is used for constructing a three-phase inverter model and a circuit topology, and based on the model, a mathematical model of the three-phase inverter under a two-phase static coordinate system is obtained by Clark transformation;
the control module is used for obtaining an optimal control law equation and a feedback gain matrix by adopting a composite control method combining PR control and state feedback control based on the mathematical model;
The LQR algorithm module is used for solving and obtaining an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm based on the feedback gain matrix;
And the observer module is used for establishing a generalized integral extended state observer GI-ESO based on the state feedback coefficient and the resonance controller parameter, and controlling and counteracting the output voltage harmonic wave so as to inhibit the three-phase inverter power supply output voltage harmonic wave.
In general, the above technical solutions conceived by the present invention, compared with the prior art, enable the following beneficial effects to be obtained:
1. the method of the invention can quickly track and respond to the change of the system state and improve the overall performance of the system while inhibiting the specific frequency harmonic wave by adopting a composite control method combining PR control and state feedback control; the stability of the system can be further improved, the sensitivity of the system to parameter changes and external interference is reduced, and no static error tracking is realized;
2. the method provided by the invention has the advantages that through an LQR optimal control algorithm, the control scheme is simple in structure and easy to realize, can be suitable for processing the multi-objective optimization problem in a linear system, is high in reaction speed and small in overshoot, and has good robustness;
3. The method of the invention uses Clark transformation to transform the output variable of the three-phase inverter into a two-phase stationary coordinate system Under, let at/>The system structure of the three-phase inverter under the coordinate system has no coupling among variables, decoupling control is not needed, and the operation intensity is reduced;
4. The method of the invention comprises the following steps of Shaft sum/>Under the condition that the shaft is completely decoupled, the generalized integral extended state observer is utilized to identify the rapidly-changing sinusoidal interference, so that the method has higher estimation precision and stronger robustness and has greater flexibility in practical application.
Drawings
FIG. 1 is a flow chart of a method for suppressing output voltage harmonics of a three-phase inverter according to an embodiment of the present invention;
FIG. 2 is a flowchart showing the step S100 according to the embodiment of the present invention;
FIG. 3 is a topology diagram of a three-phase inverter according to an embodiment of the present invention;
FIG. 4 is a graph showing the relationship between three-phase stationary and two-phase stationary coordinate systems according to an embodiment of the present invention;
FIG. 5 is a flowchart showing a step S200 according to an embodiment of the present invention;
FIG. 6 is a schematic block diagram of a LQR-based composite control strategy in accordance with an embodiment of the present invention;
FIG. 7 is a flowchart showing the step S400 according to the embodiment of the present invention;
FIG. 8 is a block diagram of a controller according to an embodiment of the present invention;
FIG. 9 is a diagram illustrating a GI-ESO structure according to an embodiment of the present invention;
FIG. 10 is a schematic diagram of a three-phase inverter composite control system based on LQR in accordance with an embodiment of the present invention;
Fig. 11 is a system configuration diagram for suppressing output voltage harmonics of a three-phase inverter according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a method for inhibiting output voltage harmonic waves of a three-phase inverter power supply, which is shown in fig. 1 and comprises the following steps:
S100, constructing a three-phase inverter model and circuit topology, and obtaining a mathematical model of the three-phase inverter under a two-phase static coordinate system by using Clark transformation based on the model;
s200, based on the mathematical model, an optimal control law equation and a feedback gain matrix are obtained by adopting a composite control method combining proportional resonance control and state feedback control;
s300, solving to obtain an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm based on the feedback gain matrix;
S400, utilizing the state feedback coefficient and the resonance controller parameter, combining a generalized integral extended state observer, realizing dead-difference-free tracking of output voltage, reducing output voltage harmonic wave, and obtaining an inverter overall control block diagram.
Referring to fig. 2, in step S100, the following steps are included:
S101, constructing a three-phase inverter model and a structure topology, and setting model parameters;
S102, based on the model, constructing a mathematical equation of the three-phase inverter under a three-phase static coordinate system according to the kirchhoff voltage law and the kirchhoff voltage law;
s103, based on a mathematical equation of the three-phase inverter under a three-phase static coordinate system, acquiring a state space equation and a model of the three-phase inverter under the three-phase static coordinate system;
s104, converting the output variable of the three-phase inverter into a two-phase static coordinate system by using Clark conversion And (3) downwards.
In particular, the method comprises the steps of,
S101, constructing a three-phase inverter model and a structure topology, and setting model parameters;
The three-phase inverter adopts a three-phase three-wire system H-bridge inversion structure, the circuit topology of the three-phase three-wire system H-bridge inversion structure is shown in figure 3, la, lb and Lc are output filter inductors, ca, cb and Cc are filter capacitors, R is a filter equivalent resistor, and the direct current input voltage is The midpoint output voltage of the H bridge arm is/>、/>、/>The currents flowing through the filter inductance are respectively/>、/>、/>The filter capacitor terminal voltages are respectively/>、/>、/>Three-phase inverter output currents are/>, respectively、/>、; The filter adopts an LC filtering structure; the filter capacitors are connected in a star shape;
Since the frequency response of the LCL filter has a peak at the resonance frequency, the stability of the system is reduced, and an LC filter structure is adopted; in terms of a filter capacitor connection structure, capacitors are connected in a star shape from the viewpoint of reliability; the H-bridge inversion portion may be approximately equivalent to a proportional link.
Further, S102, based on the model in S101, a kirchhoff voltage law and a kirchhoff voltage law are adopted to build a mathematical equation of the three-phase inverter under a three-phase stationary coordinate system:
（1），
（2），
wherein C is a filter capacitor, R is a filter equivalent resistor, and the DC input voltage is The midpoint output voltage of the H bridge arm is/>、/>、/>The currents flowing through the filter inductance are respectively/>、/>、/>The filter capacitor terminal voltages are respectively/>、/>、/>Three-phase inverter output currents are/>, respectively、/>、/>。
Further, S103, based on a mathematical equation of the three-phase inverter in the three-phase stationary coordinate system, obtaining a state space equation and a model of the three-phase inverter in the three-phase stationary coordinate system;
arranging the formula (1) and the formula (2) to obtain a state space equation of the three-phase inverter under a three-phase static coordinate system;
（3），
The simplification of formula (3) can be obtained:
（4），
Wherein, ，/>，/>，/>，/>；
Setting output filter capacitor voltage and inductor current as state variables to obtain a state space model of the inverter:
（5），
Wherein, ，/>，/>，/>，/>，/>，。
Further, referring to fig. 4, S104, a Clark transformation is utilized to transform the three-phase inverter state space equation into a state space equation under a two-phase stationary coordinate system;
Establishing a coordinate system, and making The axis coincides with the a-axis, the resultant vector/>, under a three-phase stationary coordinate systemAt angular velocity/>Rotating counterclockwise; at any time/> ，/>Is projected to/>, by vector decomposition, for the included angle between the rotating voltage vector and the a-axis of the three-phase static coordinate systemOn the coordinate system, clark conversion is carried out to obtain the three-phase inverter at/>Mathematical model under coordinate system:
（6），
Wherein, ，/>，/>，/>，。
Referring to fig. 5, step S200 includes:
S201, constructing a resonant controller expression function and a state space model thereof;
S202, constructing a state space equation of an inverter under an external interference signal based on the state space model;
S203, combining output feedback and state feedback in the system, establishing an augmented state space equation of the inverter, and obtaining an optimal control law equation and a feedback gain matrix.
In particular, the method comprises the steps of,
Referring to fig. 6, in S201, a resonant controller expression function and a state space model thereof are constructed;
Constructing a resonance controller expression:
（7），
Wherein, For the transfer function of the resonant controller,/>And/>For the control parameters to be solved,/>Is a Laplace transform factor,/>Is angular frequency;
writing equation (7) into a state space model:
（8），
Wherein, Is a state variable of the resonance controller,/>For the output of the resonant controller,For system output/>And reference input/>Error of (2); /(I)，/>，/>，/>；/>Is 50Hz;
Further, S202, based on the state space model, constructs a state space equation of the inverter under the external interference signal;
under the condition of an external interference signal, the state space equation of the inverter is converted into:
（9），
Wherein, Representing external interference vectors,/>；
Control signal of inverterThe method comprises the following steps:
（10），
Wherein, And/>Is a state feedback coefficient.
Further, S203, in combination with the output feedback and the state feedback in the system, establishes an augmented state space equation of the inverter, and obtains an optimal control law equation and a feedback gain matrix;
and establishing an augmented state space equation of the inverter by combining output feedback and state feedback in the system:
（11），
Wherein, ,/>,/>,/>,/>,
,/>；
Establishing a performance index J function:
（12），
Obtaining an optimal control law by using an LQR optimal control method Equation:
（13），
where P is the semi-positive symmetric solution of the following Riccati equation:
（14），
Thus, the obtained feedback gain matrix is:
（15），
k is the obtained state feedback and resonance controller parameter.
Specifically, in step S300,
The LQR optimal control algorithm comprises the following specific steps:
for a linear steady system, the time interval is the whole In the method, three dimensions of voltage fluctuation in the operation process, energy loss of a control system and steady-state error of inverter output are comprehensively considered to obtain an optimal control lawSo that the performance index J reaches the minimum:
（16），
in the method, in the process of the invention, AndIs thatA weight matrix of a constant value of the dimension semi-positive definite symmetry,Is thatMaintaining a normal symmetric constant weight matrix;、 the start time and the end time of the control process are respectively realized;
Performance index J comprises three parts:
the method is used for limiting the output voltage fluctuation in the operation process of the inverter, namely, the requirement on the dynamic performance of the output voltage of the inverter is met;
representing the limitation of the control energy of the inverter system, namely reflecting the requirement on energy consumption;
the method represents the limitation of steady-state deviation and meets the requirement of the steady-state control precision of the output voltage of the inverter.
Referring to fig. 7, in step S400, the steps include:
In particular, the method comprises the steps of,
S401, adding a state observer, taking the input quantity and the output quantity of a controlled object as the input quantity of the observer, observing harmonic output signals of the controlled object, and establishing a controller structural block diagram, wherein the structural block diagram is shown in FIG. 8;
Further, in S402, a structure diagram of GI-ESO is built, and a state equation of quasi-resonant controller and GI-ESO is obtained;
the generalized integral extended state observer GI-ESO is introduced, a structure diagram of the GI-ESO is established, as shown in fig. 9, a quasi-resonant controller is adopted, and the expression of the quasi-resonant controller is as follows:
（17），
Wherein, As a quasi-resonant controller transfer function,/>Is a proportional gain,/>Is the bandwidth of the i times quasi-resonant controller,/>Is the resonant frequency of the i-order quasi-resonant controller;
Obtaining a state equation of the GI-ESO according to the structure diagram of the GI-ESO:
（18），
Wherein, And/>Is a state variable, u is an input,/>，/>Is the gain coefficient of GI-ESO,/>Is the estimated total interference,/>For the ith interference to be present,; Gain coefficient of observer/>。
Further, in S403, the state equation of the quasi-resonant controller and the GI-ESO are combined to obtain an estimation error and a transfer function thereof;
Combining equation (17) with equation (18) to obtain an estimated error:
（19），
the transfer functions of the disturbance estimation errors e2 and X2 are obtained through the state equation and the estimation errors of the quasi-resonant controller:
（20），
further, in S404, a fundamental frequency is selected to construct The GI-ESO state equation of the shaft current is obtained, and an overall control block diagram of the inverter is obtained;
selecting fundamental wave frequency, selecting fifth harmonic frequency and seventh harmonic frequency as selection frequency of quasi-resonance controller, and constructing GI-ESO equation of state for shaft current:
（21），
Wherein, And/>To augment state variables,/>And/>Is a variable in the augmented state variable; taking observer bandwidth as/>The gain factor of the observer is: /(I); Wherein/> 、/>Gain factor for GI-ESO;
In the case of the GI-ESO, 、/>And/>The method comprises the following steps of:
（22），
based on this, an inverter overall control block diagram is established, as shown in fig. 10.
Referring to fig. 11, the present invention further provides a system for suppressing output voltage harmonics of a three-phase inverter,
Comprising the following steps: the system comprises a coordinate system model module, a control module, an LQR algorithm module and an observer module;
the coordinate system model module is used for constructing a three-phase inverter model and a circuit topology, and based on the model, a mathematical model of the three-phase inverter under a two-phase static coordinate system is obtained by Clark transformation;
the control module is used for obtaining an optimal control law equation and a feedback gain matrix by adopting a composite control method combining PR control and state feedback control based on the mathematical model;
The LQR algorithm module is used for solving and obtaining an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm based on the feedback gain matrix;
and the observer module is used for establishing a generalized integral extended state observer GI-ESO based on the state feedback coefficient and the resonance controller parameter, controlling and counteracting the output voltage harmonic wave so as to inhibit the output voltage harmonic wave of the three-phase inverter power supply and obtaining an overall control block diagram of the inverter.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. A method for suppressing output voltage harmonics of a three-phase inverter, comprising the steps of:
S100, constructing a three-phase inverter model and circuit topology, and obtaining a mathematical model of the three-phase inverter under a two-phase static coordinate system by using Clark transformation based on the model;
s200, based on the mathematical model, an optimal control law equation and a feedback gain matrix are obtained by adopting a composite control method combining proportional resonance control and state feedback control;
s300, solving to obtain an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm based on the feedback gain matrix;
S400, utilizing the state feedback coefficient and the resonance controller parameter to combine the generalized integral extended state observer, realizing the static-difference-free tracking of the output voltage and reducing the output voltage harmonic wave.
2. The method of claim 1, wherein step S100 includes:
S101, constructing a three-phase inverter model and a structure topology, and setting model parameters;
the three-phase inverter adopts a three-phase three-wire system H-bridge inversion structure, la, lb and Lc are output filter inductors, ca, cb and Cc are filter capacitors, R is filter equivalent resistance, and the direct-current input voltage is The midpoint output voltage of the H bridge arm is/>、/>、The currents flowing through the filter inductance are respectively/>、/>、/>The filter capacitor terminal voltages are respectively/>、/>、Three-phase inverter output currents are/>, respectively、/>、/>; The filter adopts an LC filtering structure; the filter capacitors are connected in a star shape;
S102, based on the model in S101, constructing a mathematical equation of the three-phase inverter under a three-phase stationary coordinate system by adopting a kirchhoff voltage law and a kirchhoff voltage law:
（1），
（2），
wherein C is a filter capacitor, R is a filter equivalent resistor, and the DC input voltage is The midpoint output voltage of the H bridge arm is/>、/>、/>The currents flowing through the filter inductance are respectively/>、/>、/>The filter capacitor terminal voltages are respectively/>、/>、/>Three-phase inverter output currents are/>, respectively、/>、/>。
3. The method of suppressing harmonics of an output voltage of a three-phase inverter according to claim 2, wherein step S100 includes:
s103, based on a mathematical equation of the three-phase inverter under a three-phase static coordinate system, acquiring a state space equation and a model of the three-phase inverter under the three-phase static coordinate system;
arranging the formula (1) and the formula (2) to obtain a state space equation of the three-phase inverter under a three-phase static coordinate system;
（3），
The simplification of formula (3) can be obtained:
（4），
Wherein, ，/>，/>，/>，/>；
Setting output filter capacitor voltage and inductor current as state variables to obtain a state space model of the inverter:
（5），
Wherein, ，/>，/>，/>，/>，/>，/>。
4. A method for suppressing harmonics of an output voltage of a three-phase inverter according to claim 3, wherein step S100 comprises:
S104, converting a three-phase inverter state space equation into a state space equation under a two-phase static coordinate system by Clark conversion;
Establishing a coordinate system, and making The axis coincides with the a-axis, the resultant vector/>, under a three-phase stationary coordinate systemAt angular velocity/>Rotating counterclockwise; at any time/> ，/>Is projected to/>, by vector decomposition, for the included angle between the rotating voltage vector and the a-axis of the three-phase static coordinate systemOn the coordinate system, clark conversion is carried out to obtain the three-phase inverter at/>Mathematical model under coordinate system:
（6），
Wherein, ，/>，/>，/>，/>。
5. The method of claim 1, wherein step S200 includes:
S201, constructing a resonant controller expression function and a state space model thereof;
Constructing a resonance controller expression:
（7），
Wherein, For the transfer function of the resonant controller,/>And/>For the control parameters to be solved,/>Is a Laplace transform factor,/>Is angular frequency;
writing equation (7) into a state space model:
（8），
Wherein, Is a state variable of the resonance controller,/>For the output of the resonant controller,For system output/>And reference input/>Error of (2); /(I)，/>，，/>；/>Is 50Hz;
S202, constructing a state space equation of an inverter under an external interference signal based on the state space model;
under the condition of an external interference signal, the state space equation of the inverter is converted into:
（9），
Wherein, Representing external interference vectors,/>；
Control signal of inverterThe method comprises the following steps:
（10），
Wherein, And/>Is a state feedback coefficient.
6. The method of suppressing harmonics of an output voltage of a three-phase inverter according to claim 5, wherein step S200 includes:
S203, combining output feedback and state feedback in the system, establishing an augmented state space equation of the inverter, and obtaining an optimal control law equation and a feedback gain matrix;
and establishing an augmented state space equation of the inverter by combining output feedback and state feedback in the system:
（11），
Wherein, ,/>,/>,/>,/> ,
,/>；
Establishing performance indexFunction:
（12），
Obtaining an optimal control law by using an LQR optimal control method Equation:
（13），
where P is the semi-positive symmetric solution of the following Riccati equation:
（14），
Thus, the obtained feedback gain matrix is:
（15），
k is the obtained state feedback and resonance controller parameter.
7. The method of claim 1, wherein, in step S300,
The LQR optimal control algorithm comprises the following specific steps:
for a linear steady system, the time interval is the whole In the process, three dimensions of voltage fluctuation in the operation process, energy loss of a control system and steady-state error of inverter output are comprehensively considered to obtain the optimal control law/>So that the performance index J reaches the minimum:
（16），
in the method, in the process of the invention, And/>For/>Wiener semi-positive symmetric constant value weight matrix,/>Is/>Maintaining a normal symmetric constant weight matrix; /(I)、/>The start time and the end time of the control process are respectively realized;
Performance index J comprises three parts:
the method is used for limiting the output voltage fluctuation in the operation process of the inverter, namely, the requirement on the dynamic performance of the output voltage of the inverter is met;
representing the limitation of the control energy of the inverter system, namely reflecting the requirement on energy consumption;
the method represents the limitation of steady-state deviation and meets the requirement of the steady-state control precision of the output voltage of the inverter.
8. The method of claim 1 to 7, wherein, in step S400,
S401, adding a state observer, taking the input quantity and the output quantity of a controlled object as the input quantity of the observer, observing harmonic output signals of the controlled object, and establishing a controller structural block diagram;
S402, a structure diagram of the GI-ESO is established, and a state equation of the quasi-resonance controller and the GI-ESO is obtained;
Introducing a generalized integral extended state observer GI-ESO, establishing a structure diagram of the GI-ESO, and adopting a quasi-resonance controller:
（17），
Wherein, As a quasi-resonant controller transfer function,/>Is a proportional gain,/>Is the bandwidth of the i times quasi-resonant controller,/>Is the resonant frequency of the i-order quasi-resonant controller;
Obtaining a state equation of the GI-ESO according to the structure diagram of the GI-ESO:
（18），
Wherein, And/>Is a state variable, u is an input,/>，/>For the gain factor of the GI-ESO,Is the estimated total interference,/>For the ith interference to be present,; Gain coefficient of observer/>。
9. The method of claim 8, wherein, in step S400,
S403, combining the quasi-resonance controller type and the state equation of the GI-ESO to obtain an estimated error and a transfer function thereof;
Combining equation (17) with equation (18) to obtain an estimated error:
（19），
the transfer functions of the disturbance estimation errors e2 and X2 are obtained through the state equation and the estimation errors of the quasi-resonant controller:
（20），
S404, selecting fundamental wave frequency, constructing The GI-ESO state equation of the shaft current is obtained, and an overall control block diagram of the inverter is obtained;
selecting fundamental wave frequency, selecting fifth harmonic frequency and seventh harmonic frequency as selection frequency of quasi-resonance controller, and constructing GI-ESO equation of state for shaft current:
（21），
Wherein, And/>To augment state variables,/>And/>Is a variable in the augmented state variable; taking observer bandwidth as/>The gain factor of the observer is: /(I); Wherein/> 、/>Gain factor for GI-ESO;
In the case of the GI-ESO, 、/>And/>The method comprises the following steps of:
（22），
And thereby establishes an inverter overall control block diagram.
10. A system for suppressing the harmonic wave of the output voltage of a three-phase inverter is characterized in that,
Comprising the following steps: the system comprises a coordinate system model module, a control module, an LQR algorithm module and an observer module;
the coordinate system model module is used for constructing a three-phase inverter model and a circuit topology, and based on the model, a mathematical model of the three-phase inverter under a two-phase static coordinate system is obtained by Clark transformation;
the control module is used for obtaining an optimal control law equation and a feedback gain matrix by adopting a composite control method combining PR control and state feedback control based on the mathematical model;
The LQR algorithm module is used for solving and obtaining an optimal control law, a state feedback coefficient and a resonance controller parameter through an LQR optimal control algorithm based on the feedback gain matrix;
And the observer module is used for establishing a generalized integral extended state observer GI-ESO based on the state feedback coefficient and the resonance controller parameter, and controlling and counteracting the output voltage harmonic wave so as to inhibit the three-phase inverter power supply output voltage harmonic wave.
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