CN113630006B - Nonlinear control method for direct current converter - Google Patents

Nonlinear control method for direct current converter Download PDF

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CN113630006B
CN113630006B CN202110949531.5A CN202110949531A CN113630006B CN 113630006 B CN113630006 B CN 113630006B CN 202110949531 A CN202110949531 A CN 202110949531A CN 113630006 B CN113630006 B CN 113630006B
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coordinate
converter
direct current
variable
mode
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CN113630006A (en
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郭天宇
郭琦
郭海平
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CSG Electric Power Research Institute
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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
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
    • H02M3/1582—Buck-boost converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J1/00—Circuit arrangements for dc mains or dc distribution networks
    • 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
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac 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
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac 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 with automatic control of output voltage or current, e.g. switching regulators

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Dc-Dc Converters (AREA)

Abstract

The invention discloses a nonlinear control method of a direct current converter, which comprises the steps of establishing an increasing/decreasing affine nonlinear model containing an interference variable when the direct current converter operates in an increasing/decreasing mode by selecting direct current of the direct current converter as the interference variable; solving the relative ascending/descending order and the zero ascending/descending dynamic state of the affine nonlinear ascending/descending model, and keeping the stability of the zero ascending/descending dynamic state in a preset range; and establishing a step-up/step-down nonlinear control law that the direct current converter operates in a step-up/step-down mode to output interference decoupling, and performing decoupling control on the interference quantity according to the step-up/step-down nonlinear control law. The mathematical models of the DC converter in the boosting mode and the voltage reduction mode can be subjected to accurate linearization processing, so that the stability of control is ensured; the voltage of the direct current bus can be maintained to be stable when power disturbance occurs, and the voltage quality of the direct current bus is ensured; the control performance of the direct current converter and the electric energy quality of the system are improved.

Description

Nonlinear control method for direct current converter
Technical Field
The invention relates to the technical field of direct-current power grids, in particular to a nonlinear control method of a direct-current converter.
Background
A dc converter is a power electronic device that converts dc electrical energy into controllable dc electrical energy at a voltage or current required by a load. The DC converter chops the constant DC voltage into a series of pulse voltages by fast on-off control of the power electronic device, changes the pulse width of the pulse series by controlling the change of the duty ratio to realize the adjustment of the average value of the output voltage, and obtains the DC electric energy with controllable current or voltage on the controlled load by filtering of the output filter.
The prior art adopts a traditional linear control method to be applied to a direct current converter, when the actual operation state of a system is far away from a state point selected by approximate linearization, the control performance is not ideal, and the control stability and the electric energy quality of the system are not high.
Disclosure of Invention
The nonlinear control method of the direct current converter provided by the embodiment of the invention can improve the control stability of the direct current converter and the electric energy quality of a system, and effectively improve the control performance of the direct current converter.
An embodiment of the present invention provides a method for controlling nonlinearity of a dc converter, where the method includes:
selecting direct current of a direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode;
solving a boosting relative order and a boosting zero dynamic state of the boosting affine nonlinear model, and keeping the stability of the boosting zero dynamic state in a preset range;
and establishing a boost nonlinear control law that the direct current converter operates in a boost mode to output interference decoupling, and performing decoupling control on the interference amount according to the boost nonlinear control law.
Preferably, the selecting the direct current of the dc converter as an interference variable, and establishing a boost affine nonlinear model containing the interference variable when the dc converter operates in a boost mode specifically includes:
selecting the direct current of the direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode:
Figure BDA0003217897250000021
Figure BDA0003217897250000022
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is the second state variable in the X coordinate,
Figure BDA0003217897250000024
is the derivative of the state variable in the X coordinate, u1Is a control variable p in the X coordinate when the DC converter is operated in a boost mode1Is the disturbance variable y of the DC converter in boost mode in X coordinate1Is the output variable, f, of the DC converter in the boost mode in the X coordinate1(x) For the vector field, g, of the DC converter operating in boost mode directly related to the state variable in X coordinate1(x) For a vector field, D, of the DC converter operating in boost mode directly related to the control variable in X coordinate1(x) For a vector field, h, of the direct-current converter operating in boost mode which is directly related to the disturbance variable in the X coordinate1(x) For a vector field, u, of the DC converter operating in boost mode directly related to the output variable in X coordinateESIs the voltage on the DC supply side of the DC converter iELSIs the inductive current of the DC power supply side udcA DC bus voltage to which the DC converter is connected iE0SThe current flowing into the direct current bus; l isdcIs an inductor at the DC power supply side; cdcIs a DC bus capacitor; d1A duty cycle for a boost mode of operation of the DC converter;
Figure BDA0003217897250000023
is the reference value of the inductive current on the direct current power supply side.
Preferably, the solving of the boost relative order and the boost zero dynamics of the boost affine nonlinear model and the keeping of the stability of the boost zero dynamics within a preset range specifically includes:
computing lie derivatives of the boosted affine nonlinear model
Figure BDA0003217897250000031
Solving the boosting relative order of the boosting affine nonlinear model to be 1, and carrying out coordinate transformation
Figure BDA0003217897250000032
According to
Figure BDA0003217897250000033
Solving for η1(x)＝udc；
From non-singular Jacobian matrices
Figure BDA0003217897250000034
Solving for
Figure BDA0003217897250000035
Get z1Solving to obtain the boosting zero dynamic of the boosting affine nonlinear model
Figure BDA0003217897250000036
Controlling the voltage of the direct current bus by a constant voltage control method, and keeping the boosting zero dynamic stability in a preset range;
wherein the content of the first and second substances,
Figure BDA0003217897250000037
to find h1(x) For g1(x) The derivative of the lie of (a),
Figure BDA0003217897250000038
to seek
Figure BDA0003217897250000039
To f1(x) Derivative of lie of, [ phi ]1(x) Is the local differential homomorphism of the direct current converter in the boosting mode under the X coordinate,
Figure BDA00032178972500000310
is phi1(x) X is a state variable in the X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, z1Is the state variable, eta, of the DC converter in Z coordinate when the DC converter is in boost mode1The variable is a dimension-increasing state variable when the direct current converter operates in a boost mode under a Z coordinate;
Figure BDA00032178972500000313
the derivative of the dimension-increasing state variable when the direct current converter operates in a boost mode under the Z coordinate is obtained; h is1(x) A vector field which is directly related to an output variable under an X coordinate when the direct current converter operates in a boosting mode; f. of1(x) A vector field which is directly related to a state variable under an X coordinate when the direct current converter operates in a boosting mode; g1(x) A vector field which is directly related to a control variable under an X coordinate when the direct current converter operates in a boosting mode; eta1(x) The method comprises the steps that an dimension-increasing state variable when the direct current converter operates in a boosting mode under an X coordinate is obtained; u. ofESIs the voltage of the DC power supply side of the DC converter;
Figure BDA00032178972500000311
is the inductive current of the direct current power supply side; u. ofdcThe direct current bus voltage of the direct current converter; cdcIs a DC bus capacitor;
Figure BDA00032178972500000312
is the reference value of the inductive current on the direct current power supply side.
Preferably, the establishing of a boost nonlinear control law that the dc converter operates in a boost mode to output interference decoupling, and performing decoupling control of the output quantity to the interference quantity according to the boost nonlinear control law specifically include:
calculate h1(x) To D1(x) Derivative of lie
Figure BDA0003217897250000041
Calculate h1(x) To f1(x) Derivative of lie
Figure BDA0003217897250000042
Calculate h1(x) For g1(x) Derivative of lie
Figure BDA0003217897250000043
Establishing a boost nonlinear control law that the direct current converter operates in a boost mode and outputs interference decoupling
Figure BDA0003217897250000044
Decoupling control of the output quantity to the interference quantity is carried out according to the boosting nonlinear control law;
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, f1(x) For the vector field, g, of the DC converter operating in boost mode directly related to the state variable in X coordinate1(x) For a vector field, D, of the DC converter operating in boost mode directly related to the control variable in X coordinate1(x) For a vector field, h, of the direct-current converter operating in boost mode which is directly related to the disturbance variable in the X coordinate1(x) For a vector field, u, of the DC converter operating in boost mode directly related to the output variable in X coordinateESIs the voltage on the dc supply side of the dc converter,
Figure BDA0003217897250000045
is the inductive current of the DC power supply side udcIs the DC bus voltage, L, of the DC converterdcIs a DC power supply side inductor, CdcIs a DC bus capacitor u1(x) Outputting a non-linear control law, z, decoupled from disturbances for the DC converter operating in boost mode1And the state variable of the direct current converter in the boosting mode under the Z coordinate is shown, R is a weight matrix of the state variable under the X coordinate, and P is a solution of a Riccati equation under the X coordinate.
Another embodiment of the present invention provides a method for controlling nonlinearity of a dc converter, including:
selecting direct current of a direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode;
solving a voltage reduction relative order and a voltage reduction zero dynamic of the voltage reduction affine nonlinear model, and keeping the stability of the voltage reduction zero dynamic in a preset range;
and establishing a voltage reduction nonlinear control law of the output of the direct current converter for decoupling the interference in a voltage reduction mode, and performing decoupling control on the interference by the output quantity according to the voltage reduction nonlinear control law.
Preferably, the selecting the direct current of the dc converter as an interference variable, and establishing a step-down affine nonlinear model containing the interference variable when the dc converter operates in a step-down mode specifically includes:
selecting the direct current of the direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode:
Figure BDA0003217897250000051
Figure BDA0003217897250000052
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is the second state variable in the X coordinate,
Figure BDA0003217897250000053
is the derivative of the state variable in the X coordinate, u2Is the control variable, p, of the DC converter in the buck mode in X coordinate2Is the disturbance variable y in the X coordinate when the DC converter is operated in the buck mode2Is the output variable, f, of the DC converter in the buck mode in X coordinate2(x) For direct correlation of the state variable in the X coordinate when the DC converter is operating in buck modeVector field, g2(x) For the vector field, D, of the DC converter operating in buck mode in direct relation to the control variable in the X coordinate2(x) For a vector field, h, of the direct-current converter operating in buck mode, which is directly related to the disturbance variable in the X coordinate2(x) For a vector field, u, of direct correlation with the output variable in the X coordinate when the DC converter is operating in buck modeESIs the voltage on the dc supply side of the dc converter,
Figure BDA0003217897250000061
is the inductive current of the DC power supply side udcA dc bus voltage to which the dc converter is connected,
Figure BDA0003217897250000062
the current flowing into the direct current bus; l isdcIs an inductor at the DC power supply side; cdcIs a DC bus capacitor; d2A duty cycle for a buck mode of operation of the dc converter;
Figure BDA0003217897250000063
is the reference value of the inductive current on the direct current power supply side.
Preferably, the solving of the voltage reduction relative order and the voltage reduction zero dynamics of the voltage reduction affine nonlinear model and the keeping of the stability of the voltage reduction zero dynamics in a preset range specifically includes:
computing the lie derivative of the reduced-pressure affine nonlinear model
Figure BDA0003217897250000064
Solving the voltage reduction relative order of the voltage reduction affine nonlinear model to be 1, and carrying out coordinate transformation
Figure BDA0003217897250000065
According to
Figure BDA0003217897250000066
Solving for η2(x)＝udc；
From non-singular Jacobian matrices
Figure BDA0003217897250000067
Solving for
Figure BDA0003217897250000068
Get z1Solving to obtain the decompression zero dynamic of the decompression affine nonlinear model
Figure BDA0003217897250000069
Controlling the voltage of the direct current bus by a constant voltage control method, and keeping the dynamic stability of the voltage reduction zero in a preset range;
wherein the content of the first and second substances,
Figure BDA00032178972500000610
to find h2(x) For g2(x) The derivative of the lie of (a),
Figure BDA00032178972500000611
to seek
Figure BDA00032178972500000612
To f2(x) Derivative of lie of, [ phi ]2(x) Is the local differential homomorphism of the DC converter in the step-down mode in the X coordinate,
Figure BDA00032178972500000613
is phi2(x) X is a state variable in the X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, z2Is the state variable, η, of the DC converter in Z coordinate when it is operating in buck mode2The method comprises the steps that an dimension increasing state variable when the direct current converter operates in a voltage reduction mode under a Z coordinate is obtained;
Figure BDA00032178972500000614
is the direct current change under Z coordinateA derivative of an upscaling state variable when the converter is operating in a buck mode; h is2(x) A vector field directly related to an output variable in an X coordinate when the DC converter operates in a buck mode; f. of2(x) A vector field directly related to a state variable in an X coordinate when the direct current converter operates in a buck mode; g2(x) A vector field directly related to a control variable in an X coordinate when the direct current converter operates in a voltage reduction mode; eta2(x) The dimension increasing state variable is the dimension increasing state variable when the direct current converter operates in a voltage reduction mode under an X coordinate; u. ofESIs the voltage of the DC power supply side of the DC converter;
Figure BDA0003217897250000071
is the inductive current of the direct current power supply side; u. ofdcThe direct current bus voltage of the direct current converter; cdcIs a DC bus capacitor;
Figure BDA0003217897250000072
is the reference value of the inductive current on the direct current power supply side.
Preferably, the establishing of a step-down nonlinear control law that the dc converter operates in a step-down mode to output interference decoupling, and performing decoupling control of the output quantity to the interference quantity according to the step-down nonlinear control law specifically includes:
calculate h2(x) To D2(x) Derivative of lie
Figure BDA0003217897250000073
Calculate h2(x) To f2(x) Derivative of lie
Figure BDA0003217897250000074
Calculate h2(x) For g2(x) Derivative of lie
Figure BDA0003217897250000075
Establishing that the DC converter operates in a buck mode to output the DC linkDisturbance decoupled buck nonlinear control law
Figure BDA0003217897250000076
Decoupling control of the output quantity to the interference quantity is carried out according to the voltage reduction nonlinear control law;
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, f2(x) For the vector field, g, of the DC converter operating in buck mode directly related to the state variable in X coordinate2(x) For the vector field, D, of the DC converter operating in buck mode in direct relation to the control variable in the X coordinate2(x) For a vector field, h, of the direct-current converter operating in buck mode, which is directly related to the disturbance variable in the X coordinate2(x) For a vector field, u, of direct correlation with the output variable in the X coordinate when the DC converter is operating in buck modeESIs the voltage on the dc supply side of the dc converter,
Figure BDA0003217897250000081
is the inductive current of the DC power supply side udcIs the DC bus voltage, L, of the DC converterdcIs a DC power supply side inductor, CdcIs a DC bus capacitor u2(x) Outputting a non-linear control law, z, decoupled from disturbances for the DC converter operating in buck mode2And the state variable of the direct current converter in the voltage reduction mode under the Z coordinate is shown, R is a weight matrix of the state variable under the X coordinate, and P is a solution of a Riccati equation under the X coordinate.
The invention provides a nonlinear control method of a direct current converter, which comprises the steps of selecting direct current of the direct current converter as an interference variable, and establishing an increasing/decreasing affine nonlinear model containing the interference variable when the direct current converter operates in an increasing/decreasing mode; solving the relative ascending/descending order and the zero ascending/descending dynamic state of the affine nonlinear ascending/descending model, and keeping the stability of the zero ascending/descending dynamic state in a preset range; and establishing a step-up/step-down nonlinear control law that the direct current converter operates in a step-up/step-down mode to output interference decoupling, and performing decoupling control on the interference quantity according to the step-up/step-down nonlinear control law. The mathematical models of the DC converter in the boosting mode and the voltage reduction mode can be subjected to accurate linearization processing, so that the stability of control is ensured; the voltage of the direct current bus can be maintained to be stable when power disturbance occurs, and the voltage quality of the direct current bus is ensured; the control performance of the direct current converter and the electric energy quality of the system are improved.
Drawings
Fig. 1 is a schematic flowchart of a nonlinear control method for a dc converter according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a topology of a dc converter according to an embodiment of the present invention;
fig. 3 is a schematic flowchart of a nonlinear control method for a dc converter according to another embodiment of the present invention;
fig. 4 is a schematic view of a topology of a dc microgrid according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a dc bus voltage curve of the dc microgrid provided in the embodiment of the present invention;
fig. 6 is a graph showing a variation of a current deviation value of the dc power supply side of the dc microgrid according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An embodiment of the present invention provides a method for controlling nonlinearity of a dc converter, and referring to fig. 1, the method is a flowchart illustrating the method for controlling nonlinearity of the dc converter according to the embodiment of the present invention, where the method includes steps S101 to S103:
s101, selecting direct current of a direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode;
s102, solving a boosting relative order and a boosting zero dynamic state of the boosting affine nonlinear model, and keeping the stability of the boosting zero dynamic state in a preset range;
s103, establishing a boost nonlinear control law that the direct current converter operates in a boost mode to output interference decoupling, and performing decoupling control on the interference amount according to the boost nonlinear control law.
In the specific implementation of the embodiment, the direct current of the direct current converter in the boost mode is selected as an interference variable, and a boost affine nonlinear model containing the interference variable is established when the direct current converter operates in the boost mode;
solving to obtain a boost relative order and a boost zero dynamic of the boost affine nonlinear model, keeping the stability of the boost zero dynamic within a preset range, and ensuring the stability of the zero dynamic so as to ensure the effectiveness of nonlinear control;
the preset range can be specifically that when the parameters of the system fluctuate, other parameters are adjusted through a calculation function of the boost zero dynamic state, so that the boost zero dynamic state is kept in the preset fluctuation range;
and establishing a boost nonlinear control law that the direct current converter operates in a boost mode to output interference decoupling, and performing decoupling control on the interference amount according to the boost nonlinear control law.
The boost zero dynamic state is solved through a boost nonlinear model containing an interference variable when the direct current transformer operates in a boost mode, the boost zero dynamic stability is kept, the effectiveness of nonlinear control is ensured, decoupling of the output quantity of a control system to the interference quantity in the boost mode of the direct current transformer is realized through an established boost nonlinear control law, and the stability of the control system is ensured.
In another embodiment provided by the present invention, the step S101 specifically includes:
selecting the direct current of the direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode:
Figure BDA0003217897250000101
Figure BDA0003217897250000102
in specific implementation of this embodiment, refer to fig. 2, which is a schematic diagram of a topology structure of a dc converter provided in this embodiment of the present invention; selecting direct current of a direct current converter when the direct current converter operates in a boosting mode as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in the boosting mode;
Figure BDA0003217897250000103
Figure BDA0003217897250000104
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is the second state variable in the X coordinate,
Figure BDA0003217897250000105
is the derivative of the state variable in the X coordinate, u1Is a control variable p in the X coordinate when the DC converter is operated in a boost mode1Is the disturbance variable y of the DC converter in boost mode in X coordinate1Is the output variable, f, of the DC converter in the boost mode in the X coordinate1(x) For the vector field, g, of the DC converter operating in boost mode directly related to the state variable in X coordinate1(x) For direct correlation of the control variable in the X coordinate when the DC converter is operating in boost modeVector field, D1(x) For a vector field, h, of the direct-current converter operating in boost mode which is directly related to the disturbance variable in the X coordinate1(x) For a vector field, u, of the DC converter operating in boost mode directly related to the output variable in X coordinateESA voltage provided to an energy storage system on a DC power supply side of the DC converter,
Figure BDA0003217897250000111
is the inductive current of the DC power supply side udcA dc bus voltage to which the dc converter is connected,
Figure BDA0003217897250000112
the current flowing into the direct current bus; l isdcIs an inductor at the DC power supply side; cdcIs a DC bus capacitor; d1A duty cycle for a boost mode of operation of the DC converter;
Figure BDA0003217897250000113
the reference values of the inductance current at the direct current power supply side are S1 and S2 which are respectively a negative phase converter valve and a positive phase converter valve of the direct current converter;
and (3) carrying out statistics on analysis of a boosting affine nonlinear model containing interference variables in the boosting mode of the direct current converter, and carrying out accurate linearization processing on a mathematical model of the direct current converter, so that the stability of a control system is ensured.
In another embodiment provided by the present invention, the step S102 specifically includes:
calculating g in the boosted affine nonlinear model1(x) To h1(x) Derivative of lie
Figure BDA0003217897250000114
The relative order of the boosted affine nonlinear model with the disturbance variables is 1 and zero dynamics exists. Selecting coordinate transformation:
Figure BDA0003217897250000115
because of η1(x) Satisfies the following conditions:
Figure BDA0003217897250000116
so solving for η1(x)＝udc. Because of the jacobian matrix
Figure BDA0003217897250000117
Comprises the following steps:
Figure BDA0003217897250000118
so the Jacobian matrix
Figure BDA0003217897250000119
Non-exotic, one can obtain:
Figure BDA00032178972500001110
get z 10, the zero dynamics of the boosted affine nonlinear model can be found as:
Figure BDA00032178972500001111
controlling the voltage of the direct current bus by a constant voltage control method, and keeping the boosting zero dynamic stability in a preset range;
wherein the content of the first and second substances,
Figure BDA0003217897250000121
to find h1(x) For g1(x) The derivative of the lie of (a),
Figure BDA0003217897250000122
to seek
Figure BDA0003217897250000123
To f1(x) Derivative of lie of, [ phi ]1(x) Is the local differential homomorphism of the direct current converter in the boosting mode under the X coordinate,
Figure BDA0003217897250000124
is phi1(x) X is a state variable in the X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, z1Is the state variable, eta, of the DC converter in Z coordinate when the DC converter is in boost mode1The variable is a dimension-increasing state variable when the direct current converter operates in a boost mode under a Z coordinate;
Figure BDA0003217897250000125
the derivative of the dimension-increasing state variable when the direct current converter operates in a boost mode under the Z coordinate is obtained; h is1(x) A vector field which is directly related to an output variable under an X coordinate when the direct current converter operates in a boosting mode; f. of1(x) A vector field which is directly related to a state variable under an X coordinate when the direct current converter operates in a boosting mode; g1(x) A vector field which is directly related to a control variable under an X coordinate when the direct current converter operates in a boosting mode; eta1(x) The method comprises the steps that an dimension-increasing state variable when the direct current converter operates in a boosting mode under an X coordinate is obtained; u. ofESIs the voltage of the DC power supply side of the DC converter;
Figure BDA0003217897250000126
is the inductive current of the direct current power supply side; u. ofdcThe direct current bus voltage of the direct current converter; cdcIs a DC bus capacitor;
Figure BDA0003217897250000127
is the reference value of the inductive current on the direct current power supply side.
Boost zero dynamic i.e. dc bus voltage u of control systemdcThe boosting zero dynamic state of the voltage-boosting circuit ensures the DC bus voltage udcIs stable, i.e. can ensureThe boosting zero dynamic stability is ensured, so that the designed nonlinear control is effective, and the stability of the boosting zero dynamic state can be ensured by controlling the voltage of the direct current bus through a constant voltage control method.
It should be noted that, in this embodiment, the dc bus voltage is controlled by a constant voltage control method to ensure the stability of the boost zero dynamic state, and in other embodiments, other manners may be adopted for control, and the control is performed by the boost zero dynamic state calculated in this embodiment, which is within the protection scope of the present invention.
In another embodiment of the present invention, the step S103 specifically includes:
by calculating h in the boosted affine nonlinear model1(x) To D1(x) Derivative of lie
Figure BDA0003217897250000128
Therefore, the direct current converter meets the design condition of a nonlinear control law of output-to-interference decoupling when operating in a boost mode;
calculate h1(x) To f1(x) Derivative of lie
Figure BDA0003217897250000131
Calculate h1(x) For g1(x) Derivative of lie
Figure BDA0003217897250000132
Establishing a boost nonlinear control law that the direct current converter operates in a boost mode and outputs interference decoupling as follows:
Figure BDA0003217897250000133
and performing decoupling control of the output quantity to the interference quantity through the boost nonlinear control law.
Wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, f1(x) Is said direct currentVector field, g, directly related to the state variable in the X coordinate when the converter is operating in boost mode1(x) For a vector field, D, of the DC converter operating in boost mode directly related to the control variable in X coordinate1(x) For a vector field, h, of the direct-current converter operating in boost mode which is directly related to the disturbance variable in the X coordinate1(x) For a vector field, u, of the DC converter operating in boost mode directly related to the output variable in X coordinateESIs the voltage on the dc supply side of the dc converter,
Figure BDA0003217897250000134
is the inductive current of the DC power supply side udcIs the DC bus voltage, L, of the DC converterdcIs a DC power supply side inductor, CdcIs a DC bus capacitor u1(x) Outputting a non-linear control law, z, decoupled from disturbances for the DC converter operating in boost mode1And the state variable of the direct current converter in the boosting mode under the Z coordinate is shown, R is a weight matrix of the state variable under the X coordinate, and P is a solution of a Riccati equation under the X coordinate.
Decoupling control of the output quantity to the interference quantity is carried out through the boost nonlinear control law, so that the voltage stability of the direct-current bus can be maintained when power disturbance occurs, and the voltage quality of the direct-current bus is ensured;
the embodiment of the invention provides a nonlinear control method of a direct current converter, which comprises the steps of selecting direct current of the direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode; solving a boosting relative order and a boosting zero dynamic state of the boosting affine nonlinear model, and keeping the stability of the boosting zero dynamic state in a preset range; and establishing a boost nonlinear control law that the direct current converter operates in a boost mode to output interference decoupling, and performing decoupling control on the interference amount according to the boost nonlinear control law. The mathematical model under the boost mode of the DC converter can be subjected to accurate linearization treatment, so that the stability of control is ensured; the voltage of the direct current bus can be maintained to be stable when power disturbance occurs, and the voltage quality of the direct current bus is ensured; the control performance of the DC converter is improved.
Fig. 3 is a schematic flow chart of a nonlinear control method for a dc converter according to another embodiment of the present invention; the method comprises steps S301-S303;
s301, selecting direct current of a direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode;
s302, solving a voltage reduction relative order and a voltage reduction zero dynamic of the voltage reduction affine nonlinear model, and keeping the stability of the voltage reduction zero dynamic within a preset range;
and S303, establishing a voltage reduction nonlinear control law for outputting interference decoupling when the direct current converter operates in a voltage reduction mode, and performing decoupling control on the interference amount by the output amount according to the voltage reduction nonlinear control law.
In the specific implementation of the embodiment, the direct current of the direct current converter in the step-down mode is selected as an interference variable, and a step-down affine nonlinear model containing the interference variable is established when the direct current converter operates in the step-down mode;
solving to obtain a voltage reduction relative order and a voltage reduction zero dynamic of the voltage reduction affine nonlinear model, keeping the stability of the voltage reduction zero dynamic within a preset range, and ensuring the stability of the zero dynamic, thereby ensuring the effectiveness of nonlinear control;
the preset range can be specifically that when the parameters of the system fluctuate, other parameters are adjusted through a calculation function of the step-down zero dynamic state, so that the step-down zero dynamic state is kept in the preset fluctuation range;
and establishing a voltage reduction nonlinear control law of the output of the direct current converter for decoupling the interference in a voltage reduction mode, and performing decoupling control on the interference by the output quantity according to the voltage reduction nonlinear control law.
The dynamic state of the step-down zero is solved through a step-down nonlinear model containing an interference variable when the direct-current transformer operates in a step-down mode, the dynamic stability of the step-down zero is kept, the effectiveness of nonlinear control is ensured, decoupling of the output quantity of the control system to the interference quantity in the step-down mode of the direct-current transformer is realized through an established step-down nonlinear control law, and the stability of the control system is ensured.
In another embodiment provided by the present invention, the step S301 specifically includes:
selecting the direct current of the direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode:
Figure BDA0003217897250000151
Figure BDA0003217897250000152
in the specific implementation of the embodiment, the direct current of the direct current converter in the step-down mode is selected as an interference variable, and a step-down affine nonlinear model containing the interference variable is established when the direct current converter operates in the step-down mode;
Figure BDA0003217897250000153
Figure BDA0003217897250000154
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is the second state variable in the X coordinate,
Figure BDA0003217897250000155
is the derivative of the state variable in the X coordinate, u2Is the control variable, p, of the DC converter in the buck mode in X coordinate2As said DC converter in X-coordinateDisturbance variable, y, while operating in buck mode2Is the output variable, f, of the DC converter in the buck mode in X coordinate2(x) For the vector field, g, of the DC converter operating in buck mode directly related to the state variable in X coordinate2(x) For the vector field, D, of the DC converter operating in buck mode in direct relation to the control variable in the X coordinate2(x) For a vector field, h, of the direct-current converter operating in buck mode, which is directly related to the disturbance variable in the X coordinate2(x) For a vector field, u, of direct correlation with the output variable in the X coordinate when the DC converter is operating in buck modeESIs the voltage on the dc supply side of the dc converter,
Figure BDA0003217897250000161
is the inductive current of the DC power supply side udcA dc bus voltage to which the dc converter is connected,
Figure BDA0003217897250000162
the current flowing into the direct current bus; l isdcIs an inductor at the DC power supply side; cdcIs a DC bus capacitor; d2A duty cycle for a buck mode of operation of the dc converter;
Figure BDA0003217897250000163
is the reference value of the inductive current on the direct current power supply side.
In another embodiment provided by the present invention, the step S302 specifically includes:
calculating g in the boosted affine nonlinear model2(x) To h2(x) Derivative of lie
Figure BDA0003217897250000164
The relative order of the affine non-linear model is 1 and zero dynamics exist. Selecting coordinate transformation:
Figure BDA0003217897250000165
because of η2(x) Satisfies the following conditions:
Figure BDA0003217897250000166
so solving for η2(x)＝udc. Because of the jacobian matrix
Figure BDA0003217897250000167
Comprises the following steps:
Figure BDA0003217897250000168
so the Jacobian matrix
Figure BDA0003217897250000169
Non-exotic, one can obtain:
Figure BDA00032178972500001610
get z2The zero dynamics of the reduced-voltage affine nonlinear model can be found as:
Figure BDA00032178972500001611
controlling the voltage of the direct current bus by a constant voltage control method, and keeping the dynamic stability of the voltage reduction zero in a preset range;
wherein the content of the first and second substances,
Figure BDA00032178972500001612
to find h2(x) For g2(x) The derivative of the lie of (a),
Figure BDA00032178972500001613
to seek
Figure BDA00032178972500001614
To f2(x) Derivative of lie of, [ phi ]2(x) Is the local differential homomorphism of the DC converter in the step-down mode in the X coordinate,
Figure BDA00032178972500001615
is phi2(x) X is a state variable in the X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, z2Is the state variable, η, of the DC converter in Z coordinate when it is operating in buck mode2The method comprises the steps that an dimension increasing state variable when the direct current converter operates in a voltage reduction mode under a Z coordinate is obtained;
Figure BDA0003217897250000171
the derivative of the dimension-increasing state variable when the direct current converter operates in a voltage reduction mode under the Z coordinate; h is2(x) A vector field directly related to an output variable in an X coordinate when the DC converter operates in a buck mode; f. of2(x) A vector field directly related to a state variable in an X coordinate when the direct current converter operates in a buck mode; g2(x) A vector field directly related to a control variable in an X coordinate when the direct current converter operates in a voltage reduction mode; eta2(x) The dimension increasing state variable is the dimension increasing state variable when the direct current converter operates in a voltage reduction mode under an X coordinate; u. ofESIs the voltage of the DC power supply side of the DC converter;
Figure BDA0003217897250000172
is the inductive current of the direct current power supply side; u. ofdcThe direct current bus voltage of the direct current converter; cdcIs a DC bus capacitor;
Figure BDA0003217897250000173
is the reference value of the inductive current on the direct current power supply side.
Step-down zero dynamic, i.e. dc bus voltage u, of a control systemdcThe step-down zero dynamic state of the voltage ensures the DC bus voltage udcThe stability can be ensured, namely the dynamic stability of the step-down zero is ensured, so that the designed nonlinear control is ensured to be effective, and the stability of the step-down zero dynamic state can be ensured by controlling the voltage of the direct current bus through a constant voltage control method.
It should be noted that, in this embodiment, the dc bus voltage is controlled by a constant voltage control method to ensure the stability of the step-down zero dynamic state, and in other embodiments, other manners may be adopted for control, and the control is performed by the step-down zero dynamic state calculated in this embodiment, which is within the protection scope of the present invention.
In another embodiment provided by the present invention, step S303 specifically includes:
by calculating h in the pressure-reducing affine nonlinear model2(x) To D2(x) Lie derivative of (c):
Figure BDA0003217897250000174
therefore, when the direct current converter operates in a voltage reduction mode, the nonlinear control law design condition of output to interference decoupling is met.
Calculate h2(x) To f2(x) Lie derivative of and h2(x) For g2(x) Lie derivative of (c):
Figure BDA0003217897250000175
the nonlinear control law of the decoupling of the output to the interference is calculated as follows:
Figure BDA0003217897250000181
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, f2(x) For the vector field, g, of the DC converter operating in buck mode directly related to the state variable in X coordinate2(x) For the vector field, D, of the DC converter operating in buck mode in direct relation to the control variable in the X coordinate2(x) For a vector field, h, of the direct-current converter operating in buck mode, which is directly related to the disturbance variable in the X coordinate2(x) For a vector field, u, of direct correlation with the output variable in the X coordinate when the DC converter is operating in buck modeESIs said direct currentThe voltage on the dc supply side of the converter,
Figure BDA0003217897250000182
is the inductive current of the DC power supply side udcIs the DC bus voltage, L, of the DC converterdcIs a DC power supply side inductor, CdcIs a DC bus capacitor u2(x) Outputting a non-linear control law, z, decoupled from disturbances for the DC converter operating in buck mode2And the state variable of the direct current converter in the voltage reduction mode under the Z coordinate is shown, R is a weight matrix of the state variable under the X coordinate, and P is a solution of a Riccati equation under the X coordinate.
Decoupling control of the output quantity to the interference quantity is carried out through the voltage reduction nonlinear control law, so that the voltage stability of the direct current bus can be maintained when power disturbance occurs, and the voltage quality of the direct current bus is ensured;
the embodiment of the invention provides a nonlinear control method of a direct current converter, which comprises the steps of selecting direct current of the direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode; solving a voltage reduction relative order and a voltage reduction zero dynamic of the voltage reduction affine nonlinear model, and keeping the stability of the voltage reduction zero dynamic in a preset range; and establishing a voltage reduction nonlinear control law of the output of the direct current converter for decoupling the interference in a voltage reduction mode, and performing decoupling control on the interference by the output quantity according to the voltage reduction nonlinear control law. The mathematical model under the voltage reduction mode of the DC converter can be subjected to accurate linearization treatment, so that the stability of control is ensured; the voltage of the direct current bus can be maintained to be stable when power disturbance occurs, and the voltage quality of the direct current bus is ensured; the control performance of the DC converter is improved.
In another embodiment provided by the present invention, a simulation model of the dc converter is set up with reference to fig. 4, which is a schematic diagram of a topology structure of the dc microgrid provided by the embodiment of the present invention; the alternating current bus of the alternating current micro-grid is connected with the direct current bus of the direct current micro-grid through the AC/DC converter. The rated value of the voltage of the direct current bus is 560V, the capacitance of the direct current bus is 2000uF, the inductance L of the direct current power supply side is 1mL, the direct current load is 70kW, and S1 and S2 are respectively a negative phase converter valve and a positive phase converter valve of the direct current converter.
Before 2 seconds, the system is in steady state operation, the direct current load is 70kW, and at 2 seconds, the direct current side is cut off by 20 kW.
Referring to fig. 5, which is a schematic diagram of a dc bus voltage curve of the dc microgrid provided in the embodiment of the present invention, when a load on a dc side is reduced by 20kW, a PI is used to control the dc bus voltage to increase by 7V, and when the nonlinear control method of the dc converter provided in the present invention is used, the dc bus voltage increases by 2.5V. Compared with PI control, the nonlinear control method of the direct current converter provided by the embodiment can enable the overshoot of the direct current bus voltage to be smaller, and can recover to steady-state operation more quickly. Namely, the system has better dynamic response performance under the nonlinear control of the direct current converter with output quantity decoupled from disturbance quantity.
Before 2 seconds, the system is in steady state operation, the direct current load is 70kW, and at 2 seconds, the direct current side is cut off by 20 kW.
Referring to fig. 6, it is a graph of a variation of a current deviation value at a dc power supply side of the dc micro-grid provided in the embodiment of the present invention, where the u current deviation value is a difference between an inductive current reference value at the dc power supply side and an inductive current at the dc power supply side; when the load on the DC side is reduced by 20kW, the reference value of the inductive current on the DC power supply side
Figure BDA0003217897250000191
Inductive current with DC power supply side
Figure BDA0003217897250000192
Difference of (2)
Figure BDA0003217897250000193
When the direct current load has step disturbance, the direct current load does not change, decoupling of the output quantity to the disturbance quantity is realized, and therefore the control system has excellent dynamic response performance.
The invention provides a nonlinear control method of a direct current converter, which comprises the steps of selecting direct current of the direct current converter as an interference variable, and establishing an increasing/decreasing affine nonlinear model containing the interference variable when the direct current converter operates in an increasing/decreasing mode; solving the relative ascending/descending order and the zero ascending/descending dynamic state of the affine nonlinear ascending/descending model, and keeping the stability of the zero ascending/descending dynamic state in a preset range; and establishing a step-up/step-down nonlinear control law that the direct current converter operates in a step-up/step-down mode to output interference decoupling, and performing decoupling control on the interference quantity according to the step-up/step-down nonlinear control law. The mathematical models of the DC converter in the boosting mode and the voltage reduction mode can be subjected to accurate linearization processing, so that the stability of control is ensured; the voltage of the direct current bus can be maintained to be stable when power disturbance occurs, and the voltage quality of the direct current bus is ensured; the control performance of the direct current converter and the electric energy quality of the system are improved.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (6)

1. A method for nonlinear control of a dc converter, the method comprising:
selecting direct current of a direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode;
solving a boosting relative order and a boosting zero dynamic state of the boosting affine nonlinear model, and keeping the stability of the boosting zero dynamic state in a preset range;
establishing a boosting nonlinear control law that the direct current converter operates in a boosting mode and outputs decoupling to the interference variable, and performing decoupling control on the interference variable by the output quantity according to the boosting nonlinear control law;
solving a boost relative order and a boost zero dynamic of the boost affine nonlinear model, and keeping the stability of the boost zero dynamic within a preset range specifically comprises:
calculating the boost affineLie derivatives of non-linear models
Figure FDA0003523691070000011
Solving the boosting relative order of the boosting affine nonlinear model to be 1, and carrying out coordinate transformation
Figure FDA0003523691070000012
According to
Figure FDA0003523691070000013
Solving for η1(x)＝udc；
From non-singular Jacobian matrices
Figure FDA0003523691070000014
Solving for
Figure FDA0003523691070000015
Get z1Solving to obtain the boosting zero dynamic of the boosting affine nonlinear model
Figure FDA0003523691070000016
Controlling the voltage of the direct current bus by a constant voltage control method, and keeping the boosting zero dynamic stability in a preset range;
wherein the content of the first and second substances,
Figure FDA0003523691070000017
to find h1(x) For g1(x) The derivative of the lie of (a),
Figure FDA0003523691070000018
to seek
Figure FDA0003523691070000019
To f1(x) Derivative of lie of, [ phi ]1(x) Is the local differential homomorphism of the direct current converter in the boosting mode under the X coordinate,
Figure FDA00035236910700000110
is phi1(x) X is a state variable in the X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, z1Is the state variable, eta, of the DC converter in Z coordinate when the DC converter is in boost mode1The variable is a dimension-increasing state variable when the direct current converter operates in a boost mode under a Z coordinate;
Figure FDA0003523691070000021
the derivative of the dimension-increasing state variable when the direct current converter operates in a boost mode under the Z coordinate is obtained; h is1(x) A vector field which is directly related to an output variable under an X coordinate when the direct current converter operates in a boosting mode; f. of1(x) A vector field which is directly related to a state variable under an X coordinate when the direct current converter operates in a boosting mode; g1(x) A vector field which is directly related to a control variable under an X coordinate when the direct current converter operates in a boosting mode; eta1(x) The method comprises the steps that an dimension-increasing state variable when the direct current converter operates in a boosting mode under an X coordinate is obtained; u. ofESIs the voltage of the DC power supply side of the DC converter;
Figure FDA0003523691070000022
is the inductive current of the direct current power supply side; u. ofdcThe direct current bus voltage of the direct current converter; cdcIs a DC bus capacitor;
Figure FDA0003523691070000023
is the reference value of the inductive current on the direct current power supply side.
2. The method according to claim 1, wherein the selecting a dc current of the dc converter as an interference variable and establishing a boost affine nonlinear model containing the interference variable when the dc converter operates in a boost mode specifically comprises:
selecting the direct current of the direct current converter as an interference variable, and establishing a boosting affine nonlinear model containing the interference variable when the direct current converter operates in a boosting mode:
Figure FDA0003523691070000024
Figure FDA0003523691070000025
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is the second state variable in the X coordinate,
Figure FDA0003523691070000026
is the derivative of the state variable in the X coordinate, u1Is a control variable p in the X coordinate when the DC converter is operated in a boost mode1Is the disturbance variable y of the DC converter in boost mode in X coordinate1Is the output variable, f, of the DC converter in the boost mode in the X coordinate1(x) For the vector field, g, of the DC converter operating in boost mode directly related to the state variable in X coordinate1(x) For a vector field, D, of the DC converter operating in boost mode directly related to the control variable in X coordinate1(x) For a vector field, h, of the direct-current converter operating in boost mode which is directly related to the disturbance variable in the X coordinate1(x) For a vector field, u, of the DC converter operating in boost mode directly related to the output variable in X coordinateESIs the voltage on the dc supply side of the dc converter,
Figure FDA0003523691070000031
is the inductive current of the DC power supply side udcA dc bus voltage to which the dc converter is connected,
Figure FDA0003523691070000032
the current flowing into the direct current bus; l isdcIs an inductor at the DC power supply side; cdcIs a DC bus capacitor; d1A duty cycle for a boost mode of operation of the DC converter;
Figure FDA0003523691070000033
is the reference value of the inductive current on the direct current power supply side.
3. The method according to claim 1, wherein the establishing of the boost nonlinear control law that the dc converter operates in a boost mode and outputs a decoupling control on the disturbance variable, and the decoupling control on the disturbance variable by the output quantity according to the boost nonlinear control law specifically includes:
calculate h1(x) To D1(x) Derivative of lie
Figure FDA0003523691070000034
Calculate h1(x) To f1(x) Derivative of lie
Figure FDA0003523691070000035
Calculate h1(x) For g1(x) Derivative of lie
Figure FDA0003523691070000036
Establishing a boost nonlinear control law that the direct current converter operates in a boost mode and outputs decoupling to interference variables
Figure FDA0003523691070000041
Decoupling control of the output quantity to the interference variable is carried out according to the boosting nonlinear control law;
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, f1(x) For the vector field, g, of the DC converter operating in boost mode directly related to the state variable in X coordinate1(x) For a vector field, D, of the DC converter operating in boost mode directly related to the control variable in X coordinate1(x) For a vector field, h, of the direct-current converter operating in boost mode which is directly related to the disturbance variable in the X coordinate1(x) For a vector field, u, of the DC converter operating in boost mode directly related to the output variable in X coordinateESIs the voltage on the dc supply side of the dc converter,
Figure FDA0003523691070000042
is the inductive current of the DC power supply side udcIs the DC bus voltage, L, of the DC converterdcIs a DC power supply side inductor, CdcIs a DC bus capacitor u1(x) A non-linear control law, z, for decoupling the output of the disturbance variable when the DC converter is operating in boost mode1And the state variable of the direct current converter in the boosting mode under the Z coordinate is shown, R is a weight matrix of the state variable under the X coordinate, and P is a solution of a Riccati equation under the X coordinate.
4. A method for nonlinear control of a dc converter, the method comprising:
selecting direct current of a direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode;
solving a voltage reduction relative order and a voltage reduction zero dynamic of the voltage reduction affine nonlinear model, and keeping the stability of the voltage reduction zero dynamic in a preset range;
establishing a voltage reduction nonlinear control law that the direct current converter operates in a voltage reduction mode and outputs decoupling to an interference variable, and performing decoupling control on the interference variable according to the voltage reduction nonlinear control law;
solving the voltage reduction relative order and the voltage reduction zero dynamic of the voltage reduction affine nonlinear model, and keeping the stability of the voltage reduction zero dynamic within a preset range specifically comprises:
computing the lie derivative of the reduced-pressure affine nonlinear model
Figure FDA0003523691070000051
Solving the voltage reduction relative order of the voltage reduction affine nonlinear model to be 1, and carrying out coordinate transformation
Figure FDA0003523691070000052
According to
Figure FDA0003523691070000053
Solving for η2(x)＝udc；
From non-singular Jacobian matrices
Figure FDA0003523691070000054
Solving for
Figure FDA0003523691070000055
Get z1Solving to obtain the decompression zero dynamic of the decompression affine nonlinear model
Figure FDA0003523691070000056
Controlling the voltage of the direct current bus by a constant voltage control method, and keeping the dynamic stability of the voltage reduction zero in a preset range;
wherein the content of the first and second substances,
Figure FDA0003523691070000057
to find h2(x) For g2(x) The derivative of the lie of (a),
Figure FDA0003523691070000058
to seek
Figure FDA0003523691070000059
To f2(x) Derivative of lie of, [ phi ]2(x) Is the local differential homomorphism of the DC converter in the step-down mode in the X coordinate,
Figure FDA00035236910700000510
is phi2(x) X is a state variable in the X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, z2Is the state variable, η, of the DC converter in Z coordinate when it is operating in buck mode2The method comprises the steps that an dimension increasing state variable when the direct current converter operates in a voltage reduction mode under a Z coordinate is obtained;
Figure FDA00035236910700000511
the derivative of the dimension-increasing state variable when the direct current converter operates in a voltage reduction mode under the Z coordinate; h is2(x) A vector field directly related to an output variable in an X coordinate when the DC converter operates in a buck mode; f. of2(x) A vector field directly related to a state variable in an X coordinate when the direct current converter operates in a buck mode; g2(x) A vector field directly related to a control variable in an X coordinate when the direct current converter operates in a voltage reduction mode; eta2(x) The dimension increasing state variable is the dimension increasing state variable when the direct current converter operates in a voltage reduction mode under an X coordinate; u. ofESIs the voltage of the DC power supply side of the DC converter;
Figure FDA00035236910700000512
is the inductive current of the direct current power supply side; u. ofdcThe direct current bus voltage of the direct current converter; cdcIs a DC bus capacitor;
Figure FDA0003523691070000061
is the reference value of the inductive current on the direct current power supply side.
5. The method according to claim 4, wherein the selecting the dc current of the dc converter as the disturbance variable and establishing the step-down affine nonlinear model containing the disturbance variable when the dc converter operates in the step-down mode specifically comprises:
selecting the direct current of the direct current converter as an interference variable, and establishing a voltage reduction affine nonlinear model containing the interference variable when the direct current converter operates in a voltage reduction mode:
Figure FDA0003523691070000062
Figure FDA0003523691070000063
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is the second state variable in the X coordinate,
Figure FDA0003523691070000064
is the derivative of the state variable in the X coordinate, u2Is the control variable, p, of the DC converter in the buck mode in X coordinate2Is the disturbance variable y in the X coordinate when the DC converter is operated in the buck mode2Is the output variable, f, of the DC converter in the buck mode in X coordinate2(x) For the vector field, g, of the DC converter operating in buck mode directly related to the state variable in X coordinate2(x) For the DC converter to operate inVector field directly related to the control variable in X coordinate in buck mode, D2(x) For a vector field, h, of the direct-current converter operating in buck mode, which is directly related to the disturbance variable in the X coordinate2(x) For a vector field, u, of direct correlation with the output variable in the X coordinate when the DC converter is operating in buck modeESIs the voltage on the dc supply side of the dc converter,
Figure FDA0003523691070000065
is the inductive current of the DC power supply side udcA dc bus voltage to which the dc converter is connected,
Figure FDA0003523691070000071
the current flowing into the direct current bus; l isdcIs an inductor at the DC power supply side; cdcIs a DC bus capacitor; d2A duty cycle for a buck mode of operation of the dc converter;
Figure FDA0003523691070000072
is the reference value of the inductive current on the direct current power supply side.
6. The method according to claim 4, wherein the establishing of the step-down nonlinear control law that the dc converter operates in the step-down mode and outputs the decoupling of the disturbance variable, and the performing of the decoupling control of the output quantity to the disturbance variable according to the step-down nonlinear control law specifically comprises:
calculate h2(x) To D2(x) Derivative of lie
Figure FDA0003523691070000073
Calculate h2(x) To f2(x) Derivative of lie
Figure FDA0003523691070000074
Calculate h2(x) For g2(x) Derivative of lie
Figure FDA0003523691070000075
Establishing a step-down nonlinear control law of output-to-interference variable decoupling when the DC converter operates in a step-down mode
Figure FDA0003523691070000076
Decoupling control of output quantity to interference variables is carried out according to the voltage reduction nonlinear control law;
wherein X is a state variable in X coordinate, X1Is the first state variable in the X coordinate, X2Is a second state variable in the X coordinate, f2(x) For the vector field, g, of the DC converter operating in buck mode directly related to the state variable in X coordinate2(x) For the vector field, D, of the DC converter operating in buck mode in direct relation to the control variable in the X coordinate2(x) For a vector field, h, of the direct-current converter operating in buck mode, which is directly related to the disturbance variable in the X coordinate2(x) For a vector field, u, of direct correlation with the output variable in the X coordinate when the DC converter is operating in buck modeESIs the voltage on the dc supply side of the dc converter,
Figure FDA0003523691070000081
is the inductive current of the DC power supply side udcIs the DC bus voltage, L, of the DC converterdcIs a DC power supply side inductor, CdcIs a DC bus capacitor u2(x) A non-linear control law, z, for decoupling the output of the disturbance variable when the DC converter is operating in buck mode2And the state variable of the direct current converter in the voltage reduction mode under the Z coordinate is shown, R is a weight matrix of the state variable under the X coordinate, and P is a solution of a Riccati equation under the X coordinate.
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CN113036797A (en) * 2021-03-11 2021-06-25 天津大学 Direct power control method and device for multi-level converter

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