CN111555627B - Control method of high-order LCLCL direct current converter - Google Patents

Control method of high-order LCLCL direct current converter Download PDF

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CN111555627B
CN111555627B CN202010384741.XA CN202010384741A CN111555627B CN 111555627 B CN111555627 B CN 111555627B CN 202010384741 A CN202010384741 A CN 202010384741A CN 111555627 B CN111555627 B CN 111555627B
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equation
component
current
transformer
small signal
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CN111555627A (en
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戴明聪
张相军
管乐诗
王懿杰
徐殿国
袁佳音
孙宇豪
井嘉晨
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Harbin Institute of Technology
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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
    • H02M3/22—Conversion of dc power input into dc power output with intermediate conversion into ac
    • H02M3/24—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters
    • H02M3/28—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac
    • H02M3/325—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal
    • H02M3/335—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/33569—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only having several active switching elements
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters
    • H02M1/083—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters for the ignition at the zero crossing of the voltage or the current
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters
    • H02M1/088—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters for the simultaneous control of series or parallel connected semiconductor devices
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/14—Arrangements for reducing ripples from dc input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/36—Means for starting or stopping converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0048—Circuits or arrangements for reducing losses
    • H02M1/0054—Transistor switching losses
    • H02M1/0058—Transistor switching losses by employing soft switching techniques, i.e. commutation of transistors when applied voltage is zero or when current flow is zero
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

Abstract

A control method of a high-order LCLCLCL direct current converter belongs to the technical field of direct current converter control. The invention aims at the problem that the existing control method of the power converter is not suitable for an LCLCLCL high-order system. The method comprises the following steps: performing circuit transformation on the high-order LCLCLCL direct current converter to obtain an equivalent circuit; writing a nonlinear time-varying equation according to the equivalent circuit column; introducing an extended description function into the nonlinear time-varying equation to obtain an extended description time-varying equation; carrying out harmonic approximation on the extended description time-varying equation to obtain a steady-state working point equation of a nonlinear time-varying equation; adding disturbance to the steady-state operating point equation to obtain a small-signal steady-state operating point equation; then linearizing the small-signal steady-state working point equation to obtain a harmonic equation; and establishing a state space model according to the harmonic equation, and further obtaining a small signal model. The invention can ensure that the converter obtains satisfactory dynamic characteristics under different input voltages and load conditions.

Description

Control method of high-order LCLCL direct current converter
Technical Field
The invention relates to a control method of a high-order LCLCLCL direct current converter, belonging to the technical field of direct current converter control.
Background
In the field of DC/DC power converters, the power density and the efficiency of a power supply are two important indexes for evaluating the performance of the power supply. The efficiency of the switching power supply can be improved by improving the switching frequency of the converter, but the switching loss is greatly increased due to the increase of the switching frequency, and the efficiency is also greatly reduced along with the increase of the frequency, so that the high-frequency DC/DC power converter mostly adopts an LC resonance mode to realize the working state of soft switching, thereby eliminating the switching loss and improving the working efficiency of the power converter.
In a certain frequency range, the switching frequency of the power converter is changed in the existing LLC resonant converter, so that the soft switching state is not affected, and different gains are obtained at the same time, thereby ensuring that the output voltage can maintain a stable state and a higher conversion efficiency when the input voltage or load changes. But the frequency modulation range is limited, the loss of the diode is large due to large secondary side current, and the excellent soft start and overcurrent protection scheme is not provided, so that the application range is limited.
In the process of converting an input voltage and generating an output voltage by a DC/DC power converter, a certain control means is required to be combined to ensure that the DC/DC power converter can obtain satisfactory dynamic characteristics under different input voltages and different load conditions.
The existing control method for the power converter comprises the following steps: firstly, modeling is carried out based on a converter, and then control is realized based on the model. For the resonant converter, due to time domain variability, modeling methods such as a state space average method are not applicable, and then a simplified resonant modeling method is provided, namely an equivalent model of resonant capacitance and resonant inductance is established. The modeling method can obtain a rough small-signal model of the resonant converter, but the modeling result is not accurate, and particularly for a high-order LCLCLCL direct current converter, the error exceeds the fault tolerance range.
In addition, the control of the power converter also includes proportional integral control and PID control. Conventional proportional-integral (PI) control has difficulty in achieving satisfactory converter dynamics at different input voltages and under different load conditions. Even a very perfect PI parameter cannot guarantee that the down-converter has a good phase margin in different operating regions. Especially for the LCLCLCL high-order system, neither PI nor PID control can ensure that the system has enough phase margin and DC gain value.
Disclosure of Invention
The invention provides a control method of a high-order LCL direct current converter, aiming at the problem that the existing control method of a power converter is not suitable for an LCLCL high-order system.
The invention discloses a control method of a high-order LCLCLCL direct current converter, which comprises a switching tube S 1 And a switch tube S 2 Resonant capacitor C r Resonant inductor L r Transformer T, band-stop filter inductance L s Band elimination filter capacitor C s Diode D 1 Diode D 2 And an output capacitor C f ，
Band elimination filter inductance L s And a band-stop filter capacitor C s Are connected in parallel to form a band elimination filter;
switch tube S 1 Is connected with a power supply V in Positive electrode of (2), switching tube S 1 Source electrode of S is connected with a switch tube S 2 Of the drain electrode, the switching tube S 2 Is connected with a power supply V in The negative electrode of (1); resonant capacitor C r Resonant inductor L r The primary side of the transformer T and the band elimination filter are sequentially connected in series with a switching tube S 2 Between the drain and the source;
one end of the secondary side of the transformer T is connected with a diode D 1 Anode of (2), diode D 1 Cathode of (D) is connected with a diode 2 Cathode of (2), diode D 2 The anode of the transformer is connected with the other end of the secondary side of the transformer T; middle tap and diode D of transformer T secondary side 2 Is connected with an output capacitor C f (ii) a Output capacitor C f And a load resistance R L Are connected in parallel;
the control method comprises the following steps of establishing a small signal model:
performing circuit transformation on the high-order LCLCLCL direct current converter to obtain an equivalent circuit; writing a nonlinear time-varying equation according to the equivalent circuit column;
introducing an extended description function into the nonlinear time-varying equation to obtain an extended description time-varying equation; carrying out harmonic approximation on the extended description time-varying equation to obtain a steady-state working point equation of a nonlinear time-varying equation; adding disturbance to the steady-state operating point equation to obtain a small-signal steady-state operating point equation; then linearizing the steady-state working point equation of the small signal to obtain a harmonic equation;
and establishing a state space model according to the harmonic equation, and further obtaining a small signal model.
According to the control method of the high-order LCLCLCL direct current converter, the control method further comprises the following steps:
obtaining a small signal transfer function based on the small signal model; factorizing the small signal transfer function to obtain a plurality of zeros and poles, removing high-frequency zeros and poles and similar zeros and poles, and reserving the rest zeros and poles as reference zeros and reference poles; drawing a bode diagram of a small signal transfer function by the reference zero and the reference pole; designing a compensator by adopting a four-pole four-zero method based on a bode diagram of a small signal transfer function; and finally, the high-order LCLCLCL direct current converter is controlled through a compensator.
The invention has the beneficial effects that: the method comprises the steps of firstly establishing a small signal model of the LCLCL converter, writing a nonlinear time-varying equation in a column by adopting an Extended Description Function (EDF) modeling method, carrying out harmonic approximation, introducing the extended description function, acquiring a steady-state working point, increasing disturbance, linearizing a harmonic equation and finally establishing a state space model.
The method is realized based on the characteristic that the LCLCLCL direct current converter has a zero gain point, and can excellently realize soft start and overcurrent protection of the LCLCL direct current converter. The method is based on a small signal model, and the resistance of the converter to different interferences is explored; based on the established small signal model, the compensator can be further designed, so that the relation between the dynamic response speed and the stability of the LCLCLCL converter is balanced, and the satisfactory dynamic characteristics of the converter under different input voltages and different load conditions are obtained.
Drawings
FIG. 1 is a flow chart of a method of controlling a high order LCLCLCL DC converter according to the present invention;
FIG. 2 is a circuit block diagram of the high order LCLCLCL DC converter;
FIG. 3 is an equivalent circuit diagram of the high order LCLCLCL DC converter;
FIG. 4 is a diagram of a large signal model;
FIG. 5 is a plot of the transfer function of the pole-zero distribution in a particular embodiment;
FIG. 6 is a Bode plot of an acquisition based on a small signal transfer function;
FIG. 7 is a system block diagram of a compensator;
FIG. 8 is a new Bode plot compensated by a compensator for the Bode plot of FIG. 6;
FIG. 9 is a flow chart for implementing control of a high order LCLCL DC converter by a compensator;
FIG. 10 is a waveform of the dynamic response under compensator control when the load in the DC converter is reduced from 12.1A to 2.07A;
FIG. 11 is a waveform of the dynamic response under compensator control when the load in the DC converter rises from 2.07A to 12.1A;
FIG. 12 shows a resonance frequency point f s A waveform plot for the converter at 1 MHz;
FIG. 13 shows a resonance frequency point f s 1MHz position diode and switch tube oscillogram;
fig. 14 is a diode rectification waveform diagram.
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.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
In a first embodiment, referring to fig. 1, the present invention provides a method for controlling a high-order lclclcl dc converter, where the high-order lclclcl dc converter includes a switching tube S 1 Switch tube S 2 Resonant capacitor C r Resonant inductor L r Transformer T, band-stop filter inductance L s Band elimination filter capacitor C s Diode D 1 Diode D 2 And an output capacitor C f ，
Band elimination filter inductance L s And a band elimination filter capacitor C s Are connected in parallel to form a band elimination filter;
switch tube S 1 Is connected with a power supply V in Positive electrode of (2), switching tube S 1 Source electrode of S is connected with a switch tube S 2 Of the drain electrode, the switching tube S 2 Is connected with a power supply V in The negative electrode of (1); resonant capacitor C r Resonant inductor L r The primary side of the transformer T and the band elimination filter are sequentially connected in series with a switching tube S 2 Between the drain and the source;
one end of the secondary side of the transformer T is connected with a diode D 1 Anode of (2), diode D 1 Cathode of (D) is connected with a diode 2 Cathode of (2), diode D 2 The anode of the transformer is connected with the other end of the secondary side of the transformer T; middle tap of transformer T secondary side and diode D 2 Is connected with an output capacitor C f (ii) a Output capacitor C f And a load resistance R L Are connected in parallel;
the control method comprises the following steps of establishing a small signal model:
performing circuit transformation on the high-order LCLCLCL direct current converter to obtain an equivalent circuit; writing a nonlinear time-varying equation according to the equivalent circuit column;
introducing an extended description function into the nonlinear time-varying equation to obtain an extended description time-varying equation; carrying out harmonic approximation on the extended description time-varying equation to obtain a steady-state working point equation of the nonlinear time-varying equation; adding disturbance to the steady-state operating point equation to obtain a small-signal steady-state operating point equation; then linearizing the steady-state working point equation of the small signal to obtain a harmonic equation;
and establishing a state space model according to the harmonic equation, and further obtaining a small signal model.
The high-order lclclcl dc converter described in this embodiment has the ability to reduce the average current of the secondary diode. The average current can be reduced by 74% under the same load effective current, and the power supply efficiency is improved. The lclclcl converter system gain has a zero gain point. Therefore, an excellent soft start and overcurrent protection scheme can be designed accordingly.
The embodiment describes a method for establishing a small signal model of an LCLCLCL direct-current converter, and the method adopts an Extended Description Function (EDF) modeling method, writes a nonlinear time-varying equation in a column, performs harmonic approximation, introduces the extended description function, obtains a steady-state working point, increases disturbance, linearizes a harmonic equation, and finally establishes a state space model.
Further, as shown in fig. 1, the control method further includes:
obtaining a small signal transfer function based on the small signal model; factorizing the small signal transfer function to obtain a plurality of zeros and poles, removing high-frequency zeros and poles and similar zeros and poles, and reserving the rest zeros and poles as reference zeros and reference poles; drawing a bode diagram of a small signal transfer function by the reference zero and the reference pole; designing a compensator by adopting a four-pole four-zero method based on a bode diagram of a small signal transfer function; and finally, the high-order LCLCLCL direct current converter is controlled through a compensator.
In the present embodiment, a control strategy for the converter is further obtained on the basis of the small-signal model. The small signal modeling method of the variator is researched, and the resistance of the system to different interferences is researched. And designing a compensator according to the established small signal model, and balancing the relation between the dynamic response rate of the LCLCLCL system and the system stability.
The present embodiment further performs lclclcl converter compensator design: and substituting the resonance parameters, the load parameters and the existing parasitic parameters of the whole system for the obtained converter small-signal model. After the bode plot was obtained, digital compensation was performed.
Still further, the small signal model building process includes: firstly, an equivalent circuit is obtained by the high-order LCLCLCL direct current converter, the LCLCLCL direct current converter belongs to a nonlinear system, and the equivalent circuit is shown in figure 3; the state equation of each component of the equivalent circuit in the current continuous mode obtained through kirchhoff voltage law is as follows, namely a nonlinear time-varying equation:
Figure BDA0002483404370000051
Figure BDA0002483404370000052
Figure BDA0002483404370000053
Figure BDA0002483404370000054
Figure BDA0002483404370000055
Figure BDA0002483404370000056
Figure BDA0002483404370000057
v is ab For power supply V in equivalent circuit in Input voltage of i r Is a resonant inductor L r The current of (a) is measured,
Figure BDA0002483404370000058
is a resonant capacitor C r The terminal voltage of (a) is,
Figure BDA0002483404370000059
is a band-stop filter capacitor C s Terminal voltage of i p Current, sgn (i), representing the mapping of the secondary current of the transformer T back to the primary current p ) Which represents the direction of the current in the primary side of the transformer T,
Figure BDA00024834043700000510
Figure BDA00024834043700000511
which represents the voltage of the primary side of the transformer T,
Figure BDA00024834043700000512
representing the output capacitance C f Terminal voltage of
Figure BDA00024834043700000513
Voltage, L, mapped back to primary side of transformer T m Representing the excitation inductance, i, of the transformer T m Representing the excitation inductance L m Current of (i) s Representing pass band rejection filter inductance L s Current of (i) sp Is the secondary current of transformer T, r c To an output capacitor C f Parasitic resistance of v o Is a load resistance R L Voltage across, r c Is an output capacitor C f Parasitic resistance of r' c Is parasitic resistance r c And a load resistance R L Parallel equivalent resistance of r c '＝r c ||R L (Ω)。
Still further, the method for introducing an extended description function to the nonlinear time-varying equation to obtain an extended description time-varying equation includes:
performing Fourier decomposition on the nonlinear time-varying equation, and extracting a fundamental component to obtain a fundamental component expression:
i r (t)＝i r_s (t)sinω s t-i r_c (t)cosω s t，
in the formula i r_s Is a current i r Of the sinusoidal component i r_c Is a current i r Cosine component of, ω s Is the switching frequency angular frequency;
Figure BDA00024834043700000514
wherein, the lower corner mark _ s represents the sine component of the corresponding variable, and the lower corner mark _ c represents the cosine component of the corresponding variable;
i s (t)＝i s_s (t)sinω s t-i s_c (t)cos ω s t，
Figure BDA0002483404370000061
i m (t)＝i m_s (t)sinω s t-i m_c (t)cos ω s t，
and then, the expression of the fundamental component is subjected to time derivation to obtain transient characteristics of the fundamental component:
Figure BDA0002483404370000062
Figure BDA0002483404370000063
Figure BDA0002483404370000064
Figure BDA0002483404370000065
Figure BDA0002483404370000066
for non-linear parts of the above expression which cannot be directly expressed in sine and cosine form, e.g.
Figure BDA0002483404370000067
And abs (i) sp ) The fundamental component and the direct current component are approximately obtained by expanding the description function:
v ab (t)＝f 1 (d,v in )sin ω s t，
Figure BDA0002483404370000068
i sp ＝f 4 (i s_s ,i s_c )，
in the formula f 1 (d,v in )、
Figure BDA0002483404370000069
And f 4 (i s_s ,i s_c ) An extended description function of the harmonic coefficients for each state variable under the selected working condition;
in the formula, the description function is extended 1 (d,v in ) Expressed as:
Figure BDA00024834043700000610
wherein d is an expansion description operator, and theta is an arbitrary angle value;
extended description function two
Figure BDA0002483404370000071
Expressed as:
Figure BDA0002483404370000072
in the formula i s_s Is a current i s N is the transformer transformation ratio, i p_s Is a current i p Of the sinusoidal component v p_s Is a sinusoidal component of the primary voltage of the transformer;
extended description function three
Figure BDA0002483404370000073
Is shown as：
Figure BDA0002483404370000074
In the formula i s_c Is a current i s Cosine component of i p_c Is a current i p The cosine component of v p_c Is the cosine component of the primary voltage of the transformer;
primary and secondary side current relation coefficient f of transformer 4 (i s_s ,i s_c ) The following relationship is satisfied:
i sp ＝ni p 。
Figure BDA0002483404370000075
where A is the current measurement unit in amperes.
After the components are approximately equivalent, a Harmonic Balance (HB) theory can be adopted to solve the system equation of the LLC when no disturbance exists. The HB theory carries out column writing and solving on the approximated voltage and current through kirchhoff voltage and current laws of a loop.
The voltage components at the two ends of the excitation inductor are as follows:
Figure BDA0002483404370000076
Figure BDA0002483404370000077
under DC condition, v cf Can calculate to obtain:
Figure BDA0002483404370000078
when the system is free of disturbance, the first derivative of the voltage and current values of each element of the system should be 0, so that the steady state value of each component of the system in a disturbance-free state can be obtained.
Still further, the process of obtaining the steady-state operating point equation from the extended description time-varying equation is as follows:
the nonlinear time-varying equation is decomposed into sine and cosine components as follows:
Figure BDA0002483404370000081
in the formula v es Is an input voltage v ab Of the sinusoidal component v ec Is an input voltage v ab The cosine component of (a);
Figure BDA0002483404370000082
Figure BDA0002483404370000083
Figure BDA0002483404370000084
Figure BDA0002483404370000085
Figure BDA0002483404370000086
in the formula R e A secondary resistor equivalent to the primary side;
extracting resonant current i from sine component and cosine component equation r ,i s Sine and cosine component of, resonant capacitor voltage v Cr ,v Cs Sine and cosine component of and excitation current i p Obtaining a steady-state working point equation matrix expression by using the sine and cosine components:
X×Y＝U 0 ，
Figure BDA0002483404370000091
Y＝[V Cr_s V Cr_c I Lr_s I Lr_c V Cs_s V Cs_c I Ls_s I Ls_c I Lm_s I Lm_c ] T ，
in the formula V Cr_s Is a resonant capacitor C r Terminal voltage sine large signal DC expression, V Cr_c Is a resonant capacitor C r Terminal voltage cosine, I Lr_s Is a resonant inductor L r The sine large signal direct current expression form of (1);
to I Lr_c 、V Cs_s 、V Cs_c 、I Ls_s 、I Ls_c 、I Lm_s And I Lm_c The meanings of (A) are not described one by one. In the circuit theory calculation of the invention, the case expression of the same script but only variable is explained differently as follows: the upper case variable represents the (large signal) dc amount and the lower case represents the (small signal) ac amount. In the present embodiment, the upper case variable represents the steady-state quantity at the steady-state operating point in the current model, and the corresponding lower case variable represents the small semaphore.
Still further, adding disturbance to the steady-state operating point equation to obtain a small-signal steady-state operating point equation comprises:
adding a disturbance component on the basis of the large signal model to obtain a small signal relation of a corresponding state variable;
if a corresponding disturbance quantity is introduced into the input voltage of the resonant cavity, the expression is as follows:
Figure BDA0002483404370000092
in which for any of the variables a,
Figure BDA0002483404370000093
representing the disturbance amount of the variable a;
Ω s the switching frequency controlled source expression form;
the above formula is simplified, only the first order small signal component is reserved in the sorting process, and the partial derivative of the corresponding parameter is required in the sorting process of some non-linear expressions. Taking the sinusoidal component of the primary voltage as an example, for the sinusoidal component of the primary voltage:
Figure BDA0002483404370000094
are respectively to i p_s 、i p_s And v cf After a partial derivative is solved, a first-order disturbance small signal steady-state working point equation is obtained:
Figure BDA0002483404370000101
still further, the process of obtaining the small signal model is as follows:
adding small signal disturbance to a system steady-state component, assuming that an average state variable of a corresponding disturbance quantity consists of a direct current component and the small disturbance, adding the disturbance to a steady-state working point equation, eliminating the direct current component, and then neglecting second-order and above high-order components to obtain a small signal model primary expression:
Figure BDA0002483404370000102
Figure BDA0002483404370000103
Figure BDA0002483404370000104
in the formula
Figure BDA0002483404370000105
Figure BDA0002483404370000106
Figure BDA0002483404370000107
Figure BDA0002483404370000108
Figure BDA0002483404370000109
Figure BDA00024834043700001010
D is the duty ratio of the converter;
finally, obtaining a small signal model:
Figure BDA00024834043700001011
Figure BDA0002483404370000111
Figure BDA0002483404370000112
Figure BDA0002483404370000113
Figure BDA0002483404370000114
Figure BDA0002483404370000115
Figure BDA0002483404370000116
Figure BDA0002483404370000117
Figure BDA0002483404370000118
Figure BDA0002483404370000119
Figure BDA00024834043700001110
Figure BDA00024834043700001111
in the formula of omega sn In order to normalize the switching angular frequency,
Figure BDA00024834043700001112
ω r the main resonant frequency of the high-order LCLCLCL direct current converter;
Figure BDA00024834043700001113
is a load resistance R L A both-end voltage (output voltage) disturbance amount;
Figure BDA00024834043700001114
still further, the method for obtaining the small signal transfer function based on the small signal model comprises the following steps:
and substituting the operating parameters of the high-order LCLCLCL direct current converter into the small signal model to obtain a small signal transfer function.
The state space model is composed of a series of input, output and state variables, and a convenient analysis mode is provided for a multi-input and multi-output system. If the dynamic system is a linear time-varying system, the columns can be written in the form of a matrix equation set, and the state space expression of the LCLCL resonant converter is as follows:
Figure BDA0002483404370000121
Figure BDA0002483404370000122
in the formula:
Figure BDA0002483404370000123
Figure BDA0002483404370000124
the transfer function G between the system output voltage and the frequency p ：
Figure BDA0002483404370000125
In the formula, the specific expression form of each matrix is as follows:
Figure BDA0002483404370000126
B＝[-ω 0 I Lr_c ω 0 I Lr_s -ω 0 V Cr_c ω 0 V Cr_s -ω 0 I Ls_c ω 0 I Ls_s -ω 0 V Cs_c ω 0 V Cs_s -ω 0 I Lm_c ω 0 I Lm_s 0] T
Figure BDA0002483404370000127
D＝0，
substitution of A, B, C, D four matrices
Figure BDA0002483404370000131
And obtaining a small signal model.
The specific embodiment is as follows:
in order to verify the feasibility of the topology and parameter design selection of the invention, a prototype with the following indexes is built
Rated input voltage: 400V;
rated power: 400W;
series resonance frequency: 1MHz (fundamental), 3MHz (third harmonic);
parallel resonance frequency: 2 MHz;
efficiency: higher than 95%;
output voltage: 24V;
output voltage ripple: less than 200 mV;
the model number and parameters of the chip in the DC converter selected by the prototype are shown in Table 1.
TABLE 1
Figure BDA0002483404370000132
According to the parameters in the table above, the resonance parameters, the load parameters, and the parasitic parameters are substituted into the model, so as to obtain the transfer function of the distribution of the poles-zero as shown in fig. 5.
Still further, a bode graph before compensation is obtained as shown in fig. 6;
as can be seen from fig. 6, the system is unstable at crossover frequencies greater than the switching frequency, and a compensator of 4P4Z is designed for the transfer function. A system block diagram of the compensator is shown in fig. 7. The 4P4Z compensator can be programmed into a digital controller after discretization processing, and finally actual control is carried out.
In FIG. 7, the output voltage Vo is sampled and sent to an analog-to-digital converter to convert the voltage to a digital value V m With a given reference voltage V ref And comparing to obtain an error amount e, sending the error into a compensator to obtain a digital quantity voltage adjustment value, sending the voltage adjustment value into an ePWM module to obtain a working frequency adjustment value, and acting the working frequency adjustment value on a resonant cavity to play a role of a closed-loop voltage regulation and stabilization system.
The bode diagram of the compensated system is shown in fig. 8.
As can be seen from fig. 8, the cross-over frequency of the compensated system is 1/10 of the switching frequency, and the phase margin is 45 °, so that the system is stable.
With reference to fig. 9, the specific process of using the compensator for control includes: each interruption judgment is used for sequentially judging whether the system is started or not, overcurrent protection and conventional load sudden change (system closed loop is required to maintain the stability of the system).
When the soft start judgment is carried out, detecting the voltage value of the output voltage, when the output voltage does not reach the standard, continuously searching an output voltage/working frequency comparison table in a program, gradually pulling the output voltage/working frequency comparison table from 2MHz to 1MHz, when the output voltage is searched to be more than 23V, considering that the soft start is finished, and skipping to the next stage judgment; the overcurrent protection is to sample and take current through a current loop of the system, when the digital output of an analog-to-digital converter exceeds a set value, the switching frequency is firstly pulled to a zero gain point (2MHz) of the quinary resonance system to carry out the overcurrent protection without system power failure, and whether the system is closed or not is determined after the system is overhauled. And finally, load sudden change control is carried out, median digital filtering is carried out in a normal working state, the influence of interference on the system stability is prevented, and the control flow shown in the figure 7 is carried out after the load sudden change is detected.
Finally, the following indexes are realized through experiments:
(1) as shown in fig. 10 and 11. The 24V bias is set for the output voltage channel in the figure. It is seen from the figure that the resonant current converges rapidly when the load drops. After the system reaches the expected track under light load, the voltage compensation regulator eliminates the output voltage fluctuation until the output voltage fluctuation is finally stable. The system outputs 510mV of voltage overshoot in the process of load sudden change, and compared with the traditional voltage compensation control mode, the output voltage overshoot of the converter is smaller.
(2) Switch tube S 1 And S 2 Soft switching is achieved. The waveform is shown in fig. 12.
(3) The diode successfully injected the third harmonic and the loss reduction waveform is shown in fig. 13.
In the diode rectification waveform diagram shown in fig. 14, the waveforms of the high left and the low right demonstrate that the efficiency is higher when the injection of the third harmonic exists.
Experiments prove that the method can realize stable closed loop of the LCLCLCL system, and the dynamic response speed is enough excellent.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (3)

1. A control method for a high-order LCLCLCL DC converter comprises a switching tube S 1 Switch tube S 2 Resonant capacitor C r Resonant inductor L r Transformer T, band-stop filter inductance L s Band-stop filter capacitor C s Diode D 1 Diode D 2 And an output capacitor C f ，
Band elimination filter inductance L s And a band elimination filter capacitor C s Are connected in parallel to form a band elimination filter;
switch tube S 1 Is connected with a power supply V in Positive electrode of (2), switching tube S 1 Source electrode ofClosing pipe S 2 Of the drain electrode, the switching tube S 2 Is connected with a power supply V in The negative electrode of (1); resonant capacitor C r Resonant inductor L r The primary side of the transformer T and the band elimination filter are sequentially connected in series with a switching tube S 2 Between the drain and the source of (a);
one end of the secondary side of the transformer T is connected with a diode D 1 Anode of (2), diode D 1 Cathode of (2) is connected with a diode D 2 Cathode of (2), diode D 2 The anode of the transformer is connected with the other end of the secondary side of the transformer T; middle tap and diode D of transformer T secondary side 2 Is connected with an output capacitor C f (ii) a Output capacitor C f And a load resistance R L Are connected in parallel;
the control method is characterized by comprising the following steps of establishing a small signal model: performing circuit transformation on the high-order LCLCLCL direct current converter to obtain an equivalent circuit; writing a nonlinear time-varying equation according to the equivalent circuit column;
introducing an extended description function into the nonlinear time-varying equation to obtain an extended description time-varying equation; carrying out harmonic approximation on the extended description time-varying equation to obtain a steady-state working point equation of a nonlinear time-varying equation; adding disturbance to the steady-state operating point equation to obtain a small-signal steady-state operating point equation; then linearizing the steady-state working point equation of the small signal to obtain a harmonic equation;
establishing a state space model by the harmonic equation, and further obtaining a small signal model;
the nonlinear time-varying equation comprises:
Figure FDA0003712347110000011
Figure FDA0003712347110000012
Figure FDA0003712347110000013
Figure FDA0003712347110000014
Figure FDA0003712347110000015
Figure FDA0003712347110000016
Figure FDA0003712347110000021
v is ab For power supply V in equivalent circuit in Input voltage of i r Is a resonant inductor L r The current of (a) is measured,
Figure FDA0003712347110000027
is a resonant capacitor C r The terminal voltage of (a) is,
Figure FDA0003712347110000028
is a band-stop filter capacitor C s Terminal voltage of i p Current, sgn (i), representing the mapping of the secondary current of the transformer T back to the primary current p ) Which represents the direction of the current in the primary side of the transformer T,
Figure FDA0003712347110000022
representing the output capacitance C f Terminal voltage of
Figure FDA0003712347110000023
Voltage, L, mapped back to primary side of transformer T m Representing the excitation inductance, i, of the transformer T m Representing the excitation inductance L m Current of (i) s Representing the inductance L of the filter by bandstop s Current of (i) sp For secondary current of transformer T, v o Is a load resistance R L Voltage across, r c Is an output capacitor C f Parasitic resistance of r c Is a parasitic resistance r c And a load resistance R L R 'of' c ＝r c ||R L ；
The method for introducing the extended description function into the nonlinear time-varying equation to obtain the extended description time-varying equation comprises the following steps:
performing Fourier decomposition on the nonlinear time-varying equation, and extracting a fundamental component to obtain a fundamental component expression:
i r (t)＝i r_s (t)sinω s t-i r_c (t)cosω s t，
in the formula i r_s Is a current i r Of the sinusoidal component i r_c Is a current i r Cosine component of, omega s Is the switching frequency angular frequency;
v Cr (t)＝v Cr_s (t)sinω s t-v Cr_c (t)cosω s t，
wherein, the lower corner mark _ s represents the sine component of the corresponding variable, and the lower corner mark _ c represents the cosine component of the corresponding variable;
i s (t)＝i s_s (t)sinω s t-i s_c (t)cosω s t，
v Cs (t)＝v Cs_s (t)sinω s t-v Cs_c (t)cosω s t，
i m (t)＝i m_s (t)sinω s t-i m_c (t)cosω s t，
and then, the expression of the fundamental component is subjected to time derivation to obtain transient characteristics of the fundamental component:
Figure FDA0003712347110000024
Figure FDA0003712347110000025
Figure FDA0003712347110000026
Figure FDA0003712347110000031
Figure FDA0003712347110000032
to pair
Figure FDA0003712347110000033
And abs (i) sp ) The fundamental component and the direct current component are approximately obtained by expanding the description function:
v ab (t)＝f 1 (d,v in )sinω s t，
Figure FDA0003712347110000034
i sp ＝f 4 (i s_s ,i s_c )，
where the extended description function is f 1 (d,v in ) Expressed as:
Figure FDA0003712347110000035
wherein d is an expansion description operator, and theta is an arbitrary angle value;
extended description function two
Figure FDA0003712347110000039
Expressed as:
Figure FDA0003712347110000036
in the formula i s_s Is a current i s N is the transformer transformation ratio, i p_s Is a current i p Of the sinusoidal component v p_s Is a sinusoidal component of the primary voltage of the transformer;
extended description function three
Figure FDA0003712347110000037
Expressed as:
Figure FDA0003712347110000038
in the formula i s_c Is a current i s Cosine component of i p_c Is a current i p The cosine component of v p_c Is the cosine component of the primary voltage of the transformer;
primary and secondary side current relation coefficient f of transformer 4 (i s_s ,i s_c ) The following relationship is satisfied: i all right angle sp ＝ni p ；
The process of obtaining the steady-state operating point equation from the extended description time-varying equation is as follows:
decomposing the nonlinear time-varying equation into sine and cosine components as follows:
Figure FDA0003712347110000041
in the formula v es Is an input voltage v ab V is a sinusoidal component of ec For an input voltage v ab The cosine component of (a);
Figure FDA0003712347110000042
Figure FDA0003712347110000043
Figure FDA0003712347110000044
Figure FDA0003712347110000045
Figure FDA0003712347110000046
in the formula R e A secondary resistor equivalent to the primary side;
obtaining a large signal model according to kirchhoff's law by the sine component expression and the cosine component expression;
extracting current i from sine component and cosine component equation r ,i s Sine and cosine component of (1), capacitor voltage v Cr ,v Cs Sine and cosine component of and exciting current i m Obtaining a steady-state working point equation matrix expression by using the sine and cosine components:
X×Y＝U 0 ，
Figure FDA0003712347110000051
Figure FDA0003712347110000052
in the formula V Cr_s Is a resonant capacitor C r Terminal voltage sine large signal DC expression, V Cr_c Is a resonant capacitor C r Terminal voltage cosine;
adding disturbance to the steady-state operating point equation to obtain a small-signal steady-state operating point equation comprises:
adding a disturbance component on the basis of the large signal model to obtain a small signal relation of a corresponding state variable;
introducing a corresponding disturbance quantity into the input voltage of the resonant cavity, wherein the expression is as follows:
Figure FDA0003712347110000053
in which for any of the variables a,
Figure FDA0003712347110000054
representing the disturbance amount of the variable a;
Ω s the expression form is a switching frequency controlled source;
simplifying the above equation, retaining the first order small signal component, for the primary voltage sinusoidal component:
Figure FDA0003712347110000055
are respectively to i p_s 、i p_s And v cf After a partial derivative is solved, a first-order disturbance small signal steady-state working point equation is obtained:
Figure FDA0003712347110000056
the process of obtaining the small signal model is as follows:
assuming that the average state variable of the corresponding disturbance quantity consists of a direct-current component and small disturbance, adding the disturbance into a steady-state working point equation, eliminating the direct-current component, and then neglecting second-order and above high-order components to obtain a small-signal model preliminary expression:
Figure FDA0003712347110000061
Figure FDA0003712347110000062
Figure FDA0003712347110000063
in the formula
Figure FDA0003712347110000064
Figure FDA0003712347110000065
Figure FDA0003712347110000066
Figure FDA0003712347110000067
D is the duty ratio of the converter;
finally, obtaining a small signal model:
Figure FDA0003712347110000068
Figure FDA0003712347110000069
Figure FDA00037123471100000610
Figure FDA00037123471100000611
Figure FDA00037123471100000612
Figure FDA00037123471100000613
Figure FDA0003712347110000071
Figure FDA0003712347110000072
Figure FDA0003712347110000073
Figure FDA0003712347110000074
Figure FDA0003712347110000075
Figure FDA0003712347110000076
in the formula of omega sn In order to normalize the switching angular frequency,
Figure FDA0003712347110000077
ω r the main resonant frequency of the high-order LCLCLCL direct current converter;
Figure FDA0003712347110000078
is a load resistance R L Voltage disturbance quantity at two ends;
Figure FDA0003712347110000079
2. the method of controlling a high order LCLCLCL DC converter according to claim 1, further comprising:
obtaining a small signal transfer function based on the small signal model; factorizing the small signal transfer function to obtain a plurality of zeros and poles, removing high-frequency zeros and poles and similar zeros and poles, and reserving the rest zeros and poles as reference zeros and reference poles; drawing a bode diagram of a small signal transfer function by the reference zero and the reference pole; designing a compensator by adopting a four-pole four-zero method based on a bode diagram of a small signal transfer function; and finally, the high-order LCLCLCL direct current converter is controlled through a compensator.
3. The method of controlling a higher order LCLCLCL DC converter according to claim 2,
the method for obtaining the small signal transfer function based on the small signal model comprises the following steps:
and substituting the operating parameters of the high-order LCLCL direct current converter into the small signal model to obtain a small signal transfer function.
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