CN111310398B - LLC resonant converter closed loop stability analysis method - Google Patents

LLC resonant converter closed loop stability analysis method Download PDF

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CN111310398B
CN111310398B CN202010076478.8A CN202010076478A CN111310398B CN 111310398 B CN111310398 B CN 111310398B CN 202010076478 A CN202010076478 A CN 202010076478A CN 111310398 B CN111310398 B CN 111310398B
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resonant converter
llc resonant
transfer matrix
equation set
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CN111310398A (en
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李虹
邹颖
孙绍哲
郝瑞祥
张波
郑琼林
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Beijing Jiaotong University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • 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
    • 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

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  • Dc-Dc Converters (AREA)

Abstract

The invention discloses a closed-loop stability analysis method of an LLC resonant converter based on Floquet theory, comprising the following steps: performing linear modeling on the LLC resonant converter through extended description function modeling to obtain a system state equation set and a steady-state working point; solving a linear term of a Taylor expansion of a state equation set by applying disturbance at a steady-state working point to obtain a perturbation equation set of the system; obtaining a system state transfer matrix by solving a Jacobian matrix of a perturbation equation set so as to take the system state transfer matrix as a stability analysis model; and determining the stable range of the LLC resonant converter closed-loop control parameters by analyzing the mode length of the maximum eigenvalue of the state transfer matrix. The method can accurately provide the stable range of the closed-loop control parameters of the LLC resonant converter system, judge the critical stable state of the LLC resonant converter system, and the analysis process is completely based on the time domain, so that the solution of the high-order transfer function of the LLC resonant converter is avoided, the complexity of judging the stability of the LLC resonant converter is effectively reduced, and the result is accurate.

Description

LLC resonant converter closed loop stability analysis method
Technical Field
The invention relates to the technical field of PFM (Pulse Frequency Modulation) type resonant converters, in particular to a closed loop stability analysis method of an LLC resonant converter.
Background
With the development of power electronic technology, the LLC resonant converter is widely applied to systems such as electric vehicle charging piles, photovoltaic system dc converters, data center dc power supplies, and the like, due to its inherent advantages of soft switching capability, high power density, low switching loss, easiness in magnetic integration, and the like. For the resonant converter, the control mode mainly adopts frequency conversion control, and the resonant network mainly depends on fundamental wave to transmit energy, so that the traditional state space average modeling method cannot be applied. Subsequently, many methods for modeling and stabilizing the resonant converter system, such as Extended Description Function (EDF), state plane analysis, time domain analysis, etc., have been introduced. However, the modeling and stability analysis methods are limited to frequency domain open loop analysis, and the physical concepts thereof are blurred.
In the related art, an Extended Description Function (EDF) approximately expresses a frequency modulation signal in a system into an amplitude modulation signal, extracts an effective energy transfer component of a nonlinear quantity in the system through fourier expansion, and further obtains a small signal model of the system through harmonic balance and disturbance linearization processing. The method is widely applied to modeling and stability analysis of the resonant converter.
However, the method needs to solve the high-order transfer function of the system, and only a numerical transfer function can be obtained, so that an algebraic transfer function is difficult to derive, and the physical concept of the stability analysis model is not clear enough, so that the method has certain limitation. The stability analysis method based on the state plane analysis also has the defect. The time domain simulation method obtains an amplitude-frequency curve and a phase-frequency curve of the system by frequency sweeping modeling on a simulation platform, a physical model is not clear, and the timeliness and the precision of the time domain simulation method are limited by simulation software.
Disclosure of Invention
The present application is based on the recognition and discovery by the inventors of the following problems:
different from the extended description function method in the background art, the stability analysis method based on the Floquet theory judges the stability of the system by judging the characteristic value of the system state transfer matrix, the physical concept is clear, the closed loop stability range can be accurately given, the stability analysis process is directly based on the time domain, and the complexity of stability analysis is reduced to a certain extent.
Therefore, the stability analysis method based on the Floquet theory becomes an important tool for analyzing the stability of the periodic system, and is currently applied to single-stage DC-AC inverters and cascaded DC-DC converters. The stability analysis method based on the Floquet theory is applied to the resonant converter for the first time and is used for analyzing the stability problem of closed-loop operation of the half-bridge LLC resonant converter.
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, the invention aims to provide an analysis method for the closed-loop stability of the LLC resonant converter, which can accurately judge the stability of a converter system, provide a stable range of closed-loop control parameters and effectively improve the accuracy of a judgment result.
In order to achieve the above object, an embodiment of the present invention provides a method for analyzing closed-loop stability of an LLC resonant converter, including the following steps: performing linear modeling on the LLC resonant converter through extended description function modeling to obtain a system state equation set and a steady-state working point; obtaining a linear term of a Taylor expansion of a state equation set by applying disturbance at the steady-state working point to obtain a perturbation equation set of the system; obtaining a system state transfer matrix by solving a Jacobian matrix of the perturbation equation set so as to take the system state transfer matrix as a stability analysis model; and determining the stable range of the LLC resonant converter closed-loop control parameters by analyzing the mode length of the maximum eigenvalue of the state transfer matrix.
The method for analyzing the closed-loop stability of the LLC resonant converter can accurately judge the stable condition of the system and provide the stable range of the closed-loop control parameters of the LLC resonant converter system, and the analysis process is completely based on the time domain, so that the solution of a high-order transfer function of the LLC resonant converter is avoided, the complexity of judging the stability of the LLC resonant converter is effectively reduced, and the result is accurate.
In addition, the LLC resonant converter closed-loop stability analysis method according to the above embodiment of the present invention may further have the following additional technical features:
further, in an embodiment of the present invention, the determining a stable range of the LLC resonant converter closed-loop control parameter by analyzing a mode length of a maximum eigenvalue of the state transfer matrix includes: deriving a system Jacobian matrix according to the perturbation equation, deriving a system state transfer matrix according to the Jacobian matrix, and calculating the maximum eigenvalue according to the state transfer matrix; and obtaining a closed loop stability result of the LLC resonant converter according to the size relation between the modular length of the maximum characteristic value and 1.
Further, in an embodiment of the present invention, the obtaining the closed-loop stability result of the LLC resonant converter by the magnitude relation between the mode length of the maximum eigenvalue and 1 includes: when the maximum characteristic value modular length is smaller than 1, the LLC resonant converter is judged to be in a stable state; when the mode length is larger than 1, the LLC resonant converter is judged to be in a destabilization state; and when the mode length is equal to 1, determining that the LLC resonant converter is in a critical stable state.
Further, in one embodiment of the present invention, the system of state equations is represented as:
Figure BDA0002378612900000021
where t is time and x is a column vector consisting of system state variables.
Further, in one embodiment of the present invention, the calculation formula of the perturbation equation set is:
Figure BDA0002378612900000022
wherein,
Figure BDA0002378612900000023
representing the amount of photographing, xpIs a steady state periodic solution vector of the system equation of state, also known as the steady state operating point, JFIs a jacobian matrix.
Further, in one embodiment of the present invention, the jacobian matrix will be derived from the following equation:
Figure BDA0002378612900000031
further, in an embodiment of the present invention, the state transfer matrix is:
Figure BDA0002378612900000032
wherein T is the system period.
Further, in one embodiment of the present invention, the maximum eigenvalue is found by the following formula:
|λI-C|＝0，
wherein, λ is the characteristic value of the state transfer matrix, and I is the identity matrix.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a method for analyzing the closed loop stability of an LLC resonant converter according to an embodiment of the invention;
FIG. 2 is a flow chart of a method for analyzing the closed loop stability of an LLC resonant converter according to an embodiment of the invention;
FIG. 3 is an equivalent circuit topology of a half-bridge LLC resonant converter system according to an embodiment of the invention;
FIG. 4 shows a half-bridge LLC resonant converter according to an embodiment of the invention with a fixed integral parameter (k)i60) a graph of the time-dependent change of the maximum eigenvalue mode length of the system state transfer matrix;
FIG. 5 is a graph of a half-bridge LLC resonant converter according to an embodiment of the invention at a fixed ratio parameter (k)p0.01) system state transfer matrix maximum eigenvalue mode length is in a time-varying relation graph;
FIG. 6 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.05，kiSimulating a waveform diagram of the output voltage under 60;
FIG. 7 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.05，kiA partial enlarged view of the output voltage simulation waveform under 60;
FIG. 8 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.07，kiSimulating a waveform diagram of the output voltage under 60;
FIG. 9 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.07，kiA partial enlarged view of the output voltage simulation waveform under 60;
FIG. 10 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.01，kiSimulating a waveform diagram of the output voltage under 150;
FIG. 11 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.01，kiA partial enlarged view of an output voltage simulation waveform under 150;
FIG. 12 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.01，kiOutput voltage simulation oscillogram under 170;
FIG. 13 shows a half-bridge LLC resonant converter at k according to an embodiment of the inventionp＝0.01，kiA partial enlarged view of the output voltage simulation waveform under 170;
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The method for analyzing the closed loop stability of the LLC resonant converter proposed by the embodiment of the invention is described below with reference to the accompanying drawings.
Fig. 1 is a flow chart of an LLC resonant converter closed loop stability analysis method according to an embodiment of the present invention.
As shown in fig. 1, the LLC resonant converter closed-loop stability analysis method includes the following steps:
in step S101, linear modeling is performed on the LLC resonant converter through extended description function modeling to obtain a system state equation set and a steady-state operating point.
The LLC resonant converter system is a half-bridge LLC resonant converter, and the feedback loop is provided with a PI controller and a VCO voltage-controlled oscillator equivalent proportion link.
It can be understood that, as shown in fig. 2, the embodiment of the present invention linearly models the power stage and the control loop of the half-bridge LLC resonant converter shown in fig. 3 by using the extended description function modeling method to obtain the system state equation set and the steady-state operating point x thereofp。
Further, in an embodiment of the present invention, a system of state equations is obtained according to topology, control parameters, closed-loop feedback mode conditions, frequency modulation signal approximation processing, fourier expansion approximation processing of nonlinear quantity, and harmonic balance of the LLC resonant converter, wherein the system of state equations is:
Figure BDA0002378612900000041
wherein:
Figure BDA0002378612900000051
Figure BDA0002378612900000052
Figure BDA0002378612900000053
wherein irsBeing the sinusoidal component of the resonant inductor current, ircIs the cosine component of the resonant inductor current, imsBeing the sinusoidal component of the exciting inductor current, imcIs the cosine component of the exciting inductor current, vCrsIs the sinusoidal component of the resonant capacitor voltage, vCrcIs the cosine component of the resonant capacitor voltage, ipsIs a sinusoidal component of the primary side current of the transformer, ipcIs the cosine component of the primary side current of the transformer, ippIs the amplitude of the primary side current of the transformer, iRpIs the maximum value of the current of the rectifier diode, vCoTo output the filter capacitor voltage. L isrIs a resonant inductance value, LmTo values of exciting inductance, CrIs a resonance capacitance value, RoTo output a load resistance value, rsIs parasitic resistance of resonant network, rcFor outputting filter capacitor parasitic resistance, omegasFor the system switching angular frequency, n is the transformer transformation ratio, EvFor the half-bridge midpoint input voltage cosine component amplitude, GVCOIs the proportional coefficient, k, of an equivalent voltage controlled oscillatorpIs the proportionality coefficient, k, of a PI regulatoriIs the integral coefficient of the PI regulator, voFor the system output voltage, vrefIs the system control loop reference voltage.
Furthermore, the above system of state equations can be represented by the following simplified equations:
Figure BDA0002378612900000054
further, since the steady state operating point of the system is uniquely determined by the circuit parameters, by setting the differential amount in the system state equation set to zero, i.e.: and G (t, x) is 0, and the steady-state operating point of the system can be obtained.
In step S102, a linear term of a taylor expansion of the state equation set is obtained by applying a disturbance at the steady-state operating point, and a perturbation equation set of the system is obtained.
It can be appreciated that the system perturbation equation set is obtained by superimposing the perturbations at the steady state operating point, as shown in FIG. 2, and substituting into the state equation set to solve the linear terms of the Taylor expansion of the state equation set.
Wherein the perturbation equation set is shown as the following formula:
Figure BDA0002378612900000055
Figure BDA0002378612900000056
Figure BDA0002378612900000061
wherein:
Figure BDA0002378612900000062
Figure BDA0002378612900000063
Figure BDA0002378612900000064
it should be noted that the definitions of the variables in the perturbation equation set are consistent with those defined in the state equation set, and the superscript of the variable is
Figure BDA0002378612900000065
Expressed as the amount of uptake.
In step S103, a system state transfer matrix is obtained by solving the jacobian matrix of the perturbation equation set to use the system state transfer matrix as a stability analysis model.
It can be understood that the Jacobian matrix J of the perturbation equation system is solved based on Floquet theory as shown in FIG. 2FAnd further obtaining a system state transfer matrix C as a stability analysis model:
Figure BDA0002378612900000066
Figure BDA0002378612900000071
Figure BDA0002378612900000072
Figure BDA0002378612900000073
according to the Floquet theory, since the jacobian matrix is a constant matrix, the state transfer matrix is:
Figure BDA0002378612900000074
wherein T is the system period.
In step S104, the stable range of the LLC resonant converter closed-loop control parameter is determined by analyzing the mode length of the maximum eigenvalue of the state transfer matrix.
It can be understood that, as shown in fig. 2, the stability of the half-bridge LLC resonant converter is analyzed by plotting the maximum eigenvalue modulo length of the system state transfer matrix versus time.
Further, in an embodiment of the present invention, determining the stable range of the LLC resonant converter closed-loop control parameter by analyzing the mode length of the maximum eigenvalue of the state transfer matrix includes: deducing a system Jacobian matrix according to a perturbation equation, deducing a system state transfer matrix according to the Jacobian matrix, and calculating a maximum eigenvalue according to the state transfer matrix; and obtaining a closed loop stability result of the LLC resonant converter according to the size relation between the modular length of the maximum characteristic value and 1.
Specifically, the method includes the steps of substituting a steady-state operating point and a circuit parameter table into a state transfer matrix of a computing system, and judging the stability of the closed loop of the LLC resonant converter by analyzing the mode length of the maximum eigenvalue of the state transfer matrix, and specifically includes the following steps: when the maximum eigenvalue mode length of the state transfer matrix is smaller than 1, determining that the LLC resonant converter system is in a stable state; when the maximum eigenvalue mode length of the state transfer matrix is greater than 1, determining that the LLC resonant converter closed-loop system is in a destabilization state; and when the maximum eigenvalue mode length of the state transfer matrix is equal to 1, determining that the LLC resonant converter closed-loop system is in a critical stable state.
Furthermore, a relationship graph of the maximum characteristic value modular length of the state transfer matrix changing along with time is drawn, so that the stability analysis result is more visual.
For example, in one embodiment of the present invention, the system integration parameter (k) is fixedi60), the system is plotted at different scale parameters (k)p) The maximum eigenvalue modulo length of the lower transfer matrix is plotted against time, as shown in fig. 4. When k ispWhen the modulus length of the maximum eigenvalue of the system transfer matrix is less than or equal to 0.05, the modulus length is all less than 1, and the system is monotonically decreased along with time, and the system is judged to be in a stable state; when k ispWhen the modulus length of the maximum eigenvalue of the system transfer matrix is more than 1 when the modulus length is more than 0.05, the system transfer matrix monotonically increases along with time, and the system is judged to be in a destabilization state.
For example, in another embodiment of the present invention, the system scaling parameter (k) is fixedp0.01), the system is plotted at different scale parameters (k)i) The maximum eigenvalue modulo length of the lower transfer matrix is plotted against time, as shown in fig. 5. When k isiWhen the transfer matrix length is less than or equal to 150, the maximum eigenvalue modular length of the system transfer matrix is less than 1, and the maximum eigenvalue modular length monotonically decreases along with time, and the system is judged to be in a stable state; when k isiWhen the transfer matrix length is more than 150, the maximum eigenvalue modular length of the system transfer matrix is more than 1, and the transfer matrix length is monotonically increased along with time, and the system is judged to be in a destabilization state.
Next, Simulation verification is performed on the LLC resonant converter stability analysis result based on Floquet theory by means of PSIM (Power Simulation) software. The simulation parameter table is shown in table 1.
TABLE 1
Figure BDA0002378612900000081
Wherein the first set of PI parameters is: k is a radical ofp＝0.05，kiThe PSIM simulation was performed under this parameter at 60, and the simulation results are shown in fig. 6 and 7. Under the parameter, the output voltage waveform of the system is stable.
The second set of PI parameters is: k is a radical ofp＝0.07，kiThe PSIM simulation was performed under this parameter at 60, and the simulation results are shown in fig. 8 and 9. Under the parameter, the output voltage waveform of the system oscillates, and the secondary side separation phenomenon occurs, so that the system is judged to be in an unstable state at the moment.
The two simulation results are consistent with the first analysis result of the stability analysis of the LLC resonant converter based on the Floquet theory in the embodiment of the present invention.
The third set of PI parameters is: k is a radical ofp＝0.01，kiThe PSIM simulation was performed under this parameter at 150, and the simulation results are shown in fig. 10 and 11. Under the parameter, the output voltage waveform of the system is stable.
The fourth set of PI parameters is: k is a radical ofp＝0.01，kiThe PSIM simulation was performed under this parameter, and the simulation results are shown in fig. 12 and 13. Under the parameter, the output voltage waveform of the system oscillates, and the secondary side separation phenomenon occurs, so that the system is judged to be in an unstable state at the moment.
The two simulation results are consistent with the second analysis result of the stability analysis of the LLC resonant converter based on the Floquet theory in the embodiment of the present invention.
Through the analysis, when the system is judged to be in a stable state and an unstable state respectively, verification is obtained through circuit simulation according to the analysis result obtained by the stability analysis method based on the Floquet theory, the result coincidence degree is high, and the accuracy of the stability analysis method based on the Floquet theory is proved.
According to the stability analysis method of the LLC resonant converter based on the Floquet theory, provided by the embodiment of the invention, the system stability discrimination is converted into the stability discrimination of the zero solution of the perturbation equation of the system, the Jacobian matrix of the system is used for deducing the state transfer matrix of the system, and then the stability of the system is discriminated according to the size relation between the maximum eigenvalue mode length of the state transfer matrix of the system and 1. Therefore, in the stability analysis process, the stability control range of the closed-loop parameters of the system can be conveniently determined by the LLC resonant converter stability analysis method based on the Floquet theory, the analysis process is relatively easy, and the method can be popularized to other resonant converters.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (6)

1. A method for analyzing the stability of a closed loop of an LLC resonant converter is characterized by comprising the following steps:
performing linear modeling on the LLC resonant converter through extended description function modeling to obtain a system state equation set and a steady-state working point;
the system state equation set is expressed as:
Figure FDA0003528173250000011
wherein t is time and x is a column vector consisting of system state variables;
alternatively, the system of state equations is represented as:
Figure FDA0003528173250000012
wherein:
Figure FDA0003528173250000013
Figure FDA0003528173250000014
Figure FDA0003528173250000015
wherein t is time, irsBeing the sinusoidal component of the resonant inductor current, ircIs the cosine component of the resonant inductor current, imsBeing the sinusoidal component of the exciting inductor current, imcIs the cosine component of the exciting inductor current, vCrsIs the sinusoidal component of the resonant capacitor voltage, vCrcIs the cosine component of the resonant capacitor voltage, ipsIs a sinusoidal component of the primary side current of the transformer, ipcIs the cosine component of the primary side current of the transformer, ippIs the amplitude of the primary side current of the transformer, iRpIs the maximum value of the current of the rectifier diode, vCoFor outputting the filter capacitor voltage, LrIs a resonant inductance value, LmTo values of exciting inductance, CrIs a resonance capacitance value, RoTo output a load resistance value, rsIs parasitic resistance of resonant network, rcFor outputting filter capacitor parasitic resistance, omegasFor the system switching angular frequency, n is the transformer transformation ratio, EvFor the half-bridge midpoint input voltage cosine component amplitude, GVCOIs the proportional coefficient, k, of an equivalent voltage controlled oscillatorpIs the proportionality coefficient, k, of a PI regulatoriIs the integral coefficient of the PI regulator, voFor the system output voltage, vrefA system control loop reference voltage;
setting the differential quantity in the system state equation set to zero to obtain a system steady-state working point;
obtaining a linear term of a Taylor expansion of a state equation set by applying disturbance at the steady-state working point to obtain a perturbation equation set of the system; determining the perturbation equation set according to:
Figure FDA0003528173250000021
Figure FDA0003528173250000022
Figure FDA0003528173250000023
wherein:
Figure FDA0003528173250000024
Figure FDA0003528173250000025
Figure FDA0003528173250000026
wherein, the upper label
Figure FDA0003528173250000031
Expressed as amount of uptake, xpIs a steady state periodic solution vector of the system equation of state, also known as the steady state operating point, JFIs a Jacobian matrix;
obtaining a system state transfer matrix by solving a Jacobian matrix of the perturbation equation set so as to take the system state transfer matrix as a stability analysis model; and
and determining the stable range of the LLC resonant converter closed-loop control parameters by analyzing the mode length of the maximum eigenvalue of the state transfer matrix.
2. The method according to claim 1, wherein said determining a stable range of the LLC resonant converter closed-loop control parameter by analyzing a mode length of a maximum eigenvalue of the state transfer matrix comprises:
deriving a system Jacobian matrix according to the perturbation equation, deriving a system state transfer matrix according to the Jacobian matrix, and calculating the maximum eigenvalue according to the state transfer matrix;
and obtaining a closed loop stability result of the LLC resonant converter according to the size relation between the modular length of the maximum characteristic value and 1.
3. The method according to claim 1 or 2, wherein obtaining the closed-loop stability result of the LLC resonant converter by the relation between the modular length of the maximum eigenvalue and the magnitude of 1 comprises:
when the maximum characteristic value modular length is smaller than 1, the LLC resonant converter is judged to be in a stable state;
when the mode length is larger than 1, the LLC resonant converter is judged to be in a destabilization state;
and when the mode length is equal to 1, determining that the LLC resonant converter is in a critical stable state.
4. The method of claim 1, wherein the jacobian matrix is to be derived from the following equation:
Figure FDA0003528173250000032
5. the method of claim 4, wherein the state transfer matrix is:
Figure FDA0003528173250000033
wherein T is the system period.
6. The method of claim 5, wherein the maximum eigenvalue is found by:
|λI-C|＝0，
wherein, λ is the characteristic value of the state transfer matrix, and I is the identity matrix.
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双模式逆变器母线电压补偿及控制策略研究;卢雄伟;《中国优秀硕士学位论文全文数据库 工程科技II辑》;20160315(第3期);第C042-408页 *
并网逆变器小信号建模方法对比及其适用性分析;刘倪等;《电力系统自动化》;20181025(第23期);第204-213页 *

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