CN114244137A - Control method of LLC resonant matrix converter based on alternating current link - Google Patents

Control method of LLC resonant matrix converter based on alternating current link Download PDF

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CN114244137A
CN114244137A CN202111568449.4A CN202111568449A CN114244137A CN 114244137 A CN114244137 A CN 114244137A CN 202111568449 A CN202111568449 A CN 202111568449A CN 114244137 A CN114244137 A CN 114244137A
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voltage
resonant
current
resonance
llc
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CN114244137B (en
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张政权
张家瑜
刘庆想
王利民
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Southwest 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
    • 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
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/32—Means for protecting converters other than automatic disconnection
    • 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
    • H02M1/42—Circuits or arrangements for compensating for or adjusting power factor in converters or inverters
    • 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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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Ac-Ac Conversion (AREA)
  • Dc-Dc Converters (AREA)

Abstract

The invention relates to a control method of an LLC resonant matrix converter based on an alternating current link, which comprises the following steps: dividing three-phase input phase voltage into a plurality of intervals, and configuring instantaneous values of the three-phase input phase voltage to obtain excited high-line voltage and low-line voltage; calculating high line voltage and low line voltage according to a charge distribution principle to obtain equivalent synthetic voltage; obtaining an LLC resonant converter gain curve by a fundamental equivalent analysis method, and obtaining the switch working frequency and the voltage value of the resonant capacitor in different modes by combining a resonant current curve; working time of high line voltage and low line voltage is calculated, and the LLC resonant matrix converter is excited together according to the respective working time; and configuring the switch working states of the switch matrix according to the difference of the three-phase input phase voltages in different intervals. The frequency conversion control method can realize better voltage regulation capability, higher power factor and lower harmonic current, so that the circuit has wider application scenes.

Description

Control method of LLC resonant matrix converter based on alternating current link
Technical Field
The invention relates to the technical field of converters, in particular to a control method of an LLC resonant matrix converter based on an alternating current link.
Background
The power supply is used as a basic component for electric energy conversion, and is continuously developed towards miniaturization, and the switching power supply has high power density, so the switching power supply is widely applied to power supply products based on power electronic technology, wherein an AC-DC converter plays an important role in switching power supply integration; however, a bridge rectifier bridge is generally adopted as an input rectification circuit in a conventional AC-DC converter, which may result in low conversion efficiency, and may also cause pollution to the power grid environment due to higher harmonics in the current, and a DC energy storage link exists in the conversion of electric energy, requiring a huge electrolytic capacitor.
Therefore, the matrix converter without intermediate direct-current energy storage becomes an object of attention of researchers, and has the advantages of bidirectional energy transmission, adjustable input power factor, low harmonic content, small size and the like. Meanwhile, the soft switching technology based on the resonance principle improves the high-frequency performance and dynamic response, reduces the switching loss and improves the working frequency. The LLC resonant converter can respectively realize the voltage boosting function and the voltage reducing function under different working frequencies, and particularly can realize ZVS of a switching tube and ZCS of a secondary rectifier diode when the working frequency is higher than a cut-off frequency and lower than an LC resonant frequency, so that the switching loss is reduced, and the conversion efficiency is improved. LLC is also favored by researchers because of its high efficiency, high power density, and soft switching characteristics.
Better AC-DC conversion performance can be achieved by using the characteristics of the matrix converter and the LLC resonant converter. However, the matrix converter usually adopts multi-level excitation, and the switching tubes are bidirectional switching tubes connected back to back, so that the number of the switching tubes in three-phase alternating current is large. However, the traditional control strategy of the LLC resonant converter is usually to use a fundamental equivalent analysis method or an extended function analysis method for the two-level excitation, the fundamental equivalent analysis method is too simplified, high harmonics in the circuit are ignored, the error may be larger in the high-frequency operating mode, the extended function analysis method has higher modeling accuracy, but the modeling process is relatively complex, and both methods are to integrally control the switch, and therefore cannot be applied to the matrix converter, and a new control method applied to the LLC resonant matrix converter needs to be studied.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a control method of an LLC resonant matrix converter based on an alternating current link, and solves the problems of the prior art.
The purpose of the invention is realized by the following technical scheme: a control method of an ac link based LLC resonant matrix converter, the control method comprising:
s1, dividing the three-phase input phase voltage into a plurality of intervals, and carrying out instantaneous value V on the collected three-phase input phase voltage according to the magnitude relation of the phase voltage in each intervala、Vb、VcConfiguring to obtain excited high-line voltage VnAnd low line voltage Vm；
S2, dividing the high line voltage V according to the charge distribution principlenAnd low line voltage VmCalculating to obtain equivalent synthetic voltage Vin；
Specifically, the quantity of electric charge transferred when high line voltage excitation in a half period is set to be Q1The amount of charge transferred when energized by low line voltage is Q2According to the principle of charge distribution, the ratio of the amount of charge flowing in each phase should be equal to the absolute value of the ratio of the voltages of each phase, and therefore can be set as:
Figure BDA0003422572050000021
the equivalent synthetic voltage is:
Figure BDA0003422572050000022
s3, obtaining an LLC resonant converter gain curve through a fundamental wave equivalent analysis method, and combining the LLC resonant converter gain curve with resonant currentObtaining the voltage value V of the switch working frequency and the resonant capacitor under different voltage boosting and reducing modes by a curvecr；
S4, calculating high line voltage VnAnd low line voltage VmAccording to the working time of the LLC resonant matrix converter, the LLC resonant matrix converter is excited together according to the respective working time;
and S5, generating corresponding PWM waves according to the difference and the working time of the three-phase input phase voltages in different intervals, and configuring the switch working state of the switch matrix.
Obtaining an LLC resonant converter gain curve by a fundamental equivalent analysis method, and obtaining a switching working frequency and a voltage peak value V of a resonant capacitor under different modes of voltage boosting and voltage reducing by combining a resonant current curvecrThe method comprises the following steps:
obtaining a gain curve according to a fundamental equivalent analysis method
Figure BDA0003422572050000023
Wherein, therein
Figure BDA0003422572050000024
Figure BDA0003422572050000025
LrIs a resonant inductor, LmFor exciting the inductance, frIs the resonant frequency, fsTo the operating frequency, ZrIs a resonant impedance, RacIs an equivalent load;
obtaining the effective value of the resonance current of the step-down mode as the curve according to the resonance current of the LLC resonance converter in the step-up mode and the step-down mode
Figure BDA0003422572050000026
And boost mode resonant current effective value
Figure BDA0003422572050000027
Figure BDA0003422572050000028
When resonant current and excitationWhen the inductive currents are equal, the voltage value of the resonant capacitor in the voltage reduction mode is obtained through integration
Figure BDA0003422572050000029
And the voltage value of the resonant capacitor in the boost mode is
Figure BDA00034225720500000210
Wherein ω isrTo resonate angular velocity, CrIs a resonant capacitor, V0Is rated output voltage, n is transformer transformation ratio, R is load, T is work period obtained by gain curve, TrIs the resonance period.
The calculated high line voltage VnAnd low line voltage VmAnd jointly exciting the LLC resonant matrix converters in dependence on the respective operating times comprises:
solving a differential equation of the LLC resonant converter to obtain a voltage and current solution V of the buck mode resonant capacitorcr＝Vin-sgn(ir-im)nVo+(V-Vin+sgn(ir-im)nVo)cos(ωrt)+iZ1sin(ωrt)，
Figure BDA0003422572050000031
In the boost mode, an excitation inductor participates in resonance, and the on-off of the voltage and the current of a resonance capacitor is V respectivelycr＝Vin+(V'-Vin)cos(ωt)+i'Z2sin(ωt)，
Figure BDA0003422572050000032
Figure BDA0003422572050000033
Where V, i is the initial voltage and initial current in buck mode,
Figure BDA0003422572050000034
for the resonant impedance, V ', i' are the initial voltage and initial current in boost mode,
Figure BDA0003422572050000035
is the common resonant impedance;
for the voltage reduction mode, according to the trigonometric function relation of the general solution, the resonance capacitor voltage is taken as the abscissa, the resonance current and the resonance impedance Z are taken as the abscissa in the plane rectangular coordinate system1The product of the two is a state plan constructed by the ordinate, corresponding track graphs are drawn, and the working time of each part is obtained according to the radian of the track in the track graphs;
for the boosting mode, according to the trigonometric function relation of the general solution, a state plan is constructed in a plane rectangular coordinate system, a corresponding track graph is drawn, the abscissa represents the voltage of the resonant capacitor, and the ordinate represents the resonant current and the resonant impedance Z1Product of (2) and resonant current and resonant impedance Z2And calculating the working time of each track according to the resonance period and the common resonance period.
The working time of each part obtained according to the radian of the track in the track graph comprises the following steps:
respectively expressed as V in O1n-nV0、O2＝Vm-nV0、O3＝-Vn-nV0As the center of circle, in r1、r2、r3Drawing a track graph for the radius, and setting the initial voltage of the first part of the track graph as V1The second part initial voltage is-V4The third part has an initial voltage of V2End voltage is V3；
Obtained according to the charge distribution principle
Figure BDA0003422572050000036
The function relation existing in the locus diagram is r1 2-(V2-O1)2＝r2 2-(V2-O2)2，r3 2-(V3-O3)2＝r2 2-(V3-O2)2，r3 2-(V4-O3)2＝r1 2-(V4+O1)2；
To function relationLine solution to obtain
Figure BDA0003422572050000037
Figure BDA0003422572050000038
And according to the resonant frequency TrAnd the radian of each track obtains the working time of each part
Figure BDA0003422572050000039
Figure BDA00034225720500000310
The calculating the working time of each track according to the resonance period and the common resonance period comprises:
respectively expressed as V in O1n-nV0、O2＝Vm-nV0、VmAs the center of circle, in r1、r2、r3Drawing a track graph for the radius, and setting the initial voltage of the first part of the track graph as V1The second part has initial voltage V2The third part has an initial voltage of V3End voltage is V4；
Obtained according to the charge distribution principle
Figure BDA00034225720500000311
The function relation existing in the locus diagram is r1 2-(V2-O1)2＝r2 2-(V2-O2)2，[r3 2-(V3-Vm)2]Z1＝[r2 2-(V3-O2)2]Z2，[r3 2-(V4-Vm)2]Z1＝[r1 2-(V4+O1)2]Z2；
Solving the functional relation to obtain
Figure BDA0003422572050000041
Figure BDA0003422572050000042
According to the resonance period TrAnd a common resonance period Tr' working time given to each trajectory can be calculated as
Figure BDA0003422572050000043
Figure BDA0003422572050000044
In step S1, the three-phase input phase voltage is divided into 12 sections, and the high line voltage V of each sectionnAnd low line voltage VmIs set as follows:
interval 1: va≥0，Vb<0，Vc≥0，Va<Vc，VH＝Vb，VM＝Va，VL＝Vc；
Interval 2: va≥0，Vb<0，Vc≥0，Va>Vc，VH＝Vb，VM＝Vc，VL＝Va；
Interval 3: va>0，Vb≤0，Vc≤0，Vb<Vc，VH＝Va，VM＝Vc，VL＝Vb；
Interval 4: va>0，Vb≤0，Vc≤0，Vb>Vc，VH＝Va，VM＝Vb，VL＝Vc；
Interval 5: va≥0，Vb≥0，Vc<0，Va>Vb，VH＝Vc，VM＝Vb，VL＝Va；
Interval 6: va≥0，Vb≥0，Vc<0，Va<Vb，VH＝Vc，VM＝Va，VL＝Vb；
Interval 7: va≤0，Vb>0，Vc≤0，Va>Vc，VH＝Vb，VM＝Va，VL＝Vc；
Interval 8: va≤0，Vb>0，Vc≤0，Va<Vc，VH＝Vb，VM＝Vc，VL＝Va；
Interval 9: va<0，Vb≥0，Vc≥0，Vb>Vc，VH＝Va，VM＝Vc，VL＝Vb；
Interval 10: va<0，Vb≥0，Vc≥0，Vb<Vc，VH＝Va，VM＝Vb，VL＝Vc；
Interval 11: va≤0，Vb≤0，Vc>0，Va<Vb，VH＝Vc，VM＝Vb，VL＝Va；
Interval 12: va≤0，Vb≤0，Vc>0，Va>Vb，VH＝Vc，VM＝Va，VL＝Vb；
Wherein, high line voltage Vn＝|VH-VLL, low line voltage Vm＝|VH-VM|。
The control method is realized based on an LLC resonant matrix converter, wherein the LLC resonant matrix converter comprises a three-phase power grid, an input filter, a bidirectional switch matrix, an LLC resonant circuit, a high-frequency transformer, a high-frequency rectifier and a load; the three-phase input phase voltage is connected with a matrix converter with 12 switches through an input filter, LLC resonance is excited by a switch matrix, energy is transferred by the LLC resonance through a transformer, and finally a filter capacitor and a load are charged by a high-frequency rectifier.
The invention has the following advantages: the control method of the LLC resonant matrix converter based on the alternating current link technology can realize better voltage regulation capability, higher power factor and lower harmonic current, so that the circuit has wider application scenes. Compared with the traditional matrix converter, the characteristics of equivalent synthetic voltage and LLC resonant frequency conversion work are utilized, so that the load voltage can be regulated while the high power factor of the three-phase input phase voltage is maintained. Compared with the traditional LLC resonant converter, the working frequency of the switch can be determined more accurately by analyzing the common solution of the differential equations of the voltage and the current of the resonant capacitor in the two modes of voltage reduction and voltage boosting, and the error is smaller under the high-frequency condition.
Drawings
FIG. 1 is a schematic diagram of an LLC resonant matrix converter topology based on AC link technology;
FIG. 2 is a schematic diagram of a 12 sector division of three phase input phase voltages;
FIG. 3 is a circuit diagram of the fundamental equivalent analysis of a full-bridge LLC resonant converter;
FIG. 4 is a gain curve graph of the LLC resonant converter obtained by a fundamental equivalent analysis;
FIG. 5 is a schematic diagram of a buck mode resonant current of the LLC resonant converter;
FIG. 6 is a schematic diagram of a boost mode resonant current of the LLC resonant converter;
FIG. 7 is a plan view of the operation state of the buck mode of the LLC resonant matrix converter based on the AC link technique;
FIG. 8 is a plan view of the operation state of the boost mode of the LLC resonant matrix converter based on the AC link technique;
FIG. 9 is a PWM schematic of 12 switches in buck mode;
fig. 10 is a PWM schematic of 12 switches in boost mode.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the present application provided below in connection with the appended drawings is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application. The invention is further described below with reference to the accompanying drawings.
The converter circuit topology structure adopted by the invention is shown in figure 1, three-phase input phase voltage is connected with a matrix converter with 12 switches through an input filter, LLC resonance is excited by a switch matrix, energy is transmitted by the LLC resonance through a transformer, and finally a filter capacitor and a load are charged by a high-frequency rectifier. The specific parameters are as follows: three-phase input voltage is 220V/50Hz, output voltage is 500V, output power is 15Kw, and resonant inductor Lr34.4189uH, resonant capacitance Cr294.377nF, excitation inductance Lm＝103.2567uH。
In the matrix converter, the configuration of three-phase input phase voltages can be realized through switches, and corresponding excitation voltages are obtained. Therefore, in order to implement the control strategy of the present invention, the operating state of the input excitation voltage needs to be specified. According to the relative magnitude relationship of three-phase input phase voltages, each input phase voltage period can be divided into 12 sectors as shown in fig. 2:
interval 1: va≥0，Vb<0，Vc≥0，Va<Vc，VH＝Vb，VM＝Va，VL＝Vc；
Interval 2: va≥0，Vb<0，Vc≥0，Va>Vc，VH＝Vb，VM＝Vc，VL＝Va；
Interval 3: va>0，Vb≤0，Vc≤0，Vb<Vc，VH＝Va，VM＝Vc，VL＝Vb；
Interval 4: va>0，Vb≤0，Vc≤0，Vb>Vc，VH＝Va，VM＝Vb，VL＝Vc；
Interval 5: va≥0，Vb≥0，Vc<0，Va>Vb，VH＝Vc，VM＝Vb，VL＝Va；
Interval 6: va≥0，Vb≥0，Vc<0，Va<Vb，VH＝Vc，VM＝Va，VL＝Vb；
Interval 7: va≤0，Vb>0，Vc≤0，Va>Vc，VH＝Vb，VM＝Va，VL＝Vc；
Interval 8: va≤0，Vb>0，Vc≤0，Va<Vc，VH＝Vb，VM＝Vc，VL＝Va；
Interval 9: va<0，Vb≥0，Vc≥0，Vb>Vc，VH＝Va，VM＝Vc，VL＝Vb；
Interval 10: va<0，Vb≥0，Vc≥0，Vb<Vc，VH＝Va，VM＝Vb，VL＝Vc；
Interval 11: va≤0，Vb≤0，Vc>0，Va<Vb，VH＝Vc，VM＝Vb，VL＝Va；
Interval 12: va≤0，Vb≤0，Vc>0，Va>Vb，VH＝Vc，VM＝Va，VL＝Vb；
Defining a high line voltage Vn＝|VH-VLI and Low line Voltage Vm＝|VH-VML, wherein VHIs the phase with the maximum voltage absolute value, VMIs the voltage absolute value minimum phase, VLIs the voltage absolute value centered phase. Three-phase input phase voltage V acquired in real timea、Vb、VcThrough the division of 12 sectors, a high line voltage and a low line voltage are obtained, and the two voltages jointly excite the LLC resonance. In order to make the excitation mode have higher power factor, the charge quantity transferred when high-line voltage excitation in a half period is assumed to be Q according to the charge distribution principle1The amount of charge transferred when energized by low line voltage is Q2The ratio of the amount of charge flowing in each phase should be equal to the absolute value of the ratio of the phase voltages of each phase, and therefore can be defined:
Figure BDA0003422572050000061
at the same time due to the equivalent resultant voltage VinThe transmitted energy is equal to obtain:
VnQ1+VmQ2＝Vin(Q1+Q2)，
the equivalent resulting voltage can be derived as:
Figure BDA0003422572050000062
when the output voltage is constant, the equivalent combination is usedThe gain | G | of the converter can be obtained through voltage forming, and the working frequency of the switch can be correspondingly predicted through a fundamental equivalent analysis method. A fundamental wave equivalent analysis model of a full-bridge LLC resonant converter is shown in FIG. 3, and an input voltage V is obtainedinPerforming Fourier series expansion, and taking the first term to obtain the input voltage of a model as follows:
Figure BDA0003422572050000071
Figure BDA0003422572050000072
the secondary side voltage of the transformer obtained by performing Fourier series expansion on the load voltage is as follows:
Figure BDA0003422572050000073
Figure BDA0003422572050000074
the secondary side current of the transformer obtained by the same method is as follows:
Figure BDA0003422572050000075
therefore, after the voltage and the current of the secondary side of the transformer are equivalent to the primary side of the transformer, the equivalent output voltage is obtained as follows:
Figure BDA0003422572050000076
the equivalent load is:
Figure BDA0003422572050000077
according to the fundamental wave equivalent model, the direct current gain of the LLC circuit can be deduced as follows:
Figure BDA0003422572050000078
wherein
Figure BDA0003422572050000079
The gain curve is shown in fig. 4, when the circuit parameters are known, the gain | G | is related to the frequency ratio x, assuming that h is 3. However, the solution of the high-order equation is difficult, so that the frequency ratio under different equivalent synthetic voltage conditions can be obtained by solving the curve difference, and the working frequency of the switch can be predicted through the circuit resonance parameters.
Due to the switching of the switches in the switch matrix, the predicted switching frequency cannot be directly applied to the switch matrix. The on-time of each switch can be further determined by analysis of the LLC resonant converter differential equation. However, when the LLC resonant converter operates at different frequencies, the voltage and the current on the resonant capacitor have certain differences, and therefore, it is necessary to separately discuss a step-down mode in which the operating frequency is higher than the resonant frequency and a step-up mode in which the operating frequency is lower than the resonant frequency and higher than the cut-off frequency. The buck mode resonant current is shown in fig. 5, and it can be assumed that the resonant current is:
Figure BDA00034225720500000710
the exciting inductance current is:
Figure BDA00034225720500000711
where the resonant current is equal to the magnetizing inductor current at time t 1.
Making the charge transferred in and out equal, the equation can be derived:
Figure BDA00034225720500000712
the calculation can obtain:
Figure BDA00034225720500000713
when the resonant current and the exciting inductor current are equal at time t 1:
Figure BDA0003422572050000081
the effective value of the resonant current is therefore:
Figure BDA0003422572050000082
the peak value of the resonant capacitor voltage obtained by integrating the resonant current is:
Figure BDA0003422572050000083
boost mode resonant current as shown in fig. 6, the resonant current can be assumed to be:
Figure BDA0003422572050000084
the exciting inductance current is:
Figure BDA0003422572050000085
the difference from the step-down mode is that the voltage of the resonant capacitor needs to be divided into two parts, firstly, the part of the excitation inductor participating in resonance is ignored, and the working period of the switch is the resonance period TrMaking the charge transferred in and out equal, the equation can be derived:
Figure BDA0003422572050000086
the calculation can obtain:
Figure BDA0003422572050000087
when the resonant current and the exciting inductor current are equal at time t 1:
Figure BDA0003422572050000088
the effective value of the resonant current is therefore:
Figure BDA0003422572050000089
meanwhile, when the excitation inductor participates in resonance, the resonance current is basically kept consistent, so that the current at the moment is considered as follows:
Figure BDA00034225720500000810
by the period T found by the gain curve, i can be calculatedmThe duration of (c). The peak value of the resonant capacitor voltage obtained by adding the two parts of voltages is as follows:
Figure BDA00034225720500000811
wherein ω isrTo resonate angular velocity, CrIs a resonant capacitor, V0Is rated output voltage, n is transformer transformation ratio, R is load, T is work period obtained by gain curve, TrIs the resonance period.
The differential to establish the LLC resonant circuit is:
Figure BDA0003422572050000091
Figure BDA0003422572050000092
Figure BDA0003422572050000093
solving the system of equations yields:
Vcr＝Vin-sgn(ir-im)nVo+(V-Vin+sgn(ir-im)nVo)cos(ωrt)+iZ1sin(ωrt)，
Figure BDA0003422572050000094
where V, i is the initial voltage and initial current,
Figure BDA0003422572050000095
is the resonant impedance.
The voltage-reducing mode is illustrated in plan view in fig. 7, where O1 ═ Vn-nV0，O2＝Vm-nV0，O3＝-Vn-nV0，r1＝O1+VcrWherein the voltage V at time t01＝-V3And the voltage is-V at the time t14And the voltage is-V at the time t2crAnd the voltage is V at the time t32。
By comparing the output with the synthesized input voltage, a curve of gain and frequency is introduced to obtain the work period T of the synthesized voltage, and the resonant current is equal to the exciting inductor current at the moment of T1, then:
Figure BDA0003422572050000096
the graphical functional relationship can therefore be used to derive:
Figure BDA0003422572050000097
due to the constraints of the grid-side charge distribution, it is possible to obtain:
Figure BDA0003422572050000098
then there are:
Figure BDA0003422572050000099
the functional relationship also exists:
r1 2-(V2-O1)2＝r2 2-(V2-O2)2，
r3 2-(V3-O3)2＝r2 2-(V3-O2)2，
r3 2-(V4-O3)2＝r1 2-(V4+O1)2，
the above several formulas can be solved simultaneously respectively:
Figure BDA00034225720500000910
Figure BDA00034225720500000911
resonant period T due to resonant frequencyrAnd a common resonance period Tr' determination, the operating times of the high and low lines can be calculated respectively:
Figure BDA0003422572050000101
Figure BDA0003422572050000102
Figure BDA0003422572050000103
Figure BDA0003422572050000104
the boost mode differs from the buck mode in that when the magnetizing inductance participates in resonance:
Vcr＝Vin+(V′-Vin)cos(ωt)+i′Z2sin(ωt)，
Figure BDA0003422572050000105
where V ', i' are the initial voltage and initial current,
Figure BDA0003422572050000106
is the common resonant impedance.
The state plan is shown in fig. 8, where O1 ═ Vn-nV0，O2＝Vm-nV0，r1＝O1+VcrWherein the voltage V at time t01＝-V4And the voltage is-V at the time t1crAnd the voltage is V at the time t22And the voltage is V at the time t33. Since the impedance is different from the time t3 to the time t4, but the current is still continuous, the impedance is put into a coordinate system after finishing.
The analysis considers that the time t3-t4 is the time when the switch work period exceeds the resonance period. Meanwhile, as the resonant current and the exciting inductance current can be regarded as being kept unchanged, the following steps are provided:
Figure BDA0003422572050000107
the graphical functional relationship can therefore be used to derive:
Figure BDA0003422572050000108
Figure BDA0003422572050000109
due to the constraints of the grid-side charge distribution, it is possible to obtain:
Figure BDA00034225720500001010
then there are:
Figure BDA00034225720500001011
the functional relationship also exists:
r1 2-(V2-O1)2＝r2 2-(V2-O2)2，
[r3 2-(V3-Vm)2]Z1＝[r2 2-(V3-O2)2]Z2，
[r3 2-(V4-Vm)2]Z1＝[r1 2-(V4+O1)2]Z2，
the formula above can be combined to obtain:
Figure BDA0003422572050000111
Figure BDA0003422572050000112
the parameters in the state plan are obtained, and the working time of the high line and the low line can be calculated respectively due to the determination of the resonant frequency:
Figure BDA0003422572050000113
Figure BDA0003422572050000114
Figure BDA0003422572050000115
Figure BDA0003422572050000116
and according to the division of the interval, generating corresponding PWM (pulse width modulation) according to the control time obtained by the calculation and configuring the PWM to the corresponding switch. Taking the three-phase input phase voltage in sector 3 as an example, the operation of the switch in the buck mode and the boost mode will be described below. When V isa＝273.8V、Vb＝-12.3V、VcWhen it is-261.9V can be calculatedinWhen the LLC resonance is in buck mode, 524.6, t is calculated as described above0-1＝0.2546μs，t1-2＝1.3142μs，t2-3＝7.4064μs，t3-40.3463 mus. All in onea＝294.0V、Vb＝-71.5V、VcWhen it is-222.5V can be calculatedin479.8, when the LLC resonance will operate in boost mode, t0-1＝1.4651μs，t1-2＝6.3713μs，t2-3＝1.6624μs，t3-4＝0.4179μs。
Finally, the switching time is configured to be corresponding PWM, and for the buck mode, the PWM is as shown in fig. 9, and the working process is as follows:
time t0-t 1: zero current turning-on of the switches Q1 and Q8 before the time of t0 is prepared for reverse freewheeling, other switches are turned off at the time of t0, the resonant current and the exciting inductance current keep the original directions, zero voltage turning-on of the switches Q4 and Q11 is achieved, and at the moment, the current flows through Q8, Q11, the exciting inductance, the transformer, the resonant capacitor, the resonant inductance, Q1 and Q4. The resonant current continuously decreases to zero, and the exciting inductor current increases in the time t0-t1 because the resonant current is larger than the exciting inductor current in the time t0-t 1. So that the input voltage is a positive high line voltage VabThe primary side voltage of the transformer is-nV0；
time t1-t 2: the resonant current remains unchanged and the inductive current is excitedDecreasing during time t1-t 2. So that the input voltage is a positive high line voltage Vab(ii) a Primary side voltage of the transformer is + nV0；
time t2-t 3: keeping the switch on, the current flows through Q1, Q4, excitation inductance, transformer, resonant capacitor, resonant inductance, Q8, Q11, and resonant current becomes forward, and excitation inductance current reduces to zero in the reverse direction first, then becomes forward and increases gradually. Before the time t3 of clamping the high line, the switch Q12 is switched on at zero current to prepare for switching the low line;
time t3-t 4: and at the time of t3, turning off the Q8 and the Q11, naturally commutating the current, turning on the switch Q9 at zero voltage, and enabling the current to flow through the Q1, the Q4, the excitation inductor, the transformer, the resonant capacitor, the resonant inductor, the Q12 and the Q9. The switches Q5, Q10 are turned on with zero current before time t4 in preparation for the negative half cycle.
For boost mode PWM, as shown in fig. 10, the operation process is:
time t0-t 1: zero current of switches Q1 and Q8 is turned on to prepare for reverse freewheeling before the time of t0, other switches are turned off at the time of t0, the resonant current and the exciting inductance current keep the original directions, and dead time t is passeddAnd zero voltage opening of the switches Q4 and Q11 is realized, and at the moment, current flows through Q8 and Q11, the excitation inductor, the transformer, the resonant capacitor, the resonant inductor, Q1 and Q4. The resonant current is continuously reduced to zero, and the exciting inductance current is continuously reduced. The voltage at the input end is positive high-line voltage Vab(ii) a Primary side voltage of the transformer is + nV0；
time t1-t 2: keeping the switch on, the current flows through Q1, Q4, excitation inductance, transformer, resonant capacitor, resonant inductance, Q8, Q11, and resonant current becomes forward, and excitation inductance current reduces to zero in the reverse direction first, then becomes forward and increases gradually. Before the time t2 of clamping the high line, the switch Q12 is switched on at zero current to prepare for switching the low line;
time t2-t 3: turning off the Q8 and the Q11 at the time of t2, naturally commutating current, realizing a zero-voltage turn-on switch Q9, and enabling the current to flow through Q1, Q4, an excitation inductor, a transformer, a resonant capacitor, a resonant inductor, Q12 and Q9;
time t3-t 4: resonant current and excitation at time t3The inductive currents are equal, and no current passes through the transformer. At the time t3-t4, the exciting inductor current is basically kept unchanged, so that the circuit can be regarded as that the resonant inductor and the exciting inductor jointly participate in resonance, the resonance period changes, and the voltage of the input end is the positive low-line voltage Vac. The switches Q5, Q10 are turned on with zero current before time t4 in preparation for the negative half cycle.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (7)

1. A control method of an LLC resonant matrix converter based on an AC link is characterized in that: the control method comprises the following steps:
s1, dividing the three-phase input phase voltage into a plurality of intervals, and carrying out instantaneous value V on the collected three-phase input phase voltage according to the magnitude relation of the phase voltage in each intervala、Vb、VcConfiguring to obtain excited high-line voltage VnAnd low line voltage Vm；
S2, dividing the high line voltage V according to the charge distribution principlenAnd low line voltage VmCalculating to obtain equivalent synthetic voltage Vin；
S3, obtaining an LLC resonant converter gain curve through a fundamental wave equivalent analysis method, and obtaining a switch working frequency and a voltage value V of a resonant capacitor under different modes of voltage boosting and voltage reducing by combining a resonant current curvecr；
S4, calculating high line voltage VnAnd low line voltage VmAccording to the working time of the LLC resonant matrix converter, the LLC resonant matrix converter is excited together according to the respective working time;
and S5, generating corresponding PWM waves according to the difference and the working time of the three-phase input phase voltages in different intervals, and configuring the switch working state of the switch matrix.
2. A method of controlling an ac link based LLC resonant matrix converter in accordance with claim 1, characterized by: obtaining an LLC resonant converter gain curve by a fundamental equivalent analysis method, and obtaining a switching working frequency and a voltage peak value V of a resonant capacitor under different modes of voltage boosting and voltage reducing by combining a resonant current curvecrThe method comprises the following steps:
obtaining a gain curve according to a fundamental equivalent analysis method
Figure FDA0003422572040000011
Wherein, therein
Figure FDA0003422572040000012
Figure FDA0003422572040000013
LrIs a resonant inductor, LmFor exciting the inductance, frIs the resonant frequency, fsTo the operating frequency, ZrIs a resonant impedance, RacIs an equivalent load;
obtaining the effective value of the resonance current of the step-down mode as the curve according to the resonance current of the LLC resonance converter in the step-up mode and the step-down mode
Figure FDA0003422572040000014
And boost mode resonant current effective value
Figure FDA0003422572040000015
Figure FDA0003422572040000016
When the resonant current is equal to the exciting inductance current, the voltage value of the resonant capacitor in the voltage reduction mode is obtained by integration
Figure FDA0003422572040000017
And the voltage value of the resonant capacitor in the boost mode is
Figure FDA0003422572040000018
Wherein ω isrTo resonate angular velocity, CrIs a resonant capacitor, V0Is rated output voltage, n is transformer transformation ratio, R is load, T is work period obtained by gain curve, TrIs the resonance period.
3. A method of controlling an ac link based LLC resonant matrix converter in accordance with claim 1, characterized by: the calculated high line voltage VnAnd low line voltage VmAnd jointly exciting the LLC resonant matrix converters in dependence on the respective operating times comprises:
solving a differential equation of the LLC resonant converter to obtain a voltage and current solution V of the buck mode resonant capacitorcr＝Vin-sgn(ir-im)nVo+(V-Vin+sgn(ir-im)nVo)cos(ωrt)+iZ1sin(ωrt)，
Figure FDA0003422572040000021
In the boost mode, an excitation inductor participates in resonance, and the on-off of the voltage and the current of a resonance capacitor is V respectivelycr＝Vin+(V′-Vin)cos(ωt)+i′Z2sin(ωt)，
Figure FDA0003422572040000022
Figure FDA0003422572040000023
Where V, i is the initial voltage and initial current in buck mode,
Figure FDA0003422572040000024
is a resonant impedance, V'),i' is the initial voltage and initial current in boost mode,
Figure FDA0003422572040000025
is the common resonant impedance;
for the voltage reduction mode, according to the trigonometric function relation of the general solution, the resonance capacitor voltage is taken as the abscissa, the resonance current and the resonance impedance Z are taken as the abscissa in the plane rectangular coordinate system1The product of the two is a state plan constructed by the ordinate, corresponding track graphs are drawn, and the working time of each part is obtained according to the radian of the track in the track graphs;
for the boosting mode, according to the trigonometric function relation of the general solution, a state plan is constructed in a plane rectangular coordinate system, a corresponding track graph is drawn, the abscissa represents the voltage of the resonant capacitor, and the ordinate represents the resonant current and the resonant impedance Z1Product of (2) and resonant current and resonant impedance Z2And calculating the working time of each track according to the resonance period and the common resonance period.
4. A method of controlling an ac link based LLC resonant matrix converter as claimed in claim 3, characterized in that: the working time of each part obtained according to the radian of the track in the track graph comprises the following steps:
respectively expressed as V in O1n-nV0、O2＝Vm-nV0、O3＝-Vn-nV0As the center of circle, in r1、r2、r3Drawing a track graph for the radius, and setting the initial voltage of the first part of the track graph as V1The second part initial voltage is-V4The third part has an initial voltage of V2End voltage is V3；
Obtained according to the charge distribution principle
Figure FDA0003422572040000026
The function relation existing in the locus diagram is r1 2-(V2-O1)2＝r2 2-(V2-O2)2，r3 2-(V3-O3)2＝r2 2-(V3-O2)2，r3 2-(V4-O3)2＝r1 2-(V4+O1)2；
Solving the functional relation to obtain
Figure FDA0003422572040000027
Figure FDA0003422572040000028
And according to the resonant frequency TrAnd the radian of each track obtains the working time of each part
Figure FDA0003422572040000029
Figure FDA00034225720400000210
5. A method of controlling an ac link based LLC resonant matrix converter as claimed in claim 3, characterized in that: the calculating the working time of each track according to the resonance period and the common resonance period comprises:
respectively expressed as V in O1n-nV0、O2＝Vm-nV0、VmAs the center of circle, in r1、r2、r3Drawing a track graph for the radius, and setting the initial voltage of the first part of the track graph as V1The second part has initial voltage V2The third part has an initial voltage of V3End voltage is V4；
Obtained according to the charge distribution principle
Figure FDA00034225720400000211
The function relation existing in the locus diagram is r1 2-(V2-O1)2＝r2 2-(V2-O2)2，[r3 2-(V3-Vm)2]Z1＝[r2 2-(V3-O2)2]Z2，[r3 2-(V4-Vm)2]Z1＝[r1 2-(V4+O1)2]Z2；
Solving the functional relation to obtain
Figure FDA0003422572040000031
Figure FDA0003422572040000032
According to the resonance period TrAnd a common resonance period Tr' working time given to each trajectory can be calculated as
Figure FDA0003422572040000033
Figure FDA0003422572040000034
6. A control method for an AC link based LLC resonant matrix converter according to any of claims 1-5, characterized by: in step S1, the three-phase input phase voltage is divided into 12 sections, and the high line voltage V of each sectionnAnd low line voltage VmIs set as follows:
interval 1: va≥0，Vb＜0，Vc≥0，Va＜Vc，VH＝Vb，VM＝Va，VL＝Vc；
Interval 2: va≥0，Vb＜0，Vc≥0，Va＞Vc，VH＝Vb，VM＝Vc，VL＝Va；
Interval 3: va＞0，Vb≤0，Vc≤0，Vb＜Vc，VH＝Va，VM＝Vc，VL＝Vb；
Interval 4: va＞0，Vb≤0，Vc≤0，Vb＞Vc，VH＝Va，VM＝Vb，VL＝Vc；
Interval 5: va≥0，Vb≥0，Vc＜0，Va＞Vb，VH＝Vc，VM＝Vb，VL＝Va；
Interval 6: va≥0，Vb≥0，Vc＜0，Va＜Vb，VH＝Vc，VM＝Va，VL＝Vb；
Interval 7: va≤0，Vb＞0，Vc≤0，Va＞Vc，VH＝Vb，VM＝Va，VL＝Vc；
Interval 8: va≤0，Vb＞0，Vc≤0，Va＜Vc，VH＝Vb，VM＝Vc，VL＝Va；
Interval 9: va＜0，Vb≥0，Vc≥0，Vb＞Vc，VH＝Va，VM＝Vc，VL＝Vb；
Interval 10: va＜0，Vb≥0，Vc≥0，Vb＜Vc，VH＝Va，VM＝Vb，VL＝Vc；
Interval 11: va≤0，Vb≤0，Vc＞0，Va＜Vb，VH＝Vc，VM＝Vb，VL＝Va；
Interval 12: va≤0，Vb≤0，Vc＞0，Va＞Vb，VH＝Vc，VM＝Va，VL＝Vb；
Wherein, high line voltage Vn＝|VH-VLL, low line voltage Vm＝|VH-VM|。
7. A control method for an AC link based LLC resonant matrix converter according to claim 6, characterized by: the control method is realized based on an LLC resonant matrix converter, wherein the LLC resonant matrix converter comprises a three-phase power grid, an input filter, a bidirectional switch matrix, an LLC resonant circuit, a high-frequency transformer, a high-frequency rectifier and a load; the three-phase input phase voltage is connected with a matrix converter with 12 switches through an input filter, LLC resonance is excited by a switch matrix, energy is transferred by the LLC resonance through a transformer, and finally a filter capacitor and a load are charged by a high-frequency rectifier.
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