CN114362531A - Numerical calculation method of single-phase single-stage AC/DC resonant converter - Google Patents

Numerical calculation method of single-phase single-stage AC/DC resonant converter Download PDF

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CN114362531A
CN114362531A CN202210029914.5A CN202210029914A CN114362531A CN 114362531 A CN114362531 A CN 114362531A CN 202210029914 A CN202210029914 A CN 202210029914A CN 114362531 A CN114362531 A CN 114362531A
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李想
郭留牛
郎天辰
胡海兵
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Nanjing University of Aeronautics and Astronautics
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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
    • H02M3/305—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 thyratron or thyristor type requiring extinguishing means
    • H02M3/315—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 thyratron or thyristor type requiring extinguishing means using semiconductor devices only
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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    • 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
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
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Abstract

The invention discloses a numerical calculation method of a single-phase single-stage AC/DC resonant converter. The phase of the continuously variable input voltage is divided into N equal parts. Because the time length of each phase interval is short enough, the external excitation of adjacent periods can be assumed to be fixed, the resonance variable change conditions of each switching period in each interval are basically similar, each phase interval can be described by adopting the switching period condition corresponding to the phase, and the problems that the number of switching periods contained in each phase interval is unknown and the initial state and the tail state of the resonant cavity of each switching period are also unknown are solved. And carrying out numerical calculation through the equivalent relation and the equation unknown quantity existing in the switching period to obtain the one-to-one corresponding relation of the working mode of the resonant cavity, the change condition of each resonant variable of the resonant cavity and the switching frequency-input phase. And sorting the calculation results according to the phase continuous change sequence by means of numerical calculation software to obtain corresponding results under different phases.

Description

Numerical calculation method of single-phase single-stage AC/DC resonant converter
Technical Field
The invention relates to the technical field of converter numerical calculation, in particular to a numerical calculation method of a single-phase single-stage AC/DC LLC converter based on input voltage division.
Background
With the explosive growth of distributed energy storage, micro-grid and electric automobile and power grid (V2G) applications, the isolated A C/DC converter has attracted great attention from the industry and academia. The single-phase single-stage AC/DC resonant converter is an isolated AC/DC converter with high efficiency, high power density and low cost, has research and practical values, and is used for obtaining the soft switching condition of a high-frequency switching tube and realizing the control of alternating current input current and direct current output voltage by using an LLC resonant circuit.
However, such a single-phase single-stage AC/DC resonant converter is different from a conventional DC/DC resonant converter. The resonant cavity input and output voltages of the traditional DC/DC converter are stable and have no change, and the LLC resonant cavity operation state has no change in a static period. The resonant cavity input voltage and power of the single-phase single-stage AC/DC converter are time-varying, and the output voltage fluctuates, so that the LLC resonant cavity in a static period is complex in operation state, and further the analysis of the single-phase single-stage AC/DC resonant converter is complex. Meanwhile, the traditional resonance transformation analysis method cannot obtain an accurate circuit analysis result:
conventional resonance transformation analysis methods are classified into frequency domain analysis methods and time domain analysis methods. The fundamental wave analysis (FHA) is the most common frequency domain analysis method, and the state plane method and the numerical analysis method belong to the time domain analysis method. To simplify the analysis of the resonant converter, FHA assumes that the voltage and current waveforms in the resonant cavity are purely sinusoidal, and thus a simplified and well-defined set of equations can be solved to describe the current. However, when the switching frequency is much higher than the resonant frequency, the voltage and current of the resonant cavity cannot be approximated to a sinusoidal waveform, and the analysis result of the fundamental wave analysis (FHA) will have a large error. FHA is therefore not suitable for resonant converters with a wide switching frequency range, such as single-phase single-stage AC/DC converters. In order to increase the analysis accuracy of FHA, enhanced FHA and multi-harmonic approximation analysis methods are proposed in the literature [ Liu J, Zhang J, Zheng T Q, et al. However, these methods are not only complicated in analysis but also fail to obtain accurate analysis results. The state plane analysis method is a method For converting a complex mathematical expression of a Resonant cavity into an intuitive geometric track, and can accurately draw Voltage and current tracks [ Xu, Peng, Xia, et al. However, this method cannot obtain the voltage gain of the resonant cavity, cannot obtain the characteristics between the control variable (switching frequency fs) and each resonant variable, and cannot describe the characteristics of the resonant converter. As for the numerical analysis method, it is the most accurate analysis method of the DC/DC resonant converter compared with other analysis methods. The document [ Fang X, Hu H, Shen Z J, et al, operation Mode Analysis and Peak Gain optimization of th e LLC resonance Converter [ J ]. IEEE Transactions on Power Electronics,2012,27(4):1985 and 1995 ] studies the numerical Analysis method of DC/DC LLC Resonant converters and optimizes the design of LLC Resonant cavities using the numerical Analysis method. However, there are many problems in applying the numerical analysis method to the single-phase single-stage AC/DC resonant converter: 1) the input voltage and power to the cavity are time-varying and cannot be calculated numerically for one switching cycle to represent the entire converter. 2) The output voltage of a single-phase single-stage AC/DC resonant converter fluctuates, and the equivalent circuit of the converter is different from that of a DC/DC resonant converter; 3) continuous numerical calculation of each switching cycle of a single-phase single-stage AC/DC resonant converter causes accumulation of errors, which in turn causes deviation of the calculation result.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a numerical calculation method of a single-phase single-stage AC/DC resonant converter. The phase of the continuously variable input voltage is divided into N equal parts. Because the time length of each phase interval is short enough, the external excitation (input voltage, output voltage and input power) of adjacent periods can be assumed to be fixed and unchanged, the resonance variable change conditions of each switching period in each interval are basically similar, each phase interval can be described by adopting the switching period condition corresponding to the phase, and the problems that the number of switching periods contained in each phase interval is unknown and the initial state and the tail state of the resonant cavity of each switching period are also unknown are solved. And carrying out numerical calculation through the equivalent relation and the equation unknown quantity existing in the switching period to obtain the one-to-one corresponding relation of the working mode of the resonant cavity, the change condition of each resonant variable of the resonant cavity and the switching frequency-input phase. And sorting the calculation results according to the phase continuous change sequence by means of numerical calculation software to obtain corresponding results under different phases.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a numerical calculation method of a single-phase single-stage AC/DC resonant converter, which is applied to a single-phase single-stage AC/DC resonant converter based on an LLC resonant structure, the resonant converter comprising: alternating current power supply, low pass filter circuit, the two-way switch tube of upper bridge arm, the split capacitor of lower bridge arm, LLC resonant cavity circuit structure, secondary side full wave rectifier circuit and output filter capacitor and direct current load, wherein LLC resonant cavity circuit structure includes: resonant inductor LrResonant capacitor CrAnd the excitation inductance L of the transformerm。
The numerical calculation method includes the steps of:
1) a static period (1/2 power frequency periods) of AC/DC conversion is divided into N equal phase intervals, the input voltage, the output voltage and the power in each phase interval are assumed to be constant values, and meanwhile, the switching period corresponding to each phase is assumed to be approximate to the switching period of a DC/DC LLC circuit, wherein the positive half period and the negative half period of the DC/DC conversion are unequal in input voltage.
2) Selecting a switching period as a representative from each phase interval to carry out numerical calculation, and presuming the operation mode of each LLC switching period according to the conditions of input voltage, output voltage and power, wherein the operation mode is combined by three basic resonance states (P state, N state and O state), and the state equation of each variable in the three basic resonance states in the period is found out.
3) And finding out the equivalent relation among variables in the switching period according to the operation mode of each LLC switching period and the conditions of input voltage, output voltage and power, and expressing the equivalent relation by a numerical equation set.
4) And solving an equation set of each LLC switching period by using a numerical calculation method and determining the operation mode of the period.
5) And sorting the numerical calculation results of all LLC switching periods according to the continuously-changed alternating current input phases to obtain the numerical relation between the switching frequency and the alternating current input phases under different power conditions, describing the characteristics of the converter and guiding the parameter design and the control strategy design of the converter resonant cavity.
Further, the operating mode is composed of three basic resonance states, specifically:
1) p state: output voltage u of resonant cavityoAnd its input voltage uiSame direction resonant inductance LrResonant capacitor CrResonance maintaining, exciting inductance LmIs charged by voltage uoClamping, per unit value of each variable (resonant current i in P state)LrPnExciting current iLmPnResonant capacitor voltage uCrPnOutput voltage uoPn) The time domain expression is:
Figure BDA0003465931720000041
2) n state, output voltage u of the resonatoroBecomes equal to the input voltage uiResonant inductance L in the opposite directionrResonant capacitor CrAlso maintaining resonance, but exciting inductance LmThe direction of the clamping voltage is also changed, and the per unit value of each variable (the resonant current i in the N state)LrNnExciting current iLmNnResonant capacitor voltage uCrNnOutput voltage uoNn) The time domain expression is:
Figure BDA0003465931720000042
3) o state, LLC resonant cavity and secondary side DC side disconnection, excitation inductance LmAdded to the resonant inductor LrAnd a resonance capacitor CrIn the resonance process of (2), the per unit value of each variable (resonance current i in O state)LrOnExciting current iLmOnResonant capacitor voltage uCrOnOutput voltage uoOn) The time domain expression is:
Figure BDA0003465931720000051
according to different input/output voltage and power conditions, LLC switching cycle operation modes of a single-phase single-stage AC/DC LLC converter can be divided into 4 conditions, namely a mode NP, a mode NOP, a mode PO and a mode OPO.
Further, the LLC switching frequency (about 100kHz) of a single-phase single-stage AC/DC LLC converter is much greater than the input/output voltage and current variation frequency (about 50Hz) in the AC/DC converter, so that the input/output voltage, current and power are assumed to be constant values every LLC switching cycle, and the numerical calculation method summarizes the equivalent relationship among the variables as follows:
the first type: all the inductance current and the capacitance voltage are continuously changed at all times and do not change suddenly at any time, and the resonance variables (the resonance current i in the X1 state) at the termination time of the previous state are assumed to be adjacent basic resonance states in the same half period in X1 and Y1LrX1nExciting current iLmX1nResonant capacitor voltage uCrX1nOutput voltage uoX1n) And the resonance variable at the initial time of the next state (resonance current i in the Y1 state)LrY1nExciting current iLmY1nResonant capacitor voltage uCrY1nOutput voltage uoY1n) The values are equal, and the equivalent relation formula of the continuous change of the variable is as follows:
Figure BDA0003465931720000052
assume Z1 and X2 are the fundamental resonant states before and after positive and negative half-switching cycle switching. Resonance variable at the end of the previous state (resonance current i in the Z1 state)LrZ1nExciting current iLmZ1nResonant capacitor voltage uCrZ1n) And the resonance variable at the initial time of the next state (resonance current i in X2 state)LrX2nExciting current iLmX2nResonant capacitor voltage uCrX2n) The values are equal, the value of the output voltage is equal to the output voltage of the corresponding phase, and the equivalent relational expression of the continuous change of the variables is as follows:
Figure BDA0003465931720000061
the second type: energy conservation is ensured in the LLC resonant cavity, energy generated by input current and resonant cavity input energy are conserved in each half switching cycle, assuming X, Y, Z states are three resonant states which sequentially form a positive half cycle, the energy conservation relationship being expressed as:
Figure BDA0003465931720000062
meanwhile, the input energy and the output energy of the LLC resonant cavity are conserved in each half period, wherein the output current of the LLC resonant cavity is the difference value of the resonant current and the exciting current. Assuming that the Y-state is the state O of three-element resonance, the resonance current is equal to the excitation current. The input/output energy conservation relationship is expressed as:
Figure BDA0003465931720000063
in the third category: the positive half cycle and the negative half cycle respectively account for 50% of fixed duty ratio, and assume delta tx1、Δty1And Δ tz1Expressed as the duration, Δ t, of state X1, state Y1, and state Z1, respectively, during the positive half-switching cyclex2、Δty2And Δ tz1Respectively expressed as state X2 and state Y in the positive half switching period2 and state Z2, this equivalence relation being expressed as:
Δtx1+Δty1+Δtz1＝Δtx2+Δty2+Δtz2＝Ts/2。
compared with the prior art, the invention has the advantages that:
1) the method can accurately describe the change of each variable in all switching periods in the AC/DC energy conversion process by using the numerical value, is favorable for mastering the change rule of each variable in the single-phase AC/DC conversion process and further guides the selection design of each device;
2) the obtained result can accurately obtain the switching frequency variation range and the variation rule along with the phase variation, so as to guide the parameter design and the control strategy design of the resonant cavity of the single-phase single-stage AC/DC LLC converter, and the method is simple, reliable and easy to realize;
3) the relationship between various parameters in such a single-phase single-stage AC/DC LLC converter, such as the influence of power and output voltage on the variation of its switching frequency, can be accurately reflected.
Drawings
FIG. 1 is a structural diagram of a single-phase single-stage AC/DC LLC converter according to an embodiment of the invention;
FIG. 2 is a flow chart of a numerical calculation method according to an embodiment of the present invention
FIG. 3 is a schematic diagram of an embodiment of the present invention that divides a quiescent period (half power frequency period) into N equally divided phase intervals;
FIG. 4 is a flow chart of the present invention for determining the operating mode of each phase-mapped switch within a quiescent period (half the power frequency period);
FIG. 5 is a diagram of the mode of operation of an LLC switching cycle of the invention, wherein (a) is in a P state, (b) is in an N state, and (c) is in an O state;
FIG. 6 is a graph illustrating the operation of the present invention in numerically calculating different switching cycles under different loading conditions, wherein (a) is the mode NP (pi/2 full load), (b) is the mode PO (pi/4 full load), (c) is the mode OPO (pi/4 half load), and (d) is the mode NOP (pi/2 10% load);
FIG. 7 is a graph of the numerical relationship between the switching frequency and the AC input phase obtained by numerical calculations for an embodiment of the present invention, wherein (a) is a full load condition, (b) is a half load condition, and (c) is a 10% load condition;
fig. 8 is an experimental waveform diagram of a single-phase single-stage AC/DC LLC converter according to an embodiment of the present invention, where (a) is a main waveform of a power frequency period, (b) is a waveform calculated by experimental values and numerical values of a switching frequency, and (c) is a main waveform of a switching period.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings by way of examples.
The single-phase single-stage AC/DC LLC converter structure according to the present invention is shown in fig. 1, and includes: alternating current power supply 1, low-pass filter circuit 2, two groups of bidirectional switching tubes 3 of upper bridge arm, split capacitor 4 of lower bridge arm, LLC circuit structure (resonance inductor L)rResonant capacitor CrAnd the excitation inductance L of the transformerm)5, a secondary side full-wave rectifying circuit 6, an output filter capacitor and a direct current load 7.
The method is suitable for the numerical calculation method of the converter, each switching period in the whole static period is calculated according to the numerical value of a flow chart shown in figure 2, the operation mode of each switching period and the corresponding equivalent equation set are determined, and the method is realized by the following steps:
1) dividing the AC input voltage and power phase which are continuously changed at 50Hz into 360 equal parts, as shown in FIG. 3, selecting a special working point which takes pi/2 of the AC input voltage and power as the maximum value and outputs voltage equal to the average value in 360 equal phase intervals in the static cycle, and taking the working point as the starting point of numerical calculation of the whole static cycle.
2) The parameter (u) will be knowni(π/2),uo(π/2),pi(pi/2)) are sequentially substituted into the equivalent equation set of 4 operational modes in the order shown in fig. 4 (from NP mode to OPO mode) and the numerical equation set is sequentially solved. In these equivalence equations are known: firstly, the inductive current and the capacitor voltage are always kept continuous; secondly, energy in the converter is conserved in one switching period; positive and negative half switching cycles each account for a fixed 50%. All meters using numerical calculationAnd determining the operation mode of the switching period according to whether the calculation result meets the following two conditions (whether the duration of each state is greater than 0, and the resonant current and the capacitor voltage are continuously changed).
The mode of operation is composed of three basic resonant states (P-state, N-state and O-state), as shown in figure 5,
1) p-state (fig. 5 (a)): output voltage u of resonant cavityoAnd its input voltage uiSame direction resonant inductance LrResonant capacitor CrResonance maintaining, exciting inductance LmIs charged by voltage uoClamping, per unit value of each variable (resonant current i in P state)LrPnExciting current iLmPnResonant capacitor voltage uCrPnOutput voltage uoPn) The time domain expression is:
Figure BDA0003465931720000091
2) n state (fig. 5(b)), output voltage u of the resonatoroBecomes equal to the input voltage uiResonant inductance L in the opposite directionrResonant capacitor CrAlso maintaining resonance, but exciting inductance LmThe direction of the clamping voltage is also changed, and the per unit value of each variable (the resonant current i in the N state)LrNnExciting current iLmNnResonant capacitor voltage uCrNnOutput voltage uoNn) The time domain expression is:
Figure BDA0003465931720000092
3) o state (FIG. 5(c)), the LLC resonant cavity and the secondary side are disconnected on the DC side, and the excitation inductance L ismAdded to the resonant inductor LrAnd a resonance capacitor CrIn the resonance process of (2), the per unit value of each variable (resonance current i in O state)LrOnExciting current iLmOnResonant capacitor voltage uCrOnOutput voltage uoOn) The time domain expression is:
Figure BDA0003465931720000093
according to different input/output voltage and power conditions, LLC switching cycle operation modes of a single-phase single-stage AC/DC LLC converter can be divided into 4 conditions, namely a mode NP, a mode NOP, a mode PO and a mode OPO.
3) After the numerical calculation of each of the LLC switching cycles at the operating points is completed, the numerical solutions are sequentially stored and the phase angle θ is increased (or decreased) according to the flow shown in fig. 6. Updating the known quantity (u)i(θ),uo(θ),pi(θ)) and begins calculating the value for the next LLC switching cycle. The time interval between adjacent LLC switching cycles is very short, the corresponding input/output voltage and instantaneous power variations are also very small, and the operating modes of adjacent LLC switching cycles are identical. The operating mode calculated at the last operating point is first used to calculate the switching period. If the calculation is still satisfactory, the model will be used to solve the equation for the next switching cycle. And switching to the equation of the next operation mode according to the flow shown in fig. 6 until the result is not in accordance with the requirement until a correct calculation result is found.
The numerical calculation method of the invention has the following operation conditions (operation modes and various quantity change conditions) of different switching cycles under different load conditions: the switching cycle corresponding to the phase pi/2 under the full load condition is the mode NP (a), the switching cycle corresponding to the phase pi/4 is the mode PO (b), the switching cycle corresponding to the phase pi/4 under the half load condition is the mode OPO (c), and the switching cycle corresponding to the phase pi/2 under the 10% load condition is the mode NOP (d). All states have a duration greater than 0 and the inductor current and capacitor voltage remain continuous as shown in fig. 7.
The numerical relation between the switching frequency and the alternating current input phase obtained by applying the numerical calculation method of the invention is as follows: 1) f. ofs>frPhase region and f corresponding to the mode of operation (mode NP or NOP)s<frIn the case of a phase region corresponding to the operating mode (mode PO or OPO) always at fs＝frAs a boundary line; 2) mode of operation under extremely light load(modal NP or NOP) phase region. In the region (0-pi/2), the input voltage increases along with the phase, and the converter enables the gain switching frequency to meet the requirement of direct-current voltage gain in the AC/DC conversion process. In the region [ pi/2-pi ], the switching frequency decreases with increasing phase and the input voltage is symmetric about pi/2, the switching frequency is asymmetric. As shown in fig. 7.
The numerical calculation method of the invention is experimentally verified, and fig. 8 shows an experimental waveform of the single-phase single-stage AC/DC LLC converter. Fig. 8(a) is the input current waveform, the resonant current, and the output voltage waveform for the full load case. Fig. 8(b) is a comparison of the corresponding switching frequency values at different phases and the switching frequency waveform obtained by numerical analysis, the two switching frequencies being almost coincident. Fig. 8 c is a comparison of the operation modes of the switching cycles in different phases with the operation modes (modes NP, PO, OPO) obtained in fig. 6.
The results are obtained by means of FIG. 8: the input current control and the output voltage control of the single-stage AC/DC converter based on input voltage division can be realized by applying the numerical calculation method to control the switching frequency change of the converter. The numerical calculation method provided by the invention is also proved to be capable of accurately calculating the numerical relation of variables in the single-phase single-stage AC/DC LLC converter. The numerical relation can describe the characteristics of the converter and guide the parameter design and the control strategy design of the resonant cavity of the converter, and the method is simple, reliable and easy to implement.
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (3)

1. A numerical calculation method of a single-phase single-stage AC/DC resonant converter is characterized by comprising the following steps: the numerical calculation method is applied to a single-phase single sheet based on an LLC resonance structureA stepped AC/DC resonant converter, the resonant converter comprising: the device comprises an alternating current power supply, a low-pass filter circuit, a bidirectional switch tube of an upper bridge arm, a split capacitor of a lower bridge arm, an LLC resonant cavity circuit structure, a secondary side full-wave rectification circuit, an output filter capacitor and a direct current load; wherein LLC resonant cavity circuit structure includes: resonant inductor LrResonant capacitor CrAnd the excitation inductance L of the transformerm；
The numerical calculation method includes the steps of:
1) dividing a static cycle of AC/DC conversion into N equal-divided phase intervals, assuming that input voltage, output voltage and power in each phase interval are constant values, and assuming that a switching cycle corresponding to each phase is approximate to a DC/DC LLC switching cycle with unequal positive and negative half-cycle input voltages;
2) selecting a switching period as a representative from each phase interval to carry out numerical calculation, and presuming the operation mode of each LLC switching period according to the conditions of input voltage, output voltage and power, wherein the operation mode is a state equation of each variable in three basic resonance states in the period by the combination of three basic resonance states, a P state, an N state and an O state;
3) according to the operation mode of each LLC switching period and the conditions of input voltage, output voltage and power, finding out the equivalent relation among variables in the switching period, and expressing the equivalent relation by a numerical equation set;
4) solving an equation set of each LLC switching period by using a numerical calculation method and determining the operation mode of the period;
5) and sorting the numerical calculation results of all LLC switching periods according to the continuously-changed alternating current input phases to obtain the numerical relation between the switching frequency and the alternating current input phases under different power conditions, describing the characteristics of the converter and guiding the parameter design and the control strategy design of the converter resonant cavity.
2. A numerical calculation method according to claim 1, characterized in that: the operation mode is composed of three basic resonance states, specifically:
1) p state: resonant cavity inputOutput voltage uoAnd its input voltage uiSame direction resonant inductance LrResonant capacitor CrResonance maintaining, exciting inductance LmIs charged by voltage uoAnd clamping, wherein the time domain expression of per unit value of each variable is as follows:
Figure FDA0003465931710000021
resonant current in P-state is iLrPnExcitation current of iLmPnResonant capacitor voltage of uCrPnOutput voltage of uoPn；
2) N state, output voltage u of the resonatoroBecomes equal to the input voltage uiResonant inductance L in the opposite directionrResonant capacitor CrAlso maintaining resonance, but exciting inductance LmThe direction of the clamping voltage is also changed, and the time domain expression of the per unit value of each variable is as follows:
Figure FDA0003465931710000022
resonant current of i in N stateLrNnExcitation current of iLmNnResonant capacitor voltage of uCrNnOutput voltage of uoNn；
3) O state, LLC resonant cavity and secondary side DC side disconnection, excitation inductance LmAdded to the resonant inductor LrAnd a resonance capacitor CrIn the resonance process, the time domain expression of each variable per unit value is as follows:
Figure FDA0003465931710000023
resonant current of i in O stateLrOnExcitation current of iLmOnResonant capacitor voltage of uCrOnOutput voltage of uoOn；
According to different input/output voltage and power conditions, LLC switching cycle operation modes of a single-phase single-stage AC/DC LLC converter can be divided into 4 conditions, namely a mode NP, a mode NOP, a mode PO and a mode OPO.
3. A numerical calculation method according to claim 1, characterized in that: in each LLC switching period, input/output voltage, current and power are assumed to be constant values, and the numerical calculation method summarizes equivalent relations among the variables as follows:
the first type: all the inductance current and the capacitance voltage are continuously changed and do not change suddenly at any time, and assuming that X1 and Y1 are adjacent basic resonance states in the same half period, the resonance variable at the ending time of the previous state and the resonance variable at the initial time of the next state are equal in value, and the equivalent relation of the continuous change of the variables is as follows:
Figure FDA0003465931710000031
the resonance variable at the end of the previous state is the resonance current i in the X1 stateLrX1nExcitation current iLmX1nVoltage u of resonant capacitorCrX1nOutput voltage uoX1n；
And the resonance variable at the initial time of the next state is the resonance current i in the Y1 stateLrY1nExcitation current iLmY1nVoltage u of resonant capacitorCrY1nOutput voltage uoY1n；
Assuming that Z1 and X2 are basic resonance states before and after positive and negative half switching cycle switching; the resonance variable at the ending moment of the previous state is equal to the resonance variable at the initial moment of the next state in value, the output voltage value is equal to the output voltage of the corresponding phase, and the equivalent relational expression of the continuous change of the variables is as follows:
Figure FDA0003465931710000032
the resonance variable at the end of the previous state isResonant current i in the Z1 stateLrZ1nExcitation current iLmZ1nVoltage u of resonant capacitorCrZ1n；
The resonance variable at the initial time of the next state is the resonance current i in the X2 stateLrX2nExcitation current iLmX2nVoltage u of resonant capacitorCrX2n；
The second type: energy conservation is ensured in the LLC resonant cavity, energy generated by input current and resonant cavity input energy are conserved in each half switching cycle, assuming X, Y, Z states are three resonant states which sequentially form a positive half cycle, the energy conservation relationship being expressed as:
Figure FDA0003465931710000041
meanwhile, the input energy and the output energy of the LLC resonant cavity are conserved in each half period, wherein the output current of the LLC resonant cavity is the difference value of the resonant current and the exciting current; assuming that the Y state is a state O in which three elements resonate, the resonant current is equal to the exciting current; the input/output energy conservation relationship is expressed as:
Figure FDA0003465931710000042
in the third category: the positive half cycle and the negative half cycle respectively account for 50% of fixed duty ratio, and assume delta tx1、Δty1And Δ tz1Expressed as the duration, Δ t, of state X1, state Y1, and state Z1, respectively, during the positive half-switching cyclex2、Δty2And Δ tz1Expressed as the duration of state X2, state Y2, and state Z2, respectively, during the positive half of the switching cycle, this equivalence relationship is expressed as:
Δtx1+Δty1+Δtz1＝Δtx2+Δty2+Δtz2＝Ts/2。
CN202210029914.5A 2022-01-12 2022-01-12 Numerical calculation method of single-phase single-stage AC/DC resonant converter Pending CN114362531A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115473442A (en) * 2022-11-15 2022-12-13 四川大学 Numerical analysis modeling and boundary power control method for LLC single-stage AC-DC converter
CN116345920A (en) * 2023-05-30 2023-06-27 深圳市永联科技股份有限公司 Single-stage isolated power conversion circuit and power equipment

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
XIANG LI等: "Steady-State Characterization of LLC-Based Single-Stage AC/DC Converter Based on Numerical Analysis", IEEE TRANSACTIONS ON POWER ELECTRONICS, vol. 36, no. 9, pages 9970 - 9983, XP011858217, DOI: 10.1109/TPEL.2021.3058694 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115473442A (en) * 2022-11-15 2022-12-13 四川大学 Numerical analysis modeling and boundary power control method for LLC single-stage AC-DC converter
CN115473442B (en) * 2022-11-15 2023-01-31 四川大学 LLC single-stage AC-DC converter numerical analysis modeling and boundary power control method
CN116345920A (en) * 2023-05-30 2023-06-27 深圳市永联科技股份有限公司 Single-stage isolated power conversion circuit and power equipment
CN116345920B (en) * 2023-05-30 2023-08-18 深圳市永联科技股份有限公司 Single-stage isolated power conversion circuit and power equipment

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