CN110798067B - Design method of intrinsically safe Buck-Boost converter considering filter capacitor ESR - Google Patents

Design method of intrinsically safe Buck-Boost converter considering filter capacitor ESR Download PDF

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CN110798067B
CN110798067B CN201911076936.1A CN201911076936A CN110798067B CN 110798067 B CN110798067 B CN 110798067B CN 201911076936 A CN201911076936 A CN 201911076936A CN 110798067 B CN110798067 B CN 110798067B
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皇金锋
李林鸿
张鹏超
董锋斌
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Qinzhi Electronic Information Technology (Shenzhen) Co.,Ltd.
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Shaanxi University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
    • H02M3/1582—Buck-boost converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/14—Arrangements for reducing ripples from dc input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/32—Means for protecting converters other than automatic disconnection

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Abstract

The invention provides a design method of an intrinsic safety type Buck-Boost converter considering filter capacitor ESR, which comprises the following steps: s1: determining an input voltage V of a converteriRange, load R range, output voltage VoOperating frequency f, RCMaximum value of RC,max(ii) a S2: specifying ripple voltage index Vpp,maxAnd calculating the minimum discharge energy W required by the converterB(ii) a S3: the minimum inductance L required to satisfy the converter operating mode is determined from the above parametersmin(ii) a S4: according to the minimum inductance LminCalculating Δ V1,max(ii) a S5: will be delta V1,maxAnd the specified maximum ripple voltage index Vpp,maxMaking a comparison if Δ V1,max≥VPP,maxCalculating Lmin1Finding the minimum capacitance Cmin1(ii) a If Δ V1,max<Vpp,maxTo find the minimum capacitance Cmin2(ii) a S6: obtaining the maximum output short-circuit discharge energy WmaxW is to bemaxAnd WBComparing, and judging the intrinsic safety performance of the converter until the design is finished; s7: and carrying out simulation verification and experimental verification. The invention provides a design method of an inductor and a capacitor of a converter, which is suitable for the flammable and explosive dangerous environments such as coal mines, petrochemicals and the like.

Description

Design method of intrinsically safe Buck-Boost converter considering filter capacitor ESR
Technical Field
The invention belongs to the technical field of Buck-Boost converter design applied to inflammable and explosive environments such as coal mines, petrochemicals and the like, and particularly relates to a design method of an intrinsically safe Buck-Boost converter considering filter capacitor ESR.
Background
The switching power supply applied to inflammable and explosive environments such as coal mines, petrochemicals and the like not only needs to meet the requirement that the energy released under the most dangerous working conditions (such as output short circuit) cannot detonate the gas and other media in the dangerous environment, but also needs to meet the requirement of electrical performance indexes such as ripple voltage. The Buck-Boost converter can realize the function of wide voltage input or wide voltage output, has the advantages of small volume, high efficiency, light weight and the like, and has wide application prospect in dangerous environments such as coal mines, petrifaction and the like, which are inflammable, explosive and the like.
The research of the intrinsically safe switching converter is always a focus of attention of scholars at home and abroad, and the research of the most dangerous output short-circuit discharge working condition of the output intrinsically safe Buck-Boost converter researches the most dangerous working condition of the Buck-Boost converter; analysis and design of the output intrinsically safe Buck-Boost DC-DC converter analyze output short circuit release energy of the Buck-Boost converter, and a minimum capacitor meeting the requirement of output ripple voltage is designed through a ripple voltage expression of a Continuous Conduction Mode (CCM). As can be seen from the above documents, the capacitance of the intrinsically safe Buck-Boost converter needs to not only consider the energy released in a short time when the output occurs, but also meet the requirement of ripple voltage, and therefore, the design of the capacitance of the intrinsically safe switching converter is particularly critical.
The existing literature is based on ideal capacitance for ripple voltage analysis of the Buck-Boost converter, influence of parasitic parameters on the ripple voltage is not considered, and in order to meet the requirement of the ripple voltage, a filter capacitor with 2-4 times of allowance is generally selected, so that the size and the cost of the converter are increased, and meanwhile, energy released when the converter is in short circuit fault is increased.
A large number of experimental researches find that the influence of Equivalent Series Resistance (ESR) of the filter electrolytic capacitor on ripple voltage is very large, that is, a ripple voltage theory and experiment based on an ideal capacitor have a large error. The concrete expression is as follows: ESR can affect parameters such as output voltage gain and critical inductance of the converter; ESR also causes distortion of the ripple voltage waveform; when the working temperature of the external or switching power supply changes, the ESR of the electrolytic capacitor changes, and the shape and size of the corresponding ripple voltage also change significantly. If the ESR is large, even if the margin of 2-4 times of the capacitor is selected, the ripple voltage index requirement cannot be met.
The applicant filed patent No. 201910706895.3 at 2019.8.1, entitled method for modeling output ripple voltage of a Boost converter, considers the influence of filter capacitor ESR on the output ripple voltage of the Boost converter, and provides guidance for further optimization design of an intrinsically safe Boost converter applied to dangerous environments.
Disclosure of Invention
The invention provides a design method of an intrinsically safe Buck-Boost converter considering filter capacitor ESR, which analyzes and summarizes a ripple voltage mathematical model of the converter considering filter capacitor ESR, and provides a parameter optimization design method of the intrinsically safe Buck-Boost converter in the dynamic variation range of input voltage, load resistance and ESR, wherein the most dangerous working condition of the converter is an energy release expression during short circuit.
The technical scheme of the invention is as follows: an intrinsic safety type Buck-Boost converter design method considering filter capacitance (ESR) comprises the following steps:
s1: determining an input voltage V of a converteriRange [ V ]i,min，Vi,max]Load R range [ Rmin，Rmax]Output voltage VoOperating frequency f, determining equivalent series resistance R of filter capacitorCMaximum value of (1), namely RC,max；
S2: specifying ripple voltage index Vpp,maxAnd calculating the minimum discharge energy W required by the converterB；
S3: the minimum inductance L required to satisfy the converter operating mode is determined from the above parametersminMinimum inductance LminOften determined by the operating mode of the converter, the converter output current is generally required to be greater than a certain value IAOperating in CCM, i.e. requiring a minimum critical resistance RCM>RANamely, LminThe calculation formula is:
Figure GDA0002959466060000021
wherein R isARepresenting the critical resistance of the working mode of the converter;
s4: mixing L withminSubstituting into the calculation formula (2) to calculate Δ V1,max：
Figure GDA0002959466060000022
Wherein α ═ RminVi,min-RC,maxVo；
S5: will be delta V1,maxAnd the specified maximum ripple voltage index Vpp,maxMaking a comparison if Δ V1,max≥VPP,maxCalculating Lmin1The minimum capacitance C required in the CISM3 mode is obtainedmin1(ii) a If Δ V1,max<Vpp,maxTo find the minimum capacitance Cmin2；
S6: obtaining the maximum output short-circuit discharge energy WmaxW is to bemaxAnd WBComparing, judging the intrinsic safety performance of the converter, if the intrinsic safety performance meets the requirement, finishing the design, and if the intrinsic safety performance does not meet the requirement, resetting RC,maxOr repeating the steps from S2 until the design is finished;
s7: and building a Buck-Boost converter applied to the class I environment for simulation verification and experimental verification.
Further, in the S2, the minimum discharge energy WBThe calculation process is as follows:
Figure GDA0002959466060000031
wherein, CBIn order to ensure that the converter output meets the intrinsic safety requirements, the capacitance corresponding to the minimum ignition voltage V must be equal to V KVoAnd K is a safety factor.
Further, the safety factor K is 1.5.
Further, in the S5, the maximum output short-circuit discharge energy WmaxThe calculation process of (2) is:
Figure GDA0002959466060000032
in the formula, WCEnergy released for the capacitor at the moment of short-circuiting of the converter, WLEnergy released by the inductor at the time of short circuit, C is capacitance, ILP,maxIs the maximum value of the inductor current,
Figure GDA0002959466060000033
wherein α ═ RminVi,min-RC,maxVo。
Further, in the S5, the Δ V1,maxAnd the specified maximum ripple voltage index Vpp,maxThe process of making the comparison is:
A. if Δ V1,max≥Vpp,maxWhen making Δ V1,max＝Vpp,maxTo obtain the inductance L satisfying the ripple requirementmin1：
Figure GDA0002959466060000034
Wherein α ═ RminVi,min-RC,maxVo，
Figure GDA0002959466060000036
γ＝RminRC,max(Vi,minVo-Vi,minVPP,max+Vo 2+VoVPP,max)；
The minimum capacitance C required in the CISM3 mode is obtained according to the formula (7)min1Then, the maximum output short-circuit discharge energy W when the converter is short-circuited is obtained according to the formula (4)maxThis is compared with W calculated in S2BBy comparison, if Wmax<WBThe output circuit is intrinsically safe, if Wmax>WBThen the intrinsic safety requirement is not met, and R needs to be reduced at this timeC,maxOr the switching frequency f is increased and the design is carried out again until the requirement is met,
Figure GDA0002959466060000035
wherein α ═ RminVi,min-RC,minVo，β＝RminVo[2fLmin1(Vi,min+Vo)-RC,minVi,min]；
B. If Δ V1,max<Vpp,maxThe ripple voltage decreases with the increase of the capacitance C, R ═ Rmin，Vi＝Vi,min，RC＝RC,maxThe ripple voltage is the largest, so the minimum capacitance C required in this mode is obtained by the ripple type of CISM1 and CISM2 in formula (8)min2＝max{CCISM1，CCISM2In practice, a certain margin of capacitance is selected, i.e. C ═ λ Cmin2λ is 1.1, and the maximum output short-circuit discharge energy W at the time of short-circuit of the converter is obtained by equation (4)maxIf W ismax<WBThe output circuit is intrinsically safe, if Wmax>WBThen the intrinsic safety requirement is not met, and R also needs to be reducedC,maxOr the switching frequency f is increased and the design is carried out again until the requirement is met,
Figure GDA0002959466060000041
in the formula (I), the compound is shown in the specification,
Figure GDA0002959466060000042
t2＝(1-D)T，tm＝-b/2a，
Figure GDA0002959466060000043
Figure GDA0002959466060000044
the invention has the advantages that:
1. the invention combines the maximum output ripple voltage and the maximum short-circuit discharge energy of the converter in the dynamic range, provides a design method of the inductor and the capacitor of the converter, is suitable for the flammable and explosive dangerous environments such as coal mines, petrochemicals and the like, and has good dynamic characteristics;
2. the parameter design method of the intrinsically safe Buck-Boost converter considering the filter capacitor ESR can be applied to other intrinsically safe DC-DC converters, and can provide theoretical basis for reducing the size of other converters and reducing the explosion risk caused by short-circuit fault of a direct-current power supply.
Drawings
FIG. 1 is a Buck-Boost converter topology of the present invention;
FIG. 2 is a flow chart of Buck-Boost converter design according to the present invention;
FIG. 3 is a graph showing simulation results of the inductor current and the output ripple voltage of the electrolytic capacitor according to different parameters of the present invention;
FIG. 4 shows the experimental results of the inductive current and the output ripple voltage of the electrolytic capacitor according to different parameters of the present invention;
FIG. 5 is a graph of output ripple voltage versus load and input voltage;
FIG. 6 is a graph of output short circuit release energy versus load and output voltage.
Detailed Description
The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which a person skilled in the art can, without any creative effort, fully implement the present invention.
The specific implementation mode of the invention is as follows: as shown in fig. 1 to 6, a method for designing an intrinsically safe Buck-Boost converter considering filter capacitance ESR includes:
s1: the output filter electrolytic capacitor is equivalent to RCAnd C, the equivalent circuit of which is shown in FIG. 1, determines the input voltage V of the converteriRange [ V ]i,min，Vi,max]Load R range [ Rmin，Rmax]Output voltage VoOperating frequency f, determining equivalent series resistance R of filter capacitorCMaximum value of (1), namely RC,max；
S2: specifying ripple voltage index Vpp,maxAnd calculating the minimum discharge energy W required by the converterB；
S3: the minimum inductance L required to satisfy the converter operating mode is determined from the above parametersminMinimum inductance LminOften determined by the operating mode of the converter, the converter output current is generally required to be greater than a certain value IAOperating in CCM, i.e. requiring a minimum critical resistance RCM>RANamely, LminThe calculation formula is:
Figure GDA0002959466060000051
wherein R isARepresenting the critical resistance of the working mode of the converter;
s4: according to the minimum inductance LminCalculating Δ V1,maxSubstituting into the calculation formula (2):
Figure GDA0002959466060000052
wherein α ═ RminVi,min-RC,maxVo；
S5: will be delta V1,maxAnd the specified maximum ripple voltage index Vpp,maxMaking a comparison if Δ V1,max≥VPP,maxCalculating Lmin1The minimum capacitance C required in the CISM3 mode is obtainedmin1(ii) a If Δ V1,max<Vpp,maxTo find the minimum capacitance Cmin2；
S6: obtaining the maximum output short-circuit discharge energy WmaxW is to bemaxAnd WBComparing, judging the intrinsic safety performance of the converter, if the intrinsic safety performance meets the requirement, finishing the design, and if the intrinsic safety performance does not meet the requirement, resetting RC,maxOr repeating the steps from S2 until the design is finished;
s7: and building a Buck-Boost converter applied to the class I environment for simulation verification and experimental verification.
Further, in the S2, the minimum discharge energy WBThe calculation process is as follows:
Figure GDA0002959466060000061
wherein, CBIn order to ensure that the converter output meets the intrinsic safety requirements, the capacitance corresponding to the minimum ignition voltage V must be equal to V KVoAnd K is a safety coefficient which is 1.5.
Further, in S5, the maximum output short-circuit discharge energy WmaxThe calculation process of (2) is:
Figure GDA0002959466060000062
in the formula, WCEnergy released for the capacitor at the moment of short-circuiting of the converter, WLEnergy released by the inductor at the time of short circuit, C is capacitance, ILP,maxIs the maximum value of the inductor current,
Figure GDA0002959466060000063
wherein α ═ RminVi,min-RC,maxVo。
Further, in the S5, the Δ V1,maxAnd the specified maximum ripple voltage index Vpp,maxThe process of making the comparison is:
A. if Δ V1,max≥Vpp,maxWhen making Δ V1,max＝Vpp,maxTo obtain the inductance L satisfying the ripple requirementmin1：
Figure GDA0002959466060000064
Wherein α ═ RminVi,min-RC,maxVo，
Figure GDA0002959466060000065
γ＝RminRC,max(Vi,minVo-Vi,minVPP,max+Vo 2+VoVPP,max)；
The minimum capacitance C required in the CISM3 mode is obtained according to the formula (7)min1Then, the maximum output short-circuit discharge energy W when the converter is short-circuited is obtained according to the formula (4)maxThis is compared with W calculated in S2BBy comparison, if Wmax<WBThe output circuit is intrinsically safe, if Wmax>WBThen the intrinsic safety requirement is not met, and R needs to be reduced at this timeC,maxOr the switching frequency f is increased and the design is carried out again until the requirement is met,
Figure GDA0002959466060000066
wherein α ═ RminVi,min-RC,minVo，β＝RminVo[2fLmin1(Vi,min+Vo)-RC,minVi,min]；
B. If Δ V1,max<Vpp,maxThe ripple voltage decreases with the increase of the capacitance C, R ═ Rmin，Vi＝Vi,min，RC＝RC,maxThe ripple voltage is the largest, so the minimum capacitance C required in this mode is obtained by the ripple type of CISM1 and CISM2 in formula (8)min2Max (CCISM 1, CCISM 2), a certain margin of capacitance is actually selected, i.e., C ═ λ Cmin2λ is 1.1, and the maximum output short-circuit discharge energy W at the time of short-circuit of the converter is obtained by equation (4)maxIf W ismax<WBThe output circuit is intrinsically safe, if Wmax>WBThen the intrinsic safety requirement is not met, and R also needs to be reducedC,maxOr the switching frequency f is increased and the design is carried out again until the requirement is met,
Figure GDA0002959466060000071
in the formula (I), the compound is shown in the specification,
Figure GDA0002959466060000072
t2＝(1-D)T，tm＝-b/2a，
Figure GDA0002959466060000073
Figure GDA0002959466060000074
in order to verify the correctness of theoretical analysis, a Buck-Boost converter applied to a class I environment is built, and a main circuit is shown in a figure 1. The specific parameters are as follows: vi is 7-13V, R is 40-70 omega, Vo is 10V, f is 10kHz, Vpp,max2% Vo 200mV, requiring that the converter operates in CCM with an output current greater than 0.17A, i.e. R A60 Ω, provided that RC,maxTaking another factor K of 1.5 as 180m Ω, consider voltage V of 10 × 1.5 as 15V, CBThe minimum ignition discharge energy W required by the converter can be obtained by substituting the equation (3) for 190.0 μ F (according to the minimum ignition voltage curve of the capacitive circuit)B9.5mJ, minimum inductance Lmin958.7 μ H, mixing LminObtaining Δ V by substituting formula (2)1,max＝147.8mV<Vpp,maxThe minimum capacitance C required in this mode is obtained from equation (8)min2116.5 muF, taking the margin, and taking C as lambada Cmin2128.2 muF, the maximum energy W released by the short circuit is outputmax＝6.8mJ<WBTherefore, the output circuit meets the intrinsic safety requirements. The following were verified by simulation and experiment, respectively: the inductance L selected by simulation is 958.7 μ H, the parameters of the electrolytic capacitor are shown in table 1, the simulation results of the inductance current and the output ripple voltage are shown in fig. 3, the comparison results of the simulation and the theoretical analysis are shown in table 1, and it can be known from table 1 that the converter obtained by the simulation results and the theoretical analysisThe results of the short-circuit discharge energy and the output ripple voltage are consistent. When R is decreasedCWhen R is greater than R, the filter capacitance can be effectively reducedCWhen the output ripple voltage exceeds the standard, the output ripple voltage may not reach the standard even if a certain amount of filter capacitance is increased.
Figure GDA0002959466060000075
Figure GDA0002959466060000081
TABLE 1
The inductance L is 959 μ H, and the nominal values of the capacitance parameters are: 150 muF/35V, 100 muF/50V, 220 muF/250V, FIG. 4 shows the experimental results of the inductive current and the output ripple voltage of the electrolytic capacitors with different parameters, and the driving signal V of VT is on the left sideGSWaveform, inductive current ILAnd an output voltage VoA waveform; right side is ILAnd VoThe results of comparing the experimental and theoretical analyses are shown in table 2.
As can be seen from table 2, the experimental results are substantially consistent with the converter short-circuit discharge energy results obtained from theoretical analysis. The influence of the filter capacitor ESR on the ripple voltage can be clearly seen from fig. 4, and the error between the experimental result of the ripple voltage and the ripple result of the theoretical analysis is only about 5%. Also from the experimental results, it can be seen that when R is decreasedCWhen R is greater than R, the filter capacitance can be effectively reducedCWhen the output ripple voltage exceeds the standard, the output ripple voltage may not reach the standard even if a certain amount of filter capacitance is increased.
Figure GDA0002959466060000082
TABLE 2
When the filter capacitance takes C-132.0 μ F>λCmin2＝128.2μF、RC＝128mΩ<RC,maxWhen the output voltage is 180m omega, the converter outputs ripple voltage and outputs short circuit to release energy and loadAnd the input voltage are shown in fig. 5 and 6, respectively.
As can be seen from fig. 5, the output ripple voltage of the converter decreases with the increase of the load resistance value, and decreases with the increase of the input voltage, where R is 40 Ω and ViThe maximum value is reached when the voltage is 7V, and the output ripple voltage is 155mV<Vpp,maxThe power is 200mV, and the ripple index requirement is met.
As can be seen from fig. 6, the converter short-circuit discharge energy decreases with an increase in the load resistance value and decreases with an increase in the input voltage, where R is 40 Ω and ViThe maximum value is reached at 7V, and the short-circuit discharge energy is 7.0mJ<WB9.5mJ, and meets the requirement of intrinsic safety.
While the preferred embodiments of the invention have been described, it is to be understood that the invention is not limited to the precise embodiments described, and that equipment and structures not described in detail are understood to be practiced as commonly known in the art; any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention by those skilled in the art can be made without departing from the technical scope of the present invention, and still fall within the protection scope of the technical solution of the present invention.

Claims (3)

1. An intrinsic safety type Buck-Boost converter design method considering filter capacitor ESR is characterized by comprising the following steps:
s1: determining an input voltage V of a converteriRange [ V ]i,min，Vi,max]Load R range [ Rmin，Rmax]Output voltage VoOperating frequency f, determining equivalent series resistance R of filter capacitorCMaximum value of (1), namely RC,max；
S2: specifying ripple voltage index Vpp,maxAnd calculating the minimum discharge energy W required by the converterB；
S3: the minimum inductance L required to satisfy the converter operating mode is determined from the above parametersminMinimum inductance LminOften determined by the operating mode of the converter, generally requiredThe converter output current being greater than a value IAOperating in CCM, i.e. requiring a minimum critical resistance RCM>RANamely, LminThe calculation formula is:
Figure FDA0003064042790000011
wherein R isARepresenting the critical resistance of the working mode of the converter;
s4: mixing L withminSubstituting into the calculation formula (2) to calculate Δ V1,max：
Figure FDA0003064042790000012
Wherein α ═ RminVi,min-RC,maxVo；
S5: will be delta V1,maxAnd the specified maximum ripple voltage index Vpp,maxMaking a comparison if Δ V1,max≥VPP,maxCalculating Lmin1To find the minimum capacitance Cmin1(ii) a If Δ V1,max<Vpp,maxTo find the minimum capacitance Cmin2；
Maximum output short-circuit discharge energy WmaxThe calculation process of (2) is:
Figure FDA0003064042790000013
in the formula, WCEnergy released for the capacitor at the moment of short-circuiting of the converter, WLEnergy released by the inductor at the time of short circuit, C is capacitance, ILP,maxIs the maximum value of the inductor current,
Figure FDA0003064042790000014
wherein α ═ RminVi,min-RC,maxVo；
The Δ V1,maxAnd the specified maximum ripple voltage index Vpp,maxThe process of making the comparison is:
A. if Δ V1,max≥Vpp,maxWhen making Δ V1,max＝Vpp,maxTo obtain the inductance L satisfying the ripple requirementmin1：
Figure FDA0003064042790000015
Wherein α ═ RminVi,min-RC,maxVo，
Figure FDA0003064042790000021
γ＝RminRC,max(Vi,minVo-Vi,minVPP,max+Vo 2+VoVPP,max)；
The minimum capacitance C required in the CISM3 mode is obtained according to the formula (7)min1Then, the maximum output short-circuit discharge energy W when the converter is short-circuited is obtained according to the formula (4)max：
This is compared with W calculated in S2BBy comparison, if Wmax<WBThe output circuit is intrinsically safe, if Wmax>WBThen the intrinsic safety requirement is not met, and R needs to be reduced at this timeC,maxOr the switching frequency f is increased and the design is carried out again until the requirement is met,
Figure FDA0003064042790000022
wherein α ═ RminVi,min-RC,minVo，β＝RminVo[2fLmin1(Vi,min+Vo)-RC,minVi,min]；
B. If Δ V1,max<Vpp,maxThe ripple voltage decreases with the increase of the capacitance C, R ═ Rmin，Vi＝Vi,min，RC＝RC,maxThe ripple voltage is the largest, so the minimum capacitance C required in this mode is obtained by the ripple type of CISM1 and CISM2 in formula (8)min2＝max{CCISM1，CCISM2In practice, a certain margin of capacitance is selected, i.e. C ═ λ Cmin2λ is 1.1, and the maximum output short-circuit discharge energy W at the time of short-circuit of the converter is obtained by equation (4)maxIf W ismax<WBThe output circuit is intrinsically safe, if Wmax>WBThen the intrinsic safety requirement is not met, and R also needs to be reducedC,maxOr the switching frequency f is increased and the design is carried out again until the requirement is met,
Figure FDA0003064042790000023
in the formula (I), the compound is shown in the specification,
Figure FDA0003064042790000024
t2＝(1-D)T，tm＝-b/2a，
Figure FDA0003064042790000025
Figure FDA0003064042790000026
Figure FDA0003064042790000027
s6: obtaining the maximum output short-circuit discharge energy WmaxW is to bemaxAnd WBComparing, judging the intrinsic safety performance of the converter, if the intrinsic safety performance meets the requirement, finishing the design, and if the intrinsic safety performance does not meet the requirement, resetting RC,maxOr repeating the steps from S2 until the design is finished;
s7: and building a Buck-Boost converter applied to the class I environment for simulation verification and experimental verification.
2. The design method of the intrinsically safe Buck-Boost converter considering filter capacitor ESR as claimed in claim 1, wherein in the step S2, the minimum discharge energy W isBThe calculation process is as follows:
Figure FDA0003064042790000031
wherein, CBIn order to ensure that the converter output meets the intrinsic safety requirements, the capacitance corresponding to the minimum ignition voltage V must be equal to V KVoAnd K is a safety factor.
3. The design method of the intrinsically safe Buck-Boost converter considering the filter capacitor ESR is characterized in that the safety factor K is 1.5.
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