# Optimal Design Method for Inner-Intrinsically Safe Buck-Boost Converters Based on Ignition Capability

Authors: Yongxiu Zhao; Minggeng Li; Qi Wang
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Intrinsically safe switching converters are the best choice for low-voltage DC power supplies in explosive environments (such as coal mine). To obtain the optimal design method of the inner-intrinsically safe buck-boost converter (IISBBC), the equivalent circuits for various switching states and operating conditions of the buck-boost converter are studied, and the most dangerous inductor-disconnected discharge (IDD) condition of the buck-boost converter is obtained. Based on this condition, the IDD behavior of the IISBBC is studied. According to the minimum ignition curves (MICs) of the resistive circuit and the simple inductive circuit, the expressions describing the IDD ignition capability of the IISBBC in terms of the critical ignition power and the critical ignition energy are derived. The IDD has the strongest ignition capability based on power when the IISBBC is working at its maximum input voltage and minimum load resistance, and it has the strongest ignition capability based on energy when the IISBBC is working at its minimum input voltage and minimum load resistance. The converter is inner-intrinsically safe only when the maximum arc power is less than the critical ignition power and the inductive energy is less than its critical value. By incorporating the proposed criterion, the optimal design method for IISBBCs that meets the demands of electric and inner-intrinsic safety performance is obtained. Based on this method, the design range of the inductance and capacitance and the optimal inductance to give the IISBBC the best inner-intrinsic safety performance are obtained. The feasibility and reliability of the proposed optimal design method are demonstrated by an explosion test.


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## Body

## 1. Introduction

Electrical equipment working in explosive environments must meet explosion-proof requirements, and the intrinsically safe type is the best type of explosion-proofing [1, 2]. With the development of modern industrial control systems for integration and low power consumption, buck-boost converters are the best choice for intrinsically safe power supply because of their advantages of boost or buck output, small size, light weight, and high conversion efficiency.The inner-intrinsically safe buck-boost converter (IISBBC) must not ignite explosive gases when an inductor-disconnected discharge (IDD) occurs [3–5]. Intrinsic safety is achieved by limiting the ignition capability of components in the IISBBC [6–10]. Therefore, research on the design and optimization of the IISBBC is needed.The design principle of the IISBBC is to meet the demands of both inner-intrinsic safety and electric performance [11]. The optimal topology design methods for the buck-boost converter have been researched [12–14], and the control strategies for the buck-boost converter have also been studied [15, 16]. However, the intrinsically safe performance of buck-boost converters has not been considered.Presently, ignition capability can be evaluated by nonexplosive and explosive evaluation methods. The explosive evaluation method is accurate and reliable, but it cannot guide the design of an IISBBC. The nonexplosive evaluation method is more suitable for the analysis and design of an IISBBC. At present, the IDD ignition capability is largely described in terms of the minimum ignition energy [17–20] and the average discharge power [21]. However, the minimum ignition energy cannot explain why an IDD with a longer discharge time has a weaker ignition capability. The ignition capability evaluation according to the average discharge power is affected by the energy loss factor, which reduces the reliability of the evaluation result. Moreover, the above studies cannot be applied to time-varying nonlinear circuits such as buck-boost converters [22]. Thus, the most dangerous output short-circuit discharge conditions and the design methods of output intrinsically safe buck-boost converters have been studied [23]. However, inner-intrinsic safety was not considered, which means that output intrinsic safety converters must be equipped with an explosion-proof enclosure, which causes them to lose the advantages of intrinsic safety. The design method for intrinsically safe buck-boost converters was based on minimum ignition curves (MICs) [24]. However, this method is complicated, and large errors may arise.To obtain a reliable and feasible optimal design method for the IISBBC, equivalent circuits in different switching states and operating modes of buck-boost converters were analyzed. The most dangerous IDD conditions were obtained. The relationship between the IDD characteristics and converter parameters was then analyzed in depth. Based on the MIC of a resistive circuit and a simple inductive circuit, expressions describing the IDD ignition capability of the buck-boost converter will be derived. Then, the design method for an IISBBC meeting the demands of both inner-intrinsic safety and electric performance will be obtained. Based on the principle of the maximum safety margin of the inner-intrinsic safety, the optimal method will be obtained. The feasibility and reliability of the proposed optimal design method will be evaluated by the explosion criterion based on the International Electrotechnical Commission (IEC) spark test apparatus.


## 2. Design Consideration Based on Electric Performance Demand

### 2.1. Operating Modes of Buck-Boost Converters

The buck-boost converter schematic is shown in Figure1, where Ui represents the input voltage, Uo represents the output voltage, Io represents the output current, S represents the switch, L represents the inductance, VD represents the diode, C represents the capacitance, RL represents the load resistance, and f represents the switching frequency.Figure 1
The schematic diagram of the buck-boost converter.(1)LC=RL1−d22f=RLUi22fUi+Uo2,If the inductance currentiL drops to zero during a switching cycle, the buck-boost converter operates in the discontinuous conduction mode (DCM); otherwise, it operates in the continuous conduction mode (CCM). The critical inductance of the CCM and DCM, LC is given by [24].where d represents the switching duty cycle. If L>LC, the converter works in the CCM; if L<LC, it works in the DCM. The inductance peak current ILP of the converter in the CCM and DCM are given by [24].(2)ILPCCM=UoUi+UoRLUi+UoUi2LfUi+Uo,(3)ILPDCM=Uo2LfRL,where ILPCCM represents the inductance peak current in the CCM and ILPDCM represents the inductance peak current in the DCM. From equations (2) and (3), ILPCCM decreases with increasing Ui,L,andRL in the CCM; ILPDCM is independent of Ui and decreases with increasing RL and L in the DCM.The laws governing the change inILP with L in different operating modes according to equations (2)–(3) are shown in Figure 2.Figure 2
ILP vs. L in different operating modes.If the inductance valley currentILV is always larger than the output current Io in a switching cycle, the buck-boost converter operates in the complete inductance supply mode (CISM); otherwise, it operates in the incomplete inductance supply mode (IISM). The critical inductance LK of the CISM and IISM [24] is given by the following:(4)LK=RL1−d22fd=RLUi22fUoUi+Uo,when L>LK, the converter works in the CISM; when L<LK, it works in the IISM. Substituting equation (1) into (4), it is obvious that LC is always smaller than LK; therefore, the operating modes of the buck-boost converter according to L are shown in Figure 3.Figure 3
Operating modes vs.L.As shown in Figure3, the buck-boost converter has three operating modes: CCM-CISM, CCM-IISM, and DCM-IISM. The output ripple voltages UPP of the buck-boost converter in these three operating modes are given by [23]:(5)UPP.CCM−CISM=Uo2RLCfUo+Ui,(6)UPP.CCM−IISM=LUo2CRLUoUi+RLUi2LfUo+Ui2,(7)UPP.DCM−IISM=UofCRL1−2LfRL+Lf2RL.The laws governing the change inUPP with L in different operating modes according to equations (5)–(7) are shown in Figure 4.Figure 4
UPP vs. L in different operating modes.According to Figure4, UPP decreases with increasing L in the IISM and UPP is independent of L in the CISM.


### 2.2. Inductance Design Based on Electric Performance Demands

According to Figure3, L affects the operating modes in which the buck-boost converter works. Assuming that the range of Ui is Uimin,Uimax and the range of RL is RLmin,RLmax, the laws of the changes in the operating modes with L,Ui,andRL are shown in Figure 5.Figure 5
Operating modes vs.L, Ui, and RL.In Figure5, L1>L2>L3>L4, and the shaded area indicates that the converter is working in the CCM, and in the other areas, it works in the DCM. The larger the inductance L is, the larger the area in which the converter operates in the CCM. For each figure, the inductance valley current ILV decreases as RL and Ui increase, and after it drops to zero completely, the converter’s operating mode changes from the CCM to the DCM. According to equations (2)–(3) and Figure 4, ILP and the current stress of the switch will be too large if the converter always works in the DCM in the assumed Ui−RL area. Moreover, ILP increases with increasing Io. Therefore, to ensure that ILP will not be too large when Io is large, the converter is better designed to work in the CCM at least when the output current Io reaches the maximum. In this case, the operating mode within the assumed Ui−RL working area is shown in Figure 6.Figure 6
Operating mode to meet electric performance.Thus, the minimum inductance that meets the electric performance demandsLEmin is LC when the converter works at Uimax and RLmin. According to equation (1), LEmin is given by the following:(8)LEmin=RLminUimax22fUimax+Uo2.


### 2.3. Capacitance Design Based on Electric Performance Demands

After the inductance is determined, the capacitance should be determined based on the maximum output ripple voltageUPPmax in the assumed Ui−RL working area to meet the electric performance demand. If the converter works in the CCM when the output power is large (such as in the case of L3 in Figure 5), the maximum output ripple voltage UPPmax is obtained when the converter works at Uimax and RLmin in the CCM-IISM. Thus, the minimum capacitance CEmin that can meet the electric performance demand is given by [25]:(9)CEmin=L2mRLmin2UoUimin+RLminUimin2LfUimin+Uo2,where m=UPPmax/Uo. The change laws for CEmin according to L and m are shown in Figure 7.Figure 7
CEmin vs. L and m.According to Figure7, the larger UPPmax is, the lower CEminis. CEmin decreases first and then increases with increasing L.


## 2.1. Operating Modes of Buck-Boost Converters

The buck-boost converter schematic is shown in Figure1, where Ui represents the input voltage, Uo represents the output voltage, Io represents the output current, S represents the switch, L represents the inductance, VD represents the diode, C represents the capacitance, RL represents the load resistance, and f represents the switching frequency.Figure 1
The schematic diagram of the buck-boost converter.(1)LC=RL1−d22f=RLUi22fUi+Uo2,If the inductance currentiL drops to zero during a switching cycle, the buck-boost converter operates in the discontinuous conduction mode (DCM); otherwise, it operates in the continuous conduction mode (CCM). The critical inductance of the CCM and DCM, LC is given by [24].where d represents the switching duty cycle. If L>LC, the converter works in the CCM; if L<LC, it works in the DCM. The inductance peak current ILP of the converter in the CCM and DCM are given by [24].(2)ILPCCM=UoUi+UoRLUi+UoUi2LfUi+Uo,(3)ILPDCM=Uo2LfRL,where ILPCCM represents the inductance peak current in the CCM and ILPDCM represents the inductance peak current in the DCM. From equations (2) and (3), ILPCCM decreases with increasing Ui,L,andRL in the CCM; ILPDCM is independent of Ui and decreases with increasing RL and L in the DCM.The laws governing the change inILP with L in different operating modes according to equations (2)–(3) are shown in Figure 2.Figure 2
ILP vs. L in different operating modes.If the inductance valley currentILV is always larger than the output current Io in a switching cycle, the buck-boost converter operates in the complete inductance supply mode (CISM); otherwise, it operates in the incomplete inductance supply mode (IISM). The critical inductance LK of the CISM and IISM [24] is given by the following:(4)LK=RL1−d22fd=RLUi22fUoUi+Uo,when L>LK, the converter works in the CISM; when L<LK, it works in the IISM. Substituting equation (1) into (4), it is obvious that LC is always smaller than LK; therefore, the operating modes of the buck-boost converter according to L are shown in Figure 3.Figure 3
Operating modes vs.L.As shown in Figure3, the buck-boost converter has three operating modes: CCM-CISM, CCM-IISM, and DCM-IISM. The output ripple voltages UPP of the buck-boost converter in these three operating modes are given by [23]:(5)UPP.CCM−CISM=Uo2RLCfUo+Ui,(6)UPP.CCM−IISM=LUo2CRLUoUi+RLUi2LfUo+Ui2,(7)UPP.DCM−IISM=UofCRL1−2LfRL+Lf2RL.The laws governing the change inUPP with L in different operating modes according to equations (5)–(7) are shown in Figure 4.Figure 4
UPP vs. L in different operating modes.According to Figure4, UPP decreases with increasing L in the IISM and UPP is independent of L in the CISM.


## 2.2. Inductance Design Based on Electric Performance Demands

According to Figure3, L affects the operating modes in which the buck-boost converter works. Assuming that the range of Ui is Uimin,Uimax and the range of RL is RLmin,RLmax, the laws of the changes in the operating modes with L,Ui,andRL are shown in Figure 5.Figure 5
Operating modes vs.L, Ui, and RL.In Figure5, L1>L2>L3>L4, and the shaded area indicates that the converter is working in the CCM, and in the other areas, it works in the DCM. The larger the inductance L is, the larger the area in which the converter operates in the CCM. For each figure, the inductance valley current ILV decreases as RL and Ui increase, and after it drops to zero completely, the converter’s operating mode changes from the CCM to the DCM. According to equations (2)–(3) and Figure 4, ILP and the current stress of the switch will be too large if the converter always works in the DCM in the assumed Ui−RL area. Moreover, ILP increases with increasing Io. Therefore, to ensure that ILP will not be too large when Io is large, the converter is better designed to work in the CCM at least when the output current Io reaches the maximum. In this case, the operating mode within the assumed Ui−RL working area is shown in Figure 6.Figure 6
Operating mode to meet electric performance.Thus, the minimum inductance that meets the electric performance demandsLEmin is LC when the converter works at Uimax and RLmin. According to equation (1), LEmin is given by the following:(8)LEmin=RLminUimax22fUimax+Uo2.


## 2.3. Capacitance Design Based on Electric Performance Demands

After the inductance is determined, the capacitance should be determined based on the maximum output ripple voltageUPPmax in the assumed Ui−RL working area to meet the electric performance demand. If the converter works in the CCM when the output power is large (such as in the case of L3 in Figure 5), the maximum output ripple voltage UPPmax is obtained when the converter works at Uimax and RLmin in the CCM-IISM. Thus, the minimum capacitance CEmin that can meet the electric performance demand is given by [25]:(9)CEmin=L2mRLmin2UoUimin+RLminUimin2LfUimin+Uo2,where m=UPPmax/Uo. The change laws for CEmin according to L and m are shown in Figure 7.Figure 7
CEmin vs. L and m.According to Figure7, the larger UPPmax is, the lower CEminis. CEmin decreases first and then increases with increasing L.


## 3. Design Consideration Based on the Inner-Intrinsic Safety Demand

The buck-boost converter is a time-varying and nonlinear circuit with multiple operating modes. Therefore, it is necessary to analyze its operating characteristics to obtain the most dangerous IDD condition and the IDD characteristics in this condition.


### 3.1. The Most Dangerous Condition of the Inductor-Disconnected Discharge

The buck-boost converter has two equivalent circuits according to the switching state, as shown in Figure8.Figure 8
Equivalent circuits of the buck-boost converter. (a) Switch on. (b) Switch off.
(a)(b)Figure8 shows that the arc energy Warc is provided by the power source and the inductance in the switch-on state; thus, the switch-on state arc energy Warc.on is as follows:(10)Warc.on=WUi+WL,where WUi represents the arc energy provided by the power supply and WL represents the inductive energy.In the switch-off state,WL supplies the arc, C, and RL. Thus, the switch-off state arc energy Warc.off is given as follows:(11)Warc.off=WL−WRC,where WRC represents the energy consumed by C and RL.Comparing equations (10) and (11), it can be seen that when the IDD occurs completely in the switch-on state, Warc is maximized, and the inductive energy WL is entirely supplied to the arc. WLcan be expressed as follows:(12)WL=12LiL2,where iL represents the inductance current. According to equation (12), if iL is equal to ILP, Warc is equal to the maximum arc energy Warc.max. Therefore, the most dangerous IDD condition of the buck-boost converter is that IDD occurs when iL is equal to ILP, and the switch remains in the switch-on state.


### 3.2. Maximum Inductor-Disconnected Discharge Characteristics

Based on the above analysis, the most dangerous IDD condition of the buck-boost converter is obtained. The IDD ignition capability is strongest in the most dangerous IDD condition. Therefore, research on IDD behavior in the most dangerous condition is necessary.In the most dangerous IDD condition, the buck-boost converter is equivalent to a simple inductive circuit with wire resistance. The typical arc voltageuarc and arc current iarc waveforms of the simple inductive circuit based on the IEC spark test apparatus are shown in Figure 9.Figure 9
Typical IDD volt-amp waveform. (a) Arc voltage. (b) Arc current.
(a)(b)In Figure9, T represents the arc discharge time, uarc.max represents the maximum arc voltage, iarc.max represents the maximum arc current, and uarc.min represents the minimum arc voltage, which is mainly determined by the electrode material and is approximately 10 V in the IDD based on the IEC spark test apparatus. According to the change trend of uarc, the IDD can be divided into three stages:(I)
Arc-building stage: the electrode begins to break, the voltage at the breaking point rises rapidly from zero to the minimum arcing voltage, and the arc is formed.(II)
Arc-discharging stage: at this stage,uarc rises to uarc.max, and iarc drops to approximately zero. The process is mainly affected by the circuit parameters.(III)
Glow-discharging stage: the arc is basically extinguished, and the remaining energy (if any) oscillates back and forth between the equivalent capacitance between the inductance and the breaking electrode and is eventually consumed in the circuit resistance.Sinceiarc is approximately zero in stage III, the release of arc energy and the generation of Joule heat mainly occur in stages I and II. In these two stages, uarc increases from zero to uarc.max and finally equals Ui, whereas iarc decreases from iarc.max to zero. Therefore, uarc.max and iarc.max of the buck-boost converter in the most dangerous IDD condition are given by the following:(13)uarc.max=maxUi+UL=maxUi+Ldiarcdt,(14)iarc.max=ILP,where UL represents the IDD inductor voltage. However, uarc.max is random. Based on the linear attenuation model, it can be assumed that iarc decreases linearly from ILP to zero within the discharge time T; thus, equation (13) can be simplified as follows:(15)uarc.max=Ui+LILPT.According to equations (14) and (15), the maximum arc power Parc.max is given by the following:(16)Parc.max=uarc.maxiarc.max=UiILP+LILP2T.


### 3.3. Critical Ignition Power of the Inductor-Disconnected Discharge

The maximum arc powerParc.max of the buck-boost converter is obtained. Although the arc power Parc used in the test is random, it will never be greater than Parc.max. If Parc.max has the capability to ignite explosive gases, Parc used in the test will also have a chance of igniting explosive gases. Therefore, the inner-intrinsic safety performance of the buck-boost converter can be judged according to whether Parc.max has the capability to ignite explosive gases.The change laws for the minimum ignition currentIMIC for Ui can be obtained from the Type I MIC of the resistive circuit [26]. Based on power function regression analysis, the relationship between IMIC and Ui is approximately given by the following:(17)IMIC=22.35Vi−14−1.24.ComparingIMIC obtained by equation (17) and the Type I MIC of the resistive circuit under different Ui, the results are shown in Table 1.Table 1
Errors of IMIC between regression expression and MIC.
Ui (V)IMIC by equation (17) (A)IMIC by MIC (A)Relative error (%)202.4232.353.11300.7180.74−2.97400.3930.41−4.14500.2630.261.15600.1940.1854.86700.1520.1454.83800.1240.123.33900.1040.105−0.951000.0890.0881.142000.0340.0333.03According to Table1, the relative errors of IMIC obtained by equation (17) and the Type I MIC of the resistive circuit are less than ±5%, which proves the feasibility and accuracy of equation (17). According to equation (17), the critical ignition power PCI of the resistive circuit is given by the following:(18)PCI=UiIMIC=12.25IMIC25/31+14IMIC.According to Figure8(a) and equation (13), the buck-boost converter in the most dangerous IDD condition can be taken as the equivalent to the resistive circuit consisting of the input voltage source Ui, the controlled voltage source UL=Ldiarc/dt, and the wire resistance Rwire shown in Figure 10.Figure 10
Equivalent resistive circuit of the buck-boost converter in the most dangerous IDD condition.In Figure10, G is the discharge electrode. Based on the proposed equivalent circuit, if Parc.max is greater than PCI, the IDD of the buck-boost converter will have the capability to ignite methane-air mixtures. Combining equations (15) and (18), the following can be derived:(19)UiILP+LILP2T=Parc.max≤PCI=12.25ILP−25/31+14ILP.If equation (19) holds, then the buck-boost converter is inner-intrinsically safe based on the arc power; otherwise, it is dangerous. To explore the influence of the converter parameters on the ignition capability based on the arc power, the change laws of Parc.max and PCI in terms of Ui, RL, and L are shown in Figure 11.Figure 11
Parc.max and PCI vs. L. (a) Different Ui (T = 200 μs, Uo = 18 V, RL = 36 Ω, and f = 200 kHz). (b) Different RL (T = 200 μs, Uo = 18 V, Ui = 20 V, and f = 200 kHz).
(a)(b)WhenParc.max<PCI, the buck-boost converter is an inner-intrinsically safe converter; when Parc.max≥PCI, the converter will have the capability to ignite methane-air mixtures, and the greater the difference is between Parc.max and PCI, the stronger the ignition capability.According to Figure11, PCI decreases with increasing L and RL, is independent of Ui in the DCM, and decreases with increasing Ui in the CCM.Parc.max decreases with increasing RL, increases with increasing Ui when L is small, decreases with increasing Ui when L is large, and first decreases and then increases with increasing L. Therefore, the IDD ignition capability is strongest when the converter operates at Uimax and RLmin based on the arc power.


### 3.4. Critical Ignition Energy of the Inductor-Disconnected Discharge

For the IDD of the buck-boost converter, the effect of the arc energy on the ignition capability should also be analyzed.According to equation (12), WL is affected by L and iL. The minimum ignition current IMIC with different values of inductance L can be obtained from the Type I MIC of the simple inductive circuit [26]. Suppose Warc is equal to the critical ignition energy WCI; then, according to equations (10) and (12), the critical inductive energy WLCI is given by the following:(20)WLCI=12LIMIC2=WCI−WUi.According to the Type I MIC of the simple inductive circuit, whenILP < 0.4 A, the energy provided by the power source WUi is negligible; thus, Warc is mainly provided by L, so WLCI is approximately constant at 525 μJ; when ILP ≥ 0.4 A, WLCI is not constant. In this condition, WLCI decreases with increasing Ui when Ui < 18 V, and WLCI is independent of Ui when Ui ≥ 18 V. Therefore, based on the power function regression analysis, the change laws of  WLCI with Ui and ILP are given by the following:(21)WLCI=525×10−6,ILP<0.4A,3.28ILP22.5ILP−1.596−0.012exp0.187Ui×10−3,ILP≥0.4A,Ui<18V,0.55ILP0.05×10−3,ILP≥0.4A,Ui≥18V.ComparingWLCI obtained by equation (21) and the Type I MIC of the simple inductive circuit under different Ui and ILP, the results are shown in Table 2.Table 2
Error ofWLCI between regression expression and MIC.
Ui (V)ILP (A)WLCI by equation (21) (μJ)WLCI by MIC (μJ)Relative error (%)80.35255171.5581771.447502.86831224.3312150.77120.5568.5587.53.18121730.447004.351231085.781057.52.67180.5539.82537.50.43181589.275752.48183677.09652.53.77According to Table2, the relative errors of WLCI obtained by equation (21) and the Type I MIC of the simple inductive circuit are less than ±5%, which proves the feasibility and accuracy of equation (21). Equation (21) shows that if WL < WLCI, the buck-boost converter will be inner-intrinsically safe based on the arc energy.To investigate the influence of the converter parameters on the ignition capability based on the arc energy, the change laws ofWL and WLCI with Ui, RL, and L are shown in Figure 12.Figure 12
WLCI and WL vs. L and Ui. (a) Different Ui (T = 200 μs, UoUo = 18 V, RL = 36 Ω, and f = 200 kHz). (b) Different RL (T = 200 μs, Uo = 18 V, Ui = 20 V, and f = 200 kHz).
(a)(b)According to Figure12, WLCI and WL decrease with increasing Ui and RL; WLCI decreases and tends to be stable with increasing L; WL increases with increasing L and ILP and decreasing Ui. Therefore, the IDD ignition capability is strongest when the converter operates at Uimin and RLmin based on the arc energy. It can also be concluded that in low-voltage and large-current conditions, WLCI is not constant but changes with Ui and ILP only when ILP < 0.4 A is WLCI equal to 525 μJ. This is consistent with the conclusions regarding the Type I MIC of the simple inductive circuit.


### 3.5. Inductance Design Based on Inner-Intrinsic Safety Demands

According to Figure11, there is a maximum inductance LPmax and a minimum inductance LPmin based on power, which are shown in Figure 13.Figure 13
The inductance design range based on power (T = 200 μs, Uo = 18 V, RL = 36 Ω, and f = 200 kHz).IfL > LPmax or L < LPmin, Parc.max will be greater than PCI, and the IDD of the converter will have the capability to ignite methane-air mixtures in both conditions. According to Figure 13, the inductance design range based on power Lp is given by the following:(22)LP∈LPmin,LPmax.As shown in Figure11, LPmax decreases as Ui increases and RL decreases; LPmin increases as Ui increases and RL decreases. Therefore, the values of LPmax and LPmin when the converter is operating in the Uimax and RLmin conditions should be considered in the design.According to Figure12, there is a maximum inductance based on the energy LWmax, which is shown in Figure 14. If L > LWmax, WL will be greater than WLCI. Thus, the converter IDD will have the capability to ignite methane-air mixtures.Figure 14
The inductance design range based on energy (T = 200 μs, Uo = 18 V, RL = 36 Ω, and f = 200 kHz).By incorporating Figure14, the inductance design range based on the energy LW is given by the following:(23)LW∈0,LWmax.From Figure12, LWmax decreases as Ui and RL increase. Therefore, the value of LWmax when the converter is operating in the Uimin and RLmin conditions should be considered in the design.


### 3.6. Inductance Optimization Based on Inner-Intrinsic Safety Demands

According to Figure13, there is an optimal inductance Lopt that maximizes the power difference PΔ between PCI and Parc.max when the converter operates in the Uimax and RLmin conditions. Thus, this inductance will cause the buck-boost converter to have the maximum safety margin of the inner-intrinsic safety performance based on power.SinceL > LEmin, the converter works in the CCM when RL = RLmin. According to equation (19), the power difference PΔ can be obtained by the following:(24)PΔ=12.25ILPCCM−25/31−Uimax−LILPCCMT+14ILPCCM.For the first derivative of equation (24) is equal to zero, we can obtain(25)4.94UiUoL2fUi+UoILPCCM−25/31+Ui2Uo2L2fUi+Uo+ILPCCMUiUoLTfUi+Uo−ILPCCM2TL+ILPCCMUiUoTLLfUi+Uo+ILPCCM2LTL′TL2−UiUo12.25ILPCCM−25/31+142LfUi+Uo=0,where TL represents the discharge time T affected by the inductance L. The root of equation (25) is the optimal inductance Lopt that maximizes the power difference PΔ.To investigate the influence ofUi on the design and optimization of inductance, the laws governing the change in LP,LW, LEmin, and Lopt with Ui are shown in Figure 15. The discharge time T can be determined from the IDD time model based on the IEC spark test apparatus [27], which is given by(26)TL=2.98+1.66×103L+221.37ILP−119.38ILP2−25.67ILP3+24.1ILP4×10−6.Figure 15
LP,LW, LEmin, and Lopt vs. Ui (Uo = 18 V, RL = 36 Ω, and f = 200 kHz).In Figure15, the shaded area is the design range in which the inductance L meets the demands of inner-intrinsic safety and electric performance. To ensure that the IISBBC has the best inner-intrinsic safety performance in the most dangerous condition, the inductance L should be as close to Lopt as possible.


## 3.1. The Most Dangerous Condition of the Inductor-Disconnected Discharge

The buck-boost converter has two equivalent circuits according to the switching state, as shown in Figure8.Figure 8
Equivalent circuits of the buck-boost converter. (a) Switch on. (b) Switch off.
(a)(b)Figure8 shows that the arc energy Warc is provided by the power source and the inductance in the switch-on state; thus, the switch-on state arc energy Warc.on is as follows:(10)Warc.on=WUi+WL,where WUi represents the arc energy provided by the power supply and WL represents the inductive energy.In the switch-off state,WL supplies the arc, C, and RL. Thus, the switch-off state arc energy Warc.off is given as follows:(11)Warc.off=WL−WRC,where WRC represents the energy consumed by C and RL.Comparing equations (10) and (11), it can be seen that when the IDD occurs completely in the switch-on state, Warc is maximized, and the inductive energy WL is entirely supplied to the arc. WLcan be expressed as follows:(12)WL=12LiL2,where iL represents the inductance current. According to equation (12), if iL is equal to ILP, Warc is equal to the maximum arc energy Warc.max. Therefore, the most dangerous IDD condition of the buck-boost converter is that IDD occurs when iL is equal to ILP, and the switch remains in the switch-on state.


## 3.2. Maximum Inductor-Disconnected Discharge Characteristics

Based on the above analysis, the most dangerous IDD condition of the buck-boost converter is obtained. The IDD ignition capability is strongest in the most dangerous IDD condition. Therefore, research on IDD behavior in the most dangerous condition is necessary.In the most dangerous IDD condition, the buck-boost converter is equivalent to a simple inductive circuit with wire resistance. The typical arc voltageuarc and arc current iarc waveforms of the simple inductive circuit based on the IEC spark test apparatus are shown in Figure 9.Figure 9
Typical IDD volt-amp waveform. (a) Arc voltage. (b) Arc current.
(a)(b)In Figure9, T represents the arc discharge time, uarc.max represents the maximum arc voltage, iarc.max represents the maximum arc current, and uarc.min represents the minimum arc voltage, which is mainly determined by the electrode material and is approximately 10 V in the IDD based on the IEC spark test apparatus. According to the change trend of uarc, the IDD can be divided into three stages:(I)
Arc-building stage: the electrode begins to break, the voltage at the breaking point rises rapidly from zero to the minimum arcing voltage, and the arc is formed.(II)
Arc-discharging stage: at this stage,uarc rises to uarc.max, and iarc drops to approximately zero. The process is mainly affected by the circuit parameters.(III)
Glow-discharging stage: the arc is basically extinguished, and the remaining energy (if any) oscillates back and forth between the equivalent capacitance between the inductance and the breaking electrode and is eventually consumed in the circuit resistance.Sinceiarc is approximately zero in stage III, the release of arc energy and the generation of Joule heat mainly occur in stages I and II. In these two stages, uarc increases from zero to uarc.max and finally equals Ui, whereas iarc decreases from iarc.max to zero. Therefore, uarc.max and iarc.max of the buck-boost converter in the most dangerous IDD condition are given by the following:(13)uarc.max=maxUi+UL=maxUi+Ldiarcdt,(14)iarc.max=ILP,where UL represents the IDD inductor voltage. However, uarc.max is random. Based on the linear attenuation model, it can be assumed that iarc decreases linearly from ILP to zero within the discharge time T; thus, equation (13) can be simplified as follows:(15)uarc.max=Ui+LILPT.According to equations (14) and (15), the maximum arc power Parc.max is given by the following:(16)Parc.max=uarc.maxiarc.max=UiILP+LILP2T.


## 3.3. Critical Ignition Power of the Inductor-Disconnected Discharge

The maximum arc powerParc.max of the buck-boost converter is obtained. Although the arc power Parc used in the test is random, it will never be greater than Parc.max. If Parc.max has the capability to ignite explosive gases, Parc used in the test will also have a chance of igniting explosive gases. Therefore, the inner-intrinsic safety performance of the buck-boost converter can be judged according to whether Parc.max has the capability to ignite explosive gases.The change laws for the minimum ignition currentIMIC for Ui can be obtained from the Type I MIC of the resistive circuit [26]. Based on power function regression analysis, the relationship between IMIC and Ui is approximately given by the following:(17)IMIC=22.35Vi−14−1.24.ComparingIMIC obtained by equation (17) and the Type I MIC of the resistive circuit under different Ui, the results are shown in Table 1.Table 1
Errors of IMIC between regression expression and MIC.
Ui (V)IMIC by equation (17) (A)IMIC by MIC (A)Relative error (%)202.4232.353.11300.7180.74−2.97400.3930.41−4.14500.2630.261.15600.1940.1854.86700.1520.1454.83800.1240.123.33900.1040.105−0.951000.0890.0881.142000.0340.0333.03According to Table1, the relative errors of IMIC obtained by equation (17) and the Type I MIC of the resistive circuit are less than ±5%, which proves the feasibility and accuracy of equation (17). According to equation (17), the critical ignition power PCI of the resistive circuit is given by the following:(18)PCI=UiIMIC=12.25IMIC25/31+14IMIC.According to Figure8(a) and equation (13), the buck-boost converter in the most dangerous IDD condition can be taken as the equivalent to the resistive circuit consisting of the input voltage source Ui, the controlled voltage source UL=Ldiarc/dt, and the wire resistance Rwire shown in Figure 10.Figure 10
Equivalent resistive circuit of the buck-boost converter in the most dangerous IDD condition.In Figure10, G is the discharge electrode. Based on the proposed equivalent circuit, if Parc.max is greater than PCI, the IDD of the buck-boost converter will have the capability to ignite methane-air mixtures. Combining equations (15) and (18), the following can be derived:(19)UiILP+LILP2T=Parc.max≤PCI=12.25ILP−25/31+14ILP.If equation (19) holds, then the buck-boost converter is inner-intrinsically safe based on the arc power; otherwise, it is dangerous. To explore the influence of the converter parameters on the ignition capability based on the arc power, the change laws of Parc.max and PCI in terms of Ui, RL, and L are shown in Figure 11.Figure 11
Parc.max and PCI vs. L. (a) Different Ui (T = 200 μs, Uo = 18 V, RL = 36 Ω, and f = 200 kHz). (b) Different RL (T = 200 μs, Uo = 18 V, Ui = 20 V, and f = 200 kHz).
(a)(b)WhenParc.max<PCI, the buck-boost converter is an inner-intrinsically safe converter; when Parc.max≥PCI, the converter will have the capability to ignite methane-air mixtures, and the greater the difference is between Parc.max and PCI, the stronger the ignition capability.According to Figure11, PCI decreases with increasing L and RL, is independent of Ui in the DCM, and decreases with increasing Ui in the CCM.Parc.max decreases with increasing RL, increases with increasing Ui when L is small, decreases with increasing Ui when L is large, and first decreases and then increases with increasing L. Therefore, the IDD ignition capability is strongest when the converter operates at Uimax and RLmin based on the arc power.


## 3.4. Critical Ignition Energy of the Inductor-Disconnected Discharge

For the IDD of the buck-boost converter, the effect of the arc energy on the ignition capability should also be analyzed.According to equation (12), WL is affected by L and iL. The minimum ignition current IMIC with different values of inductance L can be obtained from the Type I MIC of the simple inductive circuit [26]. Suppose Warc is equal to the critical ignition energy WCI; then, according to equations (10) and (12), the critical inductive energy WLCI is given by the following:(20)WLCI=12LIMIC2=WCI−WUi.According to the Type I MIC of the simple inductive circuit, whenILP < 0.4 A, the energy provided by the power source WUi is negligible; thus, Warc is mainly provided by L, so WLCI is approximately constant at 525 μJ; when ILP ≥ 0.4 A, WLCI is not constant. In this condition, WLCI decreases with increasing Ui when Ui < 18 V, and WLCI is independent of Ui when Ui ≥ 18 V. Therefore, based on the power function regression analysis, the change laws of  WLCI with Ui and ILP are given by the following:(21)WLCI=525×10−6,ILP<0.4A,3.28ILP22.5ILP−1.596−0.012exp0.187Ui×10−3,ILP≥0.4A,Ui<18V,0.55ILP0.05×10−3,ILP≥0.4A,Ui≥18V.ComparingWLCI obtained by equation (21) and the Type I MIC of the simple inductive circuit under different Ui and ILP, the results are shown in Table 2.Table 2
Error ofWLCI between regression expression and MIC.
Ui (V)ILP (A)WLCI by equation (21) (μJ)WLCI by MIC (μJ)Relative error (%)80.35255171.5581771.447502.86831224.3312150.77120.5568.5587.53.18121730.447004.351231085.781057.52.67180.5539.82537.50.43181589.275752.48183677.09652.53.77According to Table2, the relative errors of WLCI obtained by equation (21) and the Type I MIC of the simple inductive circuit are less than ±5%, which proves the feasibility and accuracy of equation (21). Equation (21) shows that if WL < WLCI, the buck-boost converter will be inner-intrinsically safe based on the arc energy.To investigate the influence of the converter parameters on the ignition capability based on the arc energy, the change laws ofWL and WLCI with Ui, RL, and L are shown in Figure 12.Figure 12
WLCI and WL vs. L and Ui. (a) Different Ui (T = 200 μs, UoUo = 18 V, RL = 36 Ω, and f = 200 kHz). (b) Different RL (T = 200 μs, Uo = 18 V, Ui = 20 V, and f = 200 kHz).
(a)(b)According to Figure12, WLCI and WL decrease with increasing Ui and RL; WLCI decreases and tends to be stable with increasing L; WL increases with increasing L and ILP and decreasing Ui. Therefore, the IDD ignition capability is strongest when the converter operates at Uimin and RLmin based on the arc energy. It can also be concluded that in low-voltage and large-current conditions, WLCI is not constant but changes with Ui and ILP only when ILP < 0.4 A is WLCI equal to 525 μJ. This is consistent with the conclusions regarding the Type I MIC of the simple inductive circuit.


## 3.5. Inductance Design Based on Inner-Intrinsic Safety Demands

According to Figure11, there is a maximum inductance LPmax and a minimum inductance LPmin based on power, which are shown in Figure 13.Figure 13
The inductance design range based on power (T = 200 μs, Uo = 18 V, RL = 36 Ω, and f = 200 kHz).IfL > LPmax or L < LPmin, Parc.max will be greater than PCI, and the IDD of the converter will have the capability to ignite methane-air mixtures in both conditions. According to Figure 13, the inductance design range based on power Lp is given by the following:(22)LP∈LPmin,LPmax.As shown in Figure11, LPmax decreases as Ui increases and RL decreases; LPmin increases as Ui increases and RL decreases. Therefore, the values of LPmax and LPmin when the converter is operating in the Uimax and RLmin conditions should be considered in the design.According to Figure12, there is a maximum inductance based on the energy LWmax, which is shown in Figure 14. If L > LWmax, WL will be greater than WLCI. Thus, the converter IDD will have the capability to ignite methane-air mixtures.Figure 14
The inductance design range based on energy (T = 200 μs, Uo = 18 V, RL = 36 Ω, and f = 200 kHz).By incorporating Figure14, the inductance design range based on the energy LW is given by the following:(23)LW∈0,LWmax.From Figure12, LWmax decreases as Ui and RL increase. Therefore, the value of LWmax when the converter is operating in the Uimin and RLmin conditions should be considered in the design.


## 3.6. Inductance Optimization Based on Inner-Intrinsic Safety Demands

According to Figure13, there is an optimal inductance Lopt that maximizes the power difference PΔ between PCI and Parc.max when the converter operates in the Uimax and RLmin conditions. Thus, this inductance will cause the buck-boost converter to have the maximum safety margin of the inner-intrinsic safety performance based on power.SinceL > LEmin, the converter works in the CCM when RL = RLmin. According to equation (19), the power difference PΔ can be obtained by the following:(24)PΔ=12.25ILPCCM−25/31−Uimax−LILPCCMT+14ILPCCM.For the first derivative of equation (24) is equal to zero, we can obtain(25)4.94UiUoL2fUi+UoILPCCM−25/31+Ui2Uo2L2fUi+Uo+ILPCCMUiUoLTfUi+Uo−ILPCCM2TL+ILPCCMUiUoTLLfUi+Uo+ILPCCM2LTL′TL2−UiUo12.25ILPCCM−25/31+142LfUi+Uo=0,where TL represents the discharge time T affected by the inductance L. The root of equation (25) is the optimal inductance Lopt that maximizes the power difference PΔ.To investigate the influence ofUi on the design and optimization of inductance, the laws governing the change in LP,LW, LEmin, and Lopt with Ui are shown in Figure 15. The discharge time T can be determined from the IDD time model based on the IEC spark test apparatus [27], which is given by(26)TL=2.98+1.66×103L+221.37ILP−119.38ILP2−25.67ILP3+24.1ILP4×10−6.Figure 15
LP,LW, LEmin, and Lopt vs. Ui (Uo = 18 V, RL = 36 Ω, and f = 200 kHz).In Figure15, the shaded area is the design range in which the inductance L meets the demands of inner-intrinsic safety and electric performance. To ensure that the IISBBC has the best inner-intrinsic safety performance in the most dangerous condition, the inductance L should be as close to Lopt as possible.


## 4. Experimental Verification

### 4.1. Design of the Inner-Intrinsically Safe Buck-Boost Converter

Two groups of the main system and component parameters of the IISBBC are shown in Table3.Table 3
Main system and component parameters.
VariablesGroup 1Group 2Ui14–18 V18–22 VUo18 V18 VRL36–90 Ω36–90 Ωf200 kHz200 kHzUPP1%Uo1%UoAccording to Figure15 and Table 3, in these parameters, when Ui is higher than 24 V, L will have no value to meet the electrical performance and inner-intrinsic safety demands. Therefore, considering the working demands and voltage fluctuations, Ui of the IISBBC is set to 14–22 V and divided into two groups of low-input voltage (Group 1) and high-input voltage (Group 2). Taking Group 1 as an example, the design steps are as follows:(1)
According to the above parameters and equation (8), the inductance L must be greater than LEmin, which is given by the following:(27)L≥LEmin=RLminUimax22fUimax+Uo2=22.5μH.(2)
The inductanceL must ensure that there is no IDD ignition capability when the converter operates at Uimax and RLmin based on the arc power. Since L > LEmin, the converter works in the CCM when RL = RLmin. Combining equations (2) and (19), the maximum inductance LPmax and the minimum inductance LPmin based on the arc power can be obtained by(28)UimaxILPCCM+LILPCCM2T=12.25ILPCCM−25/31+14ILPCCM.Solving equation (28), we obtain the following:(29)LPmin=7.51μH,LPmax=813.92μH.According to equation (22), the inductance design range based on power Lp is given by the following:(30)7.51≤LP≤813.92μH.(3)
The inductanceL must ensure that there is no IDD ignition capability when the converter operates at Uimin and RLmin based on the arc energy. Since the expression of WLCI is different according to Ui and ILP, the minimum inductance peak current ILPmin needs to be determined. According to equation (2), ILP decreases to ILPmin when L is infinite, which is given by the following:(31)ILPmin=UoUimin+UoRLminUimin=1.14A > 0.4A.Combining equations (12) and (21) and substituting the parameters, the maximum inductance based on the energy LWmax can be obtained by(32)LWmax=3.28ILPCCM22.5ILPCCM−1.596−0.012exp0.187Ui×10−3.Solving equation (32), we obtain(33)LWmax=1003.11μH.According to equation (23), the inductance design range based on the energy LW is given by the following:(34)0≤LW≤1003.11μH.(4)
According to equations (25) and (26), the optimal inductance Lopt is as follows:(35)Lopt=74.05LμH.To ensure that the IISBBC has the the best inner-intrinsic safety performance, the inductanceL is taken as Lopt.(5)
According to equation (9), CEmin is 9.437 μF. Thus, we can set C equal to 22 μF to meet the electric performance demand.Similarly, the inductance design range of Group 2 can be obtained. The inductance design ranges of these two groups of IISBBC are shown in Table4.Table 4
Inductance design range of IISBBC.
VariablesGroup 1 (μH)Group 2 (μH)LEmin22.528.225LPmin7.5138.29LPmax813.92508.98LWmax1003.111100.11Lopt74.05137.78The design ranges of inductance and capacitance obtained by the proposed method and design method based on the MIC [24] are compared in Table 5.Table 5
Comparison of the inductance and capacitance design ranges.
VariablesProposed methodMethod based on the MICGroup 1L22.5 ≤L ≤ 813.92 μH22.5 ≤L ≤ 349.88 μHLopt74.05μHNoneC (if L = Lopt)9.437μF ≤ C9.437μF ≤ CGroup 2L38.29 ≤L ≤ 508.98 μHN/ALopt137.78μHC (if L = Lopt)9.355μF ≤ CThe design method based on the MIC takesLEmin as the initial value, iterates by querying the MIC after considering the safety margin λ (λ = 1.5 in Table 5), and obtains the maximum inductance that meets the inner-intrinsically safe performance demands. However, this method is more complicated, and reading errors may accumulate by querying the MIC multiple times; thus, the accuracy of the method is reduced. Moreover, according to Group 2 in Table 5, when Ui is large, there is a case where the critical ignition current IMIC corresponding to LEmin fails to meet the intrinsic safety demand, and the iteration cannot be performed. Thus, the applicability of the method is also reduced.The proposed design method considers the effect of the critical ignition power and energy on the IDD ignition capability. According to the analysis of the critical ignition power, ifL is too large or too small, the IDD can ignite methane-air mixtures, which contradicts the idea of the design method based on the MIC that L meets the intrinsically safe performance demand and should be as small as possible. Moreover, based on the principle that the converter has the largest safety margin of IDD, the optimal inductance Lopt is obtained. Thus, the inductance design method is clearer. According to the analysis of the critical ignition energy, WLCI is affected by L, ILP, and Ui. Therefore, the critical ignition energy WCI is generally not considered to be constant. The main difference between these two methods is the design consideration based on the inner-intrinsic safety performance. However, the design considerations based on the electrical performance are basically identical, so the two methods have consistent LEmin and CEmin.


### 4.2. Explosive Test Based on the IEC Spark Test Apparatus

The IISBBCs were tested by the IEC spark test apparatus. The IEC spark test apparatus [28] and its structure are shown in Figure 16, where the tungsten wire and the cadmium disk are the disconnected electrodes.Figure 16
IEC spark test apparatus. (a) Prototype appearance. (b) Structural schematic.
(a)(b)The disconnected points of the tested circuit are connected with these two electrodes. The disconnected electrodes are contacted and disconnected through the transmission gear rotates so that the circuit is turned on and off [29, 30].The steps of the explosive test are as follows:(1)
Prepare a gas mixture corresponding to an explosive environment. The Type I environment is a methane-air mixture with a concentration ratio of 8–8.6%. Clean the electrodes.(2)
Calibrate the sensitivity of the apparatus. The calibration circuit is a simple inductive circuit with parameters of supply voltageE = 24 V, inductance L = 95 mH, and current I = 110 mA. If an explosion occurs within 400 revolutions of the transmission gear, the sensitivity calibration of the apparatus is qualified. The explosive evaluation of the tested circuit can be carried out only after the apparatus sensitivity has been calibrated three times.(3)
The IISBBC is connected to the resistive load and the IEC spark test apparatus for the explosive tests. If an explosion occurs within 400 revolutions of the transmission gear, the tested circuit has ignition capability; otherwise, it is intrinsically safe.To verify the effectiveness of inductance optimization, the theoretical and experimental values of the differencePΔ between the critical ignition power PCI and the maximum arc power Parc.max under different L are shown in Figure 17.Figure 17
PΔ vs. L of the IISBBC in the explosive test (Ui = 22 V, Uo = 18V, C = 22 μF, RL = 36 Ω, and f = 200 kHz).According to Figure17, the closer L is to Lopt, the larger PΔ is, and the maximum PΔ is reached when L is equal to Lopt. The inner-intrinsic safety performance of the IISBBC has the maximum safety margin based on the arc power, which proves the effectiveness of the inductance optimization.However, it can be found that the margin of the test value is smaller than the theoretical value. This is due to the parasitic parameters of the converter, which makes the inductance peak currentILP greater than the theoretical value, which reduces the safety margin. However, the safety margin of Lopt is still the largest.To verify the feasibility and reliability of the proposed design method, explosive tests were performed on buck-boost converters with different inductances. The test results are shown in Table6.Table 6
Explosive test results (Ui = 22 V, Uo = 18 V, C = 22 μF, RL = 36 Ω, and f = 200 kHz).
Design rangeCritical valueInductance (μH)ResultsUnsafe20Exploded35UnexplodedInner-intrinsically safeLPmin38.29Unexploded50UnexplodedLopt137.78Unexploded300UnexplodedLPmax508.98UnexplodedUnsafeLWmax520Unexploded900Exploded1095.11Exploded1500ExplodedAccording to Table5, when L is within the design range that meets the inner-intrinsic safety performance demands, IDD will not have the ignition capability, which verifies the feasibility of the proposed design method.Moreover, ifL is near the boundary between the inner-intrinsic safety and dangerous range, it still does not have ignition capability. This is because the proposed method considers the most dangerous condition, and the actual IDD ignition capability is weaker than this condition, so it has a safety margin, which verifies the reliability of the proposed design method.However, the proposed design method does not consider the output intrinsic safety performance of the converter, so further research on this is needed.


## 4.1. Design of the Inner-Intrinsically Safe Buck-Boost Converter

Two groups of the main system and component parameters of the IISBBC are shown in Table3.Table 3
Main system and component parameters.
VariablesGroup 1Group 2Ui14–18 V18–22 VUo18 V18 VRL36–90 Ω36–90 Ωf200 kHz200 kHzUPP1%Uo1%UoAccording to Figure15 and Table 3, in these parameters, when Ui is higher than 24 V, L will have no value to meet the electrical performance and inner-intrinsic safety demands. Therefore, considering the working demands and voltage fluctuations, Ui of the IISBBC is set to 14–22 V and divided into two groups of low-input voltage (Group 1) and high-input voltage (Group 2). Taking Group 1 as an example, the design steps are as follows:(1)
According to the above parameters and equation (8), the inductance L must be greater than LEmin, which is given by the following:(27)L≥LEmin=RLminUimax22fUimax+Uo2=22.5μH.(2)
The inductanceL must ensure that there is no IDD ignition capability when the converter operates at Uimax and RLmin based on the arc power. Since L > LEmin, the converter works in the CCM when RL = RLmin. Combining equations (2) and (19), the maximum inductance LPmax and the minimum inductance LPmin based on the arc power can be obtained by(28)UimaxILPCCM+LILPCCM2T=12.25ILPCCM−25/31+14ILPCCM.Solving equation (28), we obtain the following:(29)LPmin=7.51μH,LPmax=813.92μH.According to equation (22), the inductance design range based on power Lp is given by the following:(30)7.51≤LP≤813.92μH.(3)
The inductanceL must ensure that there is no IDD ignition capability when the converter operates at Uimin and RLmin based on the arc energy. Since the expression of WLCI is different according to Ui and ILP, the minimum inductance peak current ILPmin needs to be determined. According to equation (2), ILP decreases to ILPmin when L is infinite, which is given by the following:(31)ILPmin=UoUimin+UoRLminUimin=1.14A > 0.4A.Combining equations (12) and (21) and substituting the parameters, the maximum inductance based on the energy LWmax can be obtained by(32)LWmax=3.28ILPCCM22.5ILPCCM−1.596−0.012exp0.187Ui×10−3.Solving equation (32), we obtain(33)LWmax=1003.11μH.According to equation (23), the inductance design range based on the energy LW is given by the following:(34)0≤LW≤1003.11μH.(4)
According to equations (25) and (26), the optimal inductance Lopt is as follows:(35)Lopt=74.05LμH.To ensure that the IISBBC has the the best inner-intrinsic safety performance, the inductanceL is taken as Lopt.(5)
According to equation (9), CEmin is 9.437 μF. Thus, we can set C equal to 22 μF to meet the electric performance demand.Similarly, the inductance design range of Group 2 can be obtained. The inductance design ranges of these two groups of IISBBC are shown in Table4.Table 4
Inductance design range of IISBBC.
VariablesGroup 1 (μH)Group 2 (μH)LEmin22.528.225LPmin7.5138.29LPmax813.92508.98LWmax1003.111100.11Lopt74.05137.78The design ranges of inductance and capacitance obtained by the proposed method and design method based on the MIC [24] are compared in Table 5.Table 5
Comparison of the inductance and capacitance design ranges.
VariablesProposed methodMethod based on the MICGroup 1L22.5 ≤L ≤ 813.92 μH22.5 ≤L ≤ 349.88 μHLopt74.05μHNoneC (if L = Lopt)9.437μF ≤ C9.437μF ≤ CGroup 2L38.29 ≤L ≤ 508.98 μHN/ALopt137.78μHC (if L = Lopt)9.355μF ≤ CThe design method based on the MIC takesLEmin as the initial value, iterates by querying the MIC after considering the safety margin λ (λ = 1.5 in Table 5), and obtains the maximum inductance that meets the inner-intrinsically safe performance demands. However, this method is more complicated, and reading errors may accumulate by querying the MIC multiple times; thus, the accuracy of the method is reduced. Moreover, according to Group 2 in Table 5, when Ui is large, there is a case where the critical ignition current IMIC corresponding to LEmin fails to meet the intrinsic safety demand, and the iteration cannot be performed. Thus, the applicability of the method is also reduced.The proposed design method considers the effect of the critical ignition power and energy on the IDD ignition capability. According to the analysis of the critical ignition power, ifL is too large or too small, the IDD can ignite methane-air mixtures, which contradicts the idea of the design method based on the MIC that L meets the intrinsically safe performance demand and should be as small as possible. Moreover, based on the principle that the converter has the largest safety margin of IDD, the optimal inductance Lopt is obtained. Thus, the inductance design method is clearer. According to the analysis of the critical ignition energy, WLCI is affected by L, ILP, and Ui. Therefore, the critical ignition energy WCI is generally not considered to be constant. The main difference between these two methods is the design consideration based on the inner-intrinsic safety performance. However, the design considerations based on the electrical performance are basically identical, so the two methods have consistent LEmin and CEmin.


## 4.2. Explosive Test Based on the IEC Spark Test Apparatus

The IISBBCs were tested by the IEC spark test apparatus. The IEC spark test apparatus [28] and its structure are shown in Figure 16, where the tungsten wire and the cadmium disk are the disconnected electrodes.Figure 16
IEC spark test apparatus. (a) Prototype appearance. (b) Structural schematic.
(a)(b)The disconnected points of the tested circuit are connected with these two electrodes. The disconnected electrodes are contacted and disconnected through the transmission gear rotates so that the circuit is turned on and off [29, 30].The steps of the explosive test are as follows:(1)
Prepare a gas mixture corresponding to an explosive environment. The Type I environment is a methane-air mixture with a concentration ratio of 8–8.6%. Clean the electrodes.(2)
Calibrate the sensitivity of the apparatus. The calibration circuit is a simple inductive circuit with parameters of supply voltageE = 24 V, inductance L = 95 mH, and current I = 110 mA. If an explosion occurs within 400 revolutions of the transmission gear, the sensitivity calibration of the apparatus is qualified. The explosive evaluation of the tested circuit can be carried out only after the apparatus sensitivity has been calibrated three times.(3)
The IISBBC is connected to the resistive load and the IEC spark test apparatus for the explosive tests. If an explosion occurs within 400 revolutions of the transmission gear, the tested circuit has ignition capability; otherwise, it is intrinsically safe.To verify the effectiveness of inductance optimization, the theoretical and experimental values of the differencePΔ between the critical ignition power PCI and the maximum arc power Parc.max under different L are shown in Figure 17.Figure 17
PΔ vs. L of the IISBBC in the explosive test (Ui = 22 V, Uo = 18V, C = 22 μF, RL = 36 Ω, and f = 200 kHz).According to Figure17, the closer L is to Lopt, the larger PΔ is, and the maximum PΔ is reached when L is equal to Lopt. The inner-intrinsic safety performance of the IISBBC has the maximum safety margin based on the arc power, which proves the effectiveness of the inductance optimization.However, it can be found that the margin of the test value is smaller than the theoretical value. This is due to the parasitic parameters of the converter, which makes the inductance peak currentILP greater than the theoretical value, which reduces the safety margin. However, the safety margin of Lopt is still the largest.To verify the feasibility and reliability of the proposed design method, explosive tests were performed on buck-boost converters with different inductances. The test results are shown in Table6.Table 6
Explosive test results (Ui = 22 V, Uo = 18 V, C = 22 μF, RL = 36 Ω, and f = 200 kHz).
Design rangeCritical valueInductance (μH)ResultsUnsafe20Exploded35UnexplodedInner-intrinsically safeLPmin38.29Unexploded50UnexplodedLopt137.78Unexploded300UnexplodedLPmax508.98UnexplodedUnsafeLWmax520Unexploded900Exploded1095.11Exploded1500ExplodedAccording to Table5, when L is within the design range that meets the inner-intrinsic safety performance demands, IDD will not have the ignition capability, which verifies the feasibility of the proposed design method.Moreover, ifL is near the boundary between the inner-intrinsic safety and dangerous range, it still does not have ignition capability. This is because the proposed method considers the most dangerous condition, and the actual IDD ignition capability is weaker than this condition, so it has a safety margin, which verifies the reliability of the proposed design method.However, the proposed design method does not consider the output intrinsic safety performance of the converter, so further research on this is needed.


## 5. Conclusion

(1)
The most dangerous IDD condition of the buck-boost converter is that IDD occurs wheniL is equal to ILP and the switch remains on. In this condition, a resistive circuit model with a controlled voltage source is proposed to represent the buck-boost converter.(2)
Expressions describing the IDD ignition capability of the buck-boost converter in terms of the critical ignition power and energy were derived.PCI decreases with increasing RL and L, is independent of Ui in the DCM, and decreases with increasing Ui in the CCM. Parc.max decreases with increasing RL, increases with increasing Ui when L is small, decreases with increasing Ui when L is large, and first decreases and then increases with increasing L.WLCI and WL decrease with increasing Ui and RL; WLCI decreases and tends to be stable with increasing L; WL increases with increasing L and ILP and decreasing Ui. Therefore, the IDD has the strongest ignition capability based on power when the buck-boost converter operates in the Uimax and RLmin conditions and has the strongest ignition capability based on energy when the converter operates in the Uimin and RLmin conditions. When Parc.max ≥ PCI or WL ≥ WLCI, the IDD of the buck-boost converter will have the capability to ignite methane-air mixtures; thus, the converter is inner-intrinsically safe only when Parc.max < PCI and WL < WLCI.(3)
The optimal method for designing an IISBBC to meet the demands of electric and inner-intrinsic safety performance was obtained. Based on this method, the ranges ofL, C, and Lopt to design an IISBBC with the best inner-intrinsic safety performance can be obtained. The increased applicability of the proposed optimal design method compared with the design method based on querying the MIC was shown; the accuracy, feasibility, and reliability of the proposed optimal design method were demonstrated by comparison in explosion tests based on the IEC spark test apparatus.



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*Source: 6678566-2021-02-24.xml*