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.
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 Figure 1, where represents the input voltage, represents the output voltage, represents the output current, S represents the switch, L represents the inductance, VD represents the diode, C represents the capacitance, represents the load resistance, and f represents the switching frequency.
If the inductance current 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, is given by [24].where d represents the switching duty cycle. If , the converter works in the CCM; if , it works in the DCM. The inductance peak current of the converter in the CCM and DCM are given by [24].where represents the inductance peak current in the CCM and represents the inductance peak current in the DCM. From equations (2) and (3), decreases with increasing in the CCM; is independent of and decreases with increasing and L in the DCM.
The laws governing the change in with L in different operating modes according to equations (2)–(3) are shown in Figure 2.
If the inductance valley current 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 of the CISM and IISM [24] is given by the following:when , the converter works in the CISM; when , it works in the IISM. Substituting equation (1) into (4), it is obvious that is always smaller than ; therefore, the operating modes of the buck-boost converter according to L are shown in Figure 3.
As shown in Figure 3, the buck-boost converter has three operating modes: CCM-CISM, CCM-IISM, and DCM-IISM. The output ripple voltages of the buck-boost converter in these three operating modes are given by [23]:
The laws governing the change in with L in different operating modes according to equations (5)–(7) are shown in Figure 4.
According to Figure 4, decreases with increasing L in the IISM and is independent of L in the CISM.
2.2. Inductance Design Based on Electric Performance Demands
According to Figure 3, L affects the operating modes in which the buck-boost converter works. Assuming that the range of is and the range of is , the laws of the changes in the operating modes with are shown in Figure 5.
In Figure 5, , 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 decreases as and 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, and the current stress of the switch will be too large if the converter always works in the DCM in the assumed area. Moreover, increases with increasing . Therefore, to ensure that will not be too large when is large, the converter is better designed to work in the CCM at least when the output current reaches the maximum. In this case, the operating mode within the assumed working area is shown in Figure 6.
Thus, the minimum inductance that meets the electric performance demands is when the converter works at and . According to equation (1), is given by the following:
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 voltage in the assumed 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 is obtained when the converter works at and in the CCM-IISM. Thus, the minimum capacitance that can meet the electric performance demand is given by [25]:where . The change laws for according to L and m are shown in Figure 7.
According to Figure 7, the larger is, the lower is. 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 Figure 8.
(a)
(b)
Figure 8 shows that the arc energy is provided by the power source and the inductance in the switch-on state; thus, the switch-on state arc energy is as follows:where represents the arc energy provided by the power supply and represents the inductive energy.
In the switch-off state, supplies the arc, C, and . Thus, the switch-off state arc energy is given as follows:where represents the energy consumed by C and .
Comparing equations (10) and (11), it can be seen that when the IDD occurs completely in the switch-on state, is maximized, and the inductive energy is entirely supplied to the arc. can be expressed as follows:where represents the inductance current. According to equation (12), if is equal to , is equal to the maximum arc energy . Therefore, the most dangerous IDD condition of the buck-boost converter is that IDD occurs when is equal to , 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 voltage and arc current waveforms of the simple inductive circuit based on the IEC spark test apparatus are shown in Figure 9.
(a)
(b)
In Figure 9, T represents the arc discharge time, represents the maximum arc voltage, represents the maximum arc current, and 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 , 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, rises to , and 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.
Since 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, increases from zero to and finally equals , whereas decreases from to zero. Therefore, and of the buck-boost converter in the most dangerous IDD condition are given by the following:where represents the IDD inductor voltage. However, is random. Based on the linear attenuation model, it can be assumed that decreases linearly from to zero within the discharge time T; thus, equation (13) can be simplified as follows:
According to equations (14) and (15), the maximum arc power is given by the following:
3.3. Critical Ignition Power of the Inductor-Disconnected Discharge
The maximum arc power of the buck-boost converter is obtained. Although the arc power used in the test is random, it will never be greater than . If has the capability to ignite explosive gases, 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 has the capability to ignite explosive gases.
The change laws for the minimum ignition current for can be obtained from the Type I MIC of the resistive circuit [26]. Based on power function regression analysis, the relationship between and is approximately given by the following:
Comparing obtained by equation (17) and the Type I MIC of the resistive circuit under different , the results are shown in Table 1.
According to Table 1, the relative errors of 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 of the resistive circuit is given by the following:
According to Figure 8(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 , the controlled voltage source , and the wire resistance shown in Figure 10.
In Figure 10, G is the discharge electrode. Based on the proposed equivalent circuit, if is greater than , 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:
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 and in terms of , , and L are shown in Figure 11.
(a)
(b)
When , the buck-boost converter is an inner-intrinsically safe converter; when , the converter will have the capability to ignite methane-air mixtures, and the greater the difference is between and , the stronger the ignition capability.
According to Figure 11, decreases with increasing L and , is independent of in the DCM, and decreases with increasing in the CCM.
decreases with increasing , increases with increasing when L is small, decreases with increasing 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 and 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), is affected by L and . The minimum ignition current with different values of inductance L can be obtained from the Type I MIC of the simple inductive circuit [26]. Suppose is equal to the critical ignition energy ; then, according to equations (10) and (12), the critical inductive energy is given by the following:
According to the Type I MIC of the simple inductive circuit, when < 0.4 A, the energy provided by the power source is negligible; thus, is mainly provided by L, so is approximately constant at 525 μJ; when ≥ 0.4 A, is not constant. In this condition, decreases with increasing when Ui < 18 V, and is independent of when Ui ≥ 18 V. Therefore, based on the power function regression analysis, the change laws of with and are given by the following:
Comparing obtained by equation (21) and the Type I MIC of the simple inductive circuit under different and , the results are shown in Table 2.
According to Table 2, the relative errors of 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 < , 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 of and with , , and L are shown in Figure 12.
(a)
(b)
According to Figure 12, and decrease with increasing and ; decreases and tends to be stable with increasing L; increases with increasing L and and decreasing . Therefore, the IDD ignition capability is strongest when the converter operates at and based on the arc energy. It can also be concluded that in low-voltage and large-current conditions, is not constant but changes with and only when < 0.4 A is 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 Figure 11, there is a maximum inductance and a minimum inductance based on power, which are shown in Figure 13.
If L > or L < , will be greater than , 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 is given by the following:
As shown in Figure 11, decreases as increases and decreases; increases as increases and decreases. Therefore, the values of and when the converter is operating in the and conditions should be considered in the design.
According to Figure 12, there is a maximum inductance based on the energy , which is shown in Figure 14. If L > , will be greater than . Thus, the converter IDD will have the capability to ignite methane-air mixtures.
By incorporating Figure 14, the inductance design range based on the energy is given by the following:
From Figure 12, decreases as and increase. Therefore, the value of when the converter is operating in the and conditions should be considered in the design.
3.6. Inductance Optimization Based on Inner-Intrinsic Safety Demands
According to Figure 13, there is an optimal inductance that maximizes the power difference between and when the converter operates in the and 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.
Since L > , the converter works in the CCM when = . According to equation (19), the power difference can be obtained by the following:
For the first derivative of equation (24) is equal to zero, we can obtainwhere represents the discharge time T affected by the inductance L. The root of equation (25) is the optimal inductance that maximizes the power difference .
To investigate the influence of on the design and optimization of inductance, the laws governing the change in , , and with 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
In Figure 15, 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 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 Table 3.
According to Figure 15 and Table 3, in these parameters, when 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, 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 , which is given by the following:(2)The inductance L must ensure that there is no IDD ignition capability when the converter operates at and based on the arc power. Since L > , the converter works in the CCM when = . Combining equations (2) and (19), the maximum inductance and the minimum inductance based on the arc power can be obtained by Solving equation (28), we obtain the following: According to equation (22), the inductance design range based on power is given by the following:(3)The inductance L must ensure that there is no IDD ignition capability when the converter operates at and based on the arc energy. Since the expression of is different according to and , the minimum inductance peak current needs to be determined. According to equation (2), decreases to when L is infinite, which is given by the following: Combining equations (12) and (21) and substituting the parameters, the maximum inductance based on the energy can be obtained by Solving equation (32), we obtain According to equation (23), the inductance design range based on the energy is given by the following:(4)According to equations (25) and (26), the optimal inductance is as follows: To ensure that the IISBBC has the the best inner-intrinsic safety performance, the inductance L is taken as .(5)According to equation (9), 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 Table 4.
The design ranges of inductance and capacitance obtained by the proposed method and design method based on the MIC [24] are compared in Table 5.
The design method based on the MIC takes as the initial value, iterates by querying the MIC after considering the safety margin ( = 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 is large, there is a case where the critical ignition current corresponding to 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, if L 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 is obtained. Thus, the inductance design method is clearer. According to the analysis of the critical ignition energy, is affected by L, , and . Therefore, the critical ignition energy 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 and .
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.
(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 voltage E = 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 difference between the critical ignition power and the maximum arc power under different L are shown in Figure 17.
According to Figure 17, the closer L is to , the larger is, and the maximum is reached when L is equal to . 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 current greater than the theoretical value, which reduces the safety margin. However, the safety margin of 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 Table 6.
According to Table 5, 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, if L 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 when is equal to 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. decreases with increasing and L, is independent of in the DCM, and decreases with increasing in the CCM. decreases with increasing , increases with increasing when L is small, decreases with increasing when L is large, and first decreases and then increases with increasing L. and decrease with increasing and ; decreases and tends to be stable with increasing L; increases with increasing L and and decreasing . Therefore, the IDD has the strongest ignition capability based on power when the buck-boost converter operates in the and conditions and has the strongest ignition capability based on energy when the converter operates in the and conditions. When ≥ or ≥ , 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 < and < .(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 of L, C, and 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.Data Availability
The data used to support the findings of this study are included within this article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (nos. 51604217 and 51777167).