Bidirectional Interleaved PWM Converter with High Voltage-Conversion Ratio and Automatic Current Balancing Capability for Single-Cell Battery Power System in Small Scientific Satellites

Single-cell battery power systems are a promising bus architecture for small scientific satellites. However, to bridge the huge voltage gap between a single-cell battery and power bus, bidirectional converters with a high voltage conversion ratio and a large current capability for the low-voltage side are necessary. This article proposes a bidirectional interleaved pulse width modulation (PWM) converter with a high voltage conversion ratio and an automatic current balancing capability. By adding capacitors to conventional interleaved PWM converters, not only are inductor currents automatically balanced without feedback control or current sensors, but also voltage conversion ratios at a given duty cycle can be enhanced. Furthermore, the added capacitors can reduce voltage stresses of switches and charged-discharged energies of inductors, realizing more efficient power conversion and reduced circuit volume in comparison with conventional converters. A 100-W prototype was built for experimental verification, and results demonstrated the fundamental characteristics and efficacy of the proposed converter.


Introduction
Vigorous research and development efforts for small scientific satellites are underway to realize frequent and low-cost scientific space missions.Traditional power systems in scientific satellites employ an unregulated bus architecture, where a rechargeable battery and load are directly connected, as illustrated in Figure 1a.The unregulated bus architecture (see Figure 1a) is advantageous over regulated bus architectures (see Figure 1b) from the viewpoint of the system simplicity, as no dedicated converter for battery regulation is necessary.However, since the battery is directly connected to the load in the unregulated bus architectures, the number of battery cells connected in a series is determined by the load voltage requirement-e.g., eight and twelve cells for 28-V and 50-V bus systems, respectively.The energy capacity of the battery in watt-hours should be adjusted by selecting or manufacturing cells with a proper capacity, hence impairing the design flexibility.The poor design flexibility is quite unfavorable for small satellites, to provide frequent scientific mission opportunities.
Although the converter count is doubled, the regulated bus architecture (see Figure 1b) is attractive from the viewpoint of battery design flexibility.The number of battery cells connected in series can be arbitrarily changed to meet the energy capacity demand, and even a single-cell battery system is theoretically feasible, as shown in Figure 1c [1].Despite the cost penalty of the additional bidirectional Energies 2018, 11, 2702 2 of 12 converter for batteries, the regulated bus system would be a promising choice to realize frequent scientific space missions demanding a wide range of power requirements.
In general, voltages of series-connected cells are gradually imbalanced due to a minor mismatch in individual cell characteristics, such as capacity, self-discharge rate, and internal impedance.Some cells with higher/lower voltages might be over-charged/discharged, likely accelerating irreversible deterioration and increasing risks of fire or, in the worst case, an explosion.To ensure years of safe operation of batteries consisting of multiple cells connected in series, a cell equalizer is indispensable to mitigate or even eliminate cell voltage imbalance.Cell equalizers are essentially a switching power converter, such as nonisolated bidirectional converters [2][3][4][5], single-input multi-output converters [6][7][8][9], etc. [10], and these add complexity to spacecraft power systems.
Energies 2018, 11, x FOR PEER REVIEW 2 of 12 bidirectional converter for batteries, the regulated bus system would be a promising choice to realize frequent scientific space missions demanding a wide range of power requirements.
In general, voltages of series-connected cells are gradually imbalanced due to a minor mismatch in individual cell characteristics, such as capacity, self-discharge rate, and internal impedance.Some cells with higher/lower voltages might be over-charged/discharged, likely accelerating irreversible deterioration and increasing risks of fire or, in the worst case, an explosion.To ensure years of safe operation of batteries consisting of multiple cells connected in series, a cell equalizer is indispensable to mitigate or even eliminate cell voltage imbalance.Cell equalizers are essentially a switching power converter, such as nonisolated bidirectional converters [2][3][4][5], single-input multi-output converters [6][7][8][9], etc. [10], and these add complexity to spacecraft power systems.In the single-cell battery system, cell voltage mismatch is no longer an issue because there is only one single cell.Hence, no cell equalizer is necessary, allowing the simplified system configuration, as shown in Figure 1c.Although the single-cell battery system offers flexible battery design and a simplified system, two major challenges concerning bidirectional converters arise.
The first issue is an extreme duty cycle operation.To bridge the huge voltage gap between the power bus (50 V) and single-cell battery (3.0-4.2V for lithium-ion cells), a conventional nonisolated pulse width modulation (PWM) converter [Figure 2a] must operate with extremely high duty cycles (e.g., duty cycle greater than 0.9).However, conventional converters with such extreme duty cycles are exposed to high voltage and current stresses, and are known to suffer from increased losses and reduced controllability [11].Coupled-or tapped-inductors [11][12][13][14] and switched-capacitor structures [15][16][17] are often employed to achieve high voltage conversion ratios at a given duty cycle.The coupled-or tapped-inductors behave as a voltage divider whose voltage conversion ratios are adjustable with the turns ratio.Although these magnetic components realize high voltage conversion ratios with relatively simple structures, the increased magnetic design difficulty is often cited as a top concern.Switched capacitors can arbitrarily increase voltage conversion ratios by adding capacitors and switches, but numerous switches are necessary to enhance its voltage gain, likely increasing the circuit complexity.
The second issue is a large current at the low-voltage battery side.A current of the low-voltage side is more than ten times greater than that of the high-voltage side, increasing current stress as well as associated Joule losses.Interleaved PWM converters, which equivalently consist of parallel-connected multiple PWM converters operating out of phase, are a favorable solution to mitigate current stresses of switches and inductors.The topology shown in Figure 2b is a In the single-cell battery system, cell voltage mismatch is no longer an issue because there is only one single cell.Hence, no cell equalizer is necessary, allowing the simplified system configuration, as shown in Figure 1c.Although the single-cell battery system offers flexible battery design and a simplified system, two major challenges concerning bidirectional converters arise.
The first issue is an extreme duty cycle operation.To bridge the huge voltage gap between the power bus (50 V) and single-cell battery (3.0-4.2V for lithium-ion cells), a conventional nonisolated pulse width modulation (PWM) converter [Figure 2a] must operate with extremely high duty cycles (e.g., duty cycle greater than 0.9).However, conventional converters with such extreme duty cycles are exposed to high voltage and current stresses, and are known to suffer from increased losses and reduced controllability [11].Coupled-or tapped-inductors [11][12][13][14] and switched-capacitor structures [15][16][17] are often employed to achieve high voltage conversion ratios at a given duty cycle.The coupled-or tapped-inductors behave as a voltage divider whose voltage conversion ratios are adjustable with the turns ratio.Although these magnetic components realize high voltage conversion ratios with relatively simple structures, the increased magnetic design difficulty is often cited as a top concern.Switched capacitors can arbitrarily increase voltage conversion ratios by adding capacitors and switches, but numerous switches are necessary to enhance its voltage gain, likely increasing the circuit complexity.
The second issue is a large current at the low-voltage battery side.A current of the low-voltage side is more than ten times greater than that of the high-voltage side, increasing current stress as well as associated Joule losses.Interleaved PWM converters, which equivalently consist of parallel-connected multiple PWM converters operating out of phase, are a favorable solution to mitigate current stresses of switches and inductors.The topology shown in Figure 2b is a conventional three-phase interleaved PWM converter, and current stresses of inductors and switches are one-third those of the traditional converter shown in Figure 2a.However, all inductor currents need to be measured using current sensors to achieve active current balancing among multiple phases [18], increasing the cost and control complexity.Otherwise, inductor currents are likely to be unbalanced, due to minor mismatches in resistive components and duty cycles, and current stresses and power conversion losses are likely to soar, due to current concentration [19].
Energies 2018, 11, x FOR PEER REVIEW 3 of 12 conventional three-phase interleaved PWM converter, and current stresses of inductors and switches are one-third those of the traditional converter shown in Figure 2a.However, all inductor currents need to be measured using current sensors to achieve active current balancing among multiple phases [18], increasing the cost and control complexity.Otherwise, inductor currents are likely to be unbalanced, due to minor mismatches in resistive components and duty cycles, and current stresses and power conversion losses are likely to soar, due to current concentration [19].
(a) (b) This article presents a bidirectional interleaved PWM converter with high voltage conversion-ratio and automatic current balancing capability for single-cell battery power systems in small scientific satellites.By adding only two capacitors to the conventional interleaved three-phase PWM converter (Figure 2b), the voltage conversion ratio at a given duty cycle is tripled, hence preventing extreme duty cycle operations.Inductor currents can be automatically balanced thanks to the added capacitors, and no current sensor is necessary for inductor current balancing.Furthermore, the added capacitors reduce voltage stresses of switches and charged-discharged energies of inductors, contributing to efficient power conversion and reduced circuit volume.
The rest of this article is organized as follows.Section 2 describes the proposed bidirectional converter topology.The detailed operation analysis, including the derivation for voltage conversion ratio and discussion about automatic current balancing, will be discussed in Section 3. Section 4 presents the quantitative comparison between proposed and conventional converters from the viewpoint of total device power rating (TDPR) and normalized charged-discharged energies in passive components-these can be metrics to quantitatively compare efficiencies and circuit volumes of different converter topologies.Experimental results of a 100-W prototype will be shown to demonstrate the proposed converter in Section 5.

Interleaved Bidirectional PWM Converter with High Voltage-Conversion Ratio and Automatic Current Balancing Capability
The proposed bidirectional interleaved PWM converter is shown in Figure 3. Three inductors, L1-L3, are connected to the battery and share the input current.Currents of these inductors are automatically balanced without feedback control, and therefore, no current sensors nor feedback control loops are necessary.The high-and low-side switches (QLi and QHi, respectively, where i = 1, …, 3) operate in a complementary mode.Three pairs of switches (QL1-QH1, QL2-QH2, QL3-QH3) and inductors operate in the interleaving manner 120° out of phase, and thus, this converter can be regarded as a three-phase interleaved converter when viewed from the battery side.Capacitors, C1 and C2, play two roles of a high voltage-conversion ratio and automatic current balancing, as will be discussed in the next section.This article presents a bidirectional interleaved PWM converter with high voltage conversion-ratio and automatic current balancing capability for single-cell battery power systems in small scientific satellites.By adding only two capacitors to the conventional interleaved three-phase PWM converter (Figure 2b), the voltage conversion ratio at a given duty cycle is tripled, hence preventing extreme duty cycle operations.Inductor currents can be automatically balanced thanks to the added capacitors, and no current sensor is necessary for inductor current balancing.Furthermore, the added capacitors reduce voltage stresses of switches and charged-discharged energies of inductors, contributing to efficient power conversion and reduced circuit volume.
The rest of this article is organized as follows.Section 2 describes the proposed bidirectional converter topology.The detailed operation analysis, including the derivation for voltage conversion ratio and discussion about automatic current balancing, will be discussed in Section 3. Section 4 presents the quantitative comparison between proposed and conventional converters from the viewpoint of total device power rating (TDPR) and normalized charged-discharged energies in passive components-these can be metrics to quantitatively compare efficiencies and circuit volumes of different converter topologies.Experimental results of a 100-W prototype will be shown to demonstrate the proposed converter in Section 5.

Interleaved Bidirectional PWM Converter with High Voltage-Conversion Ratio and Automatic Current Balancing Capability
The proposed bidirectional interleaved PWM converter is shown in Figure 3. Three inductors, L 1 -L 3 , are connected to the battery and share the input current.Currents of these inductors are automatically balanced without feedback control, and therefore, no current sensors nor feedback control loops are necessary.The high-and low-side switches (Q Li and Q Hi , respectively, where i = 1, . . ., 3) operate in a complementary mode.Three pairs of switches and inductors operate in the interleaving manner 120 • out of phase, and thus, this converter can be regarded as a three-phase interleaved converter when viewed from the battery side.Capacitors, C 1 and C 2 , play two roles of a high voltage-conversion ratio and automatic current balancing, as will be discussed in the next section.

Operation Analysis
The presented converter operates as step-up and -down converters when a battery is being discharged and charged, respectively.This section deals only with the step-up operation or battery discharging for the sake of brevity.However, the step-down operation or battery charging can be analyzed similarly.The analysis is performed with the premise that all circuit elements are ideal, with no parasitic components and that all capacitors are large enough so that their voltages are constant.

Operation Modes and Voltage Conversion Ratio
The theoretical key operation waveforms and current flow directions are shown in Figures 4  and 5, respectively.Gating signals for QL1-QL3, vgsL1-vgsL3, are applied so that at least two of three switches are simultaneously on.vgsL1-vgsL3 are 120° out of phase for the interleaving operation.One switching cycle can be divided into six operation modes, but three of them are Mode 1, during which all low-side switches are simultaneously turned on.Mode 1 (Figure 5a): vgsL1-vgsL3 are applied.All the low-side switches are on and their drain-source voltages, vQL1-vQL3, are zero.Inductor currents, iL1-iL3, linearly increase as Vbat is applied to L1-L3.The input current iin, which is the sum of iL1-iL3, also increases.

Operation Analysis
The presented converter operates as step-up and -down converters when a battery is being discharged and charged, respectively.This section deals only with the step-up operation or battery discharging for the sake of brevity.However, the step-down operation or battery charging can be analyzed similarly.The analysis is performed with the premise that all circuit elements are ideal, with no parasitic components and that all capacitors are large enough so that their voltages are constant.

Operation Modes and Voltage Conversion Ratio
The theoretical key operation waveforms and current flow directions are shown in Figures 4 and 5, respectively.Gating signals for Q L1 -Q L3 , v gsL1 -v gsL3 , are applied so that at least two of three switches are simultaneously on.v gsL1 -v gsL3 are 120 • out of phase for the interleaving operation.One switching cycle can be divided into six operation modes, but three of them are Mode 1, during which all low-side switches are simultaneously turned on.

Operation Analysis
The presented converter operates as step-up and -down converters when a battery is being discharged and charged, respectively.This section deals only with the step-up operation or battery discharging for the sake of brevity.However, the step-down operation or battery charging can be analyzed similarly.The analysis is performed with the premise that all circuit elements are ideal, with no parasitic components and that all capacitors are large enough so that their voltages are constant.

Operation Modes and Voltage Conversion Ratio
The theoretical key operation waveforms and current flow directions are shown in Figures 4  and 5, respectively.Gating signals for QL1-QL3, vgsL1-vgsL3, are applied so that at least two of three switches are simultaneously on.vgsL1-vgsL3 are 120° out of phase for the interleaving operation.One switching cycle can be divided into six operation modes, but three of them are Mode 1, during which all low-side switches are simultaneously turned on.Mode 1 (Figure 5a): vgsL1-vgsL3 are applied.All the low-side switches are on and their drain-source voltages, vQL1-vQL3, are zero.Inductor currents, iL1-iL3, linearly increase as Vbat is applied to L1-L3.The input current iin, which is the sum of iL1-iL3, also increases.Mode 1 (Figure 5a): v gsL1 -v gsL3 are applied.All the low-side switches are on and their drain-source voltages, v QL1 -v QL3 , are zero.Inductor currents, i L1 -i L3 , linearly increase as V bat is applied to L 1 -L 3 .The input current i in , which is the sum of i L1 -i L3 , also increases.Mode 2 (Figure 5b): v gsL1 is removed to turn off Q L1 .i L1 linearly decreases and flows through a channel or body diode of Q H1 .Since one of the inductor currents decreases, i in also decreases.C 1 is charged by i L1 , and the volt-sec balance on L 1 yields the voltage of C 1 , V C1 , as where d 1 is the duty cycle of Q L1 as designated in Figure 4. Mode 3 (Figure 5c): v gsL2 is at a low level to turn off Q L2 .A channel or body diode of Q H2 starts to conduct.At the same time, L 2 discharges and its current i L2 decreases.Similar to Mode 2, i in decreases due to the decrease in i L2 .i L2 , together with C 1 , charges C 2 , and the voltage of C 2 , V C2 , can be yielded from the volt-sec balance on L 2 , as where d 2 is the duty cycle of Q L2 .Mode 4 (Figure 5d): Q L3 is turned off, and Q H3 conducts.L 3 and C 2 charge C bus .i L3 discharges, and C bus is charged by i L3 and C 2 .From volt-sec balance on L 3 , the voltage of C bus , V bus , is obtained as where d 3 is the duty cycle of Q L3 .This equation dictates the step-up voltage conversion ratio of the proposed interleaved converter.
Given that all the duty cycles are identical as can be rewritten as Thus, the voltage conversion ratio of the proposed three-phase interleaved converter is three times greater than that of traditional PWM boost converters.
Energies 2018, 11, x FOR PEER REVIEW 5 of 12 Mode 2 (Figure 5b): vgsL1 is removed to turn off QL1. iL1 linearly decreases and flows through a channel or body diode of QH1.Since one of the inductor currents decreases, iin also decreases.C1 is charged by iL1, and the volt-sec balance on L1 yields the voltage of C1, VC1, as where d1 is the duty cycle of QL1 as designated in Figure 4. Mode 3 (Figure 5c): vgsL2 is at a low level to turn off QL2.A channel or body diode of QH2 starts to conduct.At the same time, L2 discharges and its current iL2 decreases.Similar to Mode 2, iin decreases due to the decrease in iL2.iL2, together with C1, charges C2, and the voltage of C2, VC2, can be yielded from the volt-sec balance on L2, as where d2 is the duty cycle of QL2.Mode 4 (Figure 5d): QL3 is turned off, and QH3 conducts.L3 and C2 charge Cbus.iL3 discharges, and Cbus is charged by iL3 and C2.From volt-sec balance on L3, the voltage of Cbus, Vbus, is obtained as where d3 is the duty cycle of QL3.This equation dictates the step-up voltage conversion ratio of the proposed interleaved converter.
Given that all the duty cycles are identical as d1 = d2 = d3 = d, (3) can be rewritten as Thus, the voltage conversion ratio of the proposed three-phase interleaved converter is three times greater than that of traditional PWM boost converters.In order to ensure the operation discussed above, all the low-side switches must be simultaneously on in every switching cycle, and more than two of them must be always on.To this end, d1-d3 must be greater than 0.667.Otherwise, inductor currents are no longer balanced.
The voltage conversion ratios of the proposed and conventional converters are compared in Figure 6.For the 50-V bus system, the required voltage conversion ratio is 12.5-16.7 for a lithium-ion single cell with 3.0-4.2V. Conventional converters need to operate with an extremely high duty cycle of d > 0.92.The duty cycle range of the proposed converter, on the other hand, is reduced to around 0.8, avoiding extreme duty cycle operations.In order to ensure the operation discussed above, all the low-side switches must be simultaneously on in every switching cycle, and more than two of them must be always on.To this end, d 1 -d 3 must be greater than 0.667.Otherwise, inductor currents are no longer balanced.
The voltage conversion ratios of the proposed and conventional converters are compared in Figure 6.For the 50-V bus system, the required voltage conversion ratio is 12.5-16.7 for a lithium-ion single cell with 3.0-4.2V. Conventional converters need to operate with an extremely high duty cycle of d > 0.92.The duty cycle range of the proposed converter, on the other hand, is reduced to around 0.8, avoiding extreme duty cycle operations.

Current Balancing Mechanism
C1 is charged by iL1 during Mode 2 (Figure 5b) and its amount of charge stored corresponds to q1 in Figure 4.During Mode 3, C1 is discharged by iL2, and a released charge amount is q2.Meanwhile, C2 receives q2 as iL2 flows through it.In Mode 4, C2 is discharged by iL3, and its released charge amount is q3 that is transferred to the bus.The charge balance on C2 and C3 yields where Ibus is the bus current designated in Figure 3. Since q1-q3 are equal to respective average inductor current IL1-IL3 multiplied by mode length, Equation ( 5) can be rewritten as This equation suggests that the balance among IL1-IL3 is dependent on d1-d 3 .If d1-d 3 are identical, the charge conservation law for C2 and C3 ensures complete current balancing for all inductors.This balancing mechanism does not rely on any active control nor current sensing, and therefore, all inductor currents are automatically balanced.Now consider the non-ideal case that d1-d 3 are slightly mismatched as d1 = d − ∆d and d2 = d3 = d, due to non-ideality of microcontrollers and gate drivers.IL2 and IL3 can be balanced to be IL, and Equation ( 6) can be rewritten as Rearrangement of Equation ( 7) yields This equation represents the degree of current imbalance due to duty cycle mismatch.For instance, even if d1 severely deviates from others as ∆d = 0.01, the inductor current imbalance is merely 5% with d = 0.8.Thus, the inductor current imbalance due to the non-ideality of microcontrollers and gate drives would be very minor.

Total Device Power Rating
Total device power rating (TDPR) is often introduced as a metric to quantitatively compare different topologies from the viewpoint of semiconductor volt-amp stresses [20,21].TDPR is the sum of the theoretical volt-amp stress of all semiconductor devices normalized by input or output power and is defined as

Current Balancing Mechanism
C 1 is charged by i L1 during Mode 2 (Figure 5b) and its amount of charge stored corresponds to q 1 in Figure 4.During Mode 3, C 1 is discharged by i L2 , and a released charge amount is q 2 .Meanwhile, C 2 receives q 2 as i L2 flows through it.In Mode 4, C 2 is discharged by i L3 , and its released charge amount is q 3 that is transferred to the bus.The charge balance on C 2 and C 3 yields where I bus is the bus current designated in Figure 3. Since q 1 -q 3 are equal to respective average inductor current I L1 -I L3 multiplied by mode length, Equation ( 5) can be rewritten as This equation suggests that the balance among I L1 -I L3 is dependent on d 1 -d 3 .If d 1 -d 3 are identical, the charge conservation law for C 2 and C 3 ensures complete current balancing for all inductors.This balancing mechanism does not rely on any active control nor current sensing, and therefore, all inductor currents are automatically balanced.Now consider the non-ideal case that d 1 -d 3 are slightly mismatched as d 1 = d − ∆d and d 2 = d 3 = d, due to non-ideality of microcontrollers and gate drivers.I L2 and I L3 can be balanced to be I L , and Equation ( 6) can be rewritten as Rearrangement of Equation ( 7) yields This equation represents the degree of current imbalance due to duty cycle mismatch.For instance, even if d 1 severely deviates from others as ∆d = 0.01, the inductor current imbalance is merely 5% with d = 0.8.Thus, the inductor current imbalance due to the non-ideality of microcontrollers and gate drives would be very minor.

Total Device Power Rating
Total device power rating (TDPR) is often introduced as a metric to quantitatively compare different topologies from the viewpoint of semiconductor volt-amp stresses [20,21].TDPR is the sum of the theoretical volt-amp stress of all semiconductor devices normalized by input or output power and is defined as where V max and I max are the theoretical maximum voltage and current stresses of a metal-oxidesemiconductor field-effect transistor (MOSFET).The lower the value of TDPR, the better the converter's performance will be, as power conversion loss reportedly increases with a sum of volt-ampere (V-A) products of switches [22].In this paper, ripple components are not taken into consideration for the sake of simplicity.
The theoretical voltage and current stresses of MOSFETs in the proposed converter are summarized in Table 1.All duty cycles d 1 -d 3 and average inductor currents I L1 -I L3 are assumed equal to d and I L , respectively.Voltage stresses can be determined from the operation modes shown in Figure 5 or values designated in Figure 4 with ( 1)-( 3).The current stresses of Q L2 and Q L3 are double those of others as can be seen in Figure 5-two out of three inductor currents flow through Q L2 and Q L3 as shown in Figure 5b,c.

Table 1.
Voltage and current stresses of metal-oxide-semiconductor field-effect transistors (MOSFETs) in the proposed interleaved converter.

Component
Voltage Current TDPRs of the proposed interleaved converter, conventional single-phase converter (Figure 2a), and conventional interleaved three-phase converter (Figure 2c) are compared in Figure 7.At a given conversion ratio higher than 9.0, the proposed converter achieves the lowest TDPR.At the voltage conversion ratio of 12.5, for example, the TDPR values of the conventional and proposed interleaved converters are 25.0 and 11.1, respectively, corresponding to 56% reduction.The lower TDPR tendency is attributable to the reduced voltage stresses, due to C 1 and C 2 .Switches in the conventional converters, on the other hand, must endure the full output voltage or the bus voltage V bus , resulting in a higher TDPR trend.where Vmax and Imax are the theoretical maximum voltage and current stresses of a metal-oxide-semiconductor field-effect transistor (MOSFET).The lower the value of TDPR, the better the converter's performance will be, as power conversion loss reportedly increases with a sum of volt-ampere (V-A) products of switches [22].In this paper, ripple components are not taken into consideration for the sake of simplicity.
The theoretical voltage and current stresses of MOSFETs in the proposed converter are summarized in Table 1.All duty cycles d1-d3 and average inductor currents IL1-IL3 are assumed equal to d and IL, respectively.Voltage stresses can be determined from the operation modes shown in Figure 5 or values designated in Figure 4 with ( 1)-( 3).The current stresses of QL2 and QL3 are double those of others as can be seen in Figure 5-two out of three inductor currents flow through QL2 and QL3 as shown in Figure 5b,c.

Component
Voltage TDPRs of the proposed interleaved converter, conventional single-phase converter (Figure 2a), and conventional interleaved three-phase converter (Figure 2c) are compared in Figure 7.At a given conversion ratio higher than 9.0, the proposed converter achieves the lowest TDPR.At the voltage conversion ratio of 12.5, for example, the TDPR values of the conventional and proposed interleaved converters are 25.0 and 11.1, respectively, corresponding to 56% reduction.The lower TDPR tendency is attributable to the reduced voltage stresses, due to C1 and C2.Switches in the conventional converters, on the other hand, must endure the full output voltage or the bus voltage Vbus, resulting in a higher TDPR trend.

Normalized Charged-Discharged Energies in Passive Components
Inductors and capacitors occupy a significant portion of the total volume of converters.Volumes of passive components of inductors and capacitors are generally proportional to their stored energies.In this section, the proposed and conventional converters are quantitatively compared on the basis of total charged-discharged energies in inductors and capacitors normalized

Normalized Charged-Discharged Energies in Passive Components
Inductors and capacitors occupy a significant portion of the total volume of converters.Volumes of passive components of inductors and capacitors are generally proportional to their stored energies.In this section, the proposed and conventional converters are quantitatively compared on the basis of total charged-discharged energies in inductors and capacitors normalized by input energy in a single switching cycle E in = V bat I bat T s .
To fairly compare various topologies, volume metrics S is introduced and is defined as where α L and α C are the ripple factors of inductor current and capacitor voltage, respectively, and β is the energy density ratio of capacitors to inductors.E L and E C are the charged-discharged energies of inductors and capacitors.Mathematical expressions of E L and E C for passive components in the proposed converter are listed in Table 2.
In general, α L is chosen in the range of 0.2-0.4 for ordinary PWM converters.To tightly regulate input and output voltages, input and output smoothing capacitors (i.e., C bat and C bus ) should be selected so that their ripple voltage α C is in the range of 0.03-0.05.Meanwhile, ripple factors of flying capacitors (C 1 and C 2 ) can be around 0.1 [23].Energy densities of discrete capacitors are in the range of more than three orders of magnitude greater than those of similarly scaled inductors [23][24][25].In the following, the comparison on S was performed with α L = 0.3, α C = 0.03 and 0.1 for smoothing and flying capacitors, respectively, and β = 100.

Component
Charged-Discharged Energy Calculated tendencies of S are shown in Figure 8. Inductors took the largest portion in all the converters.The portions taken by smoothing capacitors (C bat and C bus ) were substantial in the conventional single-phase converter and proposed interleaved converter, because C bus must be large to absorb large pulsating current at the bus side.Meanwhile, C bus in the conventional three-phase converter can be designed smaller, owing to the interleaving operation at the bus side.Although the proposed converter also operates in the interleaving manner at the battery side, the operation at the bus side is not in an interleaving manner, as can be seen in Figure 5.
Despite the increased portion of capacitors, the proposed converter exhibits the lowest S tendency.At the voltage conversion ratio of 12.5, the S values of the conventional 1-phase, 3-phase, and proposed converters were 339, 310, and 289, respectively, implying the volume of passive components would be reduced by greater than 7%.The lowest S tendency was chiefly because charged-discharged energies of inductors are significantly reduced by C 1 and C 2 .As shown in Figure 5, inductors together with capacitors contribute to power transfer, mitigating the energy storage burden of inductors.Since capacitors are far more compact than inductors (as characterized by β), reducing the burden of inductors by using capacitors translates into a reduction in total volume.tendency.At the voltage conversion ratio of 12.5, the S values of the conventional 1-phase, 3-phase, and proposed converters were 339, 310, and 289, respectively, implying the volume of passive components would be reduced by greater than 7%.The lowest S tendency was chiefly because charged-discharged energies of inductors are significantly reduced by C1 and C2.As shown in Figure 5, inductors together with capacitors contribute to power transfer, mitigating the energy storage burden of inductors.Since capacitors are far more compact than inductors (as characterized by β), reducing the burden of inductors by using capacitors translates into a reduction in total volume.

Experimental Results
A 100-W prototype of the proposed converter was built, as shown in Figure 9. Component values are listed in Table 3.The prototype operated with Vbat = 4.0 V and Vbus = 50 V at the switching frequency of 100 kHz.Gate drivers were power by an external power supply (neither by Vbus nor Vbat).Gating signals were generated using a TMS320F28335 control card (Texas Instruments, Dallas, TX, USA).

Experimental Results
A 100-W prototype of the proposed converter was built, as shown in Figure 9. Component values are listed in Table 3.The prototype operated with V bat = 4.0 V and V bus = 50 V at the switching frequency of 100 kHz.Gate drivers were power by an external power supply (neither by V bus nor V bat ).Gating signals were generated using a TMS320F28335 control card (Texas Instruments, Dallas, TX, USA).

Experimental Results
A 100-W prototype of the proposed converter was built, as shown in Figure 9. Component values are listed in Table 3.The prototype operated with Vbat = 4.0 V and Vbus = 50 V at the switching frequency of 100 kHz.Gate drivers were power by an external power supply (neither by Vbus nor Vbat).Gating signals were generated using a TMS320F28335 control card (Texas Instruments, Dallas, TX, USA).Measured key operation waveforms at full load in the step-up mode are shown in Figure 10.v QL1 -v QL3 and i L1 -i L3 were 120 • out of phase, and inductor average currents were identical, verifying the passive automatic current balancing capability.
The measured step-up voltage conversion ratio is shown and compared with the theoretical one in Figure 11.The experimental result matched satisfactorily with the theoretical one.The error was considered due to the power conversion loss in the prototype.The measured step-up voltage conversion ratio is shown and compared with the theoretical one in Figure 11.The experimental result matched satisfactorily with the theoretical one.The error was considered due to the power conversion loss in the prototype.The measured power conversion efficiency in the step-up mode is shown in Figure 12a.The efficiency steadily decreased as the output power increased.The efficiency at the full load of 100 W was as high as 90%.
The calculated loss breakdown is shown in Figure 12b.Joule losses of inductors and switches were dominant in medium to heavy load regions.Meanwhile, switching losses were insignificant in all power range, probably due to reduced voltage stresses of switches, as discussed in Section 4.1.The result suggests that the use of inductors and switches with low resistive components is a key to improving power conversion efficiency.The measured step-up voltage conversion ratio is shown and compared with the theoretical one in Figure 11.The experimental result matched satisfactorily with the theoretical one.The error was considered due to the power conversion loss in the prototype.The measured power conversion efficiency in the step-up mode is shown in Figure 12a.The efficiency steadily decreased as the output power increased.The efficiency at the full load of 100 W was as high as 90%.

Conclusions
The calculated loss breakdown is shown in Figure 12b.Joule losses of inductors and switches were dominant in medium to heavy load regions.Meanwhile, switching losses were insignificant in all power range, probably due to reduced voltage stresses of switches, as discussed in Section 4.1.The result suggests that the use of inductors and switches with low resistive components is a key to improving power conversion efficiency.

Conclusions
A bidirectional interleaved PWM converter with high voltage conversion ratio and passive automatic current balancing capability has been proposed for single-cell battery power systems in The measured power conversion efficiency in the step-up mode is shown in Figure 12a.The efficiency steadily decreased as the output power increased.The efficiency at the full load of 100 W was as high as 90%.
The calculated loss breakdown is shown in Figure 12b.Joule losses of inductors and switches were dominant in medium to heavy load regions.Meanwhile, switching losses were insignificant in all power range, probably due to reduced voltage stresses of switches, as discussed in Section 4.1.The result suggests that the use of inductors and switches with low resistive components is a key to improving power conversion efficiency.The measured step-up voltage conversion ratio is shown and compared with the theoretical one in Figure 11.The experimental result matched satisfactorily with the theoretical one.The error was considered due to the power conversion loss in the prototype.The measured power conversion efficiency in the step-up mode is shown in Figure 12a.The efficiency steadily decreased as the output power increased.The efficiency at the full load of 100 W was as high as 90%.
The calculated loss breakdown is shown in Figure 12b.Joule losses of inductors and switches were dominant in medium to heavy load regions.Meanwhile, switching losses were insignificant in all power range, probably due to reduced voltage stresses of switches, as discussed in Section 4.1.The result suggests that the use of inductors and switches with low resistive components is a key to improving power conversion efficiency.

Conclusions
A bidirectional interleaved PWM converter with high voltage conversion ratio and passive automatic current balancing capability has been proposed for single-cell battery power systems in

Conclusions
A bidirectional interleaved PWM converter with high voltage conversion ratio and passive automatic current balancing capability has been proposed for single-cell battery power systems in small scientific satellites.The proposed converter operates in an interleaving manner, and the added capacitors realize not only voltage conversion ratios three times greater than those of conventional bidirectional converters, but also automatic current balancing.A quantitative comparison of TDPR and volume metrics S was performed for the proposed and conventional converters.The comparative results revealed that TDPR and S of the proposed converter could be reduced by 56% and >7%, respectively, in comparison with conventional converters, suggesting higher power conversion efficiencies and more compact circuit design.The 100-W prototype with V bat = 4.0 V and V bus = 50 V was built for experimental verification.The average inductor currents were automatically balanced due to the added capacitors, and the measured power conversion efficiency was higher than 90% in the entire range, demonstrating the fundamental characteristics of the proposed converter.

Figure 1 .
Figure 1.Spacecraft power systems: (a) Conventional unregulated bus architecture; (b) conventional regulated bus architecture; (c) Regulated bus architecture with single-cell battery.

Figure 1 .
Figure 1.Spacecraft power systems: (a) Conventional unregulated bus architecture; (b) conventional regulated bus architecture; (c) Regulated bus architecture with single-cell battery.

Figure 3 .
Figure 3. Proposed interleaved PWM converter with high voltage conversion ratio.

Figure 3 .
Figure 3. Proposed interleaved PWM converter with high voltage conversion ratio.

12 Figure 3 .
Figure 3. Proposed interleaved PWM converter with high voltage conversion ratio.

Energies 2018 , 12 Figure 6 .
Figure 6.Theoretical step-up voltage conversion ratios of conventional and proposed converters.

Figure 6 .
Figure 6.Theoretical step-up voltage conversion ratios of conventional and proposed converters.

Figure 7 .
Figure 7.Total device power rating (TDPR) as a function of voltage step-up conversion ratio.

Figure 7 .
Figure 7.Total device power rating (TDPR) as a function of voltage step-up conversion ratio.

Figure 8 .
Figure 8. Normalized charged-discharged energies as a function of step-up voltage conversion ratio.(a) Conventional single-phase converter; (b) conventional three-phase interleaved converter; (c) proposed converter.

Figure 8 .
Figure 8. Normalized charged-discharged energies as a function of step-up voltage conversion ratio.(a) Conventional single-phase converter; (b) conventional three-phase interleaved converter; (c) proposed converter.

Figure 8 .
Figure 8. Normalized charged-discharged energies as a function of step-up voltage conversion ratio.(a) Conventional single-phase converter; (b) conventional three-phase interleaved converter; (c) proposed converter.

Figure 10 .
Figure 10.Measured key operation waveforms at full load.

Figure 11 .
Figure 11.Experimental and theoretical step-up voltage conversion ratios.

Figure 11 .
Figure 11.Experimental and theoretical step-up voltage conversion ratios.

Figure 11 .
Figure 11.Experimental and theoretical step-up voltage conversion ratios.

Figure 11 .
Figure 11.Experimental and theoretical step-up voltage conversion ratios.

Table 1 .
Voltage and current stresses of metal-oxide-semiconductor field-effect transistors (MOSFETs) in the proposed interleaved converter.

Table 2 .
Charged-discharged energies in inductors and capacitors in the proposed converter.

Table 3 .
Components used for prototype.

Table 3 .
Components used for prototype.