Double Stage Double Output DC–DC Converters for High Voltage Loads in Fuel Cell Vehicles

: This article aims to enhance the output voltage magnitude of fuel cells (FCs), since the actual generation is low. The traditional technique is too complicated and has a cascaded or parallel connection solution to achieve high voltage for multiple loads in vehicles. In this case, electronic power converters are a viable solution with compact size and cost. Hence, double or multiple output DC–DC converters with high voltage step up are required to feed multiple high voltage loads at the same time. In this article, novel double stage double output (DSDO) DC–DC converters are formulated to feed multiple high voltage loads of FC vehicular system. Four DSDO DC–DC converters called DSDO L–L, DSDO L-2L, DSDO L-2LC, and DSDO L-2LC are developed in this research work and all the converters are derived based on the arrangement of di ﬀ erent reactive networks. The primary power circuitry, conceptual operation, and output voltage gain derivation are given in detail with valid proof. The proposed converters are compared with possible parallel combinations of conventional converters and recently available conﬁguration. Comprehensive numerical simulation and experimental prototype results show that our theoretical predictions are valid and that the conﬁguration is applicable for real time application in FC technologies for ‘more-electric vehicles’.


Introduction
In electric grid, hybrid 'more-electric vehicles', automobile high-intensity discharge headlamps, uninterruptible power supply, and luxury loads application multiport and multilevel power converters popular solutions [1][2][3][4]. Some advanced predictive control based on the multilevel converter is also proposed for energy storage [5,6]. Fuel cells have many features, including compatibility, size, and modularity [7,8]. However, the amalgamation of series and parallel FCs is not a suitable solution for generating high DC voltage/current. Trade-off loss increases the cost of the system and requires a large space. Furthermore, the major obstacles facing FC technology are durability, low generated voltage, and to fulfill the voltage demand of high voltage loads in FC vehicles. In such cases, power electronic DC-DC converters with high voltage conversion ratios and high efficiency play a pivotal control role [9][10][11][12]. Theoretically, a moderate or high output voltage is obtained from a traditional boost converter by operating in an extreme duty cycle. Adverse effects at extreme duty ratio lead to reduced controllability, increased switching losses, high conduction losses, large current ripple, high current and voltage ratings, and reverse diode recovery problems [13][14][15][16]. Consequently, traditional DC-DC converters are not suitable candidates for FC electric vehicle applications.
Previous research has achieved high voltage conversion ratio by using a cascaded traditional boost converter configuration. However, cascaded converter configurations have low efficiency and high cost due to the increased number of high voltage/current rating semiconductor devices and reactive Previous research has achieved high voltage conversion ratio by using a cascaded traditional boost converter configuration. However, cascaded converter configurations have low efficiency and high cost due to the increased number of high voltage/current rating semiconductor devices and reactive elements [17,18]. Further, for implementation, they need complex control logic and increased driver modules to protect and control the semiconductor devices. Quadratic boost converters achieve a high voltage conversion ratio, but high current/voltage rating components/devices and the internal resistance of the inductors limits the output voltage [19]. Multistage diode/capacitor-based DC-DC converters have been proposed to achieve high voltage gain [20][21][22][23][24]. However, multiple discharging/charging loops of the capacitors lead to increased conduction loss, cost, and size, and reduced efficiency due to their parasitic nature. Converters have been proposed to get multiple outputs from a single input source by using push-pull, half-bridge, full-bridge, and fly-back converter topologies [25][26][27]. In all cases, high voltage is obtained with a high transformer rating on the primary side. Therefore, these converters cannot provide a proper solution for low weight/cost applications.
The parallel configurations of traditional converters such as boost, buck-boost, Cuk, single ended primary inductance converter (SEPIC), and ZETA can be possible solutions to achieve multiple outputs. The power circuitry of possible configurations without common front-end structure are shown in Figure 1a-e. These configurations provide two outputs using two different control switches. However, the voltage gain is not significantly improved, even when using a large number of components and devices. Furthermore, in order to reduce the component or device counts, common front-end structure can be a solution, as shown in Figure 1f-j. These configurations provide dual output using common front-end structures. However, only a few input side components are used, the device count is reduced, and the voltage gain is limited. Moreover, the current rating of the components is increased due to the common structure. In order to reduce the component count, hybrid converters are another possible solution. Moreover, hybrid Cuk, SEPIC, and ZETA converter configurations can achieve multiple outputs. A combination of Cuk and SEPIC converter structure was employed in [28]. Figure 2a shows the SEPIC-Cuk converter circuitry with common front-end design and dual output. A combination of ZETA and buck-boost converter structure was employed in [29].  Figure 2b shows the circuitry of a ZETA-Buck-boost converter with common front-end structure and two outputs. The combination of Cuk and boost converters is employed in [30]. The circuitry of a boost-Cuk converter with common front-end and two outputs is shown in Figure 2c. The voltage conversion ratio of these topologies is limited. Furthermore, efforts have been made to reduce the switching and to obtain multiple outputs [31][32][33]. However, these converters have low voltage conversion ratio and are more suitable for low-power applications. The "X-Y converter family" has been proposed for high voltage output and has single switching and a capacitor stack at the output side [34][35][36][37][38]. The block diagram of the X-Y converter family is depicted in Figure 2d. Notable, in XY converters, the X converter is directly connected to the input supply, and the Y converter is fed from the output voltage of the X converter. The output voltage of an X-Y converter is the sum of the output voltages of the X and Y converters. In order to achieve multiple outputs and high voltage conversion ratio, this article contributes the following: (f) boost-boost converter with common front-end structure; (g) buck-boost-buck-boost converter with common front end structure; (h) Cuk-Cuk converter with common front-end structure; (i) SEPIC-SEPIC converter with common front-end structure; (j) ZETA-ZETA converter with common front-end structure.   Figure 2b shows the circuitry of a ZETA-Buck-boost converter with common front-end structure and two outputs. The combination of Cuk and boost converters is employed in [30]. The circuitry of a boost-Cuk converter with common front-end and two outputs is shown in Figure 2c. The voltage conversion ratio of these topologies is limited. Furthermore, efforts have been made to reduce the switching and to obtain multiple outputs [31][32][33]. However, these converters have low voltage conversion ratio and are more suitable for low-power applications. The "X-Y converter family" has been proposed for high voltage output and has single switching and a capacitor stack at the output side [34][35][36][37][38]. The block diagram of the X-Y converter family is depicted in Figure 2d. Notable, in XY converters, the X converter is directly connected to the input supply, and the Y converter is fed from the output voltage of the X converter. The output voltage of an X-Y converter is the sum of the output voltages of the X and Y converters. In order to achieve multiple outputs and high voltage conversion ratio, this article contributes the following:  Figure 2b shows the circuitry of a ZETA-Buck-boost converter with common front-end structure and two outputs. The combination of Cuk and boost converters is employed in [30]. The circuitry of a boost-Cuk converter with common front-end and two outputs is shown in Figure 2c. The voltage conversion ratio of these topologies is limited. Furthermore, efforts have been made to reduce the switching and to obtain multiple outputs [31][32][33]. However, these converters have low voltage conversion ratio and are more suitable for low-power applications. The "X-Y converter family" has been proposed for high voltage output and has single switching and a capacitor stack at the output side [34][35][36][37][38]. The block diagram of the X-Y converter family is depicted in Figure 2d. Notable, in XY converters, the X converter is directly connected to the input supply, and the Y converter is fed from the output voltage of the X converter. The output voltage of an X-Y converter is the sum of the output voltages of the X and Y converters. In order to achieve multiple outputs and high voltage conversion ratio, this article contributes the following: The L-Y converters, i.e., an expanded member of the XY converter family that feeds power to two different high voltage loads. At same time, the proposed converter provides high voltage conversion ratio. A diagram of a typical fuel-cell vehicle (FCV) with a DSDO converter is shown Figure 3, where low FC voltage is fed to two high voltage loads.

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The modes of operation, characteristics waveform, and voltage gain analysis for each proposed configuration are discussed in detail.

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The performance of the proposed converters is validated through numerical simulation and experimental prototype results. • The L-Y converters, i.e., an expanded member of the XY converter family that feeds power to two different high voltage loads. At same time, the proposed converter provides high voltage conversion ratio. A diagram of a typical fuel-cell vehicle (FCV) with a DSDO converter is shown Figure 3, where low FC voltage is fed to two high voltage loads.

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The modes of operation, characteristics waveform, and voltage gain analysis for each proposed configuration are discussed in detail.

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The performance of the proposed converters is validated through numerical simulation and experimental prototype results.  The stage-2 and stage-2′ voltages are obtained across capacitors C2 and C'2, respectively. The load R1o is connected across capacitors C1, C2, and load R2o is connected across capacitors C'1 and C'2 to achieve double output voltages, i.e., V1o and V2o, from a single source input (Vi) as shown in Figure 4. The DSDO L-L converter operates in two modes: switch S turn-ON and another when switch S turn-OFF. Figure 5 shows the characteristics of inductor voltage and current obtained for one switching cycle. Time zone A-B describes the ON time of the switch and time zone B-C describes the OFF time. The equivalent circuit for turn-ON mode is shown in Figure 6a. In this mode, inductor L1 is magnetized through switch S and diode D1 from the input power of voltage Vi. At the same time,  Figure 4 depicts the power circuit of a DSDO L-L converter. In a DSDO L-L converter, a single switch S and input voltage V i are arranged in two stages. Two L-L converters are employed to obtain dual output voltage. The capacitors C 1 , C 2 , inductors L 1 , L 2 , and diodes D 1 , D 2 , D 3 are elements of L-L converter-1. The capacitors C' 1 , C' 2 , inductors L' 1 , L' 2 , and diodes D' 1 , D' 2 , D' 3 are elements of L-L converter-2. The stage-1 and stage-1 voltages are obtained across capacitors C 1 and C' 1 , respectively. The stage-2 and stage-2 voltages are obtained across capacitors C 2 and C' 2 , respectively. The load R 1o is connected across capacitors C 1 , C2, and load R 2o is connected across capacitors C' 1 and C' 2 to achieve double output voltages, i.e., V 1o and V 2o , from a single source input (V i ) as shown in Figure 4. • The L-Y converters, i.e., an expanded member of the XY converter family that feeds power to two different high voltage loads. At same time, the proposed converter provides high voltage conversion ratio. A diagram of a typical fuel-cell vehicle (FCV) with a DSDO converter is shown Figure 3, where low FC voltage is fed to two high voltage loads. The modes of operation, characteristics waveform, and voltage gain analysis for each proposed configuration are discussed in detail.

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The performance of the proposed converters is validated through numerical simulation and experimental prototype results.  The stage-2 and stage-2′ voltages are obtained across capacitors C2 and C'2, respectively. The load R1o is connected across capacitors C1, C2, and load R2o is connected across capacitors C'1 and C'2 to achieve double output voltages, i.e., V1o and V2o, from a single source input (Vi) as shown in Figure 4. The DSDO L-L converter operates in two modes: switch S turn-ON and another when switch S turn-OFF. Figure 5 shows the characteristics of inductor voltage and current obtained for one switching cycle. Time zone A-B describes the ON time of the switch and time zone B-C describes the OFF time. The equivalent circuit for turn-ON mode is shown in Figure 6a. In this mode, inductor L1 is magnetized through switch S and diode D1 from the input power of voltage Vi. At the same time, The DSDO L-L converter operates in two modes: switch S turn-ON and another when switch S turn-OFF. Figure 5 shows the characteristics of inductor voltage and current obtained for one switching cycle. Time zone A-B describes the ON time of the switch and time zone B-C describes the OFF time. The equivalent circuit for turn-ON mode is shown in Figure 6a. In this mode, inductor L 1 is magnetized through switch S and diode D 1 from the input power of voltage V i . At the same time, input voltage V i and the voltage across capacitor C 1 magnetizes the inductor L 2 . Total energy stored in capacitors C 1 and C 2 provide load R 1o . Inductor L' 1 is magnetized through switch S and diode D' 1 by the input voltage V i . At the same time, input voltage V i and voltage across capacitor C' 1 magnetizes inductor L' 2 . The energy is delivered to load R 2o by capacitors C' 1 and C' 2 . During turn-ON, capacitors C 1 , C' 1 , C 2 , and C' 2 are discharged, and inductors L 1 , L' 1 , L 2 , and L' 2 are magnetized. Throughout this mode, diodes D 1 , D' 1 are forward biased and diodes D 2 , D 3 , D' 2 , D' 3 are reverse biased.  The voltages across inductors can be obtained as follows,

DSDO L-L Converter
The equivalent circuit for turn-OFF mode is shown in Figure 6b. In this mode, the capacitor C1 is charged by stored energy in the inductor L1 through diode D2. At the same time, capacitor C2 is charged by stored energy in the inductor L2 through diode D3. Energy is provided to load R1o by the connection of inductors L1 and L2. Capacitor C'1 is charged from stored energy in inductor L'1 through diode D'2. At the same time, capacitor C'2 is charged from stored energy in inductor L'2 through diode D'3. Energy is provided to load R2o by connection of inductors L'1 and L'2. In turn-OFF mode, capacitors C1, C'1, C2, and C'2 are charged and inductors L1, L'1, L2, and L'2 are demagnetized. In this mode, diodes D1, D'1 are reverse biased and diodes D2, D3, D'2, and D'3 are forward biased.  The voltages across inductors can be obtained as follows, The equivalent circuit for turn-OFF mode is shown in Figure 6b. In this mode, the capacitor C 1 is charged by stored energy in the inductor L 1 through diode D 2 . At the same time, capacitor C 2 is charged by stored energy in the inductor L 2 through diode D 3 . Energy is provided to load R 1o by the connection of inductors L 1 and L 2 . Capacitor C' 1 is charged from stored energy in inductor L' 1 through diode D' 2 . At the same time, capacitor C' 2 is charged from stored energy in inductor L' 2 through diode D' 3 . Energy is provided to load R 2o by connection of inductors L' 1 and L' 2 . In turn-OFF mode, capacitors C 1 , C' 1 , C 2 , and C' 2 are charged and inductors L 1 , L' 1 , L 2 , and L' 2 are demagnetized. In this mode, diodes D 1 , D' 1 are reverse biased and diodes D 2 , D 3 , D' 2 , and D' 3 are forward biased.  The voltages across inductors can be obtained as follows, The equivalent circuit for turn-OFF mode is shown in Figure 6b. In this mode, the capacitor C1 is charged by stored energy in the inductor L1 through diode D2. At the same time, capacitor C2 is charged by stored energy in the inductor L2 through diode D3. Energy is provided to load R1o by the connection of inductors L1 and L2. Capacitor C'1 is charged from stored energy in inductor L'1 through diode D'2. At the same time, capacitor C'2 is charged from stored energy in inductor L'2 through diode D'3. Energy is provided to load R2o by connection of inductors L'1 and L'2. In turn-OFF mode, capacitors C1, C'1, C2, and C'2 are charged and inductors L1, L'1, L2, and L'2 are demagnetized. In this mode, diodes D1, D'1 are reverse biased and diodes D2, D3, D'2, and D'3 are forward biased.  The voltages across inductors can be obtained as follows, The output voltages V 1o and V 2o are obtained as follows, Figure 7 illustrates the power circuit of a DSDO L-2L converter. A single switch S and input voltage V i are employed with two-stage L-2L converters to obtain dual output voltage. The capacitors C 1 , C 2 inductors L 1 , L 2 , L 3 , and diodes D 1 , D 2 , . . . , and D 6 are elements of L-2L converter-1. The capacitors C' 1 , C' 2 , inductors L' 1 , L' 2 , L' 3 , and diodes D' 1 , D' 2 , . . . , and D' 6 are elements of L-2L converter-2. The stage-1 and stage-2 voltages are taken across capacitors C 1 and C 2 , respectively. The stage-1 and stage-2 voltages are taken across capacitors C' 1 and C' 2 , respectively. The two output voltages are taken across capacitors C 1 + C 2 and C' 1 + C' 2 , respectively. The load R 1o is connected across capacitors C 1 and C 2 , and load R 2o is connected across capacitors C' 1 and C' 2 .

DSDO L-2L Converter
The operation of a DSDO L-2L converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 8 shows the characteristic waveforms of voltage and current of the inductor for one switching cycle. In the characteristic waveform, time zone A-B describes the turn-ON time and time zone B-C describes the turn-OFF time. The voltages across inductors can be obtained as follows, The output voltages V1o and V2o are obtained as follows, ( ) converter-2. The stage-1 and stage-2 voltages are taken across capacitors C1 and C2, respectively. The stage-1′ and stage-2′ voltages are taken across capacitors C'1 and C'2, respectively. The two output voltages are taken across capacitors C1 + C2 and C'1 + C'2, respectively. The load R1o is connected across capacitors C1 and C2, and load R2o is connected across capacitors C'1 and C'2.

DSDO L-2L Converter
The operation of a DSDO L-2L converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 8 shows the characteristic waveforms of voltage and current of the inductor for one switching cycle. In the characteristic waveform, time zone A-B describes the turn-ON time and time zone B-C describes the turn-OFF time.  The equivalent circuit for turn-ON mode is shown in Figure 9a. Inductor L1 is magnetized by the input voltage Vi. In the same interval, the input voltage Vi and voltage across capacitor C1 The voltages across inductors can be obtained as follows, The output voltages V1o and V2o are obtained as follows, ( ) The operation of a DSDO L-2L converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 8 shows the characteristic waveforms of voltage and current of the inductor for one switching cycle. In the characteristic waveform, time zone A-B describes the turn-ON time and time zone B-C describes the turn-OFF time.  The equivalent circuit for turn-ON mode is shown in Figure 9a. Inductor L1 is magnetized by the input voltage Vi. In the same interval, the input voltage Vi and voltage across capacitor C1 The equivalent circuit for turn-ON mode is shown in Figure 9a. Inductor L 1 is magnetized by the input voltage V i . In the same interval, the input voltage V i and voltage across capacitor C 1 magnetizes inductors L 2 and L 3 . Energy is provided to load R 1o by capacitors C 1 and C 2 . Inductor L' 1 is magnetized by the input voltage V i . In the same interval, the input voltage V i and voltage across capacitor C' 1 magnetize inductors L' 2 and L' 3 . Energy is provided to load R 2o by capacitors C' 1 and C' 2 . During turn-ON mode, capacitors C 1 , C' 1 , C 2 , and C' 2 are discharged, and inductors L 1 , L' 1 , L 2 , L' 2 , L 3 , and L' 3 are magnetized. In this mode, diodes D 1 , D' 1 , D 3 , D' 3 , D 5 , and D' 5 are forward biased and diodes D 2 , D' 2 , D 4 , D' 4 , D 6 , and D' 6 are reverse biased.

DSDO L-2L Converter
The voltage across inductors can be obtained as follows, The equivalent circuit of the turn-OFF mode of a DSDO L-2L converter is shown in Figure 9b. In this mode, capacitor C 1 is charged by the stored energy of inductor L 1 . At same time, capacitor C 2 is charged by the series connection of inductors L 2 and L 3 . Energy is provided to load R 1o by inductors L 1 , L 2 , and L 3 . Capacitor C' 1 is charged by the stored energy of inductor L' 1 , whereas the capacitor C' 2 is charged by the series connection of inductors L' 2 and L' 3 . Energy is provided to load R 2o by inductors L' 1 , L' 2 , and L' 3 . In turn-OFF mode, capacitors C 1 , C' 1 , C 2 , and C' 2 are charged and inductors The voltage across inductors can be obtained as follows, The equivalent circuit of the turn-OFF mode of a DSDO L-2L converter is shown in Figure 9b. In this mode, capacitor C1 is charged by the stored energy of inductor L1. At same time, capacitor C2 is charged by the series connection of inductors L2 and L3. Energy is provided to load R1o by inductors L1, L2, and L3. Capacitor C'1 is charged by the stored energy of inductor L'1, whereas the capacitor C'2 is charged by the series connection of inductors L'2 and L'3. Energy is provided to load  The voltage across inductors can be obtained as follows, The output voltages V1o and V2o are obtained as follows, ( ) The voltage across inductors can be obtained as follows, The output voltages V 1o and V 2o are obtained as follows,  Figure 10 illustrates the power circuit of a DSDO L-2LC converter. A single switch S and input voltage V i are employed with two-stage L-2LC converters to obtain dual output voltages. The capacitors C, C 1 , and C 2 , inductors L 1 , L 2 , and L 3 , diodes D 1 , D 2 , . . . , and D 7 are elements of L-2LC converter-1. The capacitors C', C' 1 , and C' 2 , inductors L' 1 , L' 2 , and L' 3 , diodes D' 1 , D' 2 , . . . , and D' 7 are elements of L-2LC converter-2. The stage-1 and stage-2 voltages are taken across C 1 and C 2 , respectively. The stage-1 and stage-2 voltages are taken across capacitors C' 1 and C' 2 , respectively. The load R 1o is connected across capacitors C 1 and C 2 , and load R 2o is connected across capacitors C' 1 and C' 2 .

DSDO L-2LC Converter
The operation of a DSDO L-2LC converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 11 shows the characteristic waveforms of voltage and current of the inductor for one switching cycle. Time zone A-B describes the turn-ON time and time zone B-C describes the turn-OFF time of the switch. The equivalent circuit for turn-ON mode is shown in Figure 12a. In this interval, inductor L 1 is magnetized by the input voltage V i . The input voltage V i and voltage across capacitor C 1 magnetize inductors L 2 and L 3 , and charge capacitor C in parallel. Energy is provided to load R 1o by capacitors C 1 and C 2 . The inductor L' 1 magnetized by the input voltage V i . The input voltage V i and voltage across capacitor C' 1 magnetize inductors L' 2 and L' 3 and charge the capacitor C' in parallel. Energy is provided to load R 2o by capacitors C' 1 and C' 2 . In turn-ON mode, capacitors C 1 , C' 1 , C 2 , and C' 2 are discharged, capacitors C and C' are charged, and inductors L 1 , L' 1 , L 2 , L' 2 , L 3 , and L' 3 are magnetized. In this mode, diodes D 1 , D' 1 , D 3 , D' 3 , D 5 , D' 5 , D 6 , and D' 6 are forward biased and diodes D 2 , D' 2 , D 4 , D' 4 , D 7 , and D' 7 are reverse biased.

DSDO L-2LC Converter
The operation of a DSDO L-2LC converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 11 shows The voltages across the inductors are obtained as follows,    Figure 10 illustrates the power circuit of a DSDO L-2LC converter. A single switch S and input voltage Vi are employed with two-stage L-2LC converters to obtain dual output voltages. The capacitors C, C1, and C2, inductors L1, L2, and L3, diodes D1, D2, …, and D7 are elements of L-2LC converter-1. The capacitors C', C'1, and C'2, inductors L'1, L'2, and L'3, diodes D'1, D'2, …, and D'7 are elements of L-2LC converter-2. The stage-1 and stage-2 voltages are taken across C1 and C2, respectively. The stage-1′ and stage-2′ voltages are taken across capacitors C'1 and C'2, respectively. The load R1o is connected across capacitors C1 and C2, and load R2o is connected across capacitors C'1 and C'2.

DSDO L-2LC Converter
The operation of a DSDO L-2LC converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 11 shows The voltages across the inductors are obtained as follows,    The equivalent circuit for turn-OFF mode of a DSDO L-2LC converter is shown in Figure 12b. The capacitor C1 is charged by energy stored in inductor L1. The capacitor C2 is charged by the series connection of inductors L2, L3 and capacitor C. Energy is provided to load R1o by inductors L1, L2, L3, and capacitor C. The capacitor C'1 is charged by stored energy of inductor L'1. The capacitor C'2 is charged by the series connection of inductors L'2, L'3, and capacitor C'. Energy is provided to load R2o by inductors L'1, L'2, L'3, and capacitor C'. Hence, the capacitors C1, C'1, C2, and C'2 are charged, capacitors C and C' are discharged, and inductors L1, L'1, L2, L'2, L3, and L'3 are demagnetized. In this mode, diodes D1, D'1, D3, D'3, D5, D'5, D6, and D'6 are reverse biased and diodes D2, D'2, D4, D'4, D7, and D'7 are forward biased.
The voltages across the inductors can be obtained as follows, The output voltages V1o and V2o are obtained as follows, The equivalent circuit for turn-OFF mode of a DSDO L-2LC converter is shown in Figure 12b. The capacitor C 1 is charged by energy stored in inductor L 1 . The capacitor C 2 is charged by the series connection of inductors L 2 , L 3 and capacitor C. Energy is provided to load R 1o by inductors L 1 , L 2 , L 3 , and capacitor C. The capacitor C' 1 is charged by stored energy of inductor L' 1 . The capacitor C' 2 is charged by the series connection of inductors L' 2 , L' 3 , and capacitor C'. Energy is provided to load R 2o by inductors L' 1 , L' 2 , L' 3 , and capacitor C'. Hence, the capacitors C 1 , C' 1 , C 2 , and C' 2 are charged, capacitors C and C' are discharged, and inductors L 1 , L' 1 , L 2 , L' 2 , L 3 , and L' 3 are demagnetized. In this mode, diodes D 1 , D' 1 , D 3 , D' 3 , D 5 , D' 5 , D 6 , and D' 6 are reverse biased and diodes D 2 , D' 2 , D 4 , D' 4 , D 7 , and D' 7 are forward biased.
The voltages across the inductors can be obtained as follows, The output voltages V 1o and V 2o are obtained as follows,

DSDO L-2LC m Converter
The DSDO L-2LC m converter is a modified version of the DSDO L-2LC converter, obtained by eliminating two diodes. Figure 13 shows the power circuit of the DSDO L-2LC m converter in which a single switch S and input voltage V i are employed with two-stage L-2LC m converters to obtain dual output voltages. The capacitors C, C 1 , and C 2 , inductors L 1 , L 2 , and L 3 , diodes D 1 , D 2 , . . . , and D 5 are elements of L-2LC m converter-1. The capacitors C', C' 1 , and C' 2 , inductors L' 1 , L' 2 , and L' 3 , and diodes D' 1 , D' 2 , . . . , and D' 5 are elements of L-2LC m converter-2. The stage-1 and stage-2 voltages are taken across capacitors C 1 and C 2 , respectively. The stage-1 and stage-2 voltages are taken across capacitors C' 1 and C' 2 , respectively. Load R 1o is connected across capacitors C 1 and C 2 and load R 2o is connected across capacitors C' 1 and C' 2 .
The operation of a DSDO L-2LC m converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 14 shows the characteristic waveforms of voltage and current for inductors for one switching cycle. The time zone A-B describes the turn-ON time and B-C describes the turn-OFF time. The equivalent circuit for turn-ON mode is shown in Figure 15a. The inductor L 1 is magnetized by the input voltage V i . In the same interval, the inductor V i and voltage across capacitor C 1 magnetize inductors L 2 and L 3 and charge capacitor C in parallel. The energy is provided to load R 1o by capacitors C 1 and C 2 . The inductor L' 1 magnetized by the input voltage V i . In the same interval, input voltage V i and voltage across capacitor C' 1 magnetize inductors L' 2 and L' 3 and charge capacitor C' in parallel. The energy is provided to load R 2o by capacitors C' 1 and C' 2 . Capacitors C 1 , C' 1 , C 2 , and C' 2 are discharged, capacitors C and C' charged, and inductors L 1 , L' 1 , L 2 , L' 2 , L 3 , and L' 3 are magnetized. In this mode, diodes D 1 , D' 1 , D 3 , D' 3 , D 4 , and D' 4 are forward biased and diodes D 2 , D' 2 , D 5 , and D' 5 are reverse biased.
The operation of a DSDO L-2LCm converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 14 shows the characteristic waveforms of voltage and current for inductors for one switching cycle. The time zone A-B describes the turn-ON time and B-C describes the turn-OFF time. The equivalent circuit for turn-ON mode is shown in Figure 15a. The inductor L1 is magnetized by the input voltage Vi. In the same interval, the inductor Vi and voltage across capacitor C1 magnetize inductors L2 and L3 and charge capacitor C in parallel. The energy is provided to load R1o by capacitors C1 and C2. The inductor L'1 magnetized by the input voltage Vi. In the same interval, input voltage Vi and voltage across capacitor C'1 magnetize inductors L'2 and L'3 and charge capacitor C' in parallel. The energy is provided to load R2o by capacitors C'1 and C'2. Capacitors C1, C'1, C2, and C'2 are discharged, capacitors C and C' charged, and inductors
The operation of a DSDO L-2LCm converter is sectioned into two modes: one when switch S turn-ON and another when switch S turn-OFF. Figure 14 shows the characteristic waveforms of voltage and current for inductors for one switching cycle. The time zone A-B describes the turn-ON time and B-C describes the turn-OFF time. The equivalent circuit for turn-ON mode is shown in Figure 15a. The inductor L1 is magnetized by the input voltage Vi. In the same interval, the inductor Vi and voltage across capacitor C1 magnetize inductors L2 and L3 and charge capacitor C in parallel. The energy is provided to load R1o by capacitors C1 and C2. The inductor L'1 magnetized by the input voltage Vi. In the same interval, input voltage Vi and voltage across capacitor C'1 magnetize inductors L'2 and L'3 and charge capacitor C' in parallel. The energy is provided to load R2o by capacitors C'1 and C'2. Capacitors C1, C'1, C2, and C'2 are discharged, capacitors C and C' charged, and inductors    The voltages across inductors can be obtained as follows, The equivalent circuit for turn-OFF mode is shown in Figure 15b. Capacitor C 1 is charged by the energy of inductor L 1 , and capacitor C 2 is charged by the series connection of inductors L 2 , L 3 and capacitor C. Energy is provided to load R 1o by inductors L 1 , L 2 , L 3 , and capacitor C. Capacitor C' 1 is charged by energy of inductor L' 1 . Capacitor C' 2 is charged by the series connection of inductors L' 2 , L' 3 and capacitor C'. Energy is provided to load R 2o by inductors L' 1 , L' 2 , L' 3 , and capacitor C'. The capacitors C 1 , C' 1 , C 2 , and C' 2 are charged, capacitors C and C' are discharged, and inductors L 1 , L' 1 , L 2 , L' 2 , L 3 , and L' 3 are demagnetized. Throughout this mode, diodes D 1 , D' 1 , D 3 , D' 3 , D 4 , and D' 4 are reverse biased, and diodes D 2 , D' 2 , D 5 , and D' 5 are forward biased.
The voltages across inductors can be obtained as follows, The equivalent circuit for turn-OFF mode is shown in Figure 15b. Capacitor C1 is charged by the energy of inductor L1, and capacitor C2 is charged by the series connection of inductors L2, L3 and capacitor C. Energy is provided to load R1o by inductors L1, L2, L3, and capacitor C. Capacitor C'1 is charged by energy of inductor L'1. Capacitor C'2 is charged by the series connection of inductors L'2, L'3 and capacitor C'. Energy is provided to load R2o by inductors L'1, L'2, L'3, and capacitor C'. The capacitors C1, C'1, C2, and C'2 are charged, capacitors C and C' are discharged, and inductors L1, L'1, L2, L'2, L3, and L'3 are demagnetized. Throughout this mode, diodes D1, D'1, D3, D'3, D4, and D'4 are reverse biased, and diodes D2, D'2, D5, and D'5 are forward biased. The voltages across inductors can be obtained as follows, The output voltages V1o and V2o are obtained as follows, The voltages across inductors can be obtained as follows, The output voltages V 1o and V 2o are obtained as follows,

Comparative Study
In this section, the new DSDO converter configurations are compared with possible parallel combination of conventional converters and recently addressed DC-DC converters. Table 1 tabulates the comparison in terms of number of components and devices, voltage conversion ratio, and ratio of voltage across switch and input voltage. It is observed that one can achieve multiple output voltages by using conventional converters in parallel. However, the voltage conversion ratio is limited and not suitable for feeding high-voltage loads. Hybrid multiple output converters provide two different voltage levels while using common front-end structure. However, the voltage conversion ratio is not significantly improved by using a hybrid structure. The proposed converter provides a higher voltage conversion ratio compared to parallel combination of the conventional converters. In Figure 16a, the voltage conversion ratios of the converters are compared graphically. It is notable that all proposed converters provide inverting high voltage with medium duty cycle. It is observed that the DSDO L-2LC and DSDO L-2LC m converters generate higher voltage conversion ratios compared to the other proposed converters and in comparison to recent DC-DC converters. Figure 16b compares the number of diodes, control switches, inductors, and capacitors. It concludes that the DSDO L-2LC m converter requires fewer diodes than the DSDO L-2LC converter, while both provide the same voltage conversion ratio.

Simulation and Experimental Results
The principle and performance of the proposed DSDO converter configurations are validated through numerical simulation software. The converters were designed and tested with two loads, each rated to 100 W with a single input voltage of 20 V and with 25 kHz switching frequency. For simulation and prototype hardware implementation, the values of the reactive components were 220 µF for capacitors and 700 µH for inductors.
DSDO L-L converter: Figure 17a shows the voltage across the two different loads R1o and R2o. Voltage of −105 V was generated across each load with a fixed 60% duty cycle. Figure 17b,c depicts the voltage across capacitors C1, C'1, C2, and C'2. The voltage magnitude across capacitors C1 and C'1 are the same, i.e., 30 V. The voltage magnitudes across capacitors C2 and C'2 are both 75 V. Figure 17d shows that the voltage across switch S of a DSDO L-L converter is 125 V. DSDO L-2L converter:

Simulation and Experimental Results
The principle and performance of the proposed DSDO converter configurations are validated through numerical simulation software. The converters were designed and tested with two loads, each rated to 100 W with a single input voltage of 20 V and with 25 kHz switching frequency. For simulation and prototype hardware implementation, the values of the reactive components were 220 µF for capacitors and 700 µH for inductors.
DSDO L-L converter: Figure 17a shows the voltage across the two different loads R 1o and R 2o . Voltage of −105 V was generated across each load with a fixed 60% duty cycle. Figure 17b,c depicts the voltage across capacitors C 1 , C' 1 , C 2 , and C' 2 . The voltage magnitude across capacitors C 1 and C' 1 are the same, i.e., 30 V. The voltage magnitudes across capacitors C 2 and C' 2 are both 75 V. Figure 17d shows that the voltage across switch S of a DSDO L-L converter is 125 V. DSDO L-2L converter: Figure 18a shows the voltage across the two different loads R 1o and R 2o . Voltage of −180 V was generated across each load with a fixed 60% duty cycle. Figure 18b,c depicts the voltage across capacitors C 1 , C' 1 , C 2 , and C' 2 , and shows that the voltage magnitude across capacitors C 1 and C' 1 is 30 V. The voltage magnitudes across capacitors C 2 and C' 2 are 150 V. Figure 18d shows that the voltage across switch S of the DSDO L-2L converter is 200 V. DSDO L-2LC converter: Figure 19a depicts the voltage across the two different loads R 1o and R 2o . Voltage of −230 V is generated across each load with a fixed 60% duty cycle. Figure 19b,c shows the waveforms of the voltage across capacitors C 1 , C' 1 , C 2 , and C' 2 .
V. The voltage magnitudes across capacitors C2 and C'2 are 150 V. Figure 18d shows that the voltage across switch S of the DSDO L-2L converter is 200 V. DSDO L-2LC converter: Figure 19a depicts the voltage across the two different loads R1o and R2o. Voltage of −230 V is generated across each load with a fixed 60% duty cycle. Figure 19b and Figure 19c shows the waveforms of the voltage across capacitors C1, C'1, C2, and C'2. voltage across the two different loads R1o and R2o. Voltage of −230 V is generated across each load with a fixed 60% duty cycle. Figure 19b and Figure 19c shows the waveforms of the voltage across capacitors C1, C'1, C2, and C'2. The voltage magnitudes across capacitors C1 and C'1 are 30 V and the voltage across capacitors C2 and C'2 are 200 V. Figure 19d shows the voltage across switch S of the DSDO L-2LC converter and its magnitude is 250 V.
DSDO L-2LCm converter: Figure 20a shows the waveforms of the voltage across the two different loads R1o and R2o. Voltage of −230 V is generated across each load with a fixed 60% duty cycle. Figure 20b,c shows the waveforms of the voltage across capacitors C1, C'1, C2, and C'2. The voltage magnitudes across capacitors C1 and C'1 are 30 V, and voltage across capacitors C2 and C'2 are 200 V. Figure 20d shows the voltage across switch S of the DSDO L-2LCm converter and its magnitude is 250 V. Figure 21 shows the preliminary implemented hardware of the DSDO L-L converter. The designed hardware is tested with input voltage of 20 V and the output voltages are controlled at −105 V. Digitally controlled pulses are generated with the help of FPGA (Field Programmable Gate Array). Figure 22a and Figure 22b the voltages across R1o and R2o with the voltage of switch S, respectively. Using a 20 V input supply, −104.2 V is successfully generated across each load and the voltage across switch S is 124.08 V. Figure 22c depicts the voltage and current waveform of inductors L1 and L2, respectively. In the ON state, the voltage across inductor L1 is 20 V, which confirms that inductor L1 is magnetized with input voltage. In the OFF state, the voltage across inductor L1 is −30 V, i.e., inductor L1 is demagnetized to charge the capacitor C1. In the ON state, the voltage across inductor L2 is 50 V, which confirms that the inductor L2 is magnetized by the input voltage and the voltage across capacitor C1. In the OFF state, the voltage across inductor L2 is −75 V, i.e., inductor L2 is demagnetized to charge capacitor C2. Figure 22d depicts the voltage and current waveforms of inductor L'1, L'2 respectively. In the ON state, the voltage across inductor L'1 is 20 V, which confirms that inductor L'1 is magnetized by the input voltage. In the OFF state, the voltage across inductor L'1 is −30 V, i.e., inductor L'1 is demagnetized to charge capacitor C'1. In the ON state, the voltage across inductor L'2 is 50 V, which confirms that inductor L'2 is magnetized by the input voltage and the voltage across capacitor C'1. In the OFF state, the voltage across inductor L'2 is −75 V, i.e., inductor L'2 is demagnetized to charge capacitor C'2. The voltage magnitudes across capacitors C 1 and C' 1 are 30 V and the voltage across capacitors C 2 and C' 2 are 200 V. Figure 19d shows the voltage across switch S of the DSDO L-2LC converter and its magnitude is 250 V.
DSDO L-2LC m converter: Figure 20a shows the waveforms of the voltage across the two different loads R 1o and R 2o . Voltage of −230 V is generated across each load with a fixed 60% duty cycle. Figure 20b,c shows the waveforms of the voltage across capacitors C 1 , C' 1 , C 2 , and C' 2 . The voltage magnitudes across capacitors C 1 and C' 1 are 30 V, and voltage across capacitors C 2 and C' 2 are 200 V. Figure 20d shows the voltage across switch S of the DSDO L-2LC m converter and its magnitude is 250 V. Figure 21 shows the preliminary implemented hardware of the DSDO L-L converter. The designed hardware is tested with input voltage of 20 V and the output voltages are controlled at −105 V. Digitally controlled pulses are generated with the help of FPGA (Field Programmable Gate Array). Figures 22a and 22b the voltages across R 1o and R 2o with the voltage of switch S, respectively. Using a 20 V input supply, −104.2 V is successfully generated across each load and the voltage across switch S is 124.08 V. Figure 22c depicts the voltage and current waveform of inductors L 1 and L 2 , respectively. In the ON state, the voltage across inductor L 1 is 20 V, which confirms that inductor L 1 is magnetized with input voltage. In the OFF state, the voltage across inductor L 1 is −30 V, i.e., inductor L 1 is demagnetized to charge the capacitor C 1 . In the ON state, the voltage across inductor L 2 is 50 V, which confirms that the inductor L 2 is magnetized by the input voltage and the voltage across capacitor C 1 . In the OFF state, the voltage across inductor L 2 is −75 V, i.e., inductor L 2 is demagnetized to charge capacitor C 2 . Figure 22d depicts the voltage and current waveforms of inductor L' 1 , L' 2 respectively. In the ON state, the voltage across inductor L' 1 is 20 V, which confirms that inductor L' 1 is magnetized by the input voltage. In the OFF state, the voltage across inductor L' 1 is −30 V, i.e., inductor L' 1 is demagnetized to charge capacitor C' 1 . In the ON state, the voltage across inductor L' 2 is 50 V, which confirms that inductor L' 2 is magnetized by the input voltage and the voltage across capacitor C' 1 . In the OFF state, the voltage across inductor L' 2 is −75 V, i.e., inductor L' 2 is demagnetized to charge capacitor C' 2 .

Conclusions
This article developed four DSDO converter configurations for high voltage fuel-cell electric vehicular loads. The proposed converters need a single controlling semiconductor switch and are able to feed two loads with high voltage conversion ratio. The circuitry of the DSDO L-L, DSDO L-2L, DSDO L-2LC, and DSDO L-2LC m converters are developed by merging with two L-L, two L-2L, two L-2LC, and two L-2LC m converters, respectively. The operating principles of the proposed converters are discussed with detailed theoretical analysis and governing equations for the output voltage conversion ratio. Finally, it is concluded that among the proposed converters, the DSDO L-2LC and DSDO L-2LC m converters provide higher output voltage and are effective in comparison with DC-DC converters. Both simulation and experimental results show that the proposed DSDO L-L converters had the expected performance.