# Research on Energy Supply System Applied to Autonomous Underwater Observation Vehicles

Authors: Chunjie Wang; Yugeng Chai; Lin Cui
Journal: Applied Bionics and Biomechanics
 (2022)

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## Abstract

The discharge characteristics of seawater batteries can be used to prolong the working hours of autonomous underwater observation vehicles. However, the output voltage level of the seawater battery is low, so it cannot directly be used to power supply underwater observation vehicles. In this paper, a boost converter is proposed based on the seawater batteries to power supply autonomous underwater observation vehicles. The proposed converter greatly increases the voltage level of the seawater battery and directly supplies the underwater observation vehicles. Compared with the traditional boost converter, the voltage gain of the proposed converter is more than ten times higher than it under the same duty ratio condition. Its structure is asymmetric interleaved parallel, which can enable power devices to obtain lower voltage stress and ensure that the input current ripple is low. The operating principle and homeostasis property of the proposed converter are analyzed in detail. Finally, a prototype is built. Through simulation and experiment, the correctness of the theoretical design is verified and experimental results are analyzed.


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## Body

## 1. Introduction

With the improvement of people’s understanding of the ocean, the exploration and development of Marine environments covering 70% of the surface has received extensive attention. Autonomous underwater observation vehicle is an autonomous underwater equipment suitable for various environments, characterized by long working hours and wide range of activities [1–6]. Therefore, the energy supply requirements of this equipment are relatively high. Lithium battery has the characteristics of high specific energy and long cycle life [7], began to be applied to the power system of underwater vehicles in the early 21st century [8–11]. However, with the extension of the working hours of autonomous underwater observation vehicle, limited by the volume and weight of the vehicle itself [12–15], lithium battery cannot meet its requirements. Dissolved oxygen seawater battery, with seawater as the electrolyte, carbonized fibre or graphite are used to cathode, and active metal as anode, redox reactions with dissolved oxygen in seawater [16]. The reaction principle is as follows:Anodes:(1)Mg⟶Mg2++2e−Cathode:(2)O2+2H2O+4e−⟶4OH−The output voltage is 1.2-1.4 V, and the battery has an open structure and does not need to design a water pressure shell, which is conducive to generate electricity in seawater at different depths. Compared with lithium batteries, seawater batteries do not need to carry electrolyte and cathode active substance, and the specific energy (318 W h/kg) is higher than lithium batteries (160 Wh/kg) [17–20], and they have the characteristics of long discharge time (3-5 years), safe, and reliable. Therefore, it is particularly suitable for powering equipment that has been working under the sea for a long time. However, due to the low concentration of dissolved oxygen in the ocean, the output power of dissolved oxygen seawater batteries is low [21, 22], and it can only be applied to low-power underwater observation systems of vehicles. Based on the characteristics of the two types of batteries, the energy supply system of autonomous underwater observation vehicle can be designed as shown in Figure 1, lithium battery supplies power the power system of the vehicle, and dissolved oxygen seawater battery supplies power the observation system of the vehicles. Because the power supply technology of lithium battery is relatively mature, it will not be mentioned here.Figure 1
Energy supply system for autonomous underwater observation vehicles.The output voltage level of dissolved oxygen seawater battery is low, with a rated output of 1.3 V [23], and the voltage level required for observation system is high, so a high-gain DC-DC converter needs to be added to the output side of the seawater battery. The traditional boost converter voltage gain is lower; the higher voltage gain will make the duty cycle close to 1, while power device voltage stress is higher. So the researchers studied how to improve the voltage gain of the converter. Literature [24–26] introduces switched inductors in the boost converter, which increases the voltage gain, but the effect is insufficient. In literature [27, 28], interleaved parallel and switched capacitor are adopted to achieve high gain; due to absence of coupled inductors, the voltage gain of the converter is limited, and the voltage stress of the MOSFET and diode is high. In literature [29], multiset switched capacitors are proposed to obtain high-gain converter, but the increase in the number of switched capacitors undoubtedly increases the cost of circuits, and the efficiency and reliability of the converter cannot be satisfied. In literature [30, 31], coupled inductor was used to achieve high-gain conversion; due to the absence of interleaved parallel, the increase in voltage gain is still limited.In this paper, a high-gain DC-DC converter with asymmetric interleaved parallel as a framework is proposed, combined with coupled inductor and switched capacitor structure. Firstly, while the converter obtains a higher voltage gain, the voltage stress obtained by the power device is less. On the other hand, the input current ripple of the converter can effectively be suppressed by asymmetric interleaved parallel structure, thus making the seawater battery power supply system more stable. Finally, a prototype is built to verify the feasibility of the proposed converter.


## 2. Principles of Operation and Analysis

The equivalent topology of the proposed converter is shown in Figure2. The two MOSFET in the converter are controlled by the controller to realize 180° interleaved conduction; the diodes D2 and D3 and capacitors C2 and C3 constitute the switch capacitor structure and the output diode D4 as the output of the converter. The input of the converter is a dual coupled inductor structure, including leakage inductance Lk1 and Lk2, magnetizing inductance Lm1 and Lm2, and two ideal transformers; the diode D1 and the capacitor C1 form the clamping circuit. The turn ratio of the two coupled inductors can be expressed as NS1/Np1=N1 and NS2/Np2=N2.Figure 2
Equivalent topology of the proposed converter.In order to facilitate analysis, it is assumed that the effects of all parasitic elements are ignored. During a cycle, there are 8 working modes and the driving signals ofS1 and S2 are interleaved 180°. Figure 3 shows the key waveforms of the proposed converter, and the transient modes I, II, V, and VI due to leakage should be ignored. After ignoring, the modes in a cycle are III, VI, VII, and VIII. The topological stages of the circuit are shown in Figure 4.Figure 3
Key waveforms of the proposed converter.Figure 4
Operation modes of the proposed converter.
(a)(b)(c)(d)In mode III [t2−t3], at t2, MOSFET S2 is off, S1 is still open, diodes D1 and D3 are on, and diodes D2 and D4 are off, as shown in Figure 4(a). The current on the diode D3 is expressed as
(3)iD3t=iD3t2+VC3n2Lk1+Lk2t−t2.In mode VI [t5−t6], at t5, MOSFETs S1 and S2 are in conduction state, and diodes D1, D2, D3, and D4 are cut off, as shown in Figure 4(b). The magnetizing inductance Lm1 current is expressed as
(4)iLm1t=iLm1t5+VinLm1+Lk1t−t5.In mode VII [t6−t7], at time t6, MOSFET S1 is off, S2 is on, diodes D2 and D4 are on, and diodes D1 and D3 are off, as shown in Figure 4(c). Input current is expressed as
(5)iint=iint6+VC1+VC2+VC3+Vo−VinLk1+Lm1+VinLk2+Lm2t−t6.In mode VIII [t7−t8], at t7, the switch S1 is kept off, S2 remains on, diode D2 is on, and diodes D1, D3, and D4 are cut off, as shown in Figure 4(d). The energy of leakage inductance Lk1 is completely transferred to capacitor C2, and the current iS2 is expressed as
(6)iS2t=iLm1t+iLm2t.


## 3. Performance Analysis

### 3.1. Steady-State and Performance Analysis

According to magnetism chain conservation, the relationship between magnetizing inductanceLm1 and Lm2 is expressed as
(7)DuLm1−on+1−DuLm1−off=0,DuLm2−on+1−DuLm2−off=0.In the formula,D is the duty ratio of the S1 and S2.Available in formula (7),
(8)VC1=Vin1−D,VC2=N2k2Vin+N1k1VinD1−D,VC3=N1k1Vin+N2k2VinD1−D.According to mode VII, the output voltage is expressed as(9)Vo=VC1+VC2+VC3+Vin1−D.The voltage gain is expressed as(10)MCCM=2+k1N1+k2N21−D.In the actual coupling inductance design, because the coefficient of coupling is close to 1, it has little effect on the voltage gain. In order to facilitate the analysis, the leakage inductance is not considered in the following case, that is,k1=k2=1. The ideal voltage gain is expressed as
(11)MCCM=2+N1+N21−D.According to formula (11), the ideal voltage gain of the converter is related to turn ratio n and the duty ratio D. As shown in Figure 5, when D remains unchanged, the higher n, the higher the voltage gain of the converter.Figure 5
Voltage gain curve (N1=N2=n).The voltage stress pushed toS1 and S2 is expressed as
(12)VS2=VC1=Vin1−D=Vo2+N1+N2,VS1=Vin1−D=Vo2+N1+N2.The voltage stress of the diodeD1 is expressed as
(13)VD1=Vo−VC2−VC3=2Vin1−D.The voltage stress of the diodeD4 is expressed as
(14)VD4=Vo−VC2−VC3−VC1=Vin1−D.The voltage stress of the diodesD2 and D3 is expressed as
(15)VD2=VD3=VC2+VC3=N1+N21−DVin.The ratio curve in Figure6 is obtained using the ratio Vstress/Vo. It is not difficult to see that the voltage stress of all power devices is lower than output voltage. MOSFETs S1 and S2 and diodes D1 and D4 decrease with the increase of turn ratio n, and diodes D2 and D3 increase with it.Figure 6
Normalized semiconductor voltage stress versus turn ratios.


### 3.2. Comparison

The high-gain converter is proposed in this paper, fewer power devices are required, and their voltage stress is lower. To further reflect its advantage, the proposed converter is compared with many typical topologies in recent years. The performance parameters are shown in Table1.Table 1
Comparison of the proposed converter to typical converters.
TopologiesNo. of switches/diode/capacitors/inductanceVoltage gainSwitch voltage stressRef. [24]1/5/4/24/1−DVo/2Ref. [27]2/4/4/24/1−DVo/4Ref. [29]4/6/6/12n/1−DVo/2nRef. [30]1/3/4/2n+2/1−DVo/n+2Proposed2/4/4/22n+2/1−DVo/2n+2In order to compare the performance of converter, set the coupled inductor turn ration=3. The voltage gain comparison curve between the proposed converter and the other four converters is shown in Figure 7, and the proposed converter has a highest voltage gain compared with other typical of boost converters.Figure 7
Comparison of the voltage gain whenn=3. (i) Converter in [24, 27]. (ii) Converter in [29]. (iii) Converter in [30]. (iv) Proposed converter.The voltage stress comparison curve of the MOSFET is shown in Figure8. The ratio curve is obtained using the ratio Vstress/Vo. Compared with other typical converters, the proposed converter has the lowest voltage stress, so MOSFET devices with lower voltage stress can be selected at work. Devices with low voltage stress will get smaller loss.Figure 8
Voltage stress comparison of MOSFET. (i) Converter in [24]. (ii) Converter in [27]. (iii) Converter in [29]. (iv) Converter in [30]. (v) Proposed converter.


## 3.1. Steady-State and Performance Analysis

According to magnetism chain conservation, the relationship between magnetizing inductanceLm1 and Lm2 is expressed as
(7)DuLm1−on+1−DuLm1−off=0,DuLm2−on+1−DuLm2−off=0.In the formula,D is the duty ratio of the S1 and S2.Available in formula (7),
(8)VC1=Vin1−D,VC2=N2k2Vin+N1k1VinD1−D,VC3=N1k1Vin+N2k2VinD1−D.According to mode VII, the output voltage is expressed as(9)Vo=VC1+VC2+VC3+Vin1−D.The voltage gain is expressed as(10)MCCM=2+k1N1+k2N21−D.In the actual coupling inductance design, because the coefficient of coupling is close to 1, it has little effect on the voltage gain. In order to facilitate the analysis, the leakage inductance is not considered in the following case, that is,k1=k2=1. The ideal voltage gain is expressed as
(11)MCCM=2+N1+N21−D.According to formula (11), the ideal voltage gain of the converter is related to turn ratio n and the duty ratio D. As shown in Figure 5, when D remains unchanged, the higher n, the higher the voltage gain of the converter.Figure 5
Voltage gain curve (N1=N2=n).The voltage stress pushed toS1 and S2 is expressed as
(12)VS2=VC1=Vin1−D=Vo2+N1+N2,VS1=Vin1−D=Vo2+N1+N2.The voltage stress of the diodeD1 is expressed as
(13)VD1=Vo−VC2−VC3=2Vin1−D.The voltage stress of the diodeD4 is expressed as
(14)VD4=Vo−VC2−VC3−VC1=Vin1−D.The voltage stress of the diodesD2 and D3 is expressed as
(15)VD2=VD3=VC2+VC3=N1+N21−DVin.The ratio curve in Figure6 is obtained using the ratio Vstress/Vo. It is not difficult to see that the voltage stress of all power devices is lower than output voltage. MOSFETs S1 and S2 and diodes D1 and D4 decrease with the increase of turn ratio n, and diodes D2 and D3 increase with it.Figure 6
Normalized semiconductor voltage stress versus turn ratios.


## 3.2. Comparison

The high-gain converter is proposed in this paper, fewer power devices are required, and their voltage stress is lower. To further reflect its advantage, the proposed converter is compared with many typical topologies in recent years. The performance parameters are shown in Table1.Table 1
Comparison of the proposed converter to typical converters.
TopologiesNo. of switches/diode/capacitors/inductanceVoltage gainSwitch voltage stressRef. [24]1/5/4/24/1−DVo/2Ref. [27]2/4/4/24/1−DVo/4Ref. [29]4/6/6/12n/1−DVo/2nRef. [30]1/3/4/2n+2/1−DVo/n+2Proposed2/4/4/22n+2/1−DVo/2n+2In order to compare the performance of converter, set the coupled inductor turn ration=3. The voltage gain comparison curve between the proposed converter and the other four converters is shown in Figure 7, and the proposed converter has a highest voltage gain compared with other typical of boost converters.Figure 7
Comparison of the voltage gain whenn=3. (i) Converter in [24, 27]. (ii) Converter in [29]. (iii) Converter in [30]. (iv) Proposed converter.The voltage stress comparison curve of the MOSFET is shown in Figure8. The ratio curve is obtained using the ratio Vstress/Vo. Compared with other typical converters, the proposed converter has the lowest voltage stress, so MOSFET devices with lower voltage stress can be selected at work. Devices with low voltage stress will get smaller loss.Figure 8
Voltage stress comparison of MOSFET. (i) Converter in [24]. (ii) Converter in [27]. (iii) Converter in [29]. (iv) Converter in [30]. (v) Proposed converter.


## 4. Design Considerations

### 4.1. Coupled Inductor Design

The turn ratio of the coupled inductor is determined by the voltage gain and the duty ratio, expressed as follows:(16)n=Vo1−D2Vin−1.The value of magnetizing inductance depends on the acceptability of current ripple on the inductance. At the same time, due to the limitations of the characteristics of the seawater cell, the input current ripple large will lead to the unstable output voltage of the seawater cell. Therefore, the coupled inductor current ripple of the converter is set asα%. The value of magnetizing inductance is expressed as
(17)Lm=Lm1=Lm2=VinDα%Iinfs=D1−DVo2α%Iinfs.Magnetizing inductance has a great effect on suppressing current ripple, and the input current ripple coefficient under different magnetizing inductance can be obtained, as shown in Figure9:Figure 9
The relationship between the original inductor and current ripple.The current ripple of the coupled inductor will directly affect the stability of the system. Therefore, according to Figure9, magnetizing inductance value of 7 μH can be selected to suppress the current ripple and improve the stability of the system.


### 4.2. Capacitor Design

The capacitance is designed based on the voltage ripple and the output power, and the voltage ripple coefficient isμ%. The value of C1 to C4 is expressed as follows:
(18)C1≥2Poμ%VC1Vofs=2Po1−Dμ%VC1fsVin2n+2,C2≥Poμ%VC2Vofs=Po1−Dμ%VC2fsVin2n+2,C3≥Poμ%VC3Vofs=Po1−Dμ%VC3fsVin2n+2,C4≥Poμ%VC4Vofs=Po1−Dμ%VC4fsVin2n+2.According to the above calculation, based on the actual, the capacitance values ofC1 to C4 can be the same; in order to make the supply system operate stably, considering the actual circuit parasitic elements, it is necessary to add a certain margin on the basis of theoretical calculation.The theoretical values and the experiment values of each capacitance can be expressed in Table2:Table 2
Comparison of capacitance theory and actual values.
CapacitorC1C2C3C4Theoretical value (μF)20606050Experiment value (μF)100100100100Theoretical pressure resistance (V)617.617.624Experimental pressure resistance (V)50505050


## 4.1. Coupled Inductor Design

The turn ratio of the coupled inductor is determined by the voltage gain and the duty ratio, expressed as follows:(16)n=Vo1−D2Vin−1.The value of magnetizing inductance depends on the acceptability of current ripple on the inductance. At the same time, due to the limitations of the characteristics of the seawater cell, the input current ripple large will lead to the unstable output voltage of the seawater cell. Therefore, the coupled inductor current ripple of the converter is set asα%. The value of magnetizing inductance is expressed as
(17)Lm=Lm1=Lm2=VinDα%Iinfs=D1−DVo2α%Iinfs.Magnetizing inductance has a great effect on suppressing current ripple, and the input current ripple coefficient under different magnetizing inductance can be obtained, as shown in Figure9:Figure 9
The relationship between the original inductor and current ripple.The current ripple of the coupled inductor will directly affect the stability of the system. Therefore, according to Figure9, magnetizing inductance value of 7 μH can be selected to suppress the current ripple and improve the stability of the system.


## 4.2. Capacitor Design

The capacitance is designed based on the voltage ripple and the output power, and the voltage ripple coefficient isμ%. The value of C1 to C4 is expressed as follows:
(18)C1≥2Poμ%VC1Vofs=2Po1−Dμ%VC1fsVin2n+2,C2≥Poμ%VC2Vofs=Po1−Dμ%VC2fsVin2n+2,C3≥Poμ%VC3Vofs=Po1−Dμ%VC3fsVin2n+2,C4≥Poμ%VC4Vofs=Po1−Dμ%VC4fsVin2n+2.According to the above calculation, based on the actual, the capacitance values ofC1 to C4 can be the same; in order to make the supply system operate stably, considering the actual circuit parasitic elements, it is necessary to add a certain margin on the basis of theoretical calculation.The theoretical values and the experiment values of each capacitance can be expressed in Table2:Table 2
Comparison of capacitance theory and actual values.
CapacitorC1C2C3C4Theoretical value (μF)20606050Experiment value (μF)100100100100Theoretical pressure resistance (V)617.617.624Experimental pressure resistance (V)50505050


## 5. Simulation and Experimental Validation

The designed high-gain converter has a rated power of 10 W and a rated output voltage of 24 V. Seawater battery rated output voltage is 1.3 V. In order to verify the correctness of the above theoretical analysis, the system can be built as shown in Figure10:Figure 10
Control strategy for the seawater battery.


### 5.1. Effect of Simulation Parameters on Current Ripple

In order to further study the working characteristics of the converter, the optimal duty ratio and turn ratio are obtained by simulation. The input current ripple is related to duty ratio and turn ratio. When other device parameters are kept unchanged, the duty ratio of the converter and the turn ratio of the coupled inductor are changed, and the simulation results are shown in Figure11.
(a)
The current ripple is whenn = 3, D = 50%, the input current(b)
The current ripple is whenn = 2, D = 60%, the input current(c)
The current ripple is whenn = 4, D = 40%, the input currentFigure 11
Input current ripple under different duty ratio and turn number ratio.
(a)(b)(c)According to formula (17), when the duty ratio increases, the output voltage is kept unchanged, and the current ripple will change with the duty ratio. Therefore, through simulation, the optimal combination of turn ratio and duty ratio in Table 3 can be obtained. When the duty ratio is 50%, the current ripple is the lowest.Table 3
Input current ripple coefficient under different turn number ratio and duty cycle.
n (turn ratio)D (duty ratio)Current ripple coefficient260%5.3%350%1.8%440%12.3%After simulation analysis and theoretical analysis, in order to minimize the input current ripple of the system, the coupled inductor turn ratio can be set at 1 : 3. The duty ratio isD=50%.


### 5.2. Simulation Verification

According to the theoretical calculation and the above simulation conclusions, the simulation parameters of Table4 are set, and the model can be built. The simulation results are as follows.Table 4
Simulation parameters.
The proposed converter parametersValueVin (V)1.3n (turn ratio)Ns/Np=1:3Lm1,Lm2 (μH)7C1,C2,C3,C4 (μF)100fs (KHz)100D (duty ratio cycle)50%The simulation waveform of output voltage andS1,S2 voltage is shown in Figure 12. The output voltage is 24 V, as shown in Figure 12(a) and the voltage stress of switches S1,S2 is 3.8 V, as shown in Figure 12(b). Figures 13 and 14 show the diode voltage simulation waveform, diode D1 voltage stress is 5.7 V, as shown in Figure 13(a). The voltage stress of diodes D2 and D3 is 17.8 V, and diode D4 voltage stress is 3.4 V. Current simulation waveform is shown in Figure 15 and the input current ripple value is 0.15 A.Figure 12
Voltage simulation waveform.
(a)(b)Figure 13
DiodeD1 (a) and D2 (b) voltage waveform.
(a)(b)Figure 14
DiodeD3 (a) and D4 (b) voltage waveform.
(a)(b)Figure 15
Input current ripple waveform.In order to fully verify the performance of the power supply system of the seawater battery under the condition of the proposed converter, the output voltage range (1.2-1.4 V) of the seawater battery is simulated. The simulation results are shown in Table5:Table 5
Simulation results under seawater battery output conditions.
Vin (V)Iin (A)Current ripple (A)S1,S2 voltage stress (V)Duty ratio (%)Vout (V)1.28.330.313.6255241.258.000.223.5452241.37.690.153.8050241.357.410.183.7145241.47.140.293.764124After simulation, it can be obtained that under the condition that the output voltage range (1.2-1.4 V) of the seawater battery, the input current ripple of the proposed converter is maintained at 0.15-0.29 A, the current ripple is generally low, the voltage stress of the switching device is maintained at 3.54-3.76 V, and the voltage stress is low and the fluctuation is small.


### 5.3. Experiment and Results Analysis

In order to further verify the correctness of theoretical analysis and simulation parameters, a prototype is built in the laboratory, and the experimental waveform is obtained and analyzed.As shown in Figure16(a), the load voltage of the converter is about 24 V, which achieves the high gain effect of theoretical analysis. The voltage stress of the MOSFETs S1 and S2 is about 4 V. Due to the influence of the parasitic capacitance in the MOSFET, the parasitic capacitance discharge generates the spike voltage shown in Figure 16(b). Because the diode retains a safety margin for the voltage during the selection process, it has little impact on the system. The voltage stress of each diode is shown in Figure 17, the voltage stress of the diode D1 is about 6 V, D4 is about 4 V, and D3 is about 18 V compared to the actual voltage of the diode which is low compared to the theoretical analysis, but the voltage waveform meets the theoretical analysis and has good performance. Figure 18 is the input current ripple waveform of the converter. Due to the existence of parasitic inductance and parasitic resistance in the actual circuit, the current ripple is somewhat disturbed. It can be seen from the waveform that the current ripple is about 0.2 A, so the structure effectively reduces the input current ripple.Figure 16
Stress wave form of input/output voltage and switches voltage.
(a)(b)Figure 17
Diode voltage stress waveform.
(a)(b)Figure 18
Input current ripple.Other output voltage of seawater batteries is tested. Within the output voltage range of seawater batteries, the performance of the 1.2-1.4 V seawater battery power supply system is shown in Table6.Table 6
Experimental results under seawater battery output conditions.
Vin (V)Iin (A)Current ripple (A)S1,S2 voltage stress (V)Duty ratio (%)Vout (V)Efficiency (%)1.210.70.383.845723.678.21.2510.10.273.675323.879.11.39.40.24.005024.081.91.358.90.223.924624.082.51.48.50.343.864324.284.2Through the experimental results, it can be obtained that under the condition of the output voltage of the seawater battery, the current ripple range of the converter is 0.2-0.38 A, and the actual current ripple is close to the simulated current ripple. The influence of parasitic elements in the actual circuit is considered, and the range of current ripples is acceptable. The voltage stress of the switches is 3.67-4 V, compared with the simulation results, and the results are acceptable. The efficiency of the seawater battery power supply system has reached 78.2-84.2%.


### 5.4. Loss Analysis

The main loss in the converter comes from the heating of the power device, where the power device is the coupled inductor, diode, and MOSFET.


#### 5.4.1. MOSFET Loss

The on-state loss of the MOSFET mainly comes from the on resistanceRdon of the switches. The on-state loss is expressed as follows:
(19)Plosson=Rdon×ids2.In formula (19), ids is the effective value of the current flowing through the DS of the MOSFET.The shutdown loss of the MOSFETs is not only related to the frequencyfs but also related to the parasitic output capacitance Coss1; the shutdown loss is expressed as follows:
(20)Plossoff=ids2×tf2×fs48×Coss1.Thetf is the fall time of the switches.The switching status of the MOSFETsS1 and S2 is the same, and the total loss of the switches can be expressed as
(21)PS=2Ploss−on+Ploss−off.


#### 5.4.2. Diode Loss

The loss on diode is the product of currentiF and the forward voltage drop VF of diode. The loss of diode can be expressed as
(22)PD=fs×∫0TS/2VF×iFtdt.


#### 5.4.3. Transformer Loss

Transformer loss is the main part of the magnetic component loss. It mainly includes core loss and winding loss, among which core loss includes hysteresis loss and eddy current loss.The hysteresis loss is proportional to B and is expressed as follows:(23)Ph=Kh×fs×B1.6×V.Kh is the proportional coefficient related to the material.The eddy current loss in dynamic alternating magnetic field is(24)Pc=π2fs2B2d26ρ.In formula (24), d is the material density, measured in unit g/cm3, and ρ is resistivity.Core loss of the transformer may be expressed as(25)Pcore=Ph+Pc.Winding loss mainly comes from the copper loss of the primary winding and the secondary winding, which is expressed asPcu_p and Pcu_s, including the alternating current winding Rac_p and Rac_s. The ip,is is the current flowing through, and the losses of the primary side and secondary side winding are expressed as
(26)Pcu_p=ip2×Rac_p,Pcu_s=is2×Rac_s.The winding loss of a transformer is the sum of the copper loss of the primary and secondary side transformers, which is expressed as follows:(27)Pcu=Pcu_p+Pcus.The total transformer loss can therefore be expressed as(28)PT=2Pcu+Pcore


#### 5.4.4. Converter Loss Distribution

In fact, there are some other losses in the converter, such as wire loss and delay loss, but these losses are often very small and negligible. After calculation, the loss of each power device is shown in Table7.Table 7
Theoretical loss value.
ElementCoupled inductanceD1D2D3D4S1,S2Ploss (W)1.570.150.210.210.210.24The total power loss of the proposed converter can be expressed as(29)Ploss=PS+PD+PT.The loss of each power device is calculated according to the theory, and percentages are reflected in Figure19. The proportion of transformer loss is the largest. According to the loss analysis, winding loss (Pcu) is considered to be the main loss of the transformer, which is caused by the low rated power of the converter and the high carry currents of the transformer.Figure 19
Loss distribution of the converter.Under the rated state of the converter, the ideal conversion efficiency of the proposed converter can be calculated from (29), with a result of 83.1%, and the difference is 1.9% compared with the actual conversion efficiency. Due to the existence of parasitic resistance in the line and the existence of the parasitic capacitance and the parasitic diode in the switching, it has a certain impact on the efficiency of the converter, but the impact is small, and the actual value is close to the theoretical value.


## 5.1. Effect of Simulation Parameters on Current Ripple

In order to further study the working characteristics of the converter, the optimal duty ratio and turn ratio are obtained by simulation. The input current ripple is related to duty ratio and turn ratio. When other device parameters are kept unchanged, the duty ratio of the converter and the turn ratio of the coupled inductor are changed, and the simulation results are shown in Figure11.
(a)
The current ripple is whenn = 3, D = 50%, the input current(b)
The current ripple is whenn = 2, D = 60%, the input current(c)
The current ripple is whenn = 4, D = 40%, the input currentFigure 11
Input current ripple under different duty ratio and turn number ratio.
(a)(b)(c)According to formula (17), when the duty ratio increases, the output voltage is kept unchanged, and the current ripple will change with the duty ratio. Therefore, through simulation, the optimal combination of turn ratio and duty ratio in Table 3 can be obtained. When the duty ratio is 50%, the current ripple is the lowest.Table 3
Input current ripple coefficient under different turn number ratio and duty cycle.
n (turn ratio)D (duty ratio)Current ripple coefficient260%5.3%350%1.8%440%12.3%After simulation analysis and theoretical analysis, in order to minimize the input current ripple of the system, the coupled inductor turn ratio can be set at 1 : 3. The duty ratio isD=50%.


## 5.2. Simulation Verification

According to the theoretical calculation and the above simulation conclusions, the simulation parameters of Table4 are set, and the model can be built. The simulation results are as follows.Table 4
Simulation parameters.
The proposed converter parametersValueVin (V)1.3n (turn ratio)Ns/Np=1:3Lm1,Lm2 (μH)7C1,C2,C3,C4 (μF)100fs (KHz)100D (duty ratio cycle)50%The simulation waveform of output voltage andS1,S2 voltage is shown in Figure 12. The output voltage is 24 V, as shown in Figure 12(a) and the voltage stress of switches S1,S2 is 3.8 V, as shown in Figure 12(b). Figures 13 and 14 show the diode voltage simulation waveform, diode D1 voltage stress is 5.7 V, as shown in Figure 13(a). The voltage stress of diodes D2 and D3 is 17.8 V, and diode D4 voltage stress is 3.4 V. Current simulation waveform is shown in Figure 15 and the input current ripple value is 0.15 A.Figure 12
Voltage simulation waveform.
(a)(b)Figure 13
DiodeD1 (a) and D2 (b) voltage waveform.
(a)(b)Figure 14
DiodeD3 (a) and D4 (b) voltage waveform.
(a)(b)Figure 15
Input current ripple waveform.In order to fully verify the performance of the power supply system of the seawater battery under the condition of the proposed converter, the output voltage range (1.2-1.4 V) of the seawater battery is simulated. The simulation results are shown in Table5:Table 5
Simulation results under seawater battery output conditions.
Vin (V)Iin (A)Current ripple (A)S1,S2 voltage stress (V)Duty ratio (%)Vout (V)1.28.330.313.6255241.258.000.223.5452241.37.690.153.8050241.357.410.183.7145241.47.140.293.764124After simulation, it can be obtained that under the condition that the output voltage range (1.2-1.4 V) of the seawater battery, the input current ripple of the proposed converter is maintained at 0.15-0.29 A, the current ripple is generally low, the voltage stress of the switching device is maintained at 3.54-3.76 V, and the voltage stress is low and the fluctuation is small.


## 5.3. Experiment and Results Analysis

In order to further verify the correctness of theoretical analysis and simulation parameters, a prototype is built in the laboratory, and the experimental waveform is obtained and analyzed.As shown in Figure16(a), the load voltage of the converter is about 24 V, which achieves the high gain effect of theoretical analysis. The voltage stress of the MOSFETs S1 and S2 is about 4 V. Due to the influence of the parasitic capacitance in the MOSFET, the parasitic capacitance discharge generates the spike voltage shown in Figure 16(b). Because the diode retains a safety margin for the voltage during the selection process, it has little impact on the system. The voltage stress of each diode is shown in Figure 17, the voltage stress of the diode D1 is about 6 V, D4 is about 4 V, and D3 is about 18 V compared to the actual voltage of the diode which is low compared to the theoretical analysis, but the voltage waveform meets the theoretical analysis and has good performance. Figure 18 is the input current ripple waveform of the converter. Due to the existence of parasitic inductance and parasitic resistance in the actual circuit, the current ripple is somewhat disturbed. It can be seen from the waveform that the current ripple is about 0.2 A, so the structure effectively reduces the input current ripple.Figure 16
Stress wave form of input/output voltage and switches voltage.
(a)(b)Figure 17
Diode voltage stress waveform.
(a)(b)Figure 18
Input current ripple.Other output voltage of seawater batteries is tested. Within the output voltage range of seawater batteries, the performance of the 1.2-1.4 V seawater battery power supply system is shown in Table6.Table 6
Experimental results under seawater battery output conditions.
Vin (V)Iin (A)Current ripple (A)S1,S2 voltage stress (V)Duty ratio (%)Vout (V)Efficiency (%)1.210.70.383.845723.678.21.2510.10.273.675323.879.11.39.40.24.005024.081.91.358.90.223.924624.082.51.48.50.343.864324.284.2Through the experimental results, it can be obtained that under the condition of the output voltage of the seawater battery, the current ripple range of the converter is 0.2-0.38 A, and the actual current ripple is close to the simulated current ripple. The influence of parasitic elements in the actual circuit is considered, and the range of current ripples is acceptable. The voltage stress of the switches is 3.67-4 V, compared with the simulation results, and the results are acceptable. The efficiency of the seawater battery power supply system has reached 78.2-84.2%.


## 5.4. Loss Analysis

The main loss in the converter comes from the heating of the power device, where the power device is the coupled inductor, diode, and MOSFET.


### 5.4.1. MOSFET Loss

The on-state loss of the MOSFET mainly comes from the on resistanceRdon of the switches. The on-state loss is expressed as follows:
(19)Plosson=Rdon×ids2.In formula (19), ids is the effective value of the current flowing through the DS of the MOSFET.The shutdown loss of the MOSFETs is not only related to the frequencyfs but also related to the parasitic output capacitance Coss1; the shutdown loss is expressed as follows:
(20)Plossoff=ids2×tf2×fs48×Coss1.Thetf is the fall time of the switches.The switching status of the MOSFETsS1 and S2 is the same, and the total loss of the switches can be expressed as
(21)PS=2Ploss−on+Ploss−off.


### 5.4.2. Diode Loss

The loss on diode is the product of currentiF and the forward voltage drop VF of diode. The loss of diode can be expressed as
(22)PD=fs×∫0TS/2VF×iFtdt.


### 5.4.3. Transformer Loss

Transformer loss is the main part of the magnetic component loss. It mainly includes core loss and winding loss, among which core loss includes hysteresis loss and eddy current loss.The hysteresis loss is proportional to B and is expressed as follows:(23)Ph=Kh×fs×B1.6×V.Kh is the proportional coefficient related to the material.The eddy current loss in dynamic alternating magnetic field is(24)Pc=π2fs2B2d26ρ.In formula (24), d is the material density, measured in unit g/cm3, and ρ is resistivity.Core loss of the transformer may be expressed as(25)Pcore=Ph+Pc.Winding loss mainly comes from the copper loss of the primary winding and the secondary winding, which is expressed asPcu_p and Pcu_s, including the alternating current winding Rac_p and Rac_s. The ip,is is the current flowing through, and the losses of the primary side and secondary side winding are expressed as
(26)Pcu_p=ip2×Rac_p,Pcu_s=is2×Rac_s.The winding loss of a transformer is the sum of the copper loss of the primary and secondary side transformers, which is expressed as follows:(27)Pcu=Pcu_p+Pcus.The total transformer loss can therefore be expressed as(28)PT=2Pcu+Pcore


### 5.4.4. Converter Loss Distribution

In fact, there are some other losses in the converter, such as wire loss and delay loss, but these losses are often very small and negligible. After calculation, the loss of each power device is shown in Table7.Table 7
Theoretical loss value.
ElementCoupled inductanceD1D2D3D4S1,S2Ploss (W)1.570.150.210.210.210.24The total power loss of the proposed converter can be expressed as(29)Ploss=PS+PD+PT.The loss of each power device is calculated according to the theory, and percentages are reflected in Figure19. The proportion of transformer loss is the largest. According to the loss analysis, winding loss (Pcu) is considered to be the main loss of the transformer, which is caused by the low rated power of the converter and the high carry currents of the transformer.Figure 19
Loss distribution of the converter.Under the rated state of the converter, the ideal conversion efficiency of the proposed converter can be calculated from (29), with a result of 83.1%, and the difference is 1.9% compared with the actual conversion efficiency. Due to the existence of parasitic resistance in the line and the existence of the parasitic capacitance and the parasitic diode in the switching, it has a certain impact on the efficiency of the converter, but the impact is small, and the actual value is close to the theoretical value.


## 5.4.1. MOSFET Loss

The on-state loss of the MOSFET mainly comes from the on resistanceRdon of the switches. The on-state loss is expressed as follows:
(19)Plosson=Rdon×ids2.In formula (19), ids is the effective value of the current flowing through the DS of the MOSFET.The shutdown loss of the MOSFETs is not only related to the frequencyfs but also related to the parasitic output capacitance Coss1; the shutdown loss is expressed as follows:
(20)Plossoff=ids2×tf2×fs48×Coss1.Thetf is the fall time of the switches.The switching status of the MOSFETsS1 and S2 is the same, and the total loss of the switches can be expressed as
(21)PS=2Ploss−on+Ploss−off.


## 5.4.2. Diode Loss

The loss on diode is the product of currentiF and the forward voltage drop VF of diode. The loss of diode can be expressed as
(22)PD=fs×∫0TS/2VF×iFtdt.


## 5.4.3. Transformer Loss

Transformer loss is the main part of the magnetic component loss. It mainly includes core loss and winding loss, among which core loss includes hysteresis loss and eddy current loss.The hysteresis loss is proportional to B and is expressed as follows:(23)Ph=Kh×fs×B1.6×V.Kh is the proportional coefficient related to the material.The eddy current loss in dynamic alternating magnetic field is(24)Pc=π2fs2B2d26ρ.In formula (24), d is the material density, measured in unit g/cm3, and ρ is resistivity.Core loss of the transformer may be expressed as(25)Pcore=Ph+Pc.Winding loss mainly comes from the copper loss of the primary winding and the secondary winding, which is expressed asPcu_p and Pcu_s, including the alternating current winding Rac_p and Rac_s. The ip,is is the current flowing through, and the losses of the primary side and secondary side winding are expressed as
(26)Pcu_p=ip2×Rac_p,Pcu_s=is2×Rac_s.The winding loss of a transformer is the sum of the copper loss of the primary and secondary side transformers, which is expressed as follows:(27)Pcu=Pcu_p+Pcus.The total transformer loss can therefore be expressed as(28)PT=2Pcu+Pcore


## 5.4.4. Converter Loss Distribution

In fact, there are some other losses in the converter, such as wire loss and delay loss, but these losses are often very small and negligible. After calculation, the loss of each power device is shown in Table7.Table 7
Theoretical loss value.
ElementCoupled inductanceD1D2D3D4S1,S2Ploss (W)1.570.150.210.210.210.24The total power loss of the proposed converter can be expressed as(29)Ploss=PS+PD+PT.The loss of each power device is calculated according to the theory, and percentages are reflected in Figure19. The proportion of transformer loss is the largest. According to the loss analysis, winding loss (Pcu) is considered to be the main loss of the transformer, which is caused by the low rated power of the converter and the high carry currents of the transformer.Figure 19
Loss distribution of the converter.Under the rated state of the converter, the ideal conversion efficiency of the proposed converter can be calculated from (29), with a result of 83.1%, and the difference is 1.9% compared with the actual conversion efficiency. Due to the existence of parasitic resistance in the line and the existence of the parasitic capacitance and the parasitic diode in the switching, it has a certain impact on the efficiency of the converter, but the impact is small, and the actual value is close to the theoretical value.


## 6. Conclusions

In this paper, the DC/DC converter in the energy supply system of the autonomous underwater observation vehicles is taken as the research object, exploring the improvement of output voltage level of seawater batteries, through DC/DC converters, to supply power in the underwater observation vehicle. The topology of the proposed converter is studied and verified by simulation and experiment. The main conclusions are as follows:(1)
Under the range of output voltage 1.2-1.4 V of dissolved oxygen seawater battery, DC/DC converters can improve the voltage level. Under the premise of maintaining the output voltage of 24 V, the efficiency reaches 78-84%(2)
Under the asymmetric interleaved parallel structure, combined with the coupled inductor and clamping circuit, not only the input current ripple is suppressed, but also the voltage stress of the MOSFETs is controlled by about 4 V(3)
In the study of improving the voltage level, the combination of coupled inductors and switched capacitance in the topology can enable the converter to obtain higher voltage gain under low duty cycle


## 7. Future Work

Based on the current theoretical calculation and experimental results, an experimental platform for mixed power supply of seawater batteries and lithium batteries will be built. Due to the large loss of transformers in the proposed converter, it will be further optimized to improve the efficiency of the seawater battery power supply system. Further verify the correctness of the proposed system.



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*Source: 3859307-2022-06-29.xml*