A novel carbonate binder from waste hydrated cement paste for utilization of CO2

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Design, Analysis, and Modeling of an Isolated Constant-Current to Constant-Voltage Converter in Cabled Underwater Information Networks Zheng Zhang , Xuejun Zhou, Xichen Wang * and Tianshu Wu College of Electronic Engineering, Naval University of Engineering, Wuhan 430033, China * Correspondence: [email protected]; Tel.: +86-180-6254-8837 Received: 24 July 2019; Accepted: 27 August 2019; Published: 29 August 2019







Abstract: The underwater electric energy conversion modules are the equipment for distributing electric energy to the electric instruments in the cabled underwater information networks (CUINs), which are also related to the normal and stable operation of the underwater systems, the energy foundation and an important part of the network platform. Based on the classic push-pull high frequency switching circuit of constant voltage conversion, an isolated constant-current to constant-voltage (CC–CV) converter based on pulse width modulation (PWM) feedback was proposed in this paper. Through the theoretical analysis of the working principle of the CC–CV converter and the modeling of the converter circuit based on the state space method, it was verified that the designed converter can achieve the constant current to constant voltage transformation by high-frequency PWM feedback. Based on Saber simulation software, the circuit model of the CC–CV converter was built, and the feasibility of the design was proved by simulation analysis. According to the isolated high-frequency switching CC–CV converter circuit, the physical prototype was made. By adjusting the resistance value of the output load, the constant voltage (CV) characteristic of the output voltage of the converter was analyzed. Furthermore, the results show that the output voltage of the designed CC–CV converter is stable and the ripple of output voltage is less than 5%, when the input current or output load resistance is adjusted under the CC output status, which has the CV output characteristic. The CC–CV converter has good rationality and feasibility, and is suitable for the future development of the constant current remote power supply system of CUINs. Keywords: cabled underwater information networks (CUINs); constant current; short-circuit grounding high-impedance fault; fault diagnosis; point location; reliability

1. Introduction Over the last several decades, observation of oceans with traditional shipborne and airborne mobile platforms, exploration [1,2] by underwater unmanned vehicles (UUVs), satellite telemetry and other technological approaches has only explored and researched the changes of the epicontinental ocean in a one-sided and intermittent manner, which limited perspective and concepts connected to oceanic observation, understanding and development [3]. Long-term, real-time observation [4] is the requirement of the development of contemporary earth science, meanwhile, varying scientific research needs to reveal the mechanism with the process research. With the development of marine science and technology, in order to explore and understand the ocean and promote the development of marine science, the marine science community has proposed the third platform for observing the ocean [5,6]; that is, cabled underwater information networks (CUINs). CUINs have eliminated the limitations of time and space in marine research methods, with submarine cables and node equipment connected on the seafloor, which is the information and

Electronics 2019, 8, 961; doi:10.3390/electronics8090961

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power transmission network. It can provide rich power and high-data bandwidth, with standardized connection, transmission and monitoring protocols, as well as unified information, power transmission methods and device interfaces, which are convenient for hooking various observation instruments. CUINs can support multi-element, multidisciplinary, large-scale, long-term, real-time deep-sea science experiments and ocean observations [7–9], which are free from the limitations of energy, weather, ships, data delays and personal safety. In addition, it can meet people’s research requirements for long-term, continuous and all-weather observation of the ocean, which has become the focus and inevitable choice for countries to implement marine observation and scientific development [10]. The underwater remote power supply system is the energy foundation of the CUINs, and the performance of the remote power supply system determines whether the CUINs can operate normally. Currently, there are two major types of power supply system in use internationally and both are direct current (DC). In the first type, the trunk cable operates at a nominally constant voltage (CV) [11–13] and all nodes are parallel connected using seawater as a return; an example of that system is the North East Pacific Time-Integrated Undersea Networked Experiments (NEPTUNE- Canada) [14–16]. In the second type, the trunk cable operates in a constant current (CC) mode [17]. An example of that system is the Dense Ocean Network for Earthquakes and Tsunamis (DONET) [18,19]. The system using CC mode has good self-healing properties that protect against short-circuit grounding faults (parts of the system can continue to operate through a fault), and the system does not need high-medium-low voltage conversion, which has the advantages of modularization and standardization of the underwater electric energy conversion modules. In the CC remote power supply system of CUINs, the current in the trunk can be branched by the electric energy branching unit (EEBU) in the underwater primary nodes (PNs), not only keeping the current in the trunk constant, but also the secondary nodes (SNs) on the branch cables can be supplied in a CC or CV power supply mode. The underwater EEBU is mainly composed of one or more isolated high-frequency switching CC converters [9,11], which can be mainly divided into a constant-current to constant-current (CC–CC) converter and a constant-current to constant-voltage (CC–CV) converter. The CC–CC converters are mainly suitable for CUINs with complex topologies, long branches and high power requirements. When the branch cable is short, the energy demand is low, or when the PNs need to take power from the trunk cable to supply power to some transmission and observation instruments, the CC–CV converters are needed for power supply distribution. The CC–CV converter is one of the core pieces of power supply and distribution equipment of the CC remote power supply system. It is necessary to carry out analysis, design and research to obtain an efficient and reliable converter. Asakawa et al. [20,21] proposed a novel electric energy branching converter for the trunk CC remote power supply system of the ARENA observation network. K. Kawaguchi et al. [22,23] proposed a novel type of power converter for the termination units (TUs) distribution system of the DONET underwater network, and in order to prevent the observation network from the unstable condition of a secondary load; the power distribution system has a balanced converter mechanism that equalizes the TU power consumption constantly while corresponding to the change of secondary load, which has high reliability. Based on the high reliability and low operability requirements, a localization algorithm about the NEPTUNE underwater network for identifying faults in trunk cables by measuring the nonlinear equations of the main line faults at the shore station (SS) was proposed [24]. Lyu F. et al. [25–28] proposed a full-bridge DC converter based on duty-cycle-overlap control (DCOC), which achieved a bipolar positive and negative power supply consisting of eight high-frequency switching devices. Chitta et al. [29] achieved underwater wireless CC–CV transformation by creating an inductive power transfer (IPT) with series compensated coupled coils. Wang et al. [30,31] performed steady-status analysis on the topology of series resonant converters (SRCs) with CC input, and fabricated the hardware of the CC converter, and verified the design. Orekan et al. [32] conducted an analysis in depth of the design of underwater wireless power transfer (UWPT) system, and proposed a method to optimize the coil design to achieve efficient underwater wireless power supply. Saha et al. [33] proposed a CC–CV conversion circuit that uses a parallel

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resonant converter (PRC) to achieve a wide range of outputs. Xuewei P. [34] described the traditional circuit systematically. Currently, due to the blockade restrictions of power conversion technology in underwater CC remote power supply systems, the research on underwater electric energy conversion modules of remote power supply system for CUINs is still in its infancy stage, and there are few studies on the CC–CV converters for a CC remote power supply system. In this paper, theoretical research is carried out on the power demand of underwater electrical energy transformation of CC to CV and the terminal instruments in a CC remote supply system. A novel isolated CC–CV converter based on high-frequency pulse with modulation (PWM) feedback is proposed. A state space method is used to theoretically derive the converter circuit to prove the rationality of the design theory; the Saber simulation software is used to build a CC–CV converter circuit model to prove the feasibility of the design model; a physical prototype is made to verify the reliability of the design circuit. The designed CC–CV converter provides power supply and distribution equipment for the CC remote power supply system of CUINs, which ensures the efficient and reliable operation of CUINs and provides technical support for the trunk construction of CC remote supply system. 2. Design Concept of CC–CV Converter Circuit Currently, there are three main ways to obtain CV piezoelectric energy DC directly from the trunk, which is shown in Table 1. The first type, the power supply of these instruments is based on zener diodes in series connection with the trunk cable. However, with the rise of the current in the trunk, the heat flux of these zener diodes increases rapidly, bringing great threat to the reliability of the system. The second type is in the CV remote supply system, which converts the DC high voltage provided by the SS into the operating voltage of the observation instrument through a high-medium-low two-stage voltage transformation. However, this method has a high withstanding voltage requirement for equipment components; high-voltage long-term operation causes low reliability of the system. The third is to design a CC converter to perform branch power from the trunk, and to deliver CC or CV to the branch. However, the design of the CC converter, especially the CC–CV converter, currently, has poor isolation and anti-interference performance, and most converters cannot achieve the adjustment of the output voltage. Table 1. Comparison of three main ways to obtain constant voltage (CV) piezoelectric energy DC. Advantages

Disadvantages

Get power based on zener diode

Simple structure; easy to implement

Only suitable for small current systems; low power

Get power based on high-medium-low two-stage voltage transformation

Easy to implement; good research foundation; high voltage resistance; high power Standardization; modularity; high reliability; self-healing; high power; easy to expand

Get power based on CC–CV converters

Low reliability; poor standardization; poor self-healing Less research foundation; less reference prototype

The SS mainly includes shore power feeding equipment (SPFE), transmission equipment and monitoring system center. The underwater power supply and distribution system mainly includes four parts: The power supply unit of repeaters, power supply unit of PNs, power supply unit of SNs and underwater power consumption instruments. The main purpose of the CC–CV converter is for the repeaters and the PNs to take power from the trunk cable to provide operating power for the transmission, monitoring and observation instruments or to input CC into the CV for the instrument operation in the SNs. Schematic diagram of CC remote power supply system is depicted in Figure 1 [2].

The SS mainly includes shore power feeding equipment (SPFE), transmission equipment and monitoring system center. The underwater power supply and distribution system mainly includes four parts: The power supply unit of repeaters, power supply unit of PNs, power supply unit of SNs and underwater power consumption instruments. The main purpose of the CC–CV converter is for the repeaters and the PNs to take power from the trunk cable to provide operating power for the Electronics 2019, 8, 961 monitoring and observation instruments or to input CC into the CV for the instrument transmission, operation in the SNs. Schematic diagram of CC remote power supply system is depicted in Figure 1 [2].

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Figure 1. Schematic diagram typicalmesh mesh topology CCCC remote power supplysupply system.system. Figure 1. Schematic diagram of of typical topology remote power

The supply power supply of PNs mainly undertakesthe thetasks tasks of of the of of CCCC in the trunk The power unit ofunit PNs mainly undertakes thebranching branching in the trunk and and the power supply to the transmission, control and monitoring instruments in the nodes. The the power supply to the transmission, control and monitoring instruments in the nodes. The internal internal structure diagram of the equipment in PNs is illustrated in Figure 2. Current I in flows structure diagram of the equipment in PNs is illustrated in Figure 2. Current Iin flows through the PN, through the PN, which is branched by the CC–CV converter, and outputs the current I trunk in the which is branched by the CC–CV converter, and outputs the current Itrunk in the trunk, and the CC trunk, and the CC I branch or CV U branch in the branch. The output current in the trunk is kept Ibranch or CV Ubranch in the branch. The output current in the trunk is kept constant and equal to the constant and equal to the input current; that is, I in = I trunk . The constant current to constant voltage input current; that is, Iin = Itrunk . The constant current to constant voltage transformation is performed transformation is performed by the CC–CV converter in the PNs, and the corresponding standard by the CC–CV converter PNs, and the corresponding standard operating voltages V1 , V2 and V3 operating voltagesinVthe 1 , V2 and V3 are provided for the transmission module, the power are provided for the transmission module, the power management control module and the junction management control module and the junction box environment monitoring module in the PNs. 2019, 8, 961 5 of 23 boxElectronics environment monitoring module in the PNs.

Monitoring Center of SS

Transmission Equipment of SS

SPFE I in

PN

Transmission Module CC/CC Converter

Power Management Control Module

I trunk

Junction Box Environmental Monitoring Module V3

V2

V1

I branch

CC/CV Converter I branch

Standard Connection Interface for PN I branch / U branch Information Transmission Electric energy Transmission

Figure 2. Internal structure diagram of the equipment in primary nodes (PNs). Figure 2. Internal structure diagram of the equipment in primary nodes (PNs).

If the PN outputs CC to the SN, the CV transformation is performed by the CC–CV converter in thethe PNone outputs the SN, the CV is performed by theequipment, CC–CV converter the SN.IfOn hand,CC thetorated voltage V1transformation ∼ V3 is supplied to the internal and oninthe thehand, SN. On the one hand, the rated voltage to observation the internal equipment, on thethe 3 is supplied other the rated operating voltage V4 ∼ V V17isVsupplied to the instrumentand through other hand, the rated operating voltage V4  V7 is supplied to the observation instrument through the standard connection interfaces in SN. Internal structure diagram of the equipment in SNs is shown in Figure 3. I branch −in

CC/CV Converter

SN I branch −out

Information Transmission Electric energy Transmission

Figure 2. Internal structure diagram of the equipment in primary nodes (PNs). Electronics 2019, 8, 961 If the PN outputs CC to the SN, the CV transformation is performed by the CC–CV converter in5 of 21

the SN. On the one hand, the rated voltage V1  V3 is supplied to the internal equipment, and on the other hand, the rated operating voltage V4  V7 is supplied to the observation instrument through standard connection interfaces in SN. Internal structure diagram of the equipment in SNs is shown in the standard connection interfaces in SN. Internal structure diagram of the equipment in SNs is Figure 3. shown in Figure 3.

SN

I branch −in

V1

CC/CV Converter V2

Transmission Module

Power Management Control Module

I branch −out V3

Junction Box Environmental Monitoring Module V4  V7 Standard Connection Interface for SN

V5

V4

V6

V7 Information Transmission Electric energy Transmission

Figure 3. Internal structure diagram of the equipment in secondary nodes (SNs). Figure 3. Internal structure diagram of the equipment in secondary nodes (SNs).

In summary, as the main part of the EEBU, the CC–CV converter has the main function of In summary, as the main part of the EEBU, the CC–CV converter has the main function of transforming the CC input into the CV output, and providing the corresponding operating electric transforming the CC input into the CV output, and providing the corresponding operating electric energy for underwater electrical instruments. CC–CV converter should have output energy for underwater electrical instruments. CC–CV converter should have outputstability stabilityand andgood fault self-healing ability. When the connector loses water tightness or equipment failure, it good fault self-healing ability. When the connector loses water tightness or equipment failure,should it 2019, 8,affect 961 circuit. 6 of 23 of notElectronics affect the upper Based on the traditional push-pull high-frequency switching circuit should not the upper circuit. Based on the traditional push-pull high-frequency switching circuit of CV converter,CV an converter isolated CVbased converter based feedback on PWM feedback is designed. The circuit CV converter, an isolated on PWM is designed. The circuit schematic supplies power to theisoutput through charge and discharge in the push-pull circuit,capacitor and acts as Iin is theby C1 an to schematic diagram shown in Figure CC provided by SPFE; diagram is shown in Figure 4, where, Iin is 4, thewhere, CC provided SPFE; capacitor C1 supplies power isolation; Vs1 and Vs 2 are square wave pulse signals with phase difference of 180°, S1 and S 2 are the output through charge and discharge in the push-pull circuit, and acts as an isolation; Vs1 and Vs2 are power tubes power switch tubes controlled pulse signals inof turn, S 4 two ◦, S S 3 and aretwo square wave pulse signals with by phase difference 180and S2 are powerswitch switch tubes 1 and Rs inisturn, controlled PWM; a buffer push-pull circuit; Tr is a high frequency controlled by by pulse signals and S3resistor and S4 in areapower switch tubes controlled by PWM; Rs is a transformer with equal turns on both are the primary the transformer, buffer resistor in a push-pull circuit; Tr issides, a highNfrequency withends equalofturns on both sides, 1 and N 2 transformer N1 and and N32 are thesecondary primary ends of the the transformer; transformer,The andoutput N3 is the secondary of thefilter transformer; is the end of filter circuit is end a π-type circuit Thecomposed output filter circuit is a π-type filter circuit composed of the capacitor C , an inductor L1 in and 2 output current of the capacitor C2 , an inductor L1 and capacitor C3 ; I out −trunk is the capacitor C3 ; Iout−trunk is the output current in the trunk of the CC–CV converter mains circuit; Rload is the trunk of the CC–CV converter mains circuit; Rload is the total output total load, and the current the total output total load, and the current Iout−load flowing through Rload is set as the branch output I out −load flowing through Rload is set as the branch output current; R p1 and R p 2 form a voltage current; Rp1 and Rp2 form a voltage acquisition circuit. acquisition circuit. L1 S2

Rs

D1 I in

Vs1

C1

S1

A I out −load Rp 2

N1

C2

N3

C3

I out −trunk Rs

Push-pull current-fed multiple-output circuit

D5

Tr

N2

Vs 2

D2

L2

S3

S4

C4

PWM D3

D4

Rectifier filter circuit

Rload

R p1

B Constant voltage output circuit based on PWM

Figure 4. Schematic diagram of isolated adjustable constant-current to constant-voltage Figure 4. Schematic diagram of output-voltage isolated output-voltage adjustable constant-current to (CC–CV) converter(CC–CV) circuit based on pulse width modulation (PWM) feedback.(PWM) feedback. constant-voltage converter circuit based on pulse width modulation

In order to analyze the steady-status characteristics of the CC–CV converter, it can be assumed that the components in the circuit are ideal components, in which, the voltage drop of the switch tube is zero when the switch is turned on, and the leakage current is zero when the switch is turned off; the inductance and core loss of the transformer are neglected; the passive components in the

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In order to analyze the steady-status characteristics of the CC–CV converter, it can be assumed that the components in the circuit are ideal components, in which, the voltage drop of the switch tube is zero when the switch is turned on, and the leakage current is zero when the switch is turned off; the inductance and core loss of the transformer are neglected; the passive components in the circuit are linear and time-invariant. 3. Characteristics Analysis of CC–CV Converter Circuit The CC–CV converter circuit can be divided into two parts: (a) The CC isolation part, which mainly includes the push-pull current-fed multiple-output circuit and the rectifier filter circuit; (b) the DC constant voltage conversion part, which mainly includes the constant voltage output circuit based on PWM feedback. 3.1. Principle and Characteristic Analysis of CC Isolation Circuit In the steady-status of the CC–CV converter, since Vs1 and Vs2 are square wave pulse signals with a phase difference of 180◦ , which control switching tubes S1 and S2 with alternated turn-on, the operating process of the circuit is divided into four stages. Suppose Ts denotes a switch period, and t1 is the start time of one period, at which point S1 starts to conduct, whereas S2 is cut off; at time t2 , S1 changes from on to off, and S2 is still off. At time t3 , S2 changes from off to on whereas S1 is turn off. At time t4 , S2 changes from on to off, and S1 is off. t5 is theElectronics end time of this period, and at that moment, both S1 and S2 are turned off. According to the 2019, 8, 961 7 of 23 operating status of the CC isolation circuit, ideal waveforms of the voltages of the main components in voltages of period the maincan components in theand circuit in one period can be the circuit in one be obtained depicted in Figure 5.obtained and depicted in Figure 5.

Figure 5. Principle waveforms of the voltages of of the the gate between the source and the drain Figure 5. Principle waveforms of the voltages gateand and between the source and theofdrain of Tr power switch tubes and ; the primary and secondary ends of the transformer and S S 1 2 power switch tubes S1 and S2 ; the primary and secondary ends of the transformer Tr and thethe capacitor withvariation respect to time variation in the constant-current C1 withcapacitor respect toC1time in the constant-current isolation isolation circuit. circuit.

Vs1 Vand V are square wave pulse signals of two power switch tubes S and S In Figure In Figure 5, Vs1 5,and s2 ares 2square wave pulse signals of two power switch tubes1 S1 and2 S2 with ◦ with phase difference of 180°; between the source drainof ofSS11 and S2 ; DSDS2 1 and DS 2 are voltages phase difference of 180 ; VDS1 andVV areVvoltages between the source andand thethe drain and S 2 ; VC1 is the voltage between two terminals of capacitor C1 ; VN 1 , VN 2 and N3 are the

voltages of primary and secondary ends of the transformer. As shown in Figure 5, operation of the circuit can be divided into four phases, which can be summarized into two states: Closed status and open status. The closed status is that the switch tube S1 or S 2 is closed; that is, the period t3  t4 in the operating waveform diagram (the switch tube

S1 is turned on, the switch tube S 2 is turned off) and the period t3  t4 (the switch tube S 2 is

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VC1 is the voltage between two terminals of capacitor C1 ; VN1 , VN2 and N3 are the voltages of primary and secondary ends of the transformer. As shown in Figure 5, operation of the circuit can be divided into four phases, which can be summarized into two states: Closed status and open status. The closed status is that the switch tube S1 or S2 is closed; that is, the period t3 ∼ t4 in the operating waveform diagram (the switch tube S1 is turned on, the switch tube S2 is turned off) and the period t3 ∼ t4 (the switch tube S2 is turned on, and the switch tube S1 is turned off); The open status is when the switch tubes S1 and S2 are both switched off, which is the dead time in the operating period, corresponding to the period t2 ∼ t3 and the period t4 ∼ t5 in the operating waveform diagram. Because of the mutual inductance of transformer, the reverse voltage of each switch tube at the primary end of transformer Tr in the open-status is half of the primary voltage. The difference is only that it flows through different transformer coils, and the output current direction of the corresponding transformer secondary is opposite. In the closed status, the operating mechanism is the same in the two periods. Due to the mutual Electronics 2019, 8, 961 8 of 23 inductance of transformer, the reverse voltage of each switch in the primary end of the transformer Tr is half of the primary voltage. Theand difference, between S1output and S2current , is onlyofflowing through N 2 ; meanwhile, different transformer coils N the the secondary enddifferent of 1 transformer coils N and N ; meanwhile, the output current of the secondary end of corresponding 2 is opposite. When the circuit is in the closed status of period t  t , the 1 corresponding transformer 1 2 transformer is opposite. When the circuit is in the closed status of period t ∼ t2 , the capacitor CV1 of the capacitor C1 of the primary end of the transformer Tr is discharged, the1 pulse driving signal s1 primary end of the transformer Tr is discharged, the pulse driving signal Vs1 is in a high level status, is in a high level status, the switching tube S1 is turned on, and the voltage VDS1 between the Drain the switching tube S1 is turned on, and the voltage VDS1 between the Drain to Source (DS) poles of S1 to Source (DS) poles of S is zero. The dotted terminal of transformer coils N1 is negative is zero. The dotted terminal of 1transformer coils N1 is negative electrode. electrode. When the circuit is in the closed status of period t3 ∼ t4 , the pulse driving signal Vs2 is in a high When the circuit is in the closed status of period t  t4 , the pulse driving signal Vs 2 is in a level status, the switching transistor S2 is turned on, the 3voltage VDS2 between the DS poles of S2 is high level status, the switching transistor S is turned on, the voltage VDS 2 between the DS poles zero is zero, the dotted terminal of transformer2 coils N2 is negative electrode. In the rectifier filter part, N 2 open zero isDzero, the dotted terminal of status transformer coilsand is negative electrode. the of S 2 isdiodes the rectifier , D and D , D are in the of closed respectively, theIn capacitors 2 3 1 4 D1 , D 4 are filter part, the rectifier diodes D2 , D3 the andequivalent in the status of and open C2 , Crectifier circuit diagram of closed the constant current 3 and the inductor L1 store energy, whereas C2 , 6.C3 and the inductor L1 store energy, whereas the equivalent respectively, capacitors isolation circuit isthe shown in Figure circuit diagram of the constant current isolation circuit is shown in Figure 6. A

_

_

+

+

DC

B (a)

A

+

+

_

_

DC

B (b) Figure 6. Equivalent diagram of closed of constant isolation (a) Figure 6. Equivalent circuitcircuit diagram of closed statusstatus of constant currentcurrent isolation circuit:circuit: (a) Equivalent Equivalent circuit diagram during period; (b) equivalent circuit diagram during t  t t  t4 1 2 3 circuit diagram during t1 ∼ t2 period; (b) equivalent circuit diagram during t3 ∼ t4 period. period.

i

(t )

i

(t )

i

(t )

i

(t )

u

(t )

u

(t )

u

(t )

u

(t )

Where, C1 , C2 , C3 , L1 and C1 , C2 , C3 , L1 are the currents and voltages on capacitors C1 , C2 , C3 and inductance L1 , respectively; iA− B ( t ) is the equivalent output current of isolation circuit, RA− B is the equivalent impedance of DC constant voltage

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Where, iC1 (t), iC2 (t), iC3 (t), iL1 (t) and uC1 (t), uC2 (t), uC3 (t), uL1 (t) are the currents and voltages on capacitors C1 , C2 , C3 and inductance L1 , respectively; iA−B (t) is the equivalent output current of isolation circuit, RA−B is the equivalent impedance of DC constant voltage conversion circuit, and uA−B (t) is the equivalent voltage between points A and B. According to Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL), we can obtain:  uC (t)−uC (t)/m  d   iC1 (t) = C1 dt uC1 = 1 Rs 2 − i (t)     in  uC1 −uC2 /m   d  − iL1 (t)  iC2 (t) = C2 dt uC2 (t) = m Rs    ( ) u t C  d  iC3 (t) = C3 dt uC3 (t) = − R 3 + iL1 (t)   A−B    uL (t) = L1 d iL (t) = uC (t) − uC (t) dt

1

1

2

(1)

3

Assuming that state vector x(t) = [uC1 (t), uC2 (t), uC3 (t), iL1 (t)]T , uC1 (t), uC2 (t), uC3 (t), iL1 (t) are state variables, input vector u(t) is [iin (t)], iin (t) is the CC input variable of SPFE. Since the converter has two current outputs, the output current variable in the trunk is iout−trunk (t), and the CC isolation circuit output voltage variable is uA−B (t), then the output vector is y(t) = [iout−trunk (t), uA−B (t)]T ; the switching tube duty ratio is D. According to Equation (1), the corresponding status equation and output equations are established for the closed status: (

d xˆ close (t) = dt x(t) = A1 x(t) + B1 u(t) yclose (t) = C1 x(t) + E1 u(t)

where,                                       

    A1 =    h

1 C1 Rs 1 C2 Rs

0 0

− C 1Rs 1 − C21Rs 0 1 L

− C1

0 0 0 # 0 0 0 0 C1 = 0 0 1 0 h iT E1 = 1 0 B1 =

0 0 − C3 R1 A−B − L1 iT

(2)

 0   1   C2   1   C3   0

(3)

1

"

Similarly, when the converter is in the open status, both S1 and S2 are turned off, and capacitor C1 is in a charging status. Because the output of SPFE is a constant current source, the voltage across the capacitor rises linearly. Simultaneously, the voltages on the primary and secondary coils of the transformer are all zero, due to the influences of mutual inductance of the transformer, and the voltage VDS1 and VDS2 between the DS poles of switching transistors S1 and S2 are VC1 . The output filter circuit releases energy to provide power for the equivalent load RA−B . The equivalent circuit diagram Electronics 8, 961 circuit is as shown in Figure 7. 10 of 23 of the CC2019, isolation

A

DC

B Figure 7. Equivalent Equivalentcircuit circuitdiagram diagram open status of constant-current (CC) isolation circuit. Figure 7. ofof open status of constant-current (CC) isolation circuit.

Equally, according to the KCL and KVL, the corresponding state equation and output equation system for the open status can be established,

x open ( t ) = A2x ( t ) + B 2u ( t )  y open ( t ) = C 2x ( t ) + E 2u ( t )

(4)

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Equally, according to the KCL and KVL, the corresponding state equation and output equation system for the open status can be established,    xˆ open (t) = A2 x(t) + B2 u(t)   y (t) = C2 x(t) + E2 u(t) open

(4)

where,                                       

 0 0  0 0  1  0 0 0 − C2 A2 =  1  0 0 C3 R1A−B C3  0 L1 − L1 0 iT h 1 B2 = − C1 0 0 0 " # 0 0 0 0 C2 = 0 0 1 0 h iT E2 = 0 0

        (5)

By the application of direct weighted average method, analyzing the Equations (2) and (4), the average state equation and the average output equation of the CC isolation circuit can be obtained,   xˆ (t)        y(t)

d = dt x(t) = D[A1 x(t) + B1 u(t)] + (1 − D)[A2 x(t) + B2 u(t)] = D[C1 x(t) + E1 u(t)] + (1 − D)[C2 x(t) + E2 u(t)]

(6)

It can be concluded that, (

where,                                       

xˆ (t) = Ax + Bu y = Cx + Du

    A =   

D C1 Rs D C2 Rs

h

1−2D C1

"

0 0

0 0

h

D

0

B= C= E=

0 0

− CDRs 1 − C2DRs 0

0 0

2D−1 L

0

0

0 0 1 0 iT

0

1−2D C3 RA−B 1−2D iTL

(7)

0 1−2D C2 2D−1 C3

0

        (8)

#

In the case of DC steady-status, xˆ (t) = 0. By solving the DC steady-status equation, the DC steady-status operating equation of the underwater CC isolation circuit can be obtained as follows, (

x(t) = −A−1 Bu(t) y(t) = (E − CA−1 B)u(t)

(9)

Substituting Equation (8) into Equation (9), the relationship between input current and output voltage can be obtained,   iout−trunk (t)= Diin      (10)  iA−B (t)= iin (t)      uA−B (t)= RA−B iin (t)

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where, iout−trunk (t) and iA−B (t) are the output currents of the DC steady-status operation of the primary and secondary ends of the transformer; uA−B (t) is the equivalent output voltage of the CC isolation circuit. In summary, the output current of the trunk iout−trunk (t) is proportional to the input current Iin , and the proportional coefficient is the duty cycle D. Therefore, in order to maintain the CC characteristics of the constant current remote supply system, it is not feasible to adjust the duty cycle in the CC isolation circuit; meanwhile, the equivalent output voltage of the CC isolation circuit is independent of the duty cycle D. When the duty ratio D is changed, the output current iA−B (t) is the same as the input current Iin . The CC isolation circuit can isolate a branch of constant current in the trunk, but according to Equation (10), the output voltage is related to the turn ratio of transformer and input constant current, and it is impossible to achieve constant voltage output by adjusting duty cycle of switch tube. However, the designed constant voltage conversion circuit realizes the constant current to constant voltage transformation with WPM feedback. Therefore, the CC and CV topologies need to be combined. 3.2. Principle and Characteristic Analysis of DC Constant Voltage Conversion Circuit Based on the above analysis, when the CC–CV converter operates steadily, a cycle period of DC constant voltage conversion circuit can be divided into four stages, in which the switching tube S1 or S2 closes, such as the period t1 ∼ t2 (switching tube S1 turns on and switching tube S2 turns off), and the period t3 ∼ t4 (switching tube S2 turns on and switching tube S1 turns off) is in closed12 status. Electronics 2019, 8, 961 of 23 When the system is in the open status, the switching tube S1 and S2 are open; that is, the dead time in the operating period, corresponding to the period t2 ∼ t3 and t4 ∼ tt5 in the operating waveform is, the dead time in the operating period, corresponding to period the period 2  t3 and period t4  t5 in diagram, the operating waveform diagram of the DC constant voltage conversion circuit is illustrated the operating waveform diagram, the operating waveform diagram of the DC constant voltage in Figure 8. conversion circuit is illustrated in Figure 8.

Figure 8. Principle waveforms of the voltages of the gate of power switch tubes S3 and S4 , the capacitor Figure 8. Principle waveforms of the voltages of the gate of power switch tubes S 3 and S 4 , the C4 , and the voltage and current of the load Rload with respect to time variation in the constant-current capacitor C4 , and the voltage and current of the load Rload with respect to time variation in the isolation circuit. constant-current isolation circuit.

When the circuit is in closed status, the cc source has no load, and because of the zener diode D5 , When the is in closed cc .source no load, and of thethe zener diode the capacitor C4circuit will discharge onlystatus, to loadthe Rload When has the circuit is in thebecause open status, switching D5 , the capacitor C4 will discharge only to load Rload . When the circuit is in the open status, the

switching tubes S3 and S 4 are open, the CC source supplies power to the load Rload , and the capacitor C4 is charged. The operating status equivalent circuit of the DC constant voltage conversion circuit is depicted in Figure 9. Because the load is in charged and discharged status, the

Figure 8. Principle waveforms of the voltages of the gate of power switch tubes S 3 and S 4 , the capacitor C4 , and the voltage and current of the load Rload with respect to time variation in the constant-current isolation circuit. Electronics 2019, 8, 961 When the circuit

of 21 is in closed status, the cc source has no load, and because of the zener 11 diode D5 , the capacitor C4 will discharge only to load Rload . When the circuit is in the open status, the

Rload , andC4the switching tubes and Sthe thesupplies CC source supplies to , the S3 open, 4 are tubes S3 and S4 are CCopen, source power to the power load Rload andload the capacitor is C4 is charged. The operating the DC constant voltage conversion is capacitor charged.status The equivalent operating circuit status of equivalent circuit of the DC constantcircuit voltage depicted in circuit Figureis9.depicted Because in theFigure load is charged discharged status, current direction of conversion 9. in Because theand load is in charged andthe discharged status, the capacitor C in the closed status is opposite to that in the open status. 4 current direction of capacitor C in the closed status is opposite to that in the open status. 4

DC

DC

(a)

(b)

thethe equivalent circuit of the statusstatus of the of DCthe constant voltage Figure 9. 9. Schematic Schematicdiagram diagramofof equivalent circuit of working the working DC constant conversion circuit: (a) Equivalent circuit of closed equivalent circuit of openof status. voltage conversion circuit: (a) Equivalent circuit ofstatus; closed(b) status; (b) equivalent circuit open status.

Where, iC4 (t) and uC4 (t) are current and voltage on capacitor C4 respectively; and iload (t) is the equivalent output current of DC constant voltage conversion circuit. According to the KCL and KVL, the corresponding state equation and output equation system for the closed status can be established,  uC (t)  d   C4 dt uC4 (t) = − R 4 = −iload (t) load (11)    u ( t ) = uC ( t ) load 4 0

Assuming that state vector x (t) = [uC4 (t)], uC4 (t) is state variable, input vector u(t) is [iin 0 (t)], iin (t) is the CC input variable of the DC constant voltage conversion circuit; then, the output vector is 0 y (t) = [uload (t)]; the switching tube duty ratio is D0 . According to Equation (10), the corresponding status equation and output equations are established for the closed status: 0

(

where,

0

0

0

d xˆ 0close (t) = dt x (t) = A1 0 x (t) + B1 0 u (t) 0 y close (t) = C1 0 x0 (t) + E1 0 u0 (t)

 h i  1 0 0   A1 = − C4 Rload , B1 = [0]    C1 0 = [1], E1 0 = [0]

(12)

(13)

Similarly, according to the KCL and KVL, the corresponding state equation and output equation system for the open status can be obtained:

where,

 0 0 0 0 0    xˆ open (t) = A2 x (t) + B2 u (t)  0 0 0   y open (t) = C2 x (t) + E2 0 u0 (t)

(14)

 h i h i  1 1 0 0   A2 = C4 Rload , B2 = C4    C2 0 = [1], E2 0 = [0]

(15)

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By the application of direct weighted average method, analyzing the Equations (12) and (14), the average state equation and the average output equation of the DC constant voltage conversion circuit can be obtained, (

0

d 0 xˆ (t) = dt x (t) = D0 [A1 x0 (t) + B1 u0 (t)] + (1 − D0 )[A2 x0 (t) + B2 u0 (t)] 0 0 y (t) = D [C1 x0 (t) + E1 u0 (t)] + (1 − D0 )[C2 x0 (t) + E2 u0 (t)]

It can be concluded that, (

where,

(16)

0

xˆ (t) = A0 x0 + B0 u0 y0 = C0 x0 + D0 u0

(17)

 i h i h  1−D0 1−2D0 0 0   A = Rload C4 , B = C4    C0 = [ 1 ] , E 0 = [ 0 ]

(18)

0

In the case of DC steady-status, xˆ (t)= dx0 (t)/dt = 0. By solving the DC steady-status equation, the DC steady-status operating equation of the underwater DC constant voltage conversion circuit can be obtained— ( 0 x (t) = −A0 −1 B0 u0 (t) (19) y0 (t) = (E0 − C0 A0 −1 B0 )u0 (t) Substituting Equations (18) into (19), the relationship between input current and output voltage of load can be obtained, ( 1−D0 iload (t) = 2D 0 −1 iin (t) (20) 1−D0 uload (t) = 2D 0 −1 Rload iin (t) According to Equation (20), when duty cycle D0 is more than 50%, the output voltage uload (t) of DC constant voltage conversion circuit is not only proportional to resistance of load Rload and input current iin (t) of CC source, but also related to duty cycle D0 of switch tube in DC constant voltage conversion circuit. When the resistance of load changes, the input current iin (t) is constant. The voltage Vp1 can be sampled and adjusted by PWM feedback mode to compare with the reference voltage. The duty cycle of S3 and S4 can be adjusted to maintain the constant output voltage of the system and realize the CC to CV conversion of the system. Rload ↑→ Vload ↑→ Vp1 ↑→ PWM → D0 ↑→

1 − D0 ↓→ Vload ↓ 2D0 − 1

(21)

In summary, the CC isolation circuit achieved electrical isolation of a branch of CC source, which ensures the reliability and anti-interference of the output of system; the CC to CV transformation of the CC source is realized by the DC constant voltage conversion circuit. Combining the CC isolation circuit and DC constant voltage conversion circuit, the result can realize the CV branch output of the current in the trunk of the constant current remote supply system and ensure the current in the trunk is constant. 4. Analysis and Research of Modeling Simulation and Verification of Physical Prototype Based on the theoretical analysis, the simulation model of isolated CC–CV converter proposed in this paper is built with the Saber simulation software, and the feasibility and rationality of the proposed circuit are verified by simulation analysis. Furthermore, the prototype of the physical circuit is fabricated based on the CC remote power supply system; the experimental verification design converter has electrical isolation and CC to CV conversion function.

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4.1. Modeling and Simulation Analysis of CC–CV Converter Circuit Based on the references [7–9,34] and the test adjustment of the prototype, assume that some of the electronic component parameters in the circuit are: C1 = 3 uF, C2 = 1 uF, C3 = 2 uF, C4 = 100 uF, L1 = L2 = 6 mH, the buffer resistance Rs between the drain (D) and the source (S) of the switching Electronics 2019, 8, 961 15 of 23 tubes S1 and S2 is 5 Ω. As As shown shown in in Figure Figure 4, 4, performing performing current current output output analysis analysis on on the the CC CC isolation isolation circuit, circuit, and and select select three sets of tests for the duty cycle of switching tube S and S are 60%, 80% and 100% respectively. 2 1 three sets of tests for the duty cycle of switching tube S1 and S2 are 60%, 80% and 100% The current iA−B (t), between nodes A and B, is simulated and analyzed, while the simulation results respectively. The current i ( t ) , between nodes A and B, is simulated and analyzed, while the are as shown in Figure 10. A − B simulation results are as shown in Figure 10.

(a)

(b) current isolation isolation circuit: circuit: (a) Schematic Figure 10. Schematic diagram of simulation results of constant current diagram of of current current simulation simulationbetween betweennodes nodesAAand andBB(the (theduty dutycycle cycleof ofswitching switchingtubes tubesS1Sand S2 diagram S2 are 1 and 60%, 80%80% and and 100%); (b) schematic diagram of simulation results for voltages of Drain to Source (DS) are 60%, 100%); (b) schematic diagram of simulation results for voltages of Drain to Source poles of switching tubestubes (the duty is 100%). (DS) poles of switching (the cycle duty cycle is 100%).

Figure Figure 10 10 shows shows the the schematic schematic diagram diagram of of the the simulation simulation results results of of the the CC CC isolation isolation circuit circuit under the condition of adjusting duty cycle D. Assuming that the input constant current is 1.5 A, A, under the condition of adjusting duty cycle D . Assuming that the input constant current is 1.5 the equivalent resistance between loads is adjusted to 100 Ω. When duty cycle changes, the simulation the equivalent resistance between loads is adjusted to 100 Ω . When duty cycle changes, the output current of CC isolation circuit is basically same as the thatsame of theoretical Theanalysis. output simulation output current of CC isolation circuit the is basically as that ofanalysis. theoretical current is stable, and the fluctuation of current is less than 1.5% of the theoretical value, which is as The output current is stable, and the fluctuation of current is less than 1.5% of the theoretical value, shown in Figure 10a. It can be determined that the output current of constant current isolation circuit which is as shown in Figure 10a. It can be determined that the output current of constant current is DC constant isolation circuitcurrent. is DC constant current.

After the converter is in stable operation, the driving circuit controls the switching tubes S1 and S 2 to be turned on, and the capacitor C1 is charged and discharged accordingly, and the voltage VC1 is charged and discharged with a small amplitude at a voltage of about 150 V according to the opening and closing of the light-emitting tube. The voltage value of the load Vload should be

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After the converter is in stable operation, the driving circuit controls the switching tubes S1 and S2 to be turned on, and the capacitor C1 is charged and discharged accordingly, and the voltage VC1 is Electronics 2019, 8, 961 of 23 charged and discharged with a small amplitude at a voltage of about 150 V according to the16opening and closing of the light-emitting tube. The voltage value of the load Vload should be 150 V, and the are substantially as the theoretical values. Comparing Figure and Figure 10,. obviously, open-status voltagetheofsame switching tubes S1 and S2 should be twice as4much as Vload As shownit in can be seen that the simulation waveform of the designed constant current isolation circuit is similar Figure 10b, the voltages of VDS1 and VDS2 in the open-status are about 300 V, which are substantially to that of the theoretical waveform. The simulation results show that the circuit can achieve constant the same as the theoretical values. Comparing Figures 4 and 10, obviously, it can be seen that the current isolation output. simulation waveform of the designed constant current isolation circuit is similar to that of the theoretical When the CC isolation circuit outputs constant current, the DC constant voltage conversion waveform. The simulation results show that the circuit can achieve constant current isolation output. circuit is simulated and analyzed. The voltage V p1 at both ends of the sampling resistance R p1 is When the CC isolation circuit outputs constant current, the DC constant voltage conversion circuit S3 compared withanalyzed. the reference fedboth backends by PWM. duty cycle of switching is simulated and Thevoltage voltageVREF Vp1, at of theThe sampling resistance Rp1 istubes compared and is adjusted to maintain the constant of cycle the system and realize the SCC to CV with theS4reference voltage VREF , fed back by output PWM. voltage The duty of switching tubes S4 is 3 and adjusted to maintain the constant output voltage of the system and realize the CC to CV conversion conversion of the system. Assuming that the load resistance Rload varies, set to 100 Ω , 200 Ω , 300 of the Assuming thethe loadsampling resistance Rload varies, to 100 2002k Ω, Ω 300and Ω, 400 and Ω , system. 400 Ω and 500 Ωthat , and resistances R p1setand R p 2Ω,are 60kΩΩ 500 Ω, and the sampling resistances Rp1 and Rp2 are 2k Ω and 60k Ω respectively, the reference voltage respectively, the reference voltage VREF = 5.1 V . Having simulation and analysis of the DC constant VREF = 5.1 V. Having simulation and analysis of the DC constant voltage conversion circuit, the voltage conversion circuit, the simulation results are as shown in Figure 11. simulation results are as shown in Figure 11.

(a)

(b) Figure Schematicdiagram diagram of of simulation simulation results results of and Figure 11.11.Schematic of the the relationship relationshipbetween betweenload loadvoltage voltage and resistance change DCconstant constantvoltage voltageconversion conversion circuit: circuit: (a) of of resistance change ininDC (a)Curve Curveofofchange changeininthe theresistance resistance Ω ,200 Ω and load; voltage curves theload load(R ( Rload = = 100 200Ω,Ω300 , 300 , 400 500 Ω ). load; (b)(b) voltage curves ofofthe 100 Ω, Ω,Ω 400 Ω and 500 Ω). load

Figure shows theSchematic Schematicdiagram diagram of of simulation simulation results conversion Figure 1111 shows the resultsof ofDC DCconstant constantvoltage voltage conversion Rload. Assuming circuit case adjusting the resistanceofofload loadRload . Assumingaaconstant constantinput inputcurrent current of of 1.5 1.5 A, circuit in in thethe case of of adjusting the resistance as A, shown in Figure 11a, the output load resistance is R = 100 Ω, 200 Ω, 300 Ω, 400 Ω, and 500 as shown in Figure 11a, the output load resistance isloadRload = 100 Ω, 200 Ω, 300 Ω, 400 Ω, and 500 Ω; theΩ;equivalent voltage value at both ends is basically the same as the theoretical load the equivalent voltage value at both endsofofthe theload load RR load is basically the same as the theoretical analysis, and the output current is stable. It can be determined thatthe theoutput outputofofthe theDC DC constant analysis, and the output current is stable. It can be determined that constant voltage conversion circuit is a DC constant voltage. When the load R = 100 Ω is set, the driving load = 100 Ω is set, the driving voltage conversion circuit is a DC constant voltage. When the load Rload ◦ circuit and the switching tubes S3 and S4 are 180 out of phase, and when the switching tube is circuit and the switching tubes S3 and S4 are 180° out of phase, and when the switching tube is in the closed state, the voltage on the switching tube is zero. When the switch tube is in the open status, S3 and S4 are connected in parallel, and the voltages at both ends of the tubes are the same, which

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in the closed state, the voltage on the switching tube is zero. When the switch tube is in the open Electronics 8, S961are connected in parallel, and the voltages at both ends of the tubes are the17same, of 23 status, S32019, andwith 4 the output load voltage, as shown in Figure 12. Comparing the analysis of Figures is consistent which is consistent with thewaveform output load voltage, as shown in Figure 12. Comparing thedesigned analysis 5, 11 and 12, the simulation of the DC constant voltage conversion circuit of the is consistent with the output load voltage, as shown in Figure 12. Comparing the analysis of Figures of Figures 5, 11 and 12, the simulation waveform of the DC constant voltage conversion circuit of CC–CV converter is similar to the theoretical waveform; that is, the designed CC–CV converter has 5, 11 and 12, the simulation waveform of the DC constant voltage conversion circuit of the designed the designed CC–CV converter is similar to the theoretical waveform; that is, the designed CC–CV CV output characteristics. CC–CV converter is similar to the theoretical waveform; that is, the designed CC–CV converter has converter has CV output characteristics. CV output characteristics.

Figure 12. Schematic diagram of simulation curves of square wave pulse signals Vs 3 and Vs 4 , voltage constant conversion circuit. between the DS polesdiagram of S 3 and S 4 ( Rload =100 Ω ) in Figure Schematic of simulation simulation curves ofDC square wavevoltage pulse signals signals V and Vs4 , voltage Figure 12. 12. Schematic diagram of curves of square wave pulse Vs3 s 3 and Vs 4 , voltage between the DS poles of S3 and S4 (Rload = 100 Ω) in DC constant voltage conversion circuit. between the DS poles of S 3 and S 4 ( Rload =100 Ω ) in DC constant voltage conversion circuit.

Through simulation analysis, it can be concluded that the isolated high-frequency switching Through simulation analysis, it can concluded the isolated switching CC–CV converter can multi-branch the be constant inputthat current, which high-frequency can not only ensure the Through simulation analysis, it can be concluded that the isolated high-frequency CC–CV can multi-branch theinconstant input which can only ensure theswitching constant constantconverter characteristics of the current the trunk, butcurrent, also maintain the not requirement of future mesh CC–CV converter multi-branch thebut constant input the current, which can not only topological ensure the characteristics of thecan current trunk, maintain requirement topological structure of the in CCthe network. Thealso output DC constant voltage of is future stable,mesh which can meet constant characteristics of theThe current in the butvoltage also maintain the requirement ofthe future mesh structure of theelectricity CC network. DCtrunk, constant isand stable, which operating the operating demand output of underwater instruments, provide a can newmeet technical method topological structure of the CC network. The output DC constant voltage is stable, which can meet electricity of underwater andCC provide a new technical method for power supply for power demand supply and distributioninstruments, of underwater remote system in CUINs. the operating electricity demand of underwater instruments, and provide a new technical method and distribution of underwater CC remote system in CUINs. for power supply and distribution of underwater CC remote system in CUINs. 4.2. Research on Verification of Prototype of CC–CV Converter 4.2. Research on Verification of Prototype of CC–CV Converter 4.2. Research on the Verification of Prototype of CC–CV Converter Based on proposed CC–CV converter circuit design and simulation analysis, a principle Based on the proposed CC–CV converter circuit design and simulation analysis, a principle prototype prototype converter was built in the laboratory to further verify the rationality and feasibility of the Basedwas on built the proposed CC–CV to converter circuitthe design and simulation analysis, principle converter in the laboratory further verify rationality and feasibility of thea proposed proposed CC–CV converter circuit. The principle prototype of the CC–CV converter is as shown in prototype converter was built in the laboratory to further verify the rationality and feasibility of the CC–CV converter circuit. The principle prototype of the CC–CV converter is as shown in Figure 13. Figure 13. proposed CC–CV converter circuit. The principle prototype of the CC–CV converter is as shown in rectifier filter circuit Figure 13. rectifier filter circuit

push-pull current-fed multiple-output circuit

the constant voltage output circuit based on PWM feedback

push-pull current-fed multiple-output circuit

(a)

Figure (a) 13. Cont.

the constant voltage output circuit based on PWM feedback

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(b)

Figure of CC–CV converter: Principle prototype prototype ofof CC–CV converter; (b) construction of Figure 13. Test13.ofTest CC–CV converter: (a)(a)Principle CC–CV converter; (b) construction of laboratory test environment. laboratory test environment.

According to the designed prototype, the CV output characteristics were verified by

According to the designed prototype, the CV output characteristics were verified by experiments. experiments. Adjusting the duty cycle D of the switching tubes in the CC isolation circuit to 80%, the resistance Adjusting the duty cycle D of the switching tubes in the CC isolation circuit to 80%, the of load value was 100 Ω; values of sampling resistorsresistors Rp1 andRRp2and wereR adjusted; resistance values of sampling resistance ofset loadtovalue wasthe set resistance to 100 Ω ; the p1 p2 Electronics 2019, 8, U 961 19 of 23tubes the output voltage was set to 150 V. Furthermore, the voltage signal curves of the switching load were adjusted; the output voltage U load was set to 150 V. Furthermore, the voltage signal curves of in the CC isolation circuit and the DC constant voltage conversion circuit were acquired and analyzed, the switching tubes in the CC isolation circuit and the DC constant voltage conversion circuit were which are depicted in Figurewhich 14. are depicted in Figure 14. acquired and analyzed,

(a)

(a) 1

1. The GS terminal voltage of S 3 2. The DS terminal voltage of S 3

1. The GS terminal voltage of S 3 2. The DS terminal voltage of S 3

1 2

2

(b)

(b)

(c) Figure 14. Voltage acquisition testcurve curveof ofGate Gate to and Drain to Source (DS) (DS) polespoles of S1 of S Figure 14. Voltage acquisition test to Source Source(GS) (GS) and Drain to Source 1 andoutput the output of load in CC–CV converter: (a) (a) voltage curves between the the GS and DS S 3 ,the Rload and Sand , and of load R in CC–CV converter: voltage curves between GS and DS 3 load ; (b) voltage curves between andDS DSpoles poles of of SS 3; ;(c) (c)output output voltage load. polespoles of S1of ; (b)S1voltage curves between thethe GSGS and voltagecurve curveofof load. 3

Comparing Figure 14a,b with Figure 5 and Figure 8, the voltage acquisition waveform of the prototype is nearly the same as that of the theoretical derivation and simulation analysis. In the CC isolation circuit, when the switching tubes are closed by the square wave pulse signals, the Drain to Source (DS) voltage of the tubes is zero, whereas the DS voltage is twice as much as the voltage of

capacitor C1 , which is about 300 V, when the tubes are open. By adjusting duty cycle of DC constant voltage converter through sampling circuit and PWM feedback circuit, the output voltage can be constant. As shown in Figure 14c, the output voltage is stable at about 150 V and fluctuates within 5%, which is a good CV characteristic and can meet the requirement for the operating Electronics 2019, 8, 961 17 of 21 power-stability of underwater electrical instruments. According to the requirement of the experiment, the stability and practicability of the constant current-constant voltage14a,b converter need to5be further testing the constant of characteristic of Comparing Figure with Figures and 8, theverified voltageby acquisition waveform the prototype Rload . analysis. thenearly output bythat changing resistance value ofand the load SamplingIn resistance was set, is thevoltage same as of the the theoretical derivation simulation the CC isolation circuit, when theset switching areload closed by the square pulseand signals, the Drain to Source Rload iswave CV output was at 150 V,tubes output resistance adjusted, a constant characteristic (DS) voltage of the tubes is zero, whereas the DS voltage is twice as much as the voltage of capacitor test of load polarity output voltage with seven different resistance values was set. The test scenario is C , which is about 300 V, when the tubes are open. By adjusting duty cycle of DC constant voltage 1 depicted in Figure 12b. The experimental results, are shown in Table 2 and Figure 15. converter through sampling circuit and PWM feedback circuit, the output voltage can be constant. As shown in Figure 14c, 2. the output voltage is stable about 150 V and fluctuates within 5%, which is a Table Experimental test data in theatdifferent resistance values of load. good CV characteristic and can meet the requirement for the operating power-stability of underwater /Ω 150 Ω 200 Ω 300 Ω 500 Ω 750 Ω 1k Ω 100 Ω load electrical Rinstruments. According requirement of the experiment, the stability1.503 and practicability of1.500 the constant 1.504 1.503 1.499 1.501 I in /A to the 1.500 current-constant converter need to be further verified testing the1.503 constant characteristic 1.482 1.491 1.496 1.498 by1.498 1.509 I A− B /A voltage of the output voltage by changing the resistance value of the load Rload . Sampling resistance was set, 1.499 0.998 0.748 0.509 0.303 0.199 0.149 I out − load /A CV output was set at 150 V, output load resistance Rload is adjusted, and a constant characteristic test 171.985 121.460 95.056 69.101 47.917 35.924 30.982 U in /V of load polarity output voltage with seven different resistance values was set. The test scenario is /V 13b. 160.013 109.631 results, 84.373are shown 57.948in Table 37.952 27.96415. 22.868 B depicted U inA−Figure The experimental 2 and Figure 149.946 150.032 150.073 150.022 150.047 150.033 149.986 U out − load /V Table 2. Experimental test data in the different resistance values of load.

As shown in Table 2, with the increase of load resistance value Rload , the output voltage of the

Rload /Ω 100 Ω 150 Ω 200 Ω 300 Ω 500 Ω 750 Ω 1k Ω load U out − load remains unchanged because of the constant voltage output characteristic of the

/A 1.500 of the 1.504 1.499 1.503 1.501 converter;Iinbesides, because constant1.503 current characteristic of the trunk line and1.500 the isolation IA−B /A 1.482 1.491 1.496 1.498 1.498 1.503 1.509 I circuit, Ithe input current of the system and the output current of the isolation circuit I A− B in /A 1.499 0.998 0.748 0.509 0.303 0.199 0.149 out−load

Uin /V 171.985 121.460 30.982 voltage U in , the output remain unchanged. According to , the input69.101 voltage of47.917 the system35.924 P = U 2 / R95.056 U

/V

160.013

109.631

84.373

57.948

37.952

27.964

22.868

A−B of the CC isolation circuit and U current of the load decreases with the 149.986 increase of the A− B , the output U /V 149.946 150.032 150.073 150.022 150.047 150.033

load.

out−load

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(a)

(b) 15. Curve Curve of of relationship relationshipbetween betweenresistance resistancevalue valueofofload load and output voltages and currents Figure 15. and output voltages and currents of load, CCCC isolation circuit and the trunk: of load, isolation circuit and the trunk:(a) (a)Curve Curveofofrelationship relationshipbetween betweenload loadand andthe the voltages voltages of load, trunk; (b)(b) curve of relationship between loadload and the of load, load, CC CCisolation isolationcircuit circuitand andthe the trunk; curve of relationship between andcurrents the currents of CC isolation circuit and the trunk. load, CC isolation circuit and the trunk.

As shown in Figure 15a,b, when the value of load resistance changes, the output current of the CC isolation circuit remains unchanged, which is nearly the same as that of the trunk and has good CC characteristics. The output voltage of the DC constant voltage conversion circuit remains unchanged under load changes, and the CV output characteristics of the CC–CV converter are excellent. The input voltage of the CC–CV converter and output current of load are linearly related

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(b)

As shown in Table 2, with the increase of load resistance value Rload , the output voltage of Figure 15. Curve of relationship between resistance value of load and output voltages and currents the load Uout−load remains unchanged because of the constant voltage output characteristic of the of load, CC isolation circuit and the trunk: (a) Curve of relationship between load and the voltages of converter; besides, because of the constant current characteristic of the trunk line and the isolation load, CC isolation circuit and the trunk; (b) curve of relationship between load and the currents of circuit, the input current of the system Iin and the output current of the isolation circuit IA−B remain load, CC isolation circuit and the trunk. unchanged. According to P = U2 /R, the input voltage of the system Uin , the output voltage of the CC isolation circuit in and UA−B15a,b, , the output of of theload loadresistance decreaseschanges, with the the increase of current the load.of the As shown Figure when current the value output As shown in Figure 15a,b, when the value of load resistance changes, the output current CC CC isolation circuit remains unchanged, which is nearly the same as that of the trunk and of hasthe good isolation circuit remains which nearly same as that of conversion the trunk and has good CC CC characteristics. The unchanged, output voltage of isthe DC the constant voltage circuit remains characteristics. The output voltage of the DC constant voltage conversion circuit remains unchanged unchanged under load changes, and the CV output characteristics of the CC–CV converter are under loadThe changes, the CV output characteristics theoutput CC–CV converter are excellent. Therelated input excellent. input and voltage of the CC–CV converter of and current of load are linearly voltage of the CC–CV converter andvoltage outputvalue current of load are related to the power resistance of to the resistance of load. The input of the SPFE is linearly related to the output of the load. The input voltage value of the SPFE is related to the output power of the load, and the SPFE load, and the SPFE does not need to output high voltage, while more the underwater equipment is does not needbytothe output voltage, while more underwater equipment is less affectedand by the less affected highhigh voltage. Furthermore, thethe system reliability is greatly improved, the high voltage. the system greatly andnetwork the current in the trunk is current in the Furthermore, trunk is constant, and thereliability power ofiscable lossimproved, in the whole is constant, which constant, and the power of cable loss in the whole network is constant, which is beneficial to the system is beneficial to the system fault determination. As shown in Figure 16, with the decrease of load, 2 /R fault determination. As2 shown in Figure 16, with the decrease of load, according to Pload = Uload load , according to Pload = U load / Rload , the loss of the converter is basically stable. With the increase of load the loss of the converter is basically stable. With the increase of load power, the output efficiency of the power, the output efficiency of the converter is improved. The designed CC–CV converter has high converter is improved. The designed CC–CV converter has high conversion efficiency, and the loss of conversion efficiency, and the loss of the full module conversion is controlled within 30 W. In the the full module conversion is controlled within 30 W. In the condition of a full load, the conversion condition of a full load, the conversion efficiency exceeds 90%, and the output power of a single efficiency exceeds 90%, and the output power of a single converter is up to 230 W. converter is up to 230 W.

Figure 16. Curve converter. Curve of relationship between load and the output efficiency of the CC–CV converter.

The CC isolation circuit and the DC constant voltage conversion conversion circuit circuit are are analyzed analyzed separately, separately, and Sections sections 2 and 3 prove that the theory theory of of isolated isolated circuit circuit is is feasible. feasible. In response to the isolated isolated power converters proposed, the simulation is carried carried out out and and the the prototype prototype isis designed. designed. Through Through comprehensive theoretical derivation, simulation analysis and experimental verification, it can be verified that the proposed proposed isolated isolated CC–CV converter has reliable and efficient constant current transformation function for a branch, by combining the theory and simulation analysis of a constant current-constant voltage converter and building a test circuit circuit prototype. prototype. On the basis of maintaining the CC underwater current in the the CC–CV converter realizesrealizes electric electric energy CCcharacteristics characteristicsofof underwater current in trunk, the trunk, the CC–CV converter conversion; the CC–CV can provide andstable reliable power supply for branch energy conversion; the converter CC–CV converter canstable provide and reliable power supplyobservation for branch equipment without high-medium-low voltage conversion, and the CC–CV converter has the advantages of standardization, modularization, high power, easy expansion and high reliability. At the same time, the electrical isolation characteristic ensures that the converter is free from electromagnetic interference caused by a branch fault or current fluctuation, and ensures the stability and reliability of the constant current in the trunk. Moreover, through series-parallel redundancy of multiple converters, a high working-power can be stabilized for future high-power underwater observation equipment.

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5. Conclusions With the continuous development of cabled underwater information networks, the supply and distribution equipment of remote power supply system has become an important part of system operation and maintenance. Based on Kirchhoff’s current law and Kirchhoff’s voltage law, this paper carries out the theoretical analysis of the proposed constant current-constant voltage converter. The simulation circuit module is established, and the rationality and feasibility of the converter are verified by analyzing the simulation. The physical prototype of a constant current-constant voltage converter is fabricated, and the test environment is built. Furthermore, the reliability and practicability of the design are verified by changing the magnitude of load resistance and duty cycle. The designed constant current-constant voltage converter, which can be used in the constant current remote power supply system, can provide the required operating electric energy for underwater observation instruments, and has high practical value. Currently, this method has passed the initial testing; in order to test and verify the design and power supply adaptability of the designed converter, the next step would be to build the multi-node prototype test platform for constant current remote supply system, and furthermore, to verify the practical application performance of the converter in this paper through experiments. Author Contributions: Conceptualization, Z.Z. and X.Z.; data curation, T.W.; formal analysis, Z.Z. and X.W.; Writing—Original Draft, Z.Z.; Writing—Reviewing and Editing, X.Z. and X.W. Funding: This work was supported in part by the National Natural Science Foundation of China under Grant number 61871473 and number 61803379, and the Natural Science Foundation of Hubei Province, China under Grant number 4251181107. Conflicts of Interest: The authors declare no conflict of interest.

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