Minimum-Output-Current-Ripple Control of Current-Fed Three-Level Phase-Shift Full-Bridge Converter

: Electriﬁed ports using medium-voltage DC (MVDC) renewable energy microgrids require current-fed dc/dc converters in application scenarios such as battery or ultracapacitor charging units and hydrogen production systems. This paper designs a three-level phase-shift full-bridge (TL-PSFB) converter that interfaces with the MVDC microgrid. Its operation in the current source mode requires a wide output voltage range and small output current ripple. Firstly, the dual-output TL-PSFB topology is introduced


Introduction
Inland and offshore shipping is facing an energy transition due to the economic and environmental concerns of fossil fuels.Currently, there are some new energy vessels [1] and electrified port projects applied [2].Compared with the port microgrid directly supplied by the power grid, the addition of renewable energy can significantly reduce the utilization rate of fossil fuel.Port microgrids using renewable energy generation have immediate environmental benefits as well as long-term economic benefits.Due to the large randomness of power supply and load of renewable energy microgrid, the AC microgrid is prone to frequency fluctuation and grid oscillation problems.As a new form of network formation, a medium-voltage DC (MVDC) microgrid can avoid the above problems and has the advantages of high reliability of power supply, fast response, and scalability.The typical structure of an MVDC renewable energy microgrid is shown in Figure 1.
The wind power generation, photovoltaic power generation, and hydroelectric power generation on the source side of the renewable energy microgrid, and the charging device on the load side all have strong intermittensity.The connection of the source side to the public network can solve the short-term high power demand of the load, while the hydrogen production system on the load side can effectively solve the local consumption of renewable energy generation and bring new energy types.Ships with different working scenarios can choose energy sources such as hydrogen fuel, battery, and ultracapacitor storage.The wind power generation, photovoltaic power generation, and hydroelectric power generation on the source side of the renewable energy microgrid, and the charging device on the load side all have strong intermittensity.The connection of the source side to the public network can solve the short-term high power demand of the load, while the hydrogen production system on the load side can effectively solve the local consumption of renewable energy generation and bring new energy types.Ships with different working scenarios can choose energy sources such as hydrogen fuel, battery, and ultracapacitor storage.
MVDC input dc/dc converters for load-side charging devices or hydrogen production power sources are important components of medium-voltage DC renewable energy microgrids.The common topologies include the non-isolated Buck converter and Boost converter, isolated series resonant converter, phase-shift full-bridge converter, and bidirectional full bridge converter, etc.In MVDC applications, series or multi-level connections are usually used on the basis of the above topologies to increase output voltage level.Switching device withstand voltage is half of the bus voltage in the three-level phase-shift full-bridge (TL-PSFB) topology which can meet the requirements of MVDC input [3,4].The TL-PSFB topology adopts an intermediate frequency transformer to achieve isolation and voltage transformation, and can flexibly configure the output side voltage according to the power of the electrolyzer or the voltage of the energy storage device.Magnetic coupling can effectively isolate source and load faults.
Some scholars have performed much research on the TL-PSFB converter controlled in voltage mode.The TL-PSFB converter and the basic topological derivation are described by Prof. Xinbo Ruan in [4].In [5], a three-phase TL-PSFB converter topology was designed with voltage mode control.Literature [6] proposes a first-order sliding mode controller, which can eliminate the output voltage error by adding an integrator and achieve a better control effect.The principle analysis, modeling, and control strategy of the voltage mode controlled TL-PSFB converter are studied in the literature mentioned above.
Higher power density and efficiency has always been the goal of the power electronic converter.Increasing the switching frequency of the power device is the most direct method, however, it will cause a sharp increase in the loss caused by hard switching of MVDC input dc/dc converters for load-side charging devices or hydrogen production power sources are important components of medium-voltage DC renewable energy microgrids.The common topologies include the non-isolated Buck converter and Boost converter, isolated series resonant converter, phase-shift full-bridge converter, and bidirectional full bridge converter, etc.In MVDC applications, series or multi-level connections are usually used on the basis of the above topologies to increase output voltage level.Switching device withstand voltage is half of the bus voltage in the three-level phase-shift full-bridge (TL-PSFB) topology which can meet the requirements of MVDC input [3,4].The TL-PSFB topology adopts an intermediate frequency transformer to achieve isolation and voltage transformation, and can flexibly configure the output side voltage according to the power of the electrolyzer or the voltage of the energy storage device.Magnetic coupling can effectively isolate source and load faults.
Some scholars have performed much research on the TL-PSFB converter controlled in voltage mode.The TL-PSFB converter and the basic topological derivation are described by Prof. Xinbo Ruan in [4].In [5], a three-phase TL-PSFB converter topology was designed with voltage mode control.Literature [6] proposes a first-order sliding mode controller, which can eliminate the output voltage error by adding an integrator and achieve a better control effect.The principle analysis, modeling, and control strategy of the voltage mode controlled TL-PSFB converter are studied in the literature mentioned above.
Higher power density and efficiency has always been the goal of the power electronic converter.Increasing the switching frequency of the power device is the most direct method, however, it will cause a sharp increase in the loss caused by hard switching of switching devices.Therefore, many scholars have been studying soft switching strategies, and the main methods can be divided into two categories: proposing a new modulation strategy and improving the topology structure.The new modulation strategies reported in the literature mainly include an asymmetric duty cycle modulation strategy [7], double phase-shift modulation strategy [8], and triple phase-shift modulation strategy [9], etc.These strategies can extend the soft-switching range of the converter to a certain extent without changing the topology or adding additional energy storage elements, but they cannot achieve soft-switching in the full operating range.In [10][11][12][13][14][15], LLC resonant TL-PSFB Energies 2022, 15, 6444 3 of 16 converter was studied to achieve a wider range of soft switching with the help of resonant element energy storage.Dr. Bor-Ren Lin designed a new hybrid topology, including a three-level half-bridge converter and unregulated voltage half-bridge converter structure, which has the advantages of small circulation, wide soft-switching range, and small output current ripple [16][17][18].In addition, soft switching of the primary-side switching device can be achieved by adding a clamp diode [19] or fly-across capacitor to the primary side [20][21][22].Prof. Yan Li's focus is on the intermediate AC side.She proposed a hybrid TL-PSFB converter to accommodate a wide range of output voltages by adding a clamp inductor on the AC side, and the converter has good soft switching performance [23].Soft switching of the secondary diode has also been noticed in the literature [24][25][26].In addition, some scholars have done some improving research on the topology in some other aspects.Literature [27,28] proposed an improved modulation strategy to equalize the thermal stress of power devices or supporting capacitors.A modulation strategy to reduce the common-mode voltage was proposed in the literature [29].In order to solve the reverse recovery problem of the secondary rectifying diode, the active clamping strategy was proposed in [30,31].
Only literature [19] (hundred kW class) and [5] (MW class) have publicly reported the application of TL-PSFB converter in large-capacity DC conversion applications.Largecapacity TL-PSFB converters have high losses and complex heat dissipation design.Traditional topology with improved modulation or control strategy do not fundamentally solve the problem of narrow soft-switching range and are prone to soft-switching failure.Resonant topology or other improved topology increases power loop components, has complex topology and low reliability, and the added devices also bring losses.Therefore, the soft switching strategy is not the focus of the design of a large capacity TL-PSFB converter.
Previous research has focused on the voltage-mode controlled TL-PSFB converter, while hydrogen power or energy storage converters require a current source, the major difference between them is that current mode control has no static operating point.In addition, the output current ripple of the converter directly affects the efficiency of the electrolyzer or energy storage system, which requires the converter to have a smaller output current ripple.
This paper is organized as follows.In Section 2, a dual-output TL-PSFB topology is proposed.The principle of phase-shift pulse width modulation (PS-PWM) is introduced, and the design method of the traditional CCDC strategy is analyzed.In Section 3, the relationship between output current ripple and conducting-duty cycle and phase-shift duty cycle is analytically calculated, and a constant current control with the MOCR strategy is proposed.Section 4 compares and analyzes the performance of the two strategies in terms of output current ripple, filter inductance parameters, DC voltage utilization, and the total harmonic distortion (THD) of primary voltage.In Section 5, the proposed modulation method's effectiveness is verified by experiments.Finally, Section 6 summarizes the main work of this paper.

Topology and Principle of PS-PWM
In order to improve the power density of the converter, a dual-output TL-PSFB converter topology is designed in this paper, as shown in Figure 2. The dual-output TL-PSFB converter mainly includes support capacitors, diode-clamped three-level H-bridge, threewinding medium-frequency transformer, uncontrolled rectifier bridge, output filter inductor, and input and output diodes.The diode-clamped three-level H-bridge inverter unit converts the input DC voltage into a bipolar five-level square wave with adjustable pulse width, which is divided into two output channels after the step-down by the three-winding medium-frequency transformer.Then it is connected to two independent sets of uncontrolled rectifier bridges.Only inductive filtering is used at the rectifier output, reducing unnecessary passive components compared to previous LC or LCL filters.
unit converts the input DC voltage into a bipolar five-level square wave with pulse width, which is divided into two output channels after the step-down b winding medium-frequency transformer.Then it is connected to two indepen uncontrolled rectifier bridges.Only inductive filtering is used at the rectifier ducing unnecessary passive components compared to previous LC or LCL filt PS-PWM is adopted in the dual-output TL-PSFB converter, and its princip in Figure 3.In the figure, dθ is the conducting-duty cycle, dα is the phase-shift and Ts is the switching period.The diode-clamped three-level H-bridge in Fi the same dθ for the odd-numbered switching devices and a complementary c duty cycle 1−dθ for the even-numbered switching devices.The driving pulse bridge leg lags behind that of the left bridge leg, and the phase difference of pulse of the left and right bridge legs' switches is changed by controlling the c time of the right bridge leg dαTs.PS-PWM consists of two degrees of freedom both in the range of [0, 1/2].
By analyzing the corresponding relationship between dθ and dα, the out of the diode-clamped three-level H-bridge can be obtained, including the thr shown in Figure 4.In order to distinguish different conditions of output vol clearly, the clamping duty cycle dγ is introduced, where dγ = 1/2 −dθ.By analyzing the corresponding relationship between d θ and d α , the output voltage of the diode-clamped three-level H-bridge can be obtained, including the three cases as shown in Figure 4.In order to distinguish different conditions of output voltages more clearly, the clamping duty cycle d γ is introduced, where Energies 2022, 15, 6444

CCDC Strategy
The design principle of the CCDC strategy is to minimize THD of the primary voltage u ab .The root mean square (RMS) of the nth harmonic component of u ab is noted as U nrms (n = 1, 2, 3 . . .).THD of u ab is defined as, where the relationship between the rms value U rms of u ab and the rms value of each harmonic component is, as known from the calculation, (3) According to the waveform of u ab in Figure 4, the Fourier series expression of u ab can be obtained by analytical calculation shown in (4).
Energies 2022, 15, 6444 6 of 16 In addition, the relationship between the RMS value of u ab , d θ and d α is shown in (5).
Partial differential solution of ( 6) is performed; that is, let ∂THD/∂d α = 0 and ∂THD/∂d θ = 0, it can be obtained, Two sets of solutions can be obtained by combining ( 7) and ( 8) as follows: the first extremum point is: d θ1 = 0.42, d α1 = 0.35; the second one is: d θ2 = 0.35 and d α2 = 0.42, which are the two extreme points shown in Figure 5.
Energies 2022, 15, 6444 7 of 18 Two sets of solutions can be obtained by combining ( 7) and ( 8) as follows: the first extremum point is: dθ1 = 0.42, dα1 = 0.35; the second one is: dθ2 = 0.35 and dα2 = 0.42, which are the two extreme points shown in Figure 5.The primary voltage is input to the uncontrolled rectifier bridge via the mediumfrequency transformer.Similarly, the Fourier decomposition of the rectifier bridge output voltage ur is performed according to the relative relationship between dθ and dα.
According to (9), the maximum DC component of the output voltage of the rectifier bridge is determined by dθ, and the output voltage can be regulated within the range of the maximum DC component by adjusting dα under the condition that dθ remains un- The primary voltage is input to the uncontrolled rectifier bridge via the mediumfrequency transformer.Similarly, the Fourier decomposition of the rectifier bridge output voltage u r is performed according to the relative relationship between d θ and d α .
According to (9), the maximum DC component of the output voltage of the rectifier bridge is determined by d θ , and the output voltage can be regulated within the range of the maximum DC component by adjusting d α under the condition that d θ remains unchanged.
The d θ of the CCDC strategy is fixed at one of the two minimum points in Figure 5, and the upper limit of the DC component of the output voltage of the rectifier bridge is determined by d θ according to (9).In order to improve the utilization of the DC voltage at the primary side and obtain a wider regulation range, the CCDC strategy is usually set d θ = 0.42 and d α = 0.35.

MOCR Strategy
In this section, the output current ripple of the converter is analytically calculated, and the variation trend of the output current ripple with d θ and d α is analyzed.Then, a MOCR strategy is proposed, and a constant current control with the MOCR strategy is designed.

Analysis of Output Voltage and Current Ripple of the Rectifier Bridge
According to (9), the output voltage of the rectifier bridge is a DC component superimposed several times of AC harmonic components, so the DC component of the output voltage can be ignored when analyzing the harmonics of the filter inductor, and the load side can be equivalent to a series of resistor and capacitor.Different loads (such as ultracapacitors, batteries, electrolyzers, etc.) affect the RC parameters.The equivalent circuit at the output end of the rectifier bridge is shown in Figure 6.

MOCR Strategy
In this section, the output current ripple of the converter is analytically c and the variation trend of the output current ripple with dθ and dα is analyze MOCR strategy is proposed, and a constant current control with the MOCR s designed.

Analysis of Output Voltage and Current Ripple of the Rectifier Bridge
According to (9), the output voltage of the rectifier bridge is a DC compon imposed several times of AC harmonic components, so the DC component of t voltage can be ignored when analyzing the harmonics of the filter inductor, an side can be equivalent to a series of resistor and capacitor.Different loads (suc capacitors, batteries, electrolyzers, etc.) affect the RC parameters.The equivalen the output end of the rectifier bridge is shown in Figure 6.Transform the AC harmonic component of the output voltage of the rectifier bridge obtained by ( 9) into a complex domain expression, The harmonic component of the output current is, • Energies 2022, 15, 6444 8 of 16 Substitute ( 10) into (11) to obtain, • where, Express the output current harmonics into the form in the real number field as Figure 7 shows the comparison between the calculated waveforms and the simulated waveforms for the output currents at different d θ and d α , the trend of the calculated results is generally consistent with that of the simulation results, which proves the correctness of the calculated results.There is a certain error between the calculated and simulated results, which is mainly due to the fact that the calculated results do not take into account non-ideal factors such as duty cycle loss.The output current ripple is equal to the maximum value of the filter inductor current minus the minimum value in one cycle.Combining ( 14) and ( 15), the variation of output current ripple under different combinations of dθ and dα can be calculated, as shown in Figures 8 and 9.The output current ripple is equal to the maximum value of the filter inductor current minus the minimum value in one cycle.
Combining ( 14) and ( 15), the variation of output current ripple under different combinations of d θ and d α can be calculated, as shown in Figures 8 and 9.  Combining ( 14) and ( 15), the variation of output current ripple under different combinations of dθ and dα can be calculated, as shown in Figures 8 and 9.

Route I RouteII
Combining ( 14) and ( 15), the variation of output current ripple under different combinations of dθ and dα can be calculated, as shown in Figures 8 and 9.

Constant Current Control Combined with the MOCR Strategy
As can be seen from Figure 9, as d θ and d α increase, there is a changing path that minimizes the output current ripple.That is, Equation ( 16) is the mathematical description of the minimum output current ripple control rate.Since d θ determines the upper limit of the output voltage, transition path Route II→Route III is selected to ensure that the control variable is unique.That is, when d θ is less than 1/4, maintain d θ = 1/4 and adjust d α to control the output voltage.As the output voltage increases, control d θ is equal to d α .
Combined with the above analysis, this paper designs a constant current control combined with the MOCR strategy, as shown in Figure 10.The controller collects the output current for feedback, and d α is calculated by the PI controller, and d θ is calculated by the MOCR strategy.Since the converter adopts a secondary dual output structure, a two-output maximum current feedback strategy is used to prevent the output from being overloaded during actual operation.In Figure 10, d δ is limited to zero level, which is set to prevent the same level jump as the bus voltage.In engineering, the value is set according to the dv/dt limit of switching devices and transformers.bined with the MOCR strategy, as shown in Figure 10.The controller collects the output current for feedback, and dα is calculated by the PI controller, and dθ is calculated by the MOCR strategy.Since the converter adopts a secondary dual output structure, a two-output maximum current feedback strategy is used to prevent the output from being overloaded during actual operation.In Figure 10, dδ is limited to zero level, which is set to prevent the same level jump as the bus voltage.In engineering, the value is set according to the dv/dt limit of switching devices and transformers.

Output Current Ripple and Filter Inductor Characterization
Since dα can only be adjusted within the range less than dθ in the CCDC strategy, the output ripple of the two control strategies is compared below in the range [0, 0.42).Figure 11 shows the comparison of the normalized results of output current ripple under the same filtering inductance condition.It can be seen from the figure that the maximum ripple current modulated by the MOCR strategy is 28% smaller than that controlled by the traditional CCDC strategy, and the ripple current modulated by the MOCR strategy is all less than the CCDC strategy in the whole range of working conditions.In Figure 11, dα corresponding to the maximum current ripple under the two gies is obtained by the analytical calculation method, thus, the minimum filter indu value satisfying the maximum ripple index can be calculated.Table 1 compares the of minimum filter inductance corresponding to the two modulation methods und ferent output current ripple indexes.According to the data in the table, under d output current ripple indexes, the MOCR strategy can reduce the value of the min output filter inductance by about 23%.
According to the inductor multi-objective optimization design method studied and the parameters in Table 1, the output filter inductor is designed.Figure 12 sho comparison of the volume and weight of the minimum inductance required by t strategies corresponding to different output current ripple indexes.It can be seen fr figure that the volume and weight of the output filter inductor can be optimized to tain extent by using the MOCR strategy studied in this paper under different requir of ripple indexes, which will improve the power density of the converter.In Figure 11, d α corresponding to the maximum current ripple under the two strategies is obtained by the analytical calculation method, thus, the minimum filter inductance value satisfying the maximum ripple index can be calculated.Table 1 compares the values of minimum filter inductance corresponding to the two modulation methods under different output current ripple indexes.According to the data in the table, under different output current ripple indexes, the MOCR strategy can reduce the value of the minimum output filter inductance by about 23%.According to the inductor multi-objective optimization design method studied in [32] and the parameters in Table 1, the output filter inductor is designed.Figure 12 shows the comparison of the volume and weight of the minimum inductance required by the two strategies corresponding to different output current ripple indexes.It can be seen from the figure that the volume and weight of the output filter inductor can be optimized to a certain extent by using the MOCR strategy studied in this paper under different requirements of ripple indexes, which will improve the power density of the converter.1.
The loss of filter inductor mainly includes core loss and winding loss.The w losses can be decomposed into the sum of ac and dc losses, where Rdc is the dc resistance of the filter inductor, and this parameter can be cal from the average turn length and resistivity of the inductor winding.Rdc-n is the w ac resistance corresponding to the ripple current of different frequencies.The relat tween ac resistance and ac resistance is shown in (18).FR is the ac resistivity, which obtained by the Dowell model [33].
Generally, core loss is calculated by loss separation theory and mainly includ teresis loss, eddy current loss, and other losses.According to the calculation form magnetic core loss derived in [32], combined with (17), the total loss of inductance calculated.Figure 13 shows a comparison of the output filter inductance loss with ent parameters.It can be seen from the figure that, under the same output curren index requirements, the MOCR strategy can reduce the loss of output filtering in by up to 29.31%, which improves the efficiency of the converter to a certain extent  1.
The loss of filter inductor mainly includes core loss and winding loss.The winding losses can be decomposed into the sum of ac and dc losses, where R dc is the dc resistance of the filter inductor, and this parameter can be calculated from the average turn length and resistivity of the inductor winding.R dc-n is the winding ac resistance corresponding to the current of different frequencies.The relation between ac resistance and ac resistance is shown in (18).F R is the ac resistivity, which can be obtained by the Dowell model [33].
Generally, core loss is calculated by loss separation theory and mainly includes hysteresis loss, eddy current loss, and other losses.According to the calculation formula of magnetic core loss derived in [32], combined with (17), the total loss of inductance can be calculated.Figure 13 shows a comparison of the output filter inductance loss with different parameters.It can be seen from the figure that, under the same output current ripple index requirements, the MOCR strategy can reduce the loss of output filtering inductor by up to 29.31%, which improves the efficiency of the converter to a certain extent.magnetic core loss derived in [32], combined with (17), the total loss of inductan calculated.Figure 13 shows a comparison of the output filter inductance loss w ent parameters.It can be seen from the figure that, under the same output curr index requirements, the MOCR strategy can reduce the loss of output filtering by up to 29.31%, which improves the efficiency of the converter to a certain exte   1.

Utilization of DC Voltage and THD of Primary Voltage Characterization
The utilization of DC voltage is the ratio of the fundamental wave amplitude of u ab to U d .Combining with (4).The variation of DC voltage utilization with d θ and d α can be obtained by combining (4).
The theoretical regulation range of both d θ and d α is [0, 0.5).A fixed d θ of 0.42 for the CCDC strategy leads to lower utilization of the primary-side DC voltage.This leads to a larger transformer ratio required to achieve the designed output voltage, which will increase the primary side current and, in turn, leads to an increased transformer and primary side switching device losses.Besides, the circuit parameters of the converter are designed according to the rated working condition in general.However, d α in the light load working condition is far away from 0.35, which will result in the increase of the THD of u ab , as shown in Figure 14, which violates the initial design principle.

Utilization of DC Voltage and THD of Primary Voltage Characterization
The utilization of DC voltage is the ratio of the fundamental wave amplitude o to Ud. Combining with (4).The variation of DC voltage utilization with dθ and dα ca obtained by combining (4).  The theoretical regulation range of both dθ and dα is [0, 0.5).A fixed dθ of 0.42 for CCDC strategy leads to lower utilization of the primary-side DC voltage.This leads larger transformer ratio required to achieve the designed output voltage, which wil crease the primary side current and, in turn, leads to an increased transformer and mary side switching device losses.Besides, the circuit parameters of the converter are signed according to the rated working condition in general.However, dα in the light working condition is far away from 0.35, which will result in the increase of the TH uab, as shown in Figure 14, which violates the initial design principle.Figure 14 compares the THD of uab with the CCDC and MOCR strategies, res tively, over the full range of operating conditions, and it can be seen from the figure the difference in THD performance between the two strategies under the correspond operating conditions is not significant.However, it should be noted that the CCDC s Figure 14 compares the THD of u ab with the CCDC and MOCR strategies, respectively, over the full range of operating conditions, and it can be seen from the figure that the difference in THD performance between the two strategies under the corresponding operating conditions is not significant.However, it should be noted that the CCDC strategy is optimized for the THD of u ab , but the optimization range is limited to the operating conditions around d θ of 0.42 and d α of 0.35.The CCDC strategy does not bring optimal performance for a wide range of output requirements.

Experimental Verification
In this paper, a 1:1 test prototype is designed as shown in Figure 15, and the parameters of the main circuit are shown in Table 2.The output current ripple index is designed to be less than 20% I o .The prototype experiment uses the ultracapacitor as the load and adopts the constant current charging mode.Figure 16 shows the experimental waveform of the output curren itor charged from 0 V to the rated voltage at the constant current 180 current ripple is 34.41A with the CCDC strategy and 25.37 A with th which is 26.27% less.The output current ripple in the whole charging than that of the CCDC strategy, and the trend of ripple current durin sistent with the theoretical analysis shown in Figure 11, which verifie  Figure 16 shows the experimental waveform of the output current of the ultracapacitor charged from 0 V to the rated voltage at the constant current 180 A. The maximum current ripple is 34.41A with the CCDC strategy and 25.37 A with the MOCR strategy, which is 26.27% less.The output current ripple in the whole charging process is smaller than that of the CCDC strategy, and the trend of ripple current during charging is consistent with the theoretical analysis shown in Figure 11, which verifies the correctness of the above theoretical analysis.current ripple is 34.41A with the CCDC strategy and 25.37 A with the MOCR stra which is 26.27% less.The output current ripple in the whole charging process is sm than that of the CCDC strategy, and the trend of ripple current during charging is sistent with the theoretical analysis shown in Figure 11, which verifies the correctne the above theoretical analysis.In the initial stage, the converter prototype is designed according to the theore analysis results of the CCDC strategy.In order to meet the output current ripple in the output filter inductor is taken to be larger, and its weight and size are also larger In the initial stage, the converter prototype is designed according to the theoretical analysis results of the CCDC strategy.In order to meet the output current ripple index, the output filter inductor is taken to be larger, and its weight and size are also larger.The physical picture is shown in Figure 17a, with a weight of 142 kg and a three-dimensional size of 211 mm (height) × 329 mm (width) × 298 mm (depth).

Conclusions
For the TL-PSFB converter operating in a current-fed mode in DC microgrid, this paper analyzes and points out the problems such as poor current ripple performance and non-compliance with the static operating point design principle of the traditional CCDC strategy.A MOCR strategy is proposed and the performance of the two strategies is quantitatively compared in four aspects.Both experimental and theoretical analyses prove that the proposed MOCR strategy has better performance than the traditional CCDC strategy.In fact, the MOCR strategy adds a degree of control freedom to the CCDC strategy.Adopting the idea of software-based hardware functions avoids the use of high-order filters when a small current ripple index is required.To a certain extent, the power density and efficiency of the converter are improved and the engineering cost is reduced.According to the theoretical analysis results and experimental results of the MOCR strategy studied in this paper, the output filter inductance value of the prototype can be reduced to 6 mH; the three-dimensional figure is shown in Figure 17b.The weight is 120 kg, and the three-dimensional size is 203 mm (height) × 309 mm (width) × 277 mm (depth).Compared with the filter inductor before optimization, weight, volume and loss are respectively reduced by 13.98%, 14.94%, and 11.54%.

Conclusions
For the TL-PSFB converter operating in a current-fed mode in DC microgrid, this paper analyzes and points out the problems such as poor current ripple performance and non-compliance with the static operating point design principle of the traditional CCDC strategy.A MOCR strategy is proposed and the performance of the two strategies is quantitatively compared in four aspects.Both experimental and theoretical analyses prove that the proposed MOCR strategy has better performance than the traditional CCDC strategy.In fact, the MOCR strategy adds a degree of control freedom to the CCDC strategy.Adopting the idea of software-based hardware functions avoids the use of high-order filters when a small current ripple index is required.To a certain extent, the power density and efficiency of the converter are improved and the engineering cost is reduced.

Figure 2 .
Figure 2. Topology of dual-output TL-PSFB converter.PS-PWM is adopted in the dual-output TL-PSFB converter, and its principle is shown in Figure3.In the figure, d θ is the conducting-duty cycle, d α is the phase-shift duty cycle, and Ts is the switching period.The diode-clamped three-level H-bridge in Figure2uses the same d θ for the odd-numbered switching devices and a complementary conducting-duty cycle 1 − d θ for the even-numbered switching devices.The driving pulse of the right bridge leg lags behind that of the left bridge leg, and the phase difference of the driving pulse of the left and right bridge legs' switches is changed by controlling the carrier delay time of the right bridge leg d α T s .PS-PWM consists of two degrees of freedom: d θ and d α , both in the range of [0, 1/2].

Figure 5 .
Figure 5. Relationship between dα, dθ and the THD of primary voltage.

Figure 5 .
Figure 5. Relationship between d α , d θ and the THD of primary voltage.

Figure 6 .
Figure 6.The output harmonic equivalent circuit of the rectifier bridge.

Figure 6 .
Figure 6.The output harmonic equivalent circuit of the rectifier bridge.
minus the minimum value in one cycle.

Figure 8 .
Figure 8.Output current ripple corresponding to different dθ and dα.

Figure 9 .
Figure 9. Output current ripple corresponding to different dθ and dα (top view).

Figure 8 .
Figure 8.Output current ripple corresponding to different d θ and d α .

Figure 8 .
Figure 8.Output current ripple corresponding to different dθ and dα.

Figure 9 .
Figure 9. Output current ripple corresponding to different dθ and dα (top view).

Figure 9 .
Figure 9. Output current ripple corresponding to different d θ and d α (top view).

Figure 10 .
Figure 10.Diagram of constant current control with the MOCR strategy.

Figure 10 .
Figure 10.Diagram of constant current control with the MOCR strategy.

Figure 11 .
Figure 11.Comparison of current ripple analytical calculations between CCDC and MOCR.

Energies 2022, 15 , 6444 Figure 12 .
Figure 12.Comparison of volume and weight of output filter inductors for different param Table1.

Figure 12 .
Figure 12.Comparison of volume and weight of output filter inductors for different parameters in Table1.

Figure 13 .
Figure 13.Comparison of losses of output filter inductors for different parameters in Tab

Figure 13 .
Figure 13.Comparison of losses of output filter inductors for different parameters in Table1.

Figure 14 .
Figure 14.Comparison of the THD of uab using MOCR and CCDC.

Figure 14 .
Figure 14.Comparison of the THD of u ab using MOCR and CCDC.

Figure 15 .
Figure 15.The physical picture of the dual-output TL-PSFB converter test pro

Figure 15 .
Figure 15.The physical picture of the dual-output TL-PSFB converter test prototype.

Figure 16 .
Figure 16.The experimental waveform of the output current of the two strategies.

Figure 16 .
Figure 16.The experimental waveform of the output current of the two strategies.

Energies 2022 ,
15, 6444 16 of 18physical picture is shown in Figure17a, with a weight of 142 kg and a three-dimensional size of 211 mm (height) ×329 mm (width) ×298 mm (depth).According to the theoretical analysis results and experimental results of the MOCR strategy studied in this paper, the output filter inductance value of the prototype can be reduced to 6 mH; the three-dimensional figure is shown in Figure17b.The weight is 120 kg, and the three-dimensional size is 203 mm (height) ×309 mm (width) ×277 mm (depth).Compared with the filter inductor before optimization, weight, volume and loss are respectively reduced by 13.98%, 14.94%, and 11.54%.

Figure 17 .
Figure 17.Three-dimensional comparison of the filter inductor before and after optimization.(a) Physical picture of the filter inductor before optimization, (b) 3D picture of the filter inductor after optimization.

Figure 17 .
Figure 17.Three-dimensional comparison of the filter inductor before and after optimization.(a) Physical picture of the filter inductor before optimization, (b) 3D picture of the filter inductor after optimization.

Table 1 .
Different output current ripple indexes requiring the value of minimum filter ind corresponding to two strategies.

Table 1 .
Different output current ripple indexes requiring the value of minimum filter inductance corresponding to two strategies.

Table 2 .
The parameters of the main circuit of the test prototype.

Table 2 .
The parameters of the main circuit of the test prototype.