With the emergence of energy shortage and environmental pollution and the increasing demand for electricity and power quality, the traditional AC distribution network faces a series of problems in solving load diversification and reducing energy loss (Boroyevich et al., 2010; Zheng, 2014; Chen, 2017). In the field of electric power, DC distribution using new energy has become the only way for the transformation and upgrading of the traditional manufacturing industry (Tong et al., 2007; Song et al., 2013; Wu et al., 2013). In recent years, China has made great efforts to develop distributed renewable energy and clean energy technology (She et al., 2013). Distributed energy has the problems of scale, dispersion, indirection, and uncertainty (Ortiz, 2010; Bahmani et al., 2016). The DC distribution network can coordinate the contradiction between distributed power and grid access well and maximize the value and benefit of distributed energy (Villar et al., 2008; Villar et al., 2009). At the same time, the DC distribution network is superior to the AC distribution network in voltage grade, control system, and equipment cost and has flexible scheduling function. Therefore, a low-voltage DC power distribution network will be the trend for future development (Heinemann, 2002; Soltau et al., 2014; Zhao et al., 2021).

The topological structure of the three-port DC–DC converter is shown in Figure 1. U _in is connected to 380 V AC and outputs 537 V DC voltage by PFC rectification. U _out is connected to a 375-V distributed energy storage system; R ₀ is connected to a 48 V low-voltage load. The DC bus and distributed energy storage system constitute a capacitor–inductor–inductor–inductor–capacitor (CLLLC) bidirectional DC–DC converter to achieve bidirectional energy flow. The isolation transformer uses a three-winding core structure for ensuring that the voltage supplied by the DC bus adequately meets the requirements of both the distributed energy storage system and low-voltage loads. Furthermore, the topology has the capacity to improve the power density and concurrently diminish the volumetric dimensions of the converter. The bidirectional CLLLC resonator ensures zero voltage on and zero current off of the switching device, further saving energy. The basic parameters of the three-port DC-DC converter and three-winding intermediate frequency transformer are shown in Table 1.

In the topology of the three-port DC–DC converter, the three-winding transformer is the core component of the converter’s energy transmission. The isolation transformer is used for energy transmission and conversion. The specific working mode can be divided into three types, as shown in Figure 2.

Energy transmission mode 1 is the 537-V DC bus to charge mode, power flow from the DC bus side to a 375-V distributed energy storage system, and 48 V low-voltage load, which can be equivalent to a CLLLC bidirectional resonant converter and one-way LLC converter running in parallel; the DC bus port and distributed energy storage port constitute the CLLLC resonant topology of forward operation. The DC bus port and the low-voltage load port form a unidirectional LLC resonant topology. Energy transmission mode 2 is the distributed energy storage feedback DC bus mode. The power flows from the 375 V distributed energy storage side to the 537 V DC bus side, and the energy in distributed energy storage is injected into the grid. In this case, the three-port converter is a CLLLC full-bridge circuit operating in reverse, and the low-voltage 48-V load does not participate in energy transmission. Energy transmission mode 3 is the 375-V distributed energy storage system charging a low-voltage 48-V load, and the power flows from the distributed energy storage side to the low-voltage load side, which can be equivalent to a one-way full-bridge LLC circuit.

There are two resonant frequencies in the converter’s forward operation. The first resonant frequency is generated by the resonance of the front resonant cavity elements L _r1 and C _r1. The second resonant frequency is generated by the resonance between excitation inductor L _m and front resonant cavity elements L _r1 and C _r1, which can be expressed as Equations 1, 2. f r 1 = 1 2 π L r 1 C r 1 , (1) f m = 1 2 π L r 1 + L m C r 1 . (2)

The output voltage is controlled by controlling the switching frequency. According to the different resonant frequencies, they are divided into three resonant working states: under-resonant f _m < f _s < f _r, quasi-resonant f _s = f _m, and over-resonant f _s > f _r.

When the three-port DC–DC converter operates forward, it can be divided into three parts: port 1 is four IGBTs that constitute the inverter unit, port 2 is four IGBTs that constitute the rectifier unit, and port 3 is four diodes that constitute the uncontrolled rectifier unit. C ₁ and C ₂ are filtering capacitors in the forward and reverse operations, respectively, and C ₃ is a filtering capacitor of port 3. L _r1 and C _r1 are the resonant inductor and the resonant capacitor at the input stage of the forefront section, respectively. L _m is the excitation inductance of the transformer. L _r2 and C _r2 are the resonant inductors and capacitors of the later stage, respectively. In order to avoid the influence of some parasitic parameters on the working state of the converter, the converter is assumed to be in stable running state first. The switching device is an ideal type device. The initial energy storage of the inductor and capacitor is 0. The filter capacitor is large enough; the output voltage is the voltage source. The forward operation of the converter can be divided into eight stages, among which the first four stages and the last four stages are completely symmetric. In order to facilitate the description of the working process, the switching tube dead time is increased. This paper only analyzes the converter’s working process under the first four time states. The working waveform under the under-resonant state is shown in Figure 3. As shown in Figure 3, the switching tube dead time is large, which can be more intuitive to observe the working process of the converter, and the actual dead time is far less than the period in the figure.

Stage 1 (t ₀–t ₁): Before t ₀, the resonator is in a resonant state, and the switching tubes S ₂ and S ₃ are closed. The resonant current is continued through S ₁ and S ₄ parallel diodes so that the voltage of the switching tubes S ₁ and S ₄ is reduced to 0. At t ₀, S ₁ and S ₄ are switched on, and ZVS is switched on because the voltage of S ₁ and S ₄ is 0. In the t ₀-t ₁ stage, the direction of the resonator current i _Lr1 decreases gradually, opposite to the reference direction, and changes with the sine rule; the direction of the current i _Lm in the excitation inductor L _m with the common reference direction increases gradually linearly with time. Since i _Lr1 changes faster than i _Lm, energy is transferred from the input side to the output side through the induced current of the medium frequency transformer. Switch tubes Q ₂ and Q ₃ and diodes D ₁ and D ₄ switch on. In this stage, the resonant inductor current i _Lr1 and the excitation inductor current i _Lm change from negative to positive until they are equal at the end of this stage. At stage 1, the front resonant inductor L _r1, resonant capacitor C _r1, the side resonant inductor L _r2, and resonant capacitor C _r1 all participate in the resonant process, while L _m does not participate. This stage is shown in Figure 4A.

Stage 2 (t ₁–t ₂): At time t ₁, switch tubes S ₁ and S ₄ are still on, and the resonant inductor current i _Lr1 is equal to the excitation inductor current i _Lm. The input current of this medium-frequency transformer is 0, and switch tubes at the secondary side will be automatically shut down as the input current is 0 so that the ZCS is turned off and the power reflux problem avoided. This stage is shown in Figure 4B.

Stage 3 (t ₂–t₃): At time t ₂, switch tubes S ₁ and S ₄ are closed and are in the off state when they enter the dead zone. The voltage of switch tubes S ₁ and S ₄ is the input voltage U _in, as shown in Figure 4C.

Stage 4 (t ₃–t ₄): At time t ₃, switch tubes S ₂ and S ₃ have zero potential, the resonant current follows the current along the parallel diodes, and the output voltage of the front resonator is U _in. At this time, switch tubes S ₂ and S ₃ can realize ZVS switch-off and reasonably design the dead time to ensure that switch tubes are ZVS on and ZCS off. At time t ₄, switch tubes S ₂ and S ₃ switch on, and at the first half cycle of time t ₁–t ₄, switch tubes S ₂ and S ₃ switch off, as shown in Figure 4D.

Since the input side switch tubes S ₁–S ₄ and output side switch tubes Q ₁–Q ₄ adopt the same duty cycle control mode, which in the t ₀–t ₄ mode and t ₄–t ₈ mode are completely symmetric when the three-port converter is running forward, this paper will not describe it in detail. Theoretically, in order to improve the efficiency of the resonant converter and reduce the switching tube loss, the converter needs to operate in the under-resonant region because of the over-resonant region problem. The parametric design of a single-directional LLC is easy to implement. Although the structure of port 1 and port 2 of the bidirectional three-port resonant converter is symmetric and the work principle is the same, the under-resonant region of port 1 and the resonant region of port 2 will overlap when port 2 runs in reverse; when port 1 forward operates in the full voltage range of the under-resonant region, port 2 reverse operates in the over-resonant region. When port 1 and port 2 operate in the same voltage range, it is almost impossible to achieve under-resonance in both positive and negative operation modes. The resonant frequency in reverse operation can be optimized by the reasonable design of resonant cavity operating parameters so as to reduce the switching tube loss caused by over-resonant operation.

The three-port DC–DC converter requires different power transmission branches in different operation modes. A simplified equivalent circuit model is adopted to study the power flow relationship between the three ports of the converter. The influence of leakage inductance and coupling capacitance, stray inductance of the circuit, and filter capacitance of the medium-frequency transformer is ignored in the equivalent model. The equivalent model is shown in Figure 5.

In Figure 5B, L′_r2 and C′_r2 are the resonant inductance and resonant capacitor converted from the secondary side to the primary side of the converter, respectively. U ₁ is the input square wave voltage at the primary side of the resonator. U ₂ and U ₃ are the output square wave voltages of the secondary side of the converter. U′₂ and U′₃ are from the secondary side converted to the primary side equivalent square wave voltages of the converter. The voltage parameters on the primary and secondary sides and resonant inductance and capacitance of the resonator after conversion are shown in Equations 3, 4. U 2 ′ = U 2 n 1 / n 2 U 3 ′ = U 3 n 1 / n 3 , (3) L r 2 ′ = L r 2 n 1 / n 2 2 C r 2 ′ = C r 2 n 1 / n 2 2 . (4)

We suppose that the equivalent parallel point voltage of the three-port medium-frequency transformer is U ₀. After the AC voltage of the three-port transformer transmits power through the respective ports, a common voltage U ₀ can be formed in the medium-frequency transformer equivalent model. The resonant inductance of the resonator is much larger than the excitation inductance of the medium-frequency transformer. In order to expediently analyze, the role of the transformer excitation inductance is ignored. The △-type equivalent circuit obtained by the Y-△ transformation of the Y-type equivalent circuit in Figure 5B is shown in Figure 6.

In Figure 6, L ₁₂, L ₁₃, and L ₃₂ are energy transfer inductors between ports. According to the Y-△ transformation equation, the inductance expression of the △-type equivalent circuit can be written as Equation 5. L 12 = L r 1 + L r 2 ′ L 13 = L r 1 L 23 = L r 2 ′ . (5)

The energy transfer between port 1 and port 2 is only related to the resonant inductors L _r1 and L _r2 of port 1 and port 2 and resonant capacitors C _r1 and C _r2 from Figure 5 but has no coupling relationship with port 3. Similarly, when charging the low-voltage load of port 3, ports 1 and 2 are only related to the resonant device of the port itself, and there is no coupling relationship between ports. Therefore, the three-port DC–DC converter can be equivalent to the simplified circuit model shown in Figure 7.

The energy transfer between the ports of the three-port converter is based on the ideal state, and the leakage inductance of the medium frequency transformer will generate cyclic power between the ports in the actual operation process, which can only be eliminated by modulation technology. Port 1 and port 2 can eliminate the cyclic power by the modulation technology. In contrast, port 3 can reduce the cyclic power of the converter only by minimizing the primary-side leakage inductance of the medium-frequency transformer as port 3 is the full-bridge uncontrolled rectifier circuit. The CLLLC resonant converter is mainly divided into three parts, the inverter side, the resonator side, and the rectifier side, as shown in Figure 8.

The converter-simplified equivalent circuit can be considered a bidirectional CLLLC converter and a unidirectional LLC converter running side by side. The forward operation principle of the bidirectional CLLLC converter is the same as that of the LLC converter. This paper considers the forward operation of the CLLLC converter as an example to analyze the frequency characteristics and voltage gain characteristics between port 1 and port 2 of the three-port converter. The resonant converter usually works near the resonant frequency point. The first harmonic analysis (FHA) method is used to decompose the square wave voltage input to the resonator by Fourier decomposition. The harmonic component is ignored. Assume that only the fundamental component completes the energy transmission of the resonant converter.

The drive signals of switch tubes S ₁ and S ₄ on the inverter side are complementary to the drive signals of switch tubes S ₂ and S ₃, and the switch tubes are conducted alternately. The input voltage at both ends of the resonator is the square wave voltage from U _in to U _in. U _AB varies with the switching tube period, as shown in Equation 6. The resonator, a filter network with frequency-selective properties, weakens the higher harmonics. The resonator input voltage U _AB mainly depends on the input voltage U _in and the fundamental component of input current i _r1 of the converter. u AB t = U in   0 < t < T s 2 − U in T s 2 < t < T s , (6) where U _in is the input voltage of the converter; T _s is the switching cycle.

Taking Fourier transform of Equation 6, Equation 7 can be obtained as follows. u AB t = 4 U in π ∑ n = 1 , 3 , 5 … 1 n sin 2 π n f s t . (7)

The equivalent resistance R _eq at the input of the resonator is expressed as Equation 8. R eq = U p 1 I p 1 = 8 n 2 π 2 R 0 . (8)

The simplified equivalent model of the converter after fundamental equivalent analysis is shown in Figure 9.

The main circuit of port 1 and port 2 of the three-port DC–DC converter is simplified into a purely resistive load resonant network driven by a sinusoidal fundamental voltage by the fundamental wave analysis method. The resonant frequency characteristics and voltage gain characteristics can be solved by the fundamental equivalent circuit based on port 1 and port 2.

The above analysis shows that the voltage gain curve of the converter contains functions of ω _n, k, Q, g, and h. In the design process of the resonator, the voltage gain of the converter running in reverse is taken as h = g = 1, which means that the resonator is completely symmetric. In the design process, ω _n, Q, and k are the key parameters affecting the performance of the converter. ω _n is selected as the control variable, which means that the voltage gain curve remains monotonic within the operating frequency range of the demand and meets the voltage gain requirements under all load conditions in the forward and backward operation modes. In addition, the ZVS condition should be satisfied. The resonator elements are determined by optimizing the quality factor Q and the resonant inductance ratio k.

The three-port converter high-voltage side input voltage is 537 V, and the voltage fluctuation range is 525–550 V; the medium-voltage side rated output voltage is 375 V, and the voltage fluctuation range is 350–400 V; the medium-voltage side output power is 18 kW, and the working frequency is 2 kHz. After the above analysis, different values of parameters k and Q were found to affect the voltage gain of the converter. In the ideal case, the transformer ratio is determined. The DC voltage gain is set as 1; when the converter works at the quasi-resonant frequency normalized resonant frequency, ω _n = 1, and the transformer theoretical ratio is determined as shown in Equation 23. n = U in U out 1 . (23)

The voltage gain values of the highest and lowest input voltages in forward operation are M _1max and M _1min, respectively as shown in Equation 24. M 1 ⁡ max = n U out 1 _ ⁡ max U in _ ⁡ min M 1 ⁡ min = n U out 1 _ ⁡ min U in _ ⁡ max . (24)

The voltage gain values of the secondary-side highest and lowest input voltages in reverse operation are M _2max and M _2min, respectively as shown in Equation 25. M 2 ⁡ max = U in _ ⁡ max n U out 1 _ ⁡ min M 2 ⁡ min = U in _ ⁡ min n U out 1 _ ⁡ max . (25)

The larger value of the maximum voltage gain and the smaller value of the minimum voltage gain are taken for forward and reverse operation modes. First, the impedance characteristics of the converter are analyzed. When the converter has no load, Q = 0, and the converter gain function taking the maximum operating frequency can be expressed as Equation 26. M ω n _ ⁡ max = 1 1 + 1 k − 1 k ω n _ ⁡ max 2 . (26)

When the converter takes the minimum voltage gain M _min, its value is greater than the no-load voltage gain M _min > M _{n_max}. The restriction condition of parameter k can be obtained from Equation 27. k < M min 1 − M min ⋅ ω n _ ⁡ max 2 ω n _ ⁡ max 2 . (27)

Assume that the maximum operating frequency of the converter is infinite and the parameter k is the maximum value as shown in Equation 28. k < M min 1 − M min . (28)

According to the parameter k limiting conditions, minimum voltage gain M _min, ω _nmax = 2πf _max/2πf _r = f _nmax, and normalized quasi-resonant frequency f _nmax = f _max/f _r, the maximum operating frequency of the converter can be determined as shown in Equation 29. f nmax = 1 1 + k 1 − 1 M min . (29)

According to Equation 28, the maximum k value is 10 when the converter has no load. When k = 10, the frequency range of the converter is too wide, which is inconsistent with the actual operation of the converter. Considering the forward and backward operation modes of the converter, the maximum normalized resonant frequency f _nmax = 1.25 is taken from Equation 29, and the k value is 3.68.

The condition of the converter to realize ZVS is the switching tube current hysteresis voltage, which is the equivalent input impedance of the inductive resonator. According to Figure 9, the input impedance of the simplified model of the converter fundamental wave can be expressed as Equation 30. Z in ω n = Z 1 + Z m // Z 2 + R eq . (30)

According to the characteristic impedance Z _r and inductance coefficient k, the normalized parameter is g = h = 1; the normalized input impedance Z _n = Z _in/Z _r can be expressed as Z n ω n = Q k ω n 6 − j ω n − k + 1 ω n 3 ω n 4 + Q 2 ω n − k + 1 ω n 3 2 + Q 2 2 k + 1 ω n 2 − 1 ω n 2 − 1 + ω n 2 ω n 4 + Q 2 ω n − k + 1 ω n 3 2 . (31)

The condition for the converter to realize ZVS is the switching tube current hysteresis voltage, and the equivalent input impedance is the sensitivity. When the converter is just in the ZVS region, it means that the equivalent input impedance is purely resistive, the phase of the current and voltage is equal, and the imaginary part of Equation 31 is 0, which means that the equivalent input impedance is the dividing line of the inductive capacitance. Im Z n ω n = k + 1 ω n 2 − 1 ω n 3 + Q 2 1 − k + 1 ω n 2 2 + Q 2 2 k + 1 ω n 2 − 1 ω n 2 − 1 + ω n 2 ω n 3 + Q 2 1 − k + 1 ω n 2 2 . (32)

According to Equation 32, when the imaginary part of the normalized impedance is 0, two constraints Equations 33, 34 are obtained. In order to realize the converter ZVS and the maximum gain M _max, the Q-value selection and the minimum operating frequency f _min are discussed. k + 1 ω n 2 = 1 , (33) Q 2 2 k + 1 ω n 2 − 1 ω n 2 − 1 + ω n 2 = 0 . (34)

If Equation 33 is established, it can be concluded that when the equivalent impedance is purely resistive, ω n = 1 / k + 1 , the equivalent input impedance of the converter is purely resistive so the operating frequency range of the converter is limited to 1 / k + 1 < ω n < 1 .

If Equation 34 is established, the expression of quality factor Q _max can be obtained: Q ω n max = ω n 2 1 − ω n 2 2 k + 1 ω n 2 − 1 . (35)

Substituting Equation 35 into the voltage gain expression Equation 21 yields the minimum normalized frequency at the maximum voltage gain as shown in Equation 36: f nmin = 1 1 + k 1 − 1 M max 2 , (36)

For k = 3.5, the relationship between the maximum and minimum gain of voltage gain and the converter is shown in Figure 12.

As the normalized equivalent impedance is inductive in region 1, the AC square wave voltage across the converter resonator leads a resonant current so that power switches reach ZVS. In region 2, where the normalized equivalent impedance is inductive as well, the switch tube reaches ZVS, and rectifier diodes on the rectifier side reach ZCS. Contrastingly, in region 3, characterized by capacitive normalized equivalent impedance, the switch tube fails to achieve ZVS, and it can be observed that the voltage gain has a large variation within this region. Therefore, different Q-values should be avoided in region 3 when designing the converter resonator.

According to Equation 33, the normalized frequency of the converter is limited to the range 1 / k + 1 < ω n < 1 . According to the ZVS realization of the converter, the normalized characteristic impedance is inductive. In this case, the quality factor Q is limited to Q 2 ω n < ω n 2 1 − ω n 2 2 k + 1 ω n 2 − 1 . (37)

Let F(ω _n) = Q ²(ω _n) and find the derivative. The derivative function is equal to 0. The operating frequency ω ₀ is found within the operating frequency range 1 / k + 1 < ω n < 1 , and quality factor Q takes the extreme value. F ω n = ω n 2 1 − ω n 2 2 k + 1 ω n 2 − 1 F ′ ω n = 2 ω n 2 k + 1 ω n 4 − 1 1 − ω n 2 2 2 k + 1 ω n 2 − 1 2 . (38)

According to Equation 38, when ω 0 = 1 / 2 k + 1 4 , Q _max takes the extreme value, and the restriction condition of quality factor Q _max can be obtained by substituting it into Equation 37 as shown in Equation 39. Q max < 1 2 k + 1 − 1 . (39)

The converter operating frequency range is 1 / 2 k + 1 4 < ω n < 1 . A reasonable Q-value is selected, and it is verified that when ω 0 = 1 / 2 k + 1 4 , the voltage gain is greater than M _max; if not, the conditions are met and the Q-value is reduced.

According to Equation 23, the transformer ratio is 1.432. The forward and reverse operation voltage gains are M _1max = 1.091, M _1min = 0.0911, M _2max = 1.097, and M _2min = 0.0917.

After comprehensive consideration, the parameter is k = 3.5, and the maximum quality factor Q is calculated as 0.546. When Q = 0.4, the voltage gain is 1.249, which meets the demand.

Load resistance R ₀ and equivalent resistance R _eq are calculated as follows: R 0 = U out 1 2 P out 1 R eq = n 2 8 π 2 R 0 . (40)

According to Equation 40, the load resistance and equivalent resistance are 7.812 Ω and 12.99 Ω, respectively. The maximum and minimum resonant frequencies of the converter during rated operation are determined as follows: f min = f r 1 + k 1 − 1 M max 2 f max = f r 1 + k 1 − 1 M min . (41)

Equation 41 shows that the maximum resonant frequency of the converter is 1.585 kHz and the minimum resonant frequency is 2.465 kHz. Based on the quality factor, the resonant inductance and the resonant capacitance of the primary side of the resonator can be calculated as shown in Equations 42, 43. Q = Z r Z eq = L r 1 C r 1 R eq = 2 π f r 1 L r 1 R eq , (42) L r 1 = Q R eq 2 π f r 1 C r 1 = 1 2 π f r 1 R eq Q . (43)

The resonant inductance and capacitance of the resonator’s secondary side are calculated as Equation 44. L r 2 = L r 1 / n 2 C r 2 = n 2 C r 1 . (44)

The resonator element is calculated as L _r1 = 0.6 mH, C _r1 = 11 μF, L _r2 = 0.29 mH, and C _r2 = 22 μF.

Figure 13 shows the corresponding relationship between the voltage gain curve and normalized resonant frequency during forward and reverse operation modes. From Figure 13, the working frequencies of the forward and reverse running processes can be determined.

After discussing the value of parameters k and Q, from Figure 13, when the converter runs in the positive and negative directions, the voltage gain in the range of the under-resonant operating frequency meets the requirements.

In order to verify the rationality of theoretical analysis and parameter design, PSIM simulation software is used to simulate the forward operation of the three-port DC–DC converter under ω _n = 0.9 and different load conditions. Figure 14A shows the driving waveforms of the converter switch S ₁ and S ₃, and Figure 14B shows the waveforms of the input voltage U _in of the resonator and the voltage U _Lm of the excitation inductor.

Figure 15 shows the current waveforms of excitation inductors L _m and the original and secondary-side resonant inductors L _r1 and L _r2 under different load conditions when ω _n = 0.9. Figure 15 shows that the resonant currents i _Lr1 and i _Lr2 lag behind the excitation current i _Lm, and the switch tube realizes ZVS.

Figure 16 shows the waveforms of the input current i _pri and output current i _sec of the resonator under light-load and full-load conditions. When the load increases, the original and secondary side currents meet the power transmission requirements.

Figure 17 illustrates the output current waveform of port 2 in the three-port converter under both light-load and full-load conditions in a steady state. Figure 18 shows the resonant capacitor current waveforms on the input side and output side of the resonator under light-load and full-load conditions. The figure shows that the voltage and current of the three-port DC/DC converter can meet the power transmission requirements under both light-load and full-load conditions.

Figure 19 shows that the fixed port 1 input voltage is 537 V, and the output voltage of port 2 and port 3 is stable. U _out1 and U _out2 are stable at 375 and 48 V, respectively, when the converter runs forward.

The simulation study of the forward operation of the converter under different loads shows that the voltage and current waveforms of the resonator components meet the power output requirements, and the parameters of the resonator components are reasonable. In order to further verify the rationality of the resonator design, simulation research was conducted on the reverse operation of the converter. The fixed reverse input voltage was 375 V, and the resonator current and voltage waves during the reverse operation of the converter are shown in Figure 20.

The voltage and the current values of the resonator elements are stable in the forward and reverse operation modes, and the converter can meet the power output requirements under different loads.

Figure 21 shows the curve of DC voltage gain G _dc with normalized frequency during the forward and reverse operation modes of the converter.

The simulation results given in Figure 21 show that the forward and reverse operation modes of the converter reach the calculated value of voltage gain. The simulation of the forward and reverse operation modes of the converter verified that the resonant cavity parameters of the converter meet the design requirements under the premise of voltage gain and power transmission and realize ZVS in the under resonant range. ZVS implementation is shown in Figure 22.

On account of the above theoretical analysis and simulation investigation, a 20-kW three-port DC–DC converter experimental platform is established, as shown in Figure 23. TMS320F28335 is selected as the main control chip to validate the rationality of this design scheme.

Figure 24 shows the driving output waveform of the converter switch S ₁, where V _{gs_S1} and V _{ds_S1} are the gate voltage and drain voltage of the switch S ₁, respectively. The figure shows that the switch tube implements ZVS.

The output voltage waveforms of the medium- and low-voltage sides of the three-port DC–DC converter are shown in Supplementary Figure S1. The figure shows the stability of the output voltages at 375 and 48 V, affirming the validity of the proposed scheme.

Addressing the shortage of distributed power supply and the DC distribution network in domestic and abroad situations, this paper proposes a three-port DC-DC converter topology based on a low-voltage DC distribution network, which can effectively combine distributed energy, low-voltage load, and the DC bus. This research analyzes different energy transfer modes of the three-port DC–DC converter, and decoupling analysis is carried out on the main circuit topology structure. The working process of the equivalent model of the three-port DC–DC converter in the first half cycle of four time stages is analyzed in detail when the energy flow is forward. Then, the characteristics of the converter are studied. Based on the fundamental equivalent analysis method, the simplified equivalent model of the converter is established and the resonant frequency characteristics and voltage gain characteristics of the converter are analyzed. According to the different voltage gains, the influence of different values of the converter parameters k and Q on the gain characteristics of the converter is analyzed, and the design of the resonator is completed by choosing the parameters k and Q reasonably. Based on the theoretical derivation and using PSIM simulation software, the forward and reverse operation modes of the converter under different load conditions are simulated and analyzed. The experimental platform of a 20-kW three-port DC–DC converter is built, and experimental investigations are conducted under varied load conditions. The experimental results show that the converter can achieve stable power output under different working conditions. The use of ultra-thin silicon steel sheets in high-power intermediate-frequency applications can effectively reduce the total loss of intermediate-frequency transformers, thereby providing additional confirmation regarding the correctness and feasibility of the proposed scheme for a high-power medium-frequency converter with ultra-thin silicon steel sheets.