Multi-resonant switched capacitor efficient cooperative operation method suitable for battery active equalization

By establishing a zero-voltage soft-switching realization condition model for a single-module resonant unit, identifying multi-module current paths, and constructing an equivalent circuit model, the soft-switching problem of multi-coupling loop switch-multiplexed resonant switched capacitor topology is solved, achieving efficient and stable operating parameter boundaries and improving the efficiency and reliability of the battery active balancing system.

CN121906992APending Publication Date: 2026-04-21SHANGHAI JIAOTONG UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
SHANGHAI JIAOTONG UNIV
Filing Date
2025-12-24
Publication Date
2026-04-21

AI Technical Summary

Technical Problem

Existing multi-coupled loop switch-multiplexed multi-resonant switched capacitor topologies lack systematic analysis and design methods for soft switching, resulting in complex amplitude and direction of instantaneous current flowing through the switching transistors, making it difficult to achieve efficient operation of global soft switching.

Method used

By establishing a zero-voltage soft-switching implementation condition model for a single-module resonant unit, identifying the current paths of the top, middle, and bottom half-bridges, constructing an equivalent circuit model, and drawing the operating parameter boundaries, soft switching is ensured to be achieved in all operating modes.

Benefits of technology

This improves the operating efficiency of the switch-multiplexed multiresonant switched capacitor topology, reduces switching losses, and enhances the reliability and safety of the system.

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Abstract

The invention provides a multi-resonant switched capacitor efficient cooperative operation method suitable for battery active equalization, and the method comprises the steps: building a zero-voltage soft switching realization condition model of a single-module resonant unit, and determining the amplitude constraint and direction constraint of a soft switching current needed by a switching tube for realizing zero-voltage switching; based on topology, identifying current paths of the half bridges located at the top layer, the middle layer and the bottom layer in the soft switching transient process, and determining a mathematical relationship between the soft switching current of each layer of half bridge and the current of each resonant cavity; respectively establishing equivalent circuit models at switching moments for the top-layer half-bridge, the middle-layer half-bridge and the bottom-layer half-bridge, and solving to obtain each initial current value of the corresponding junction capacitor voltage at the switching moments; and substituting each initial current value obtained by solving into the established constraint condition, and drawing an operation parameter boundary of the topology capable of realizing soft switching in all working modes. According to the invention, by determining the operation boundaries of all half-bridge soft switches of the multi-resonant switched capacitor structure, the switching loss is reduced, and the operation efficiency is improved.
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Description

Technical Field

[0001] This application relates to the field of power electronics technology, specifically to a method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing. Background Technology

[0002] As battery energy storage systems develop towards higher voltage and larger capacity, higher demands are placed on the efficiency and power density of the energy equalization unit in the system. Resonant switched-capacitor converters have become one of the ideal choices for high-efficiency battery equalizers. In particular, the switch-multiplexed multiresonant switched-capacitor topology, through structural reuse, shows great potential in achieving efficient energy transfer between modules.

[0003] See attached document Figure 7 The diagram shows a conventional switch-multiplexed multiresonant switched capacitor structure. This structure connects half-bridges in parallel between each battery cell, enabling power transfer between adjacent cells. n battery cells require n half-bridges, totaling 2n switching devices: n-1 Lr and n-1 Cr.

[0004] However, this topology faces a significant challenge in realizing its soft-switching advantages, a challenge that single-module resonant converters do not possess. Because the topology contains multiple coupled resonant circuits, the resonant currents of each circuit are superimposed, resulting in complex time-varying characteristics in the amplitude and direction of the instantaneous current flowing through each switch.

[0005] As shown in the literature, such as the article "Improved Phase Shift Control for SiC-MOSFET Based Resonant Switched-Capacitor Converter With Parasitics Consideration" (IEEE Transactions on Industry Applications, 2020) published by X. Yang et al., the soft-switching principle of the resonant switched capacitor unit is explained.

[0006] For example, the soft switching of the decoupled multi-resonant switched capacitor topology proposed in the literature "A SiC modules based resonant switched capacitor converter" (China Electrotechnical Society, 2020) realizes the soft switching of the decoupled multi-resonant switched capacitor topology. However, this multi-resonant switched capacitor structure is essentially a combination of multiple independent resonant switched capacitor units, and its volume and active devices are about twice that of the switch multiplexing type.

[0007] Existing technologies lack systematic soft-switching analysis and design methods for multi-coupled loop topologies. Therefore, there is an urgent need for a method that can accurately analyze the soft-switching states of each switch in a multi-coupled loop and design a method that ensures a wide range of operating boundaries for global soft switching. Summary of the Invention

[0008] In view of the deficiencies in the prior art, the purpose of this application is to provide a method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing.

[0009] A first aspect of this application provides a method for efficient cooperative operation of multi-resonant switched capacitors suitable for active battery balancing. The method is based on a switch-multiplexed multi-resonant switched capacitor topology and includes: Taking the single-module resonant unit in the topology as the research object, a zero-voltage soft-switching realization condition model of the single-module resonant unit is established, and the amplitude and direction constraints of the soft-switching current required for the switching transistor to achieve zero-voltage turn-on are determined. Based on the multi-module structure of the topology, the current paths of the half-bridges located at the top, middle and bottom layers during the soft-switching transient process are identified, and the mathematical relationship between the soft-switching current of each half-bridge and the current of each resonant cavity is determined. For the top, middle and bottom half-bridges, equivalent circuit models are established at the switching time, and the changes of the corresponding junction capacitance voltage at the switching time are obtained by solving. Substitute the initial current values ​​obtained from the solution into the established constraints to plot the operating parameter boundaries of the topology that enable soft switching in all operating modes.

[0010] Optionally, the establishment of the zero-voltage soft-switching implementation condition model for the single-module resonant unit includes: The entire process of the switch turn-off delay, junction capacitance charging and discharging, and body diode freewheeling in the single-module resonant unit is analyzed. The directional constraints that the soft-switching current must satisfy during the charging and discharging phase of the junction capacitor are derived so that the voltage of the junction capacitor can be discharged to zero within the dead time. The amplitude constraint of the soft-switching current is derived so that the turn-off loss of the switching transistor can be optimized while satisfying the directional constraint.

[0011] Optionally, the determination criterion for the current direction constraint is: the discharge amount of the junction capacitance during the dead time is not less than the difference between the initial voltage of the junction capacitance and the forward conduction voltage drop of the body diode; The current amplitude constraint is determined based on the following: during the turn-off process of the switch, the voltage rise across the switch does not exceed the rated voltage of the corresponding parallel battery cell.

[0012] Optionally, the soft-switching current of the single-module resonant unit needs to satisfy: ; In the formula, i rzvs,12 This refers to the resonant circuit current. The lower current threshold for zero-voltage soft switching; The upper current limit threshold for zero-voltage soft switching; The dead time is set; This is the minimum dead time; This represents the maximum dead time.

[0013] Optionally, identifying the current paths of the half-bridge located at the top, middle, and bottom layers during soft-switching transients includes: For the top half-bridge, it is determined that the soft-switching current originates from only one resonant cavity, and the soft-switching current value of the top half-bridge depends on a shift ratio; For the intermediate layer half-bridge, it is determined that the soft-switching current originates from two adjacent resonant cavities simultaneously, and the soft-switching current value of the intermediate layer half-bridge depends on the combination of the two shift ratios. For the bottom half-bridge, it is determined that the soft-switching current also originates from only one resonant cavity, and the soft-switching current value of the bottom half-bridge depends on a shift ratio. The resonant cavity of the top half-bridge is the resonant cavity between the first battery and the adjacent battery; the resonant cavity of the bottom half-bridge is the resonant cavity between the last battery and the adjacent battery; the current path of the top half-bridge is opposite to the circuit path of the bottom half-bridge.

[0014] Optionally, in the case of the top half-bridge and the bottom half-bridge, the soft-switching current is determined by the polarity of the shift ratio corresponding to the top half-bridge and the bottom half-bridge, respectively, to determine that the soft-switching current obtains current from a resonant cavity adjacent to the top half-bridge and the bottom half-bridge; Specifically, the soft-switching current of the top half-bridge is positively correlated with the polarity of the shift phase; the soft-switching current of the bottom half-bridge is negatively correlated with the polarity of the shift phase.

[0015] Optionally, in the intermediate layer half-bridge configuration, the intermediate layer half-bridge is powered by two adjacent resonant cavities. The value of the soft-switching current needs to take into account the shift ratio of the two adjacent resonant units and is determined by the difference in the shift ratio of the two adjacent resonant units.

[0016] Optionally, the equivalent circuit models established at the switching moments for the top, middle, and bottom half-bridges respectively include: For both the top half-bridge and the bottom half-bridge, an equivalent circuit powered by a single resonant cavity is used to establish an equivalent circuit model under switching transients. For the intermediate layer half-bridge, an equivalent circuit with parallel power supply of dual resonant cavities is used to establish an equivalent circuit model under switching transients.

[0017] Optionally, for the top half-bridge and the bottom half-bridge, the initial values ​​of the single resonant cavity at the switching moment are solved by circuit analysis; For the intermediate layer half-bridge, the initial values ​​of the currents in the two adjacent resonant cavities at the switching moment are solved by circuit analysis and then algebraically added together.

[0018] Optionally, the step of drawing the operating parameter boundaries of the topology to achieve soft switching in all operating modes includes: Based on the amplitude constraints and constraint conditions of the soft switches of the half-bridges at different positions, a system of multivariable inequalities is established. Solving the system of multivariable inequalities yields the ranges of the shift ratio, resonance parameter, and dead interval. The operating parameter boundaries of the soft-opening transistor are plotted using the ranges of the shift ratio, resonance parameter, and dead interval.

[0019] This application provides a method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing. It adopts a hierarchical modeling and precise mathematical constraints based on the topology of a switch-multiplexed multi-resonant switched capacitor. By establishing a single-module zero-voltage soft-switching realization condition model, the soft-switching current constraints are clarified. The current paths of the half-bridge in each layer of the multi-module are identified and their relationship with the resonant cavity current is determined. An equivalent circuit model at the switching moment is established to solve the junction capacitor voltage change. Finally, the operating parameter boundaries of the topology to achieve soft switching in all operating modes are plotted, providing a precise design basis and reliable parameter range for the efficient and stable operation of soft switching.

[0020] Other technical effects resulting from the additional features will be further illustrated in the corresponding embodiments. Attached Figure Description

[0021] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating an efficient collaborative operation method for multi-resonant switched capacitors suitable for active battery balancing, according to an exemplary embodiment. Figure 2 This is a schematic diagram of the structure of an active balancing system for a 4-cell battery pack connected in series, according to an exemplary embodiment. Figure 3 This is a structural diagram of an RSCC cell according to an exemplary embodiment; Figure 4 This is a schematic diagram illustrating a soft-switching implementation of an RSCC unit according to an exemplary embodiment; Figure 5 This is a schematic diagram illustrating a multi-module unit soft-switching implementation according to an exemplary embodiment; Figure 6 This is a schematic diagram illustrating the implementation of soft switching at all positions of a 4-battery pack according to an exemplary embodiment; Figure 7 This is a topology diagram of a switch-multiplexed resonant switched capacitor according to an exemplary embodiment. Detailed Implementation

[0022] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application, and these all fall within the protection scope of the present application. Parts not described in detail in the following embodiments can be implemented using existing technology.

[0023] In existing technologies, due to the presence of multiple mutually coupled resonant circuits in the topology, the resonant currents of each circuit are superimposed, resulting in complex time-varying characteristics in the amplitude and direction of the instantaneous current flowing through each switch. Based on the above problems, this application provides a method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing, to solve the aforementioned issues.

[0024] This application proposes a soft-switching characteristic analysis and design method, which can determine the operating boundaries of all half-bridge soft switching in a switch-multiplexed multi-resonant switched-capacitor structure by refining the soft-switching mechanism analysis of the half-bridges at different positions of the series multi-module half-bridges, thereby reducing switching losses and improving the efficiency of its operation.

[0025] Reference Figure 1 As shown in one embodiment of this application, a method for efficient cooperative operation of multi-resonant switched capacitors suitable for active battery balancing is provided. The method is based on a switch-multiplexed multi-resonant switched capacitor topology, focusing on a single-module resonant unit within the topology, and includes: S1. Establish a zero-voltage soft-switching realization condition model for a single-module resonant unit, and determine the amplitude and direction constraints of the soft-switching current required for the switching transistor to achieve zero-voltage turn-on. S2. Based on the topology-based multi-module structure, identify the current path of the half-bridge located at the top, middle and bottom layers during the soft-switching transient process, and determine the mathematical relationship between the soft-switching current of each half-bridge and the current of each resonant cavity. S3. For the top, middle and bottom half-bridges, establish equivalent circuit models at the switching time and solve for the changes in the corresponding junction capacitance voltage at the switching time. S4. Substitute the initial current values ​​obtained from the solution into the established constraints, and draw the operating parameter boundaries of the topology that can achieve soft switching in all operating modes.

[0026] Specifically, we will first take the single-module resonant unit in a switch-multiplexed multiresonant switched-capacitor topology as the object, such as... Figure 7 In the existing switch-multiplexed multi-resonant switched capacitor topology, a zero-voltage soft-switching condition model is established for the single-module resonant unit, determining the amplitude and direction constraints of the soft-switching current required for zero-voltage turn-on of the switching transistor. Next, based on the multi-module structure of the topology, the current paths of the top, middle, and bottom half-bridges during the soft-switching transient process are identified, and the mathematical relationship between the soft-switching current of each half-bridge and the current of each resonant cavity is determined. Then, for different half-bridges, equivalent circuit models at the switching moment are constructed, and the changes in the corresponding junction capacitance voltage at the switching moment are solved. Finally, the solved initial current values ​​are substituted into the constraint conditions to plot the operating parameter boundaries that enable soft switching in all operating modes of the topology.

[0027] The embodiments described above in this application establish a zero-voltage soft-switching condition model for a single-module resonant unit, providing precise current constraints for the switching transistor to achieve zero-voltage turn-on. By identifying the current paths of different half-bridge layers and determining the mathematical relationships, the distribution and correlation of current under the multi-module structure are explained. An equivalent circuit model is constructed to solve for the junction capacitor voltage change, which can determine the voltage change at the switching moment. Finally, the operating parameter boundaries are plotted, providing design guidance for the multi-resonant switched capacitor structure to achieve soft switching in all operating modes, improving the efficiency and reliability of the circuit, and reducing switching losses.

[0028] Among them, a basic resonant switched capacitor unit in a multi-module system is taken as the research object, such as Figure 2 The illustrated active balancing system for four battery packs connected in series includes a switching transistor. S 1 -S 4. Battery B 1 -B 2. Resonant inductor L r and resonant capacitor C r A detailed analysis of its operation within one switching cycle (using...) S 1. Turn off S Taking the soft-switching transient process (taking the turn-on time as an example) as an example, an accurate mathematical model is established. Finally, a unified criterion is derived for the soft-switching current of this single module to achieve soft switching.

[0029] The specific implementation of this application is as follows: the prototype of the battery pack series battery cluster energy storage system includes: a battery pack, a DC-side filter capacitor, a DC-side parallel half-bridge, and a half-bridge AC resonant cavity.

[0030] The 4-cell battery pack has a rated voltage of 40V and a rated capacity of 314Ah, defined as follows: B 1, B 2, B 3, B Four batteries are connected in series to form a four-cell battery pack, and their voltages are respectively U 1, U 2, U 3, U 4.

[0031] B 1, B 2, B 3, B 4. Connect a filter capacitor in parallel. C It has a current rating of 10mF and its main function is to filter out high-frequency components on the current side.

[0032] B 1, B 2, B 3, B 4. Connect a pair of half-bridges in parallel, and number them as follows: S 1, S 2, S 3, S 4, S 5, S 6, S 7, S 8. The upper and lower transistors of each half-bridge module are complementary and conduct with a 50% duty cycle. At the same time, the upper transistors of two adjacent half-bridges are phase-shifted by a time difference. D 12 · T s , D 23 · T s , D 34 · T s . T s It is 10us.

[0033] The four half-bridge AC sides are each connected by three resonant cavities, and each resonant cavity has... L r , C r Its composition is as follows: 20uH and 10uF.

[0034] in, CS1 yes S Parasitic capacitance on 1, C S2 yes S Parasitic capacitance on 2. Here, u CS1 yes C S1 voltage, u CS2 yes C S2 The voltage; i CS1 yes C S1 Instantaneous current, i CS2 yes C S2 The instantaneous current; i rzvs,12 From S 1 and S The current flowing out of the AC port of the half-bridge composed of 2 components; t off_id Represents the IGBT turn-off delay time. t f It is the IGBT current fall time, and t off_uc express u CS1 The rise time u CS2 The descent time. In the following analysis, it is assumed that... C r Much larger C S1 and C S2 ,and C S1 equal C S2 And the current in t The worst-case scenario of a complete transfer at moment 1.

[0035] In some specific embodiments of this application, for establishing a zero-voltage soft-switching realization condition model for a single-module resonant unit, the amplitude and direction constraints of the soft-switching current required for the switching transistor to achieve zero-voltage turn-on are determined, including: Taking the single-module resonant unit in the topology as the research object, we analyze the entire process of the switch turn-off delay, junction capacitance charging and discharging, and body diode freewheeling in the single-module resonant unit. The directional constraints that the soft-switching current must satisfy during the junction capacitance charging and discharging phase are derived so that the junction capacitance voltage can be discharged to zero within the dead time. The amplitude constraint of the soft-switching current is derived to optimize the turn-off loss of the switching transistor while satisfying the directional constraint.

[0036] Specifically, this study focuses on a single-module resonant unit (including a switching transistor, adjacent battery cells, resonant inductor, and capacitor) in a switch-multiplexed multi-resonant switched capacitor topology. First, it analyzes the dynamic change in current transfer from the channel to the junction capacitance after the switching transistor receives the turn-off signal during the turn-off delay phase. Then, it tracks the rise and fall of the junction capacitance voltage with current flow during the junction capacitance charging and discharging phase. Finally, it derives the direction and amplitude constraints of the soft-switching current during the body diode freewheeling phase, where the current maintains a low voltage state through the body diode.

[0037] In the directional constraint, the objective is to "discharge the junction capacitance voltage to the forward conduction voltage drop of the body diode (approximately zero voltage) within the dead time". Combining the charge transfer law of junction capacitance charging and discharging, the correlation between the soft-switching current direction and the junction capacitance discharge trend is analyzed. When the current direction is consistent with the junction capacitance discharge requirement, the junction capacitance voltage will gradually decrease with the current flow. Based on this, the judgment condition of the directional constraint is derived (such as the junction capacitance discharge amount is not less than the difference between the initial voltage and the body diode voltage drop).

[0038] In amplitude constraints, based on satisfying directional constraints, the quantitative relationship between soft-switching current amplitude and voltage rise rate is analyzed for the voltage rise characteristics when the switch is turned off. When the current amplitude is too large, the voltage will rise rapidly and generate a spike after the switch is turned off, thereby deriving the upper and lower limits of amplitude constraints (e.g., the current amplitude needs to be controlled within the range that the voltage rise does not exceed the set rated voltage of the corresponding battery cell).

[0039] The embodiments described above in this application, through directional and amplitude constraints, enable the analysis of the physical essence of single-module soft switching, avoiding the problems of stage fragmentation or omission in traditional analysis, and ensuring that the subsequent model can match the timing characteristics of actual switching actions. Specifically, the derivation of directional constraints directly ensures that the switching transistor is in a near-zero voltage state before turn-on, avoiding voltage and current overlap during hard switching, reducing the switching transistor's turn-on loss, and is a prerequisite for achieving zero-voltage soft switching. Amplitude constraints, while ensuring zero-voltage turn-on, suppress voltage spikes during the switching transistor's turn-off process, avoiding abnormal increases in turn-off loss, achieving the dual soft-switching benefits of zero-voltage turn-on and low turn-off loss, and improving the operating efficiency of the single-module resonant unit.

[0040] In some specific embodiments of this application, the criteria for determining the current direction constraint are: the discharge amount of the junction capacitance during the dead time is not less than the difference between the initial voltage of the junction capacitance and the forward conduction voltage drop of the diode; the criteria for determining the current amplitude constraint are: during the turn-off process of the switch, the voltage rise across the switch does not exceed the rated voltage of the corresponding parallel battery cell.

[0041] In the above embodiments of this application, during the derivation of the soft-switching conditions for the single-module resonant unit, for the current direction constraint, the charge transfer law of the junction capacitance during the dead time is used as the basis, and the difference between the discharge amount of the junction capacitance and the forward conduction voltage drop of the body diode is used as the judgment criterion to ensure that the junction capacitance voltage can drop to the forward conduction voltage drop of the body diode (approximately zero voltage) during the dead time. For the current amplitude constraint, the voltage dynamic change characteristics when the switch is turned off are combined with the judgment criterion that the voltage rise amplitude across the switch does not exceed the rated voltage of the corresponding parallel battery cell, thereby controlling the voltage fluctuation range during the turn-off process. This achieves both setting the switch to zero voltage turn-on from the current direction dimension, avoiding the surge in losses caused by hard turn-on, and suppressing the voltage surge during turn-off from the current amplitude dimension, while adapting to the rated voltage characteristics of the battery cell. This improves the soft-switching operating efficiency of the single-module resonant unit and enhances the operating safety and reliability of the switch and battery system.

[0042] In some specific embodiments of this application, the soft-switching current of a single-module resonant unit needs to meet the following requirements: ; In the formula, i rzvs,12 For the resonant circuit current, The lower current threshold for zero-voltage soft switching; The upper current limit threshold for zero-voltage soft switching; The dead time is set; This is the minimum dead time; This represents the maximum dead time.

[0043] Specifically, refer to Figure 2 As shown, with D 12 When the voltage is >0, clarify the mechanism and implementation conditions of the single-module zero-voltage soft-start process, and combine it with Figure 2 The diagram shows a four-battery pack series system. The battery packs are connected in series from the high-potential end to the low-potential end. The top half-bridge refers to the half-bridge module (i.e., switches S1 and S2) connected to the two ends of the highest-potential battery pack B1. The bottom half-bridge refers to the half-bridge module (i.e., switches S7 and S8) connected to the two ends of the lowest-potential battery pack B4. The middle half-bridge refers to the half-bridge modules (i.e., S3 / S4 and S5 / S6) connected to the two ends of the middle-potential battery packs (B2 and B3). Taking the middle half-bridge S3 / S4 as an example, its AC side is simultaneously connected to two resonant cavities: one shared with the top half-bridge (including L...). r1 C r1 The current is I r1 ), and the resonant cavity shared with the adjacent intermediate layer half-bridge S5 / S6 (including L)r2 C r2 The current is I r2 That is, the soft-switching current is determined by the currents in both resonant cavities.

[0044] Reference Figure 3 As shown, a single module includes... S 1, S 2, S 3, S 4, B 1, B 2, L r , C r The resonant switched capacitor unit consists of battery cell B1, B2, and B3. The negative terminal of battery cell B1 is directly connected to the positive terminal of B2, and the negative terminal of battery cell B2 is directly connected to the positive terminal of B3. The negative terminal of B3 is connected to the positive terminal of B4, forming a DC voltage source in series. C1 is connected in parallel across B1 (with its two ends connected to the positive and negative terminals of B1 respectively); C2 is connected in parallel across B2; C3 is connected in parallel across B3; and C4 is connected in parallel across B4 to stabilize the voltage of the corresponding battery. B1 provides voltage U1, and B2 provides voltage U2. The switching transistor group consists of S1-S2 and S3-S4. S1 and S2 form the top-level half-bridge. The drain of S1 is connected to the positive terminal of B1, and the source of S1 is connected to the drain of S2 (forming the middle node of the half-bridge), and is simultaneously led out to the resonant inductor L. r,12 One end of the bridge; the source of S2 is connected to the negative terminal of B1, sharing the same point as the positive terminal of B2. S3 and S4 (bottom half-bridge): the drain of S3 is connected to the positive terminal of B2, sharing the same point as the source of S2); the source of S3 is connected to the drain of S4 (forming the middle node of the half-bridge), and is simultaneously led out to the resonant capacitor C. r,12 One end; the source of S4 is connected to the negative terminal of B2, and the resonant inductor L r,12 The other end is connected to the resonant capacitor C r,12 The other end is connected.

[0045] Among them, the top resonant unit L r End a is connected to the intermediate node of the top-level half-bridge S1 and S2; L r The b end is connected to C. r b end, C r The c-terminal is connected to the middle node of the intermediate layer half-bridge S3 and S4; the intermediate resonant unit L r The a-end is connected to the intermediate node of the intermediate layer half-bridge S3 and S4, L r The b end is connected to C. r The b end, C r The c-terminal is connected to the middle node of the middle layer half-bridge S5 and S6; the bottom layer resonant unit L rThe a-end is connected to the intermediate node of the top-level half-bridge S5 and S6; L r The b end is connected to C. r b end, C r The c-end is connected to the intermediate node of the intermediate layer half-bridge S7 and S8.

[0046] See attached document Figure 4 As shown, with S 1. About to be shut down S Taking the imminent commissioning time as an example, we will conduct a soft-switching analysis. The switching process of the zero-voltage soft-switching implementation model includes the following stages: exist t Before 0, the circuit operates in mode 2. S 1. Forward guidance (u) CS1 = 0), S 2. Turn off ( u CS2 = U 1).

[0047] exist t At 0 o'clock, issued S 1. Turn off the signal. At this time, the resonant circuit current... i rzvs,12 equal I r2 resonant capacitor voltage u cr,12 equal U cr2 .

[0048] exist t 0 -t During period 1, this time interval is the IGBT turn-off delay time.

[0049] exist t 1 -t During step 3, this time interval is a critical process for achieving ZVS. i rzvs,12 Start to C S1 and C S2 Charge until u CS1 Rise to U 1 and u CS2 The voltage drop to the forward conduction voltage of the internal diode decreases. V f Through the equivalent circuit, t 1 -t During period 3 u CS1 and u CS2 As shown below: .

[0050] .

[0051] In the formula, This is the voltage across the junction capacitance of the switching transistor S1; This is the rated voltage of battery B1; Characteristic impedance; ω is the angular frequency; t is the time variable. This is the steady-state resonant current; For switching transistors S The voltage across the junction capacitance of 2.

[0052] Obviously, u S1 and u S2 Depend on i rzvs ( t 1) The size and direction determine the orientation; in this case... i rzvs ( t 1) In essence, it is I r2 .if I r2 exist t If the value of 1 is too small or even negative, then S The voltage at both ends cannot discharge to zero within the dead time, such as Figure 6 As shown by the green curve in the image. Therefore, to ensure... C S2 To achieve complete discharge within a specified time, the following constraints must be met: ; In the formula, The lower current threshold for zero-voltage soft switching; The duration of the junction capacitance charging and discharging phase; This is the forward voltage drop of the switching diode.

[0053] Conversely, if I r2 If it is too large, then S The voltage across terminals 1 rises too quickly, causing S The turn-off loss of 1 increases, such as Figure 6 The blue curve in the image shows this. Therefore, to reduce... S 1. To reduce the turn-off loss and buffer the voltage rise time, under the premise of satisfying equation (5), I r2 It should also be as small as possible. t f period, SThe voltage rise across the terminals should not exceed U 20% of 1. The constraints are as follows: ; In the formula, The lower current threshold for zero-voltage soft switching; The turn-off current drop time of the switching transistor; It should be noted that in active battery balancing scenarios, the voltage rating of the switching transistor usually needs to match the rated voltage of the individual battery cells. U 1. In this embodiment, in order to achieve a balance between loss and reliability, the current drop time is set... Internally, when the switching transistor is turned off, the voltage rise across it should not exceed 20% of the battery's rated voltage to prevent overvoltage damage to the switching transistor; this should be combined with the previous switching transistor voltage formula. During the shutdown phase If the resonant current during the turn-off current fall time is approximately equal to 1 (i.e., remains constant), then... ≤ The negative sign is due to the relationship between the current direction and the voltage change direction (corresponding to the polarity of the bottom half-bridge current). Therefore, the coefficient 0.2 is a set value derived from the safety constraint of the switching transistor voltage.

[0054] Therefore, assuming I rzvs,12 For the switching time i rzvs,12 Value, for implementation S Zero-voltage turn-on of 2 I rzvs The following directional and magnitude constraints must be met: ; In the formula, This is the soft-switching current of the intermediate layer half-bridge; It should be noted that, It refers to "the current flowing through the junction capacitance of the target switch during the dead time," and its measurement point corresponds to the attached... Figure 2 Inductance L in the middle resonant cavity r12 The current is a specific value of the resonant cavity current during the dead time. When the half-bridge is in the soft-switching stage, the resonant cavity current charges and discharges through the junction capacitance. This resonant cavity current is the "soft-switching current," which needs to be considered in conjunction with the attached... Figure 2 L r12 Current correspondence Establish the correspondence between soft-switching current, resonant cavity current during dead time, and current flowing through the junction capacitance of the switching transistor (instantaneous value).

[0055] exist t At time 3, the circuit switches to mode 3. u CS1 =U 1 and u CS2 = 0.

[0056] exist t 3- t During period 4, the circuit operates in mode 3. S 2. Internal diode freewheeling. u CS2 It has resonated to a negative value and is clamped at the diode's forward voltage until... t 4 moments i CS1 The resonance will soon be negative. Therefore, S 2 needs to be t 3- t Soft turn-on (i.e., turn-on when the diode is conducting) can be achieved at any time during period 4. t After step 4, the circuit continues to operate in mode 3. S 1. Turn off, S 2. Forward navigation.

[0057] It should be noted that the circuit state of "S1 is off and the body diode of S2 is conducting freewheeling" is collectively referred to as Mode 3; specifically, during the period t3-t4, it is the freewheeling stage of the body diode of S2. At this time, the junction capacitance voltage of S2 has been discharged to zero and is maintained at a negative voltage (approximately -Vf) by its body diode.

[0058] t4 time: is the last time point at which S2 must be activated. i CS1 The resonance is about to turn negative, and the direction of the current flowing through the junction capacitance of S1 will change, which may cause the body diode of S2 to turn off naturally. If S2 is not turned on before t4, the zero-voltage turn-on window of S2 will disappear.

[0059] After t4: At this point, the drive signal for S2 has been given, and S2 transitions from the body diode freewheeling state to the forward conduction state of the MOSFET or IGBT itself. Although the conduction state of S2 has changed (from diode to switch), since S1 remains off, S2 is the only current path. Therefore, t After 4, it still reverts to mode 3 (i.e., t3-t4: the body diode freewheeling phase (the zero-voltage turn-on window of S2; at some point before t4, S2 turns on at zero voltage, in...). t 4. After that: S2 switch is in the forward conduction stage.

[0060] In summary, to achieve ZVS, the initial soft-switching current flowing into this single-module half-bridge must meet the following conditions: ; In the formula, The dead time is set; This is the minimum dead time; This represents the maximum dead time. It should be noted that during the dead time of S1 turning off and S2 turning on, the initial soft-switching current... It must be greater than the minimum current. This ensures that the junction capacitance of S2 discharges to the body diode voltage drop within the dead time, thereby achieving zero-voltage turn-on of S2. It must be less than the maximum current. This limits the charging speed of the S1 junction capacitor, preventing excessive voltage rise after S1 is turned off and reducing turn-off losses.

[0061] in,

[0062] The upper and lower limits of the soft-switching current constraint have been supplemented and are derived from the above simplified formula. The lower limit I zvs1 To achieve zero-voltage turn-on of the switching transistor, the upper limit I zvs2 This is to buffer the rising voltage of the turn-off transistor, further reduce losses, and achieve efficient operation.

[0063] In some specific embodiments of this application, for the top half-bridge, it is determined that the soft-switching current originates from only one resonant cavity, and the soft-switching current value of the top half-bridge depends on a shift ratio. For the intermediate layer half-bridge, it is determined that the soft-switching current originates from two adjacent resonant cavities simultaneously, and the soft-switching current value of the intermediate layer half-bridge depends on the combination of the two shift ratios. For the bottom half-bridge, the soft-switching current is determined to originate from only one resonant cavity, and the soft-switching current value of the bottom half-bridge depends on a shift ratio.

[0064] The resonant cavity of the top half-bridge is the resonant cavity between the first battery and the adjacent battery; the resonant cavity of the bottom half-bridge is the resonant cavity between the last battery and the adjacent battery; the current path of the top half-bridge is opposite to the circuit path of the bottom half-bridge.

[0065] Specifically, for the top-layer half-bridge, it is determined that it is only associated with a single resonant cavity between the first cell and the adjacent cell, and the soft-switching current originates solely from this resonant cavity, with the current value determined by the single shift ratio corresponding to this resonant cavity. For the middle-layer half-bridge, which is located in the middle of the topology and couples cell cells on both sides, it is determined that its soft-switching current originates simultaneously from two adjacent resonant cavities, and the current value is determined by the combination of the shift ratios corresponding to the two resonant cavities. For the bottom-layer half-bridge, it is determined that it is only associated with a single resonant cavity between the last cell and the adjacent cell, and the soft-switching current originates solely from this, with the current value determined by the corresponding single shift ratio. It is also determined that the current paths of the top-layer and bottom-layer half-bridges exhibit reverse characteristics.

[0066] The embodiments described above distinguish the soft-switching current sources, shift ratio dependencies, and current path differences of different levels of half-bridges, define the current formation logic of each level of half-bridge, avoid confusion of current characteristics in multi-module topologies, support the realization of zero-voltage soft switching of each level of half-bridge in multi-module topologies, improve the efficiency of topology control, simplify the differentiated control logic of different levels of half-bridges, and reduce the overall control complexity of multi-resonant switched capacitor topologies.

[0067] In some specific embodiments of this application, when there are top half-bridge and bottom half-bridge, the soft-switching current is determined by the polarity of the shift ratio corresponding to the top half-bridge and bottom half-bridge, respectively, to determine that the soft-switching current obtains current from a resonant cavity adjacent to the top half-bridge and bottom half-bridge.

[0068] Among them, the soft-switching current of the top half-bridge is positively correlated with the polarity of the shift ratio; the soft-switching current of the bottom half-bridge is negatively correlated with the polarity of the shift ratio.

[0069] In the embodiments described above in this application, in a switch-multiplexed multi-resonant switched-capacitor topology, for the top and bottom half-bridges that are only associated with a single resonant cavity, the acquisition method of the soft-switching current is determined by the polarity of the corresponding shift ratio. The soft-switching current of the top half-bridge is positively correlated with the polarity of the shift ratio, that is, the positive and negative currents of the shift ratio are acquired from the adjacent resonant cavities in the forward and reverse directions, respectively. The soft-switching current of the bottom half-bridge is negatively correlated with the polarity of the shift ratio, that is, the positive and negative currents of the shift ratio are acquired from the adjacent resonant cavities in the reverse and forward directions, respectively. This clarifies that the soft-switching current of both types of half-bridges is acquired from their respective adjacent single resonant cavities, establishing a correspondence between the polarity of the shift ratio and the acquisition direction of the soft-switching current. This avoids confusion between the current paths of the top and bottom half-bridges, simplifies the control logic of the soft-switching current of the two types of half-bridges, and can accurately match the current requirements of different levels of half-bridges.

[0070] In some specific embodiments of this application, when there is an intermediate layer half-bridge, the intermediate layer half-bridge is powered by two adjacent resonant cavities. The value of the soft-switching current needs to take into account the shift ratio of the two adjacent resonant units and is determined by the difference of the shift ratio of the two adjacent resonant units.

[0071] Specifically, based on the defined soft-switching of a single module, the initial soft-switching current is determined for all operating conditions of the half-bridge at different locations in the multi-module structure. The initial soft-switching current represents the voltage change of the junction capacitance of the half-bridge at different locations in the multi-module structure during the switching process. (Refer to...) Figure 5 As shown, 1) For the top-layer battery, its parallel half-bridge is powered by only one resonant cavity current. When D 12 When >0, I rzvs,top equal I r0Conversely, when D 12 When <0, I rzvs,top equal I r3 .

[0072] in, D 12 Compared to moving.

[0073] 2) For the intermediate layer battery, its parallel half-bridge will be powered by the current from the two adjacent resonant cavities. Therefore, considering both... D 12 and D 23 polarity, I rzvs,mid There are four possible scenarios: I r0 -I r1 , I r3 -I r1 , I r0- I r2 , I r3 -I r2 3) For the bottom-layer battery, its parallel half-bridge is powered by only one resonant cavity current. When D 23 When >0, I rzvs,bot equal- I r1 Conversely, when D 23 When <0, I rzvs,bot equal- I r2 .

[0074] In some specific embodiments of this application, equivalent circuit models are established at the switching moments for the top-layer, middle-layer, and bottom-layer half-bridges, respectively, including: For the top-layer half-bridge and the bottom-layer half-bridge, an equivalent circuit with single resonant cavity power supply is used to establish an equivalent circuit model under switching transients; for the middle-layer half-bridge, an equivalent circuit with dual resonant cavities connected in parallel is used to establish an equivalent circuit model under switching transients.

[0075] Among them, the equivalent circuits are respectively attached Figure 5In the diagram: c1 is the equivalent circuit model of the top-level half-bridge switch in transient state; c2 is the equivalent circuit model of the middle-level half-bridge switch in transient state; c3 is the equivalent circuit model of the bottom-level half-bridge switch in transient state.

[0076] a represents the drive signal of the switching transistor and the current waveform of each resonant cavity in the embodiment; b1 represents the actual circuit diagram at the switching moment of the top half-bridge; b2 represents the actual circuit diagram at the switching moment of the middle half-bridge; b3 represents the actual circuit diagram at the switching moment of the bottom half-bridge.

[0077] In some specific embodiments of this application, the initial current values ​​obtained at the switching moment corresponding to the junction capacitance voltage are calculated as follows: For the top-level half-bridge and the bottom-level half-bridge, the initial values ​​of the single resonant cavity at the switching moment are solved by circuit analysis; For the intermediate layer half-bridge, the initial values ​​of the currents in the two adjacent resonant cavities at the switching moment are solved by circuit analysis and then algebraically added together.

[0078] Next, we need to find the multi-module constraints that the initial soft-switching current of the half-bridge at different locations in the multi-module structure needs to satisfy during all operating conditions. That is, for the top-level, middle-level and bottom-level half-bridges, we establish equivalent circuit models at the switching moment and solve for the initial current values ​​of the corresponding junction capacitance voltage at the switching moment.

[0079] like Figure 5 As shown, the resonant current of the switching process at different positions is modeled and analyzed. An equivalent circuit model under the switching transient is established, including the top layer, middle layer and bottom layer half bridge, and the current and voltage characteristics of the half bridge at all positions are obtained.

[0080] 1) The current and voltage characteristics of the top-level equivalent circuit model are solved as follows: ; ; In the formula, This is the soft-switching current of the top-level half-bridge; For the soft-switching current of the intermediate layer half-bridge The soft-switching current value of the top-level half-bridge can be obtained using a unified criterion. I rzvs,top1 , I rzvs,top2 .

[0081] 2) The current and voltage characteristics of the intermediate layer equivalent circuit model are solved as follows: ; ; In the formula, This is the voltage across the junction capacitance of the switching transistor S3 in the intermediate layer half-bridge. This is the voltage across the junction capacitance of the switching transistor S4 in the intermediate layer half-bridge. The soft-switching current value of the intermediate layer half-bridge can be obtained using a unified criterion. I rzvs,mid1 , I rzvs,mid2 .

[0082] 3) The current and voltage characteristics of the underlying equivalent circuit model are solved as follows: ; ; In the formula, This is the voltage across the junction capacitance of the switching transistor S7 in the bottom half-bridge. This is the soft-switching current of the bottom half-bridge; This is the rated voltage of the last battery cell corresponding to the bottom half-bridge. This is the voltage across the junction capacitance of the switching transistor S8 in the bottom half-bridge. The soft-switching current value of the underlying half-bridge can be obtained using a unified criterion. I rzvs,bot1 , I rzvs,bot2。

[0083] In some specific embodiments of this application, the operating parameter boundaries for drawing the topology can achieve soft switching in all operating modes, including: Based on the amplitude constraints and constraint conditions of soft switching of half-bridges at different positions, a system of multivariable inequalities is established. Solve the system of multivariable inequalities to obtain the range of the shift ratio, resonance parameter, and dead interval; The operating parameter boundaries of the soft-opening transistor are plotted using the range of shift ratio, resonance parameter, and dead interval.

[0084] Specifically, when plotting the boundaries of soft-switching operating parameters, the soft-switching amplitude and direction constraints of the top, middle, and bottom half-bridges are first integrated. Core variables such as shift ratio, resonant parameter, and dead time are incorporated into the same analysis framework, and a system of multivariate inequalities containing these variables is established. Then, the system of inequalities is processed through algebraic solutions, numerical simulations, etc., to obtain the feasible range of each variable that satisfies the soft-switching conditions in all operating modes (such as the value range of the shift ratio, the matching range of the resonant parameter, and the reasonable range of the dead time). Finally, the range of variables is visualized in the form of curves, interval plots, etc., forming the boundaries of soft-switching operating parameters covering all operating modes.

[0085] The embodiments described above integrate the soft-switching constraints of each half-bridge layer and transform them into a solvable parameter range. This ensures that the drawn operating parameter boundaries can cover all operating modes of the topology, providing a clear feasible domain basis for the selection of shift ratio, resonance parameter, and dead time in practical applications. This avoids the blind selection of parameters and ensures that the topology can stably achieve zero-voltage soft switching under all operating conditions. It improves the operating efficiency and reliability of the battery active balancing topology and simplifies the process of topology debugging and parameter optimization.

[0086] Substituting the initial current into the constraint conditions yields the soft-switching current boundary.

[0087] ; In the formula, I zvs,top I is the soft-switching current of the top-level half-bridge at the switching moment. zvs1,top I zvs2,top Constraint I zvs,top The upper and lower limits; I zvs,mid I represents the soft-switching current of the half-bridge at the switching moment in the intermediate layer position. zvs1,mid I zvs2,mid Constraint I zvs,mid The upper and lower limits; I zvs,bot I represents the soft-switching current of the bottom-level half-bridge at the switching moment. zvs1,bot I zvs2,bot Constraint I zvs,bot The upper and lower limits.

[0088] Reference Figure 6 As shown, D 12 , D 23 , D 34 The implementation of soft switches in different locations when both are 0.1. Figure 6 (a) shows the steady-state waveforms of the current in each resonant cavity under this operating condition. Figure 6 (b1)-(b4) illustrate the implementation of soft switching in the top, second, third, and bottom half-bridges, respectively. Applying the proposed method for efficient collaborative operation of multi-resonant switched capacitors based on switch multiplexing suitable for active battery balancing, soft switching can be achieved in all half-bridge positions. All derivations not detailed above can be implemented with reference to existing technologies.

[0089] The foregoing has described some specific embodiments of this application. It should be understood that this application is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the substantive content of this application. The above-described preferred features can be used in any combination without conflict.

Claims

1. A method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing, characterized in that, The method is based on a switch-multiplexed multiresonant switched capacitor topology and includes: Establish a zero-voltage soft-switching realization condition model for a single-module resonant unit, and determine the amplitude and direction constraints of the soft-switching current required for the switching transistor to achieve zero-voltage turn-on; Based on the topology, the current paths of the half-bridges located at the top, middle and bottom layers during the soft-switching transient process are identified, and the mathematical relationship between the soft-switching current of each half-bridge and the current of each resonant cavity is determined. For the top, middle and bottom half-bridges, equivalent circuit models are established at the switching moment, and the initial current values ​​of the corresponding junction capacitance voltage at the switching moment are obtained by solving. Substitute the initial current values ​​obtained from the solution into the established constraints to plot the operating parameter boundaries of the topology that enable soft switching in all operating modes.

2. The method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing according to claim 1, characterized in that, The establishment of a zero-voltage soft-switching implementation condition model for a single-module resonant unit determines the amplitude and direction constraints of the soft-switching current required for the switching transistor to achieve zero-voltage turn-on, including: Taking the single-module resonant unit in the aforementioned topology as the research object, the entire process of the switch turn-off delay, junction capacitance charging and discharging, and body diode freewheeling in the single-module resonant unit is analyzed. The directional constraints that the soft-switching current must satisfy during the charging and discharging phase of the junction capacitor are derived so that the voltage of the junction capacitor can be discharged to zero within the dead time. The amplitude constraint of the soft-switching current is derived so that the turn-off loss of the switching transistor can be optimized while satisfying the directional constraint.

3. The efficient cooperative operation method of multi-resonant switched capacitors for active battery balancing according to claim 2, characterized in that, The criterion for determining the current direction constraint is: the discharge amount of the junction capacitor during the dead time is not less than the difference between the initial voltage of the junction capacitor and the forward conduction voltage drop of the body diode. The current amplitude constraint is determined based on the following: during the turn-off process of the switch, the voltage rise across the switch does not exceed the rated voltage of the corresponding parallel battery cell.

4. The efficient cooperative operation method of multi-resonant switched capacitors suitable for active battery balancing according to claim 3, characterized in that, The soft-switching current of the single-module resonant unit needs to satisfy: ; In the formula, i rzvs,12 For the resonant circuit current, The lower current threshold for zero-voltage soft switching; The upper current limit threshold for zero-voltage soft switching; The dead time is set; This is the minimum dead time; This represents the maximum dead time.

5. The efficient cooperative operation method of multi-resonant switched capacitors for active battery balancing according to claim 1, characterized in that, The identification of current paths in the top, middle, and bottom layers of the half-bridge during soft-switching transients includes: For the top half-bridge, it is determined that the soft-switching current originates from only one resonant cavity, and the soft-switching current value of the top half-bridge depends on a shift ratio; For the intermediate layer half-bridge, it is determined that the soft-switching current originates from two adjacent resonant cavities simultaneously, and the soft-switching current value of the intermediate layer half-bridge depends on the combination of the two shift ratios. For the bottom half-bridge, it is determined that the soft-switching current also originates from only one resonant cavity, and the soft-switching current value of the bottom half-bridge depends on a shift ratio. The resonant cavity of the top half-bridge is the resonant cavity between the first battery and the adjacent battery; the resonant cavity of the bottom half-bridge is the resonant cavity between the last battery and the adjacent battery; the current path of the top half-bridge is opposite to the circuit path of the bottom half-bridge.

6. The efficient cooperative operation method of multi-resonant switched capacitors for active battery balancing according to claim 5, characterized in that, In the case of the top half-bridge and the bottom half-bridge, the soft-switching current is determined by the polarity of the shift ratio corresponding to the top half-bridge and the bottom half-bridge, respectively, and the soft-switching current is obtained from a resonant cavity adjacent to the top half-bridge and the bottom half-bridge. Specifically, the soft-switching current of the top half-bridge is positively correlated with the polarity of the shift phase; the soft-switching current of the bottom half-bridge is negatively correlated with the polarity of the shift phase.

7. The efficient cooperative operation method of multi-resonant switched capacitors for active battery balancing according to claim 5, characterized in that, In the intermediate layer half-bridge configuration, the intermediate layer half-bridge is powered by two adjacent resonant cavities. The value of the soft-switching current needs to take into account the shift ratio of the two adjacent resonant units and is determined by the difference in the shift ratio of the two adjacent resonant units.

8. The efficient cooperative operation method of multi-resonant switched capacitors for active battery balancing according to claim 1, characterized in that, The equivalent circuit models established at the switching moments for the top, middle, and bottom half-bridges include: For both the top half-bridge and the bottom half-bridge, an equivalent circuit powered by a single resonant cavity is used to establish an equivalent circuit model under switching transients. For the intermediate layer half-bridge, an equivalent circuit with parallel power supply of dual resonant cavities is used to establish an equivalent circuit model under switching transients.

9. The efficient cooperative operation method of multi-resonant switched capacitors for active battery balancing according to claim 8, characterized in that, The solution yields the initial current values ​​corresponding to the junction capacitance voltage at the switching moment, including: For the top half-bridge and the bottom half-bridge, the initial values ​​of the single resonant cavity at the switching moment are solved by circuit analysis; For the intermediate layer half-bridge, the initial values ​​of the currents in the two adjacent resonant cavities at the switching moment are solved by circuit analysis and then algebraically added together.

10. The method for efficient coordinated operation of multi-resonant switched capacitors suitable for active battery balancing according to claim 1, characterized in that, The drawing of the topology enables the realization of soft-switching operating parameter boundaries in all operating modes, including: Based on the amplitude constraints and constraint conditions of the soft switches of the half-bridges at different positions, a system of multivariable inequalities is established. Solving the system of multivariable inequalities yields the ranges of the shift ratio, resonance parameter, and dead interval. The operating parameter boundaries of the soft-opening transistor are plotted using the ranges of the shift ratio, resonance parameter, and dead interval.