A method for designing SiC LLC resonant converter parameters with optimal turn-off current

Abstract

This application discloses a parameter design method for a SiC LLC resonant converter with optimal turn-off current. By establishing state trajectory models of the LLC resonant converter in the energy transfer and three-element resonance stages, circular and elliptical geometric trajectories are obtained respectively. Based on the trajectory geometry, analytical equations for the turn-off current of the switching transistors are derived. An approximate gain model in PO mode is constructed, establishing explicit mapping relationships between characteristic impedance, inductance ratio, operating power, operating frequency, and DC gain. The feasible region of parameters is determined by combining design specifications and device characteristics. Global optimization is performed with the goal of minimizing the turn-off current, outputting the optimal combination of resonant parameters. This application eliminates the need for simplification assumptions based on sinusoidal waves, accurately captures the real physical processes under heavy load and off-resonance conditions, avoids iterative solutions to nonlinear equations through geometric analysis, minimizes the turn-off current under zero-voltage switching conditions, effectively reduces cycling losses and switching losses, and improves the converter's efficiency across the entire load range.

Description

Technical Field

[0001] This application relates to the field of power electronics technology, specifically to a method for designing parameters of a SiC LLC resonant converter with optimal turn-off current. Background Technology

[0002] LLC resonant converters, due to their ability to achieve zero-voltage switching (ZVS) of the primary-side switches and zero-current switching (ZCS) of the secondary-side rectifiers, possess significant advantages such as a wide soft-switching range, high efficiency, high power density, and low electromagnetic interference. They have become one of the core topologies in the medium-to-high power DC-DC conversion field and are widely used in critical areas such as server power supplies, electric vehicle on-board chargers, photovoltaic inverters, energy storage systems, and communication power supplies. Among the various modulation methods of LLC resonant converters, pulse frequency modulation (PFM) has become the mainstream solution for industrial applications due to its simple control and ease of implementation. Under PFM control, the voltage gain and power transfer capability of the converter are mainly determined by the switching frequency and the resonant cavity parameters (resonant inductance L). r Resonant capacitor C r Magnetizing inductance L m The parameters of the resonant cavity are jointly determined. Therefore, the optimized design of the resonant cavity parameters is the core of LLC resonant converter design, as it directly determines the converter's voltage gain range, efficiency, and the reliability of soft switching.

[0003] Among these parameters, the instantaneous current of the primary-side switch at the turn-off moment, i.e., the turn-off current, is crucial. The magnitude of the turn-off current directly affects the turn-off loss of the switch. Furthermore, to achieve Zero-Switching (ZVS), the junction capacitance of the switch must be charged and discharged using the turn-off current during the dead time. Insufficient turn-off current may lead to ZVS failure, resulting in hard switching and causing severe switching losses and electromagnetic interference; excessive turn-off current will significantly increase turn-off losses and transformer circulating current, leading to increased conduction losses and reduced overall efficiency. Currently, the analysis and design methods for LLC resonant converters are mainly divided into three categories: frequency domain analysis, time domain analysis, and state trajectory method.

[0004] The most widely used frequency domain analysis method is the Fundamental Harmonic Approximation (FHA). FHA assumes that the voltage and current within the resonant cavity are ideal sine waves, considering only their fundamental components for modeling and analysis. This method simplifies the analysis process and has good approximation accuracy when the switching frequency is close to the series resonant frequency and the load is heavy. However, when the converter operates off-frequency (e.g., in boost or buck mode), under light load, or with a high quality factor (Q value), the current waveform within the resonant cavity becomes severely distorted and no longer approximates a sine wave. In this case, the accuracy of the FHA method drops sharply, failing to accurately predict the turn-off current, resulting in a significant deviation between the calculated turn-off current and the actual operating conditions. To ensure the reliability of ZVS, designers are often forced to reserve a very large turn-off current margin. While this ensures soft switching, it results in huge circulating energy and conduction losses within the resonant cavity, severely limiting further improvements in converter efficiency.

[0005] To improve accuracy, researchers have proposed frequency domain analysis methods with time-domain correction and pure time-domain analysis methods. Time-domain analysis accurately characterizes the physical processes of different operating modes within a switching cycle through piecewise linearization. While this method offers high accuracy, its describing equations are typically complex systems of nonlinear differential equations. Solving these equations involves iterative calculations of numerous transcendental equations, resulting in high computational costs, difficulty in guaranteeing convergence, and a lack of intuitive analytical relationships between design parameters and macroscopic performance indicators such as turn-off current and voltage gain. This makes parameter design more like a cycle of trial and error and simulation verification, lacking clear physical guidance.

[0006] Trajectory analysis, as an intuitive time-domain geometric analysis method, has attracted attention in recent years. This method maps the changes in resonant capacitor voltage and inductor current onto a two-dimensional state plane, forming a geometric trajectory. This approach transforms the problem of solving complex differential equations into an intuitive geometric analysis, aiding in understanding the converter's operation. However, existing research primarily uses state trajectories for transient control or stability analysis of converters, rarely employing them as a core tool for quantitative parameter design. While current techniques can depict the overall operating trajectory of LLC resonant converters, they lack precise geometric derivations and algebraic formulas for the critical mode switching points that determine the turn-off current, making it impossible to directly utilize the trajectory's geometric characteristics for quantitative parameter optimization.

[0007] Existing LLC resonant converter parameter design methods generally suffer from the following defects: the FHA method lacks accuracy, especially in the calculation of turn-off current under non-ideal operating conditions, which is seriously distorted; the time-domain method is complex to calculate and lacks intuitiveness; the existing state trajectory method remains at the level of qualitative analysis and fails to establish an accurate analytical relationship between turn-off current and design parameters. Summary of the Invention

[0008] The main objective of this application is to provide a method for designing parameters of a SiC LLC resonant converter with optimal turn-off current, comprising the following steps:

[0009] Step S1: Establish the state trajectory model of the LLC resonant converter in the energy transfer stage P and the three-element resonant stage O, map the resonant capacitor voltage and the resonant inductor current to the state plane, and obtain the circular trajectory corresponding to stage P and the elliptical trajectory corresponding to stage O respectively.

[0010] Step S2: Based on the state trajectory model, using the law of conservation of energy and the angle relationship of the geometric trajectory, derive the switching current I of the LLC resonant converter. off Analytical equation;

[0011] Step S3: Construct the voltage gain M of the LLC resonant converter in the PO mode with respect to the inductance ratio k, characteristic impedance Z0, operating power P, and normalized switching frequency F. n Approximate gain model;

[0012] Step S4: Determine the working mode and gain requirements based on the design specifications, and combine the approximate gain model to initially determine the feasible range of k and Z0.

[0013] Step S5: Determine the dead time and the lower limit of the turn-off current required for zero-voltage switching based on the characteristics of the switching devices, as hard constraints.

[0014] Step S6: Within the determined feasible region, minimize the turn-off current I. off The parameters are globally optimized to achieve the target, outputting the optimal inductance ratio k and characteristic impedance Z0, and the specific values ​​of resonant inductance, resonant capacitance and magnetizing inductance are calculated.

[0015] In one embodiment, the circular state trajectory equation for stage P is:

[0016]

[0017] Where i LrpN For the normalized resonant inductor current in phase P, v CrpN U is the normalized resonant capacitor voltage in the P-stage, M is the normalized DC gain, and U is the voltage across the capacitor. PN Let be the radius of the circular trajectory in phase P;

[0018] The equation for the elliptical state trajectory in stage O is:

[0019]

[0020] Where i LroN For the normalized resonant inductor current in phase 0, v CroN U is the normalized resonant capacitor voltage during phase 0. oN Let be the trajectory radius in phase O.

[0021] In one embodiment, the turn-off current I off The numerical solution is obtained by solving the following system of equations:

[0022]

[0023] Where P is the operating power of the LLC resonant converter, and V base Here, k is the voltage reference of the LLC resonant converter, Z0 is the inductance ratio of the LLC resonant converter, and F is the characteristic impedance of the LLC resonant converter. n Let be the normalized switching frequency of the LLC resonant converter; where AE, AF, EC, FC, GF, and HE represent the geometric segment lengths on the state trajectory. .

[0024] In one embodiment, the expression for the approximate gain model is:

[0025]

[0026] Where P is the operating power of the LLC resonant converter, and V base F serves as the voltage reference for the LLC resonant converter. n Let k be the normalized switching frequency of the LLC resonant converter, and k be the inductance ratio of the LLC resonant converter. .

[0027] In one embodiment, the determination of the feasible region's value range must simultaneously satisfy two constraints:

[0028] Limit the excitation inductor voltage at the turn-off moment to ensure that the LLC resonant converter operates stably in PO mode within a preset load range;

[0029] Based on the approximate gain model, the normalized gain of the LLC resonant converter at the lowest operating frequency is ensured to meet the design specifications.

[0030] In one embodiment, the step of determining the dead time and the lower limit of the turn-off current required for zero-voltage switching based on the characteristics of the switching device, as a hard constraint, includes:

[0031] Obtain the output capacitance C of the selected switching device oss and circuit dead time t dead ;

[0032] Calculate the minimum turn-off current I required to maintain the zero-voltage switching condition based on the zero-voltage switching condition. off,min The calculation formula is:

[0033]

[0034] Wherein, Vin is the input voltage of the converter;

[0035] The calculated minimum turn-off current I off,min As a hard lower limit constraint in the parameter optimization step S6, namely the turn-off current I of the final design parameters off It must be greater than or equal to the minimum turn-off current I. off,min .

[0036] In one embodiment, the step of minimizing the turn-off current I within the determined feasible region is... off The steps for performing global parameter optimization for the target, outputting the optimal inductance ratio k and characteristic impedance Z0, and calculating the specific values ​​of resonant inductance, resonant capacitance, and magnetizing inductance include:

[0037] Within the defined feasible region, the aforementioned lower limit constraint on the turn-off current is satisfied. off >=I off,min Under the conditions of the approximate gain model, a numerical optimization algorithm is used to solve for minimizing the objective function, thereby obtaining the optimal inductance ratio k and the optimal characteristic impedance Z0;

[0038] Based on the optimal inductance ratio k and the optimal characteristic impedance Z0, combined with the preset resonant frequency f r Calculate the resonant inductance L r Resonant capacitor C r and excitation inductance L m The value of .

[0039] In one embodiment, the resonant inductor L r Resonant capacitor C r and excitation inductance L m Calculate using the following formula: L r =Z0 / (2πf r ), C r =1 / (2πf r Z0), L m =kL r , where f r L is the resonant frequency. r For resonant inductance, Cr It is a resonant capacitor.

[0040] In one embodiment, the method is used to optimize LLC resonant cavity parameters in on-board chargers, server power supplies, photovoltaic inverters, or solid-state transformers to achieve zero-voltage switching across the entire load range and minimize turn-off current.

[0041] Therefore, this application has the following beneficial effects:

[0042] First, compared with the traditional fundamental wave approximation method, this method is based on an accurate time-domain state trajectory model, without the need for sine wave simplification assumptions, and can accurately capture the real physical process of LLC resonant converter under heavy load and off-resonance conditions, effectively solving the technical problem of large error in the calculation of turn-off current in traditional methods.

[0043] Secondly, this method takes minimizing the turn-off current as the core optimization objective. By establishing an analytical relationship between the turn-off current and the resonant parameters, designers do not need to blindly reserve excessive excitation current margin to ensure zero-voltage switching. This significantly reduces the circulating current in the resonant cavity, effectively reduces conduction losses and switching losses, and improves the operating efficiency of the converter across the entire load range.

[0044] Third, this method utilizes the geometric logic of the state trajectory and the derived approximate gain model to transform the complex nonlinear time-domain solution process into an intuitive algebraic mapping and geometric constraints. This avoids the iterative solution of a large number of transcendental equations in traditional time-domain methods, significantly reduces the computational complexity of parameter design, and has extremely high engineering practical value.

[0045] Fourth, this method introduces a lower limit constraint on the turn-off current based on device characteristics during the parameter optimization process, ensuring that the design results can meet the ZVS condition under all operating conditions, effectively avoiding hard switching behavior caused by improper parameter selection, and significantly improving the operational reliability of the converter. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a full-bridge LLC resonant converter topology diagram based on the SiC LLC resonant converter parameter design method with optimal turn-off current.

[0048] Figure 2This is a system flowchart of the SiC LLC resonant converter parameter design method with optimal turn-off current;

[0049] Figure 3 This is the P-mode equivalent circuit diagram of the SiC LLC resonant converter parameter design method with optimal turn-off current.

[0050] Figure 4 This is the P-mode state trajectory diagram of the SiC LLC resonant converter parameter design method with optimal turn-off current.

[0051] Figure 5 This is the O-mode equivalent circuit diagram of the SiC LLC resonant converter parameter design method with optimal turn-off current.

[0052] Figure 6 This is the O-mode state trajectory diagram of the SiC LLC resonant converter parameter design method with optimal turn-off current.

[0053] Figure 7 It is the PO mode steady-state trajectory of the SiC LLC resonant converter parameter design method with optimal turn-off current. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0055] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0056] To address the shortcomings of existing technologies, such as the fundamental wave approximation method's insufficient accuracy under heavy load and off-resonance conditions, and the time-domain analysis method's reliance on iterative solutions to numerous nonlinear equations and difficulty in establishing analytical relationships between parameters and turn-off current, this application provides a parameter design method for SiC LLC resonant converters with optimal turn-off current. This method establishes state trajectory models for the circular trajectory in the P-stage and the elliptical trajectory in the O-stage, directly deriving the analytical equation for the turn-off current using geometric relationships, and constructing an approximate gain model to establish explicit mapping relationships between parameters. Based on this, with the goal of minimizing the turn-off current, global parameter optimization is performed within the feasible region that satisfies gain requirements, mode constraints, and ZVS conditions. This application eliminates the need for sine wave simplification assumptions, avoids iterative solutions to nonlinear equations, and balances computational accuracy with engineering practicality, effectively reducing the converter's switching and cycling losses.

[0057] like Figure 1 As shown, the resonant cavity of this full-bridge LLC resonant converter mainly consists of a resonant capacitor C. r Resonant inductor L r And the magnetizing inductance L of the transformer m Composition. Based on Figure 1 The parameters of the core resonant element shown above are defined by the following formula, which shows the parameter relationships required in the converter design process:

[0058]

[0059] Where k is the inductance ratio of the converter, Z0 is the characteristic impedance, and Z1 is the characteristic impedance including the magnetizing inductance. It is the angular frequency of a binary resonant frequency; It is the angular frequency of the three-element resonant; This represents the two-element resonant frequency. By introducing an intermediate variable, the analytical calculation process of the converter under various complex operating modes is greatly simplified, reflecting the voltage gain and impedance characteristics of the converter more intuitively and clarifying the direction of parameter design.

[0060] To facilitate analysis and ensure generalizability, this application uses the normalization system shown in Table 1 for calculation.

[0061] Table 1 Normalized parameters of LLC resonant converter

[0062] Normalized value Gain Average output current Switching frequency

[0063] The normalization is mainly based on the following four benchmarks:

[0064]

[0065] Among them, C r Represents resonant capacitance, L r This represents the resonant inductance and the magnetizing inductance of the transformer, L. m , Indicates the reference voltage. Indicates the reference impedance. Indicates the reference current. Indicates the reference frequency.

[0066] This application provides a method for designing SiC LLC resonant converter parameters with optimal turn-off current, including steps S1-S6, as described above. Figure 2 , Figure 2 This is a system flowchart of a SiC LLC resonant converter parameter design method with optimal turn-off current.

[0067] Step S1: Establish the state trajectory model of the LLC resonant converter in the energy transfer stage P and the three-element resonant stage O, map the resonant capacitor voltage and the resonant inductor current to the state plane, and obtain the circular trajectory corresponding to stage P and the elliptical trajectory corresponding to stage O respectively.

[0068] Step S2: Based on the state trajectory model, using the law of conservation of energy and the angle relationship of the geometric trajectory, derive the switching current I of the LLC resonant converter. off Analytical equation;

[0069] Step S3: Construct the voltage gain M of the LLC resonant converter in the PO mode with respect to the inductance ratio k, characteristic impedance Z0, operating power P, and normalized switching frequency F. n Approximate gain model;

[0070] Step S4: Determine the working mode and gain requirements based on the design specifications, and combine the approximate gain model to initially determine the feasible range of k and Z0.

[0071] Step S5: Determine the dead time and the lower limit of the turn-off current required for zero-voltage switching based on the characteristics of the switching devices, as hard constraints.

[0072] Step S6: Within the determined feasible region, minimize the turn-off current I. off The parameters are globally optimized to achieve the target, outputting the optimal inductance ratio k and characteristic impedance Z0, and the specific values ​​of resonant inductance, resonant capacitance and magnetizing inductance are calculated.

[0073] Specifically, in this embodiment, this application provides a method for designing SiC LLC resonant converter parameters with optimal turn-off current. This method is applicable to full-bridge or half-bridge LLC resonant converters using pulse frequency modulation control. (Refer to...) Figure 2 , Figure 2 This is a system flowchart of a SiC LLC resonant converter parameter design method with optimal turn-off current provided in an embodiment of this application. The method includes the following steps S1 to S6:

[0074] Step S1: Establish a state trajectory model

[0075] First, state trajectory models of the LLC resonant converter are established during the energy transfer stage (P stage) and the three-element resonant stage (O stage). The P stage refers to the forward conduction of the secondary rectifier diodes of the converter, and the transformer magnetizing inductance L... m The system is clamped by the output voltage and does not participate in resonance; the system consists only of the resonant inductor L. r and resonant capacitor C r The operating state in which resonance occurs and energy is transferred to the load.

[0076] The O-stage refers to the secondary rectifier diode being turned off and decoupled from the load, and the magnetizing inductance L on the primary side of the transformer... m With resonant inductor L r and resonant capacitor C r The resonant capacitor voltage and resonant inductor current are mapped onto a two-dimensional state plane to obtain the circular trajectory corresponding to stage P and the elliptical trajectory corresponding to stage O, respectively. The center of the trajectory in stage P is (1-M, 0), where M is the normalized DC gain; the center of the trajectory in stage O is (1, 0).

[0077] Step S2: Derive the analytical equation for the turn-off current

[0078] Based on the aforementioned state trajectory model, and utilizing the law of conservation of energy and the rotation angle relationship of the geometric trajectory, the analytical equation for the turn-off current of the switching transistor is derived. Specifically, by analyzing the geometric segments (such as AE, AF, EC, FC, GF, HE) on the steady-state trajectory of state PO, and combining the rotation angle and time correspondence of circular and elliptical arcs, the equation for the turn-off current I of the LLC resonant converter is constructed. off This system of nonlinear equations directly relates the turn-off current to the resonant parameters, load power, switching frequency, and DC gain, allowing the determination of I without the iterative solutions required in traditional time-domain methods. off The precise value.

[0079] Step S3: Construct an approximate gain model

[0080] Construct the voltage gain M of the LLC resonant converter in the PO mode with respect to the inductance ratio k, characteristic impedance Z0, operating power P, and normalized switching frequency F. n An approximate gain model is proposed, which clarifies the analytical relationship between characteristic impedance, inductance ratio, operating frequency, and DC gain, providing an efficient computational basis for subsequent parameter design.

[0081] Step S4: Determine the feasible region

[0082] Based on the design specifications, the converter's operating mode and gain requirements are determined. Using the aforementioned approximate gain model, the feasible region range for the inductance ratio k and characteristic impedance Z0 is preliminarily determined. Specifically, this includes: substituting the minimum operating frequency and maximum gain requirement into the gain model to solve for the (k, Z0) combinations that satisfy the gain condition; simultaneously applying PO mode operation constraints to limit the excitation inductor voltage at turn-off time, and comprehensively obtaining the feasible region boundary.

[0083] Step S5: Determine the lower limit of the turn-off current

[0084] The dead time and the lower limit of the turn-off current required for zero-voltage switching are determined based on the characteristics of the switching devices, serving as hard constraints. The specific steps are: obtain the output capacitance C of the selected power device.oss and the set dead time t dead Calculate the minimum turn-off current I required to maintain ZVS based on the ZVS condition. off,min This serves as a hard lower limit constraint for subsequent optimization, ensuring that the design results can achieve soft switching under all operating conditions.

[0085] Step S6: Global parameter optimization and component calculation

[0086] Within the defined feasible region, minimize the turn-off current I. off To achieve the target, global parameter optimization is performed, outputting the optimal inductance ratio k and characteristic impedance Z0, and the resonant inductance L is calculated accordingly. r Resonant capacitor C r and excitation inductance L m The value of . This embodiment transforms the complex nonlinear time-domain solution into intuitive algebraic calculations and geometric constraints through state trajectory geometric analysis and an approximate gain model. While ensuring calculation accuracy, it significantly reduces design complexity, achieves minimization of turn-off current and reliable realization of full-range ZVS, and effectively improves the operating efficiency and reliability of LLC resonant converter.

[0087] In one embodiment, the circular state trajectory equation for stage P is:

[0088]

[0089] Where i LrpN For the normalized resonant inductor current in phase P, v CrpN U is the normalized resonant capacitor voltage in the P-stage, M is the normalized DC gain, and U is the voltage across the capacitor. PN Let be the radius of the circular trajectory in phase P;

[0090] The equation for the elliptical state trajectory in stage O is:

[0091]

[0092] Where i LroN For the normalized resonant inductor current in phase 0, v CroN U is the normalized resonant capacitor voltage during phase 0. oN Let be the trajectory radius in phase O.

[0093] Specifically, in this embodiment, the P-mode equivalent circuit is as follows: Figure 3 As shown, according to Figure 3 The parameters shown can be used to formulate the following time-domain differential equation:

[0094]

[0095]

[0096] Solving the differential equation yields the actual physical expressions for the capacitor voltage and inductor current in stage P:

[0097]

[0098]

[0099] in , The value is unknown and depends on the initial values ​​of the capacitor voltage and inductor current, as well as the phase angle. Normalizing the above formula yields the dimensionless normalized resonant capacitor voltage. and resonant inductor current expression:

[0100]

[0101]

[0102] Based on the above formula, the equation for the circular state trajectory in stage P can be obtained as follows:

[0103]

[0104] Where i LrpN For the normalized resonant inductor current in phase P, v CrpN U is the normalized resonant capacitor voltage in the P-stage, M is the normalized DC gain, and U is the voltage across the capacitor. PN Let be the radius of the circular trajectory in phase P. Figure 4 As shown, the trajectory is represented by a circle, the center of which (1-M, 0) is determined by the gain of the LLC circuit, while the radius depends on the initial conditions. .

[0105] O-mode equivalent circuit as follows Figure 5 As shown, according to Figure 5 The parameters shown can be used to formulate the following time-domain differential equation:

[0106]

[0107]

[0108] The actual physical expressions for the capacitor voltage and inductor current in stage O are obtained as follows:

[0109]

[0110]

[0111] in , The value is unknown and depends on the initial values ​​of the capacitor voltage and inductor current, as well as the phase angle, during the zero-stage. Using the same normalization factor, the dimensionless normalized resonant capacitor voltage... and resonant inductor current The expression is as follows:

[0112]

[0113]

[0114] in Based on the above formula, the equation for the elliptical state trajectory in stage O can be obtained as follows:

[0115]

[0116] Where i LroN For the normalized resonant inductor current in phase 0, v CroN U is the normalized resonant capacitor voltage during phase 0. oN Let be the trajectory radius in phase O. Since... Participating in resonance, characteristic impedance Get bigger ( Therefore, the same current factor is used. When normalized, the trajectory will be elliptical, as shown below. Figure 6 As shown, the center of the circle is fixed at (1, 0), and the radius depends on the initial conditions. .

[0117] Since the negative half-cycle operating mode is completely symmetrical with the positive half-cycle, only the time-domain equations for the positive half-cycle need to be analyzed and derived. In summary, the state trajectory under the PO mode can be plotted as follows: Figure 7 As shown, the geometric trajectories of the capacitor voltage and inductor current during the positive half-cycle consist of a circular arc and an elliptical arc, while the trajectories during the negative half-cycle are symmetrical about the center of the circle to the positive half-cycle.

[0118] In one embodiment, the turn-off current I off The system of equations is shown below:

[0119]

[0120] Where P is the operating power of the LLC resonant converter, and V base Here, k is the voltage reference of the LLC resonant converter, Z0 is the inductance ratio of the LLC resonant converter, and F is the characteristic impedance of the LLC resonant converter. n Let be the normalized switching frequency of the LLC resonant converter; where AE, AF, EC, FC, GF, and HE represent the geometric segment lengths on the state trajectory. .

[0121] Specifically, in this embodiment, according to Figure 7 The turning angle of each segment of the trajectory is related to the phase duration. Using electrical and geometric laws such as energy conservation, the final set of equations is shown below:

[0122]

[0123] Where P is the operating power of the LLC resonant converter, and V base Here, k is the voltage reference of the LLC resonant converter, Z0 is the inductance ratio of the LLC resonant converter, and F is the characteristic impedance of the LLC resonant converter. n Let be the normalized switching frequency of the LLC resonant converter; where AE, AF, EC, FC, GF, and HE represent the geometric segment lengths on the state trajectory. In the formula, AE, AF, EC, FC, GF, and HE represent the lengths of geometric line segments on the state trajectory, and their specific meanings are as follows: Figure 7 As shown: AE is the half-cycle trajectory projection, AF is the P-mode trajectory projection, EC and FC are the projection distances from H and G to the center C, GF is the trajectory geometric parameters corresponding to the intersection of P and O modes, and HE is the trajectory geometric parameters corresponding to the cutoff point.

[0124] The above set of equations is derived based on the law of conservation of energy and the geometric rotation relationship of the state trajectory. The first five equations describe the geometric constraints and energy balance between key points on the state trajectory, while the sixth equation establishes the analytical relationship between phase duration and trajectory rotation. By solving this set of equations simultaneously, given P and V... base , k, Z0, F n With parameters such as M, the turn-off current I can be directly calculated. off The numerical value of the turn-off current is obtained. Unlike traditional time-domain methods that require iterative solutions to transcendental equations, this embodiment achieves direct calculation of the turn-off current through geometric analysis, significantly reducing computational complexity while ensuring computational accuracy. This set of equations provides the core objective function calculation basis for the global parameter optimization in the subsequent step S6 of this application, making it possible to optimize the design with the goal of minimizing the turn-off current.

[0125] In one embodiment, the expression for the approximate gain model is:

[0126]

[0127] Where P is the operating power of the LLC resonant converter, and V base F serves as the voltage reference for the LLC resonant converter. n Let k be the normalized switching frequency of the LLC resonant converter, and k be the inductance ratio of the LLC resonant converter. .

[0128] Specifically, in this embodiment, the approximate gain model is obtained by solving the differential equations of the P-stage and O-stage described above. Traditional gain calculations require the calculation of a large number of differential equations, involving implicit equations and numerical iterations, which is inefficient and prone to divergence. This embodiment transforms the complex calculation process into an explicit expression through algebraic derivation, allowing the gain M to be directly calculated from the inductance ratio k, characteristic impedance Z0, switching frequency Fn, and load power P. This expression can accurately describe the gain characteristics of the LLC resonant converter in the PO mode, and is particularly suitable for applications where the impact of parameter changes on the gain curve needs to be quickly assessed during the design phase. Specifically, it can be seen from the equation set that the turn-off current is closely related to the resonant element parameters, operating frequency, circuit gain, and load conditions, and the frequency gain curve of the LLC resonant converter is uniquely determined by the load and resonant parameters. In order to determine the parameters more directly during the design phase, it is necessary to obtain an approximate gain model of the LLC resonant converter in the PO mode.

[0129] By solving the differential equations for inductor current and capacitor voltage in the P and O modes mentioned above, the approximate gain model expression for the LLC resonant converter in the PO mode can be obtained as follows:

[0130]

[0131] Where P is the operating power of the LLC resonant converter, and V base F serves as the voltage reference for the LLC resonant converter. n Let be the normalized switching frequency of the LLC resonant converter, and k be the inductance ratio of the LLC resonant converter. This is used to characterize the change in equivalent characteristic impedance when the excitation inductor participates in resonance. The approximate gain expression constructed in this application effectively overcomes the technical bottleneck of large computational volume and easy divergence in the iteration of transcendental equations in the traditional exact state trajectory method. While ensuring high computational accuracy, this expression clarifies the analytical relationship between characteristic impedance, inductance ratio, operating frequency, and DC gain, thereby reducing the dimensionality of complex constrained multivariable coupled problems. This provides a high-efficiency and easily implementable underlying mathematical model for subsequent rapid solutions to the minimum turn-off current and for multi-objective parameter optimization that balances zero-voltage turn-on and wide voltage regulation range.

[0132] In one embodiment, the determination of the feasible region's value range must simultaneously satisfy two constraints:

[0133] Limit the excitation inductor voltage at the turn-off moment to ensure that the LLC resonant converter operates stably in PO mode within a preset load range;

[0134] Based on the approximate gain model, the normalized gain of the LLC resonant converter at the lowest operating frequency is ensured to meet the design specifications.

[0135] Specifically, in this embodiment, the determination of the feasible region's value range must simultaneously satisfy two constraints, namely:

[0136] Condition 1: Limit the magnetizing inductor voltage at the turn-off moment to ensure the LLC resonant converter operates stably in PO mode within a preset load range. If the magnetizing inductor voltage is negative at the turn-off moment and its absolute value is greater than the equivalent output voltage, the secondary side will turn on again. At this time, the magnetizing inductor is reverse-clamped, and the converter no longer operates in PO mode. Therefore, it is necessary to use the formula derived from the state trajectory to ensure that the voltage V across the magnetizing inductor at the turn-off moment is... Lm The absolute value is less than the equivalent output voltage.

[0137] Condition 2: Based on the approximate gain model, ensure that the normalized gain of the LLC resonant converter at the lowest operating frequency meets the design specifications. Specifically, in the design process of the LLC resonant converter, the lowest operating frequency usually corresponds to the maximum gain requirement. The lowest operating frequency f in the design specifications... s,min (corresponding to normalized frequency F) n,min ) and maximum gain requirement M max Substituting into the above approximate gain model, we can establish inequality constraints regarding the inductance ratio k and characteristic impedance Z0: M(k,Z0,F) n,min )≥M max This inequality limits the range of (k, Z0) combinations that satisfy the gain requirement. Combining the mode constraint from condition one, and integrating the two constraints, the feasible region that simultaneously satisfies the gain requirement and the PO mode operation requirement can be defined.

[0138] In one embodiment, the step of determining the dead time and the lower limit of the turn-off current required for zero-voltage switching based on the characteristics of the switching device, as a hard constraint, includes:

[0139] Obtain the output capacitance C of the selected switching device oss and circuit dead time t dead ;

[0140] Calculate the minimum turn-off current I required to maintain the zero-voltage switching condition based on the zero-voltage switching condition. off,min The calculation formula is:

[0141]

[0142] Among them, V in The input voltage of the converter;

[0143] The calculated minimum turn-off current Ioff,min As a hard lower limit constraint in the parameter optimization step S6, namely the turn-off current I of the final design parameters off It must be greater than or equal to the minimum turn-off current I. off,min .

[0144] Specifically, in this embodiment, the output capacitance of the selected switching device and the circuit dead time t are first obtained. dead Output capacitor C oss Dead time is an inherent parasitic parameter of the switching device, and its magnitude directly affects the amount of charge required for the switching transistor to complete charging and discharging within the dead time. Designers need to select the specific power switching device model, such as a silicon carbide MOSFET, based on the converter's design requirements, and obtain the output capacitance value under rated input voltage conditions from its official datasheet. Simultaneously, a reasonable dead time is set by considering the switching speed of the switching device, the characteristics of the drive circuit, and the converter's operating frequency. A dead time that is too short may cause bridge arm shoot-through, while a dead time that is too long will increase cycle losses; it is typically set to around several hundred nanoseconds based on engineering experience. Based on the zero-voltage switching condition, the minimum turn-off current required to maintain this condition is calculated. The core requirement of zero-voltage switching is that the resonant current must provide sufficient charge within the dead time to complete the charging and discharging of the output capacitors of the four switching transistors, causing the drain-source voltage to drop to zero before the switching transistors turn on. Based on the principle of charge conservation, the product of the turn-off current and the dead time must be greater than or equal to the product of the output capacitance and the input voltage. From this relationship, the minimum turn-off current value required to maintain zero-voltage switching can be derived. This value is the physical lower limit to ensure that the converter can achieve soft switching. Any turn-off current below this value will lead to hard switching, significantly increasing switching losses.

[0145] Finally, the calculated minimum turn-off current is used as a hard lower bound constraint in the parameter optimization step. In the subsequent global optimization process, the turn-off current corresponding to all candidate parameter combinations must be greater than or equal to this minimum value. If the turn-off current calculated for a parameter combination is less than this lower bound, it must be removed from the feasible region and considered an invalid solution that does not meet the design requirements. This ensures that the final design can achieve reliable zero-voltage switching under all operating conditions, avoiding soft-switching failures caused by improper parameter selection.

[0146] In one embodiment, the step of minimizing the turn-off current I within the determined feasible region is... off The steps involve globally optimizing parameters to achieve the target, outputting the optimal inductance ratio k and characteristic impedance Z0, and calculating the specific values ​​of the resonant inductance, resonant capacitance, and magnetizing inductance. These steps include:

[0147] Within the defined feasible region, the aforementioned lower limit constraint on the turn-off current is satisfied. off >=I off,minUnder the conditions of the approximate gain model, a numerical optimization algorithm is used to solve for minimizing the objective function, thereby obtaining the optimal inductance ratio k and the optimal characteristic impedance Z0;

[0148] Based on the optimal inductance ratio k and the optimal characteristic impedance Z0, combined with the preset resonant frequency f r Calculate the resonant inductance L r Resonant capacitor C r and excitation inductance L m The value of .

[0149] Specifically, in this embodiment, firstly, within the defined feasible region, under the conditions of satisfying the lower limit constraint of the turn-off current and the approximate gain model, a numerical optimization algorithm is used to solve for the minimization of the objective function, thereby obtaining the optimal inductance ratio and the optimal characteristic impedance. Specifically, the objective function of this optimization problem is the turn-off current, the variables to be optimized are the inductance ratio and the characteristic impedance, and the constraints include the feasible region boundary, the lower limit of the turn-off current, and the gain requirement corresponding to the approximate gain model. Within the feasible region, all possible parameter combinations are traversed with a certain step size. For each set of parameters, the corresponding turn-off current is calculated, and it is checked whether it satisfies the lower limit constraint of the turn-off current. Among all candidate solutions that satisfy the constraints, the parameter combination with the minimum turn-off current is selected as the optimal solution. This process ensures that the turn-off current is minimized while satisfying the zero-voltage switching and gain requirements, thereby effectively reducing the switching losses and cycling losses of the converter.

[0150] Secondly, based on the optimal inductance ratio k and the optimal characteristic impedance Z0, and combined with the preset resonant frequency, the resonant inductance L is calculated. r Resonant capacitor C r and excitation inductance L m The values ​​of are as follows: Specifically, the resonant inductance is determined by both the characteristic impedance and the resonant frequency; the resonant capacitance is determined by both the characteristic impedance and the resonant frequency; and the magnetizing inductance is determined by both the inductance ratio and the resonant inductance. Through the above calculations, a complete resonant cavity parameter design scheme can be obtained. This scheme minimizes the turn-off current while satisfying all design constraints, thereby significantly improving the operating efficiency and reliability of the LLC resonant converter.

[0151] In one embodiment, the resonant inductor L r Resonant capacitor C r and excitation inductance L m Calculate using the following formula: L r =Z0 / (2πf r ), C r =1 / (2πf r Z0), L m =kL r , where f r L is the resonant frequency.r For resonant inductance, C r It is a resonant capacitor.

[0152] Specifically, in this embodiment, the above three formulas are executed after step S6 completes the global parameter optimization and obtains the optimal inductance ratio k and the optimal characteristic impedance Z0. Resonant inductor L r The calculation formula is based on the definitions of characteristic impedance and resonant frequency; resonant capacitance C r The calculation formula is obtained by directly transforming the characteristic impedance expression; the magnetizing inductance L m According to the definition of inductance ratio, k=L m / L r It can be calculated directly.

[0153] Substituting the optimal parameters k and Z0 into the above formula, the calculated result is the final output resonant cavity parameter design scheme, which can be directly used for the engineering fabrication and debugging of the converter. Through the method provided in this embodiment, designers can obtain the optimal resonant cavity parameter combination that minimizes the turn-off current while meeting the requirements for zero-voltage switching and gain across the entire range, significantly improving the converter's operating efficiency and reliability.

[0154] In one embodiment, the method is used to optimize LLC resonant cavity parameters in on-board chargers, server power supplies, photovoltaic inverters, or solid-state transformers to achieve zero-voltage switching across the entire load range and minimize turn-off current.

[0155] Specifically, in this embodiment, taking an on-board charger (OBC) as an example, this converter typically faces demanding operating conditions with a wide input voltage range (200V to 450V) and a wide load range (from light load to full load). Traditional FHA methods struggle to accurately predict the shutdown current when the input voltage fluctuates significantly or the load changes abruptly, forcing designers to reserve excessively large excitation current margins to ensure ZVS, thus significantly increasing cycle losses.

[0156] The method in this embodiment first establishes a state trajectory model based on the rated power and resonant frequency of the OBC. In step S1, the wide input voltage range of the OBC is mapped to different values ​​of the normalized gain M, and corresponding circular trajectories offset on the state plane are generated. In step S2, the turn-off current expression is directly derived using the trajectory geometry, avoiding the iterative solution of transcendental equations in the traditional time-domain method, thus improving computational efficiency by several times. The approximate gain model in step S3 establishes an explicit relationship between the gain requirement of the OBC and the characteristic impedance Z0 and inductance ratio k, enabling designers to quickly evaluate the impact of different parameter combinations on the gain curve. In step S4, the feasible region of k and Z0 is defined by combining the maximum gain requirement of the OBC at the lowest input voltage and the PO mode operation constraints. In step S5, the minimum turn-off current lower limit required for ZVS is calculated based on the characteristics and dead time of the SiC MOSFET device selected for the OBC. Finally, step S6 optimizes within the feasible region with the goal of minimizing the turn-off current, and outputs the optimal parameter combination.

[0157] First, the specifications of the LLC resonant converter are set as follows: rated input voltage 375V, rated output voltage 450V, rated power 4.5kW, and resonant frequency 40kHz.

[0158] Step 1: Determine the design requirements of the LLC resonant converter in this embodiment. Set its operating frequency range to 34kHz to 40kHz, and the normalized gain to a range of 1 to 1.05. Furthermore, the converter is required to operate stably in PO mode throughout the 60% to full load range, and ensure zero-voltage switching of the primary-side transistors.

[0159] The second step is to determine the feasible range of values ​​for the resonant parameter k and the characteristic impedance Z0. To define this range, the following two constraints must be met simultaneously: first, limit the excitation inductor voltage at turn-off to ensure the converter operates in PO mode throughout its entire lifecycle; second, based on the gain formula derived above, ensure that the normalized gain of the converter reaches 1.05 at the lowest operating frequency. The range defined by the above mode constraints and gain requirements will serve as the hard boundary condition for subsequent parameter optimization aimed at minimizing the turn-off current.

[0160] Step 3: Derive the dead-time constraint and turn-off current lower limit based on SiC device characteristics. Because SiC devices exhibit significant turn-on losses and extremely low turn-off losses at high frequencies, the LLC resonant converter needs to achieve zero-voltage turn-on throughout the entire operating region to ensure overall efficiency. To ensure the primary-side switch achieves ZVS, the energy stored in the drain-source capacitor must be completely released within the dead time, which requires satisfying the following formula: Dead time, This is the output capacitor of the SiC device.

[0161]

[0162] Finally, based on the output capacitance characteristics of the selected SiC device and the dead time determined above, the minimum turn-off current required to maintain ZVS can be obtained. This minimum value will serve as a hard lower limit constraint to further define the feasible range for subsequent determination of resonance parameters.

[0163] Step 4: Global parameter optimization under constraints. Based on the turn-off current model derived above, within the feasible region of parameters determined in the previous steps (i.e., the boundary that simultaneously satisfies the PO mode, gain requirements, and the lower limit of the ZVS turn-off current), the solution is performed with the objective of minimizing the turn-off current. The resonant parameter k and characteristic impedance Z0 corresponding to the minimum point of the turn-off current obtained through optimization are the optimal combination of design parameters for the final output. Finally, the optimal design parameters are determined. Z0 = 22.06Ω. Based on this, the resonant inductance L can be further calculated. r Resonant capacitor C r and excitation inductance L m The specific values ​​are respectively , , This method is also applicable to applications requiring high power density and high efficiency, such as server power supplies, photovoltaic inverters, and solid-state transformers, and has significant engineering application value.

[0164] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0165] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0166] It should be particularly noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, or of course, by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for parameter design of SiC LLC resonant converter with optimal turn-off current, characterized in that, Includes the following steps: Step S1: Establish the state trajectory model of the LLC resonant converter in the energy transfer stage P and the three-element resonant stage O, map the resonant capacitor voltage and the resonant inductor current to the state plane, and obtain the circular trajectory corresponding to stage P and the elliptical trajectory corresponding to stage O respectively. Step S2: Based on the state trajectory model, using the law of conservation of energy and the angle relationship of the geometric trajectory, derive the switching current I of the LLC resonant converter. off Analytical equation; Step S3: Construct the voltage gain M of the LLC resonant converter in the PO mode with respect to the inductance ratio k, characteristic impedance Z0, operating power P, and switching frequency F. n Approximate gain model; Step S4: Determine the working mode and gain requirements based on the design specifications, and combine the approximate gain model to initially determine the feasible range of k and Z0. Step S5: Determine the dead time and the lower limit of the turn-off current required for zero-voltage switching based on the characteristics of the switching devices, as hard constraints. Step S6: Within the determined feasible region, minimize the turn-off current I. off The parameters are globally optimized to achieve the target, outputting the optimal inductance ratio k and characteristic impedance Z0, and the specific values ​​of resonant inductance, resonant capacitance and magnetizing inductance are calculated.

2. The SiC LLC resonant converter parameter design method for optimal turn-off current according to claim 1, characterized in that, The equation for the circular trajectory in stage P is: ； Where i LrpN For the normalized resonant inductor current in phase P, v CrpN U is the normalized resonant capacitor voltage in the P-stage, M is the normalized DC gain, and U is the voltage across the capacitor. PN Let be the radius of the circular trajectory in phase P; The equation for the elliptical state trajectory in stage O is: ； where i LroN is the normalized resonant inductance current, v CroN is the normalized resonant capacitance voltage, U oN is the trajectory radius for the O phase.

3. The SiC LLC resonant converter parameter design method for optimal turn-off current according to claim 1, characterized in that, The turn-off current I in step S2 off The system of equations is as follows ； Where P is the operating power of the LLC resonant converter, and V base Here, k is the voltage reference of the LLC resonant converter, Z0 is the inductance ratio of the LLC resonant converter, and F is the characteristic impedance of the LLC resonant converter. n Let be the normalized switching frequency of the LLC resonant converter; where AE, AF, EC, FC, GF, and HE represent the geometric segment lengths on the state trajectory. .

4. The SiC LLC resonant converter parameter design method with optimal turn-off current according to claim 1, characterized in that, The expression for the approximate gain model in step S3 is: ； Where P is the operating power of the LLC resonant converter, and V base F serves as the voltage reference for the LLC resonant converter. n Let k be the normalized switching frequency of the LLC resonant converter, and k be the inductance ratio of the LLC resonant converter. .

5. The SiC LLC resonant converter parameter design method for optimal turn-off current according to claim 1, characterized in that, The determination of the feasible region value range in step S4 requires the simultaneous satisfaction of two constraints, namely: Limit the excitation inductor voltage at the turn-off moment to ensure that the LLC resonant converter operates stably in PO mode within a preset load range; Based on the approximate gain model, the normalized gain of the LLC resonant converter at the lowest operating frequency is ensured to meet the design specifications.

6. The SiC LLC resonant converter parameter design method for optimal turn-off current according to claim 1, characterized in that, The step of determining the dead time and the lower limit of the turn-off current required for zero-voltage switching based on the characteristics of the switching device, as a hard constraint, includes: acquiring an output capacitance C of the selected switching device oss and a circuit dead time t dead ; According to the zero voltage switching condition, the minimum turn-off current I required to maintain the zero voltage switching condition is calculated off,min The calculation formula is: ； wherein V in is the input voltage of the converter; The calculated minimum turn-off current I off,min As a hard lower limit constraint in the parameter optimization step S6, i.e. the turn-off current I off Satisfies the condition of being greater than or equal to the minimum turn-off current I off,min .

7. The SiC LLC resonant converter parameter design method for optimal turn-off current according to claim 1, characterized in that, Within the defined feasible region, the goal is to minimize the turn-off current I. off The steps for performing global parameter optimization for the target, outputting the optimal inductance ratio k and characteristic impedance Z0, and calculating the specific values ​​of resonant inductance, resonant capacitance, and magnetizing inductance include: Within the defined feasible region, the aforementioned lower limit constraint on the turn-off current is satisfied. off >=I off,min Under the conditions of the approximate gain model, a numerical optimization algorithm is used to solve for minimizing the objective function, thereby obtaining the optimal inductance ratio k and the optimal characteristic impedance Z0; According to the optimal inductance ratio k and the optimal characteristic impedance Z0, in combination with a preset resonant frequency f r , the values of resonant inductance L r , resonant capacitance C r and excitation inductance L m are calculated.

8. The SiC LLC resonant converter parameter design method with optimal turn-off current according to claim 1, characterized in that, The resonant inductor L r Resonant capacitor C r and excitation inductance L m Calculate using the following formula: L r =Z0 / (2πf r ), C r =1 / (2πf r Z0), L m =kLr, where f r L is the resonant frequency. r For resonant inductance, C r It is a resonant capacitor.

9. The SiC LLC resonant converter parameter design method for optimal turn-off current according to any one of claims 1 to 8, characterized in that, The method is used to optimize LLC resonant cavity parameters in on-board chargers, server power supplies, photovoltaic inverters, or solid-state transformers to achieve zero-voltage switching across the entire load range and minimize turn-off current.

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