Parameter optimization method of bidirectional CLLC resonant converter based on data driving

Abstract

The invention relates to the technical field of bidirectional CLLC resonant converter design, and discloses a parameter optimization method of a bidirectional CLLC resonant converter based on data driving. On the basis of a time domain numerical analysis method and an adaptive polynomial approximation method, under the working conditions of maximum output power and minimum input voltage of the CLLC converter, in a G2V mode and a V2G mode, an agent model of a constrained closed parameter space and total power loss of the CLLC converter is established, and meanwhile, an agent model of upper and lower boundaries of the constrained closed parameter space is established; according to the method, a resonant cavity is used as a parameter space, an upper boundary and a lower boundary of the resonant cavity parameter space and a comprehensive minimum value of total power loss in a G2V mode and a V2G mode are used as an optimization target, multi-target optimization solution is carried out by using an NSGA-II algorithm, an optimal resonance parameter scheme is further obtained, the obtained optimal resonance parameter scheme has more balanced performance, bidirectional high-efficiency operation of the CLLC converter is ensured, and the reliability of the CLLC converter is improved. And the peak efficiency is 95.8%.

Description

Technical Field

[0001] The present invention relates to the technical field of bidirectional CLLC resonant converter design, and in particular to a parameter optimization method of a bidirectional CLLC resonant converter based on data driving. Background Art

[0002] With the rapid advancement of global science and technology, the development and utilization of energy in various countries is also increasing. As far as the automotive industry is concerned, the development of electric vehicles has become an indispensable choice for the global automotive industry. V2G and G2V technologies are important components of the interaction between electric vehicles and the power grid. They improve the efficiency and stability of the power grid through two-way energy flow, and also provide economic incentives and environmentally friendly energy supply methods for electric vehicle users.

[0003] G2V technology allows the grid to provide energy to electric vehicles, and vehicles can adjust charging time and speed according to grid demand to maximize the use of clean energy and support the grid during peak hours.

[0004] V2G technology allows electric vehicles to be connected to the power grid, combining the randomness and intermittent characteristics of electric vehicle battery charging with the problem of grid load demand fluctuations, and proposes a common solution. In V2G technology, the on-board charger must have the ability to transmit energy in both directions, can charge and discharge the on-board battery according to the instructions of the power grid, and have the characteristics of high power density, high efficiency, and wide voltage gain. Therefore, it is necessary to study the circuit topology of the resonant DC / DC converter at the rear stage of the on-board charger.

[0005] The CLLC resonant converter has a simple structure, high efficiency, low electromagnetic interference, and can realize two soft switching technologies: primary zero voltage switching ZVS (Zero Voltage Switching) and secondary zero current switching ZCS (Zero Current Switching). In DC charging piles or OBCs, bidirectional DC / DC isolation modules often use CLLC resonant converters to achieve energy transmission. In order to achieve high efficiency, high power density, high switching frequency and soft switching operation of the CLLC resonant converter, it is necessary to optimize the parameters of the bidirectional CLLC resonant converter.

[0006] Existing studies have optimized the resonant cavity parameters of bidirectional CLLC resonant converters by considering the gain and loss characteristics of the converter. The literature [P. He and A. Khaligh, Comprehensive Analyses and Comparison of 1kW Isolated DC–DC Converters for Bidirectional EV Charging Systems [J]. IEEE Transactions on Transportation Electrification, vol. 3, no. 1, pp. 147-156, March 2017.] proposed a CLLC resonant converter parameter optimization design method based on time domain analysis. This method can always achieve the bidirectional voltage gain requirements of the CLLC resonant converter and soft switching operation under all working conditions. However, the optimization target only selects the total power loss of the magnetic components; the main function of the CLLC resonant converter is to achieve efficient power transmission. Therefore, the challenge of the CLLC resonant converter is not voltage regulation, but optimizing the conversion efficiency. In order to achieve high efficiency, the total power loss of the CLLC resonant converter needs to be further optimized. The literature [B. Zhao, X. Zhang, and J. Huang, AI algorithm-based two-stage optimal design methodology of high-efficiency CLLC resonant converters for the hybrid AC–DC microgrid applications [J]. IEEE Transactions on Industrial Electronics, vol. 66, no. 12, pp. 9756–9767, Dec. 2019.] established a full power loss model of the CLLC resonant converter and used an artificial intelligence algorithm to determine the optimal candidate parameter solution.However, when optimizing parameters among a large number of candidate solutions, the resonant parameters are discrete and the optimal solution is easily missed; the literature [Lin, X. Zhang and X. Li, Design Methodology for Symmetric CLLC Resonant DC Transformer Considering Voltage Conversion Ratio, System Stability, and Efficiency [J]. IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10157-10170, Sept. 2021.] proposed an optimal parameter design method for CLLC resonant converter based on artificial intelligence algorithm, with the goal of simultaneously meeting the voltage conversion ratio, system stability and system efficiency as the optimization design objectives. However, the resonant parameters are designed under a fixed input voltage, and the optimal solution cannot be guaranteed within a wide input voltage range; although ergodic parameter optimization may be a feasible strategy, the high computational cost makes this method difficult to implement. Reference [R. Wei, L. Ding, R. Liu and Y. Li, An Intuitive and Noniterative Design Methodology for CLLC Chargers Employing Simplified Operation Modes Model [J]. IEEE Transactions on Power Electronics, vol. 38, no. 6, pp. 7771-7784, June 2023.] proposes an intuitive and non-iterative CLLC resonant converter parameter optimization design method based on time domain analysis. Its optimization target is the total power loss of the circuit, and only soft switching implementation and operating mode are used as constraints. Although the existing research has made great contributions to the parameter optimization of bidirectional CLLC resonant converters, it still has the following shortcomings: 1) When performing parameter optimization design, the parameter constraint selection is not comprehensive enough; 2) The parameter optimization design is not performed within the bidirectional wide voltage operating range; 3) In the parameter optimization process, the resonant parameters are discrete, and it is easy to miss the optimal solution.

[0007] Therefore, a parameter optimization method of a bidirectional CLLC resonant converter based on data driving is proposed to solve the above problems. Summary of the invention

[0008] In view of the above problems, the purpose of the present invention is to provide a parameter optimization method for a bidirectional CLLC resonant converter based on data-driven, taking into account more comprehensive parameter constraints, within the bidirectional wide voltage operating range, based on a time domain numerical analysis method and an adaptive polynomial approximation method, taking the upper and lower boundaries of the resonant cavity parameter space, the comprehensive minimum value of the total power loss in the G2V mode and the V2G mode as the optimization target to perform parameter optimization design, and then obtain the optimal resonant parameter solution. The technical solution is as follows:

[0009] A parameter optimization method for a bidirectional CLLC resonant converter based on data drive comprises the following steps:

[0010] Step S1, determining the design range of the resonant cavity parameters;

[0011] Step S2: Based on the time domain numerical analysis method, under the working conditions of maximum output power and minimum input voltage of the bidirectional CLLC resonant converter, taking into account the working mode constraint, soft switching constraint, switching frequency constraint and resonant capacitor voltage stress constraint, the excitation inductance L is established in the G2V mode and V2G mode respectively. m , resonant inductor L r and resonant capacitor C r The closed parameter space of

[0012] Step S3: Based on the time domain numerical analysis method, under the working conditions of the maximum output power and minimum input voltage of the bidirectional CLLC resonant converter, taking into account the switch tube conduction loss P S_on , switch tube turn-off loss P S_off , Transformer core loss P T_Fe and transformer copper loss P T_Cu The total power loss P loss ;

[0013] Step S4: Use the adaptive polynomial approximation method to establish a proxy model of the parameter space, and use the adaptive polynomial approximation method to establish the parameter space and the total power loss P loss The proxy model;

[0014] Step S5: Perform multi-objective optimization using the NSGA-II algorithm to obtain the optimal parameter solution.

[0015] Furthermore, the step S1 comprises:

[0016] S11, set the primary resonant inductance L r1 Equal to the secondary resonant inductance L r2 , and unified by the resonant inductor L r Indicates; primary resonant capacitor C r1 Equal to the secondary side resonant capacitor C r2 , and unified by the resonant capacitor C rexpress;

[0017] S12, set the resonant inductance L r , resonant capacitor C r The value range and iteration step size of

[0018] S13, select the resonant inductor L r , resonant capacitor C r As an independent variable, the excitation inductance L m as the dependent variable.

[0019] Furthermore, the working mode constraint in step S2 is:

[0020] A1. Select the CLLC resonant converter to work in PO working mode for parameter optimization design;

[0021] A2, the upper boundary is the boundary between the PO working mode and the PON working mode;

[0022] A3. The lower boundary is the boundary between the PO working mode and the OPO working mode.

[0023] Furthermore, the soft switch constraint in step S2 is:

[0024] Flowing through the magnetizing inductance L m The initial value of the resonant current I m It is necessary to fully discharge the junction capacitance of the switch tube within the dead time, so the specific conditions for achieving soft switching ZVS are:

[0025]

[0026] Among them, I ZVS_min is the minimum resonant current to achieve ZVS on the primary side, t dead is the dead time between the gate level signals of the two main switches, C eq is the equivalent output capacitance of the switch tube, V in is the input voltage, i Lr1P It is the primary resonant current of the bidirectional CLLC resonant converter in P working mode.

[0027] Furthermore, the switching frequency constraint in step S2 is:

[0028] The switching frequency at the maximum output power and minimum input voltage is set as the minimum switching frequency.

[0029] Furthermore, in step S2, the voltage stress constraint of the resonant capacitor is:

[0030] When the CLLC resonant converter works in PO mode, the maximum voltage stress of the primary and secondary resonant capacitors is:

[0031]

[0032] Among them, V Cr1_MAX is the maximum voltage stress of the primary resonant capacitor, V Cr2_MAX is the maximum voltage stress of the secondary resonant capacitor, v Cr1P (t) is the normalized time domain expression of the primary resonant capacitor voltage in P mode, v Cr2P (t) is the normalized time domain expression of the secondary resonant capacitor voltage in P mode, Δt x It is the time that the bidirectional CLLC resonant converter operates in P mode.

[0033] Furthermore, the step S3 comprises:

[0034] C1. Calculate the switch conduction loss P S_on

[0035] The effective value of the primary resonant current I r_rms , the effective value of the secondary current I S_rms And the switch tube on resistance R d_on Calculate the switch conduction loss P S_on :

[0036]

[0037] Among them, Δt x is the time that the bidirectional CLLC resonant converter works in P mode, i Lr1P is the primary resonant current of the bidirectional CLLC resonant converter in P working mode, i Lr1O is the primary resonant current of the bidirectional CLLC resonant converter in the O working mode, i Lr2P is the secondary resonant current of the bidirectional CLLC resonant converter in P working mode, T s is the switching cycle;

[0038] C2. Calculate the switch off loss P S_off

[0039] Calculate the switch off current i off , the switch off current i off The expression is as follows:

[0040]

[0041] Among them, i Lm_end is the linear peak value of the excitation current of the switch tube during the dead time, t dead is the dead time between the gate level signals of the two main switches, C eq is the equivalent output capacitance of the switch tube;

[0042] Calculate the switch off voltage v off , switch off voltage v off The expression is as follows:

[0043]

[0044] The switch turns off the current i off and the switch off voltage v off Calculate the switch turn-off loss P S_off , the formula is as follows:

[0045]

[0046] Among them, f s is the operating frequency;

[0047] C3. Calculate the transformer core loss P T_Fe

[0048] Calculate the transformer core loss P using the Steinmetz formula T_Fe :

[0049] P T_Fe =C m f s α B β

[0050] Among them, C m , α, β are empirical parameters related to the magnetic core, f s is the operating frequency, B is the magnetic flux density of the core;

[0051] The magnetic flux density B of the core is:

[0052]

[0053] Among them, V o is the voltage across the transformer coil, N s is the number of turns of the transformer secondary winding, A m is the effective area of ​​the core cross section;

[0054] C4. Calculate the transformer copper loss P T_Cu

[0055] The effective value of the primary resonant current I r_rms And the transformer primary equivalent AC resistance R T_ac Calculate the transformer copper loss P T_Cu :

[0056] P T_Cu =I r_rms 2 R T_ac

[0057] C5. Calculate the total power loss P loss

[0058] Total power loss P loss Including the switch conduction loss P S_on , switch tube turn-off loss P S_off , Transformer core loss P T_Fe and transformer copper loss P T_Cu , the calculation formula is as follows:

[0059] P loss =P S_on +P S_off +P T_Fe +P T_Cu

[0060] Furthermore, in step S4, the proxy model is established using an adaptive polynomial approximation method, including the following steps:

[0061] B1. Set the error control parameter ∈;

[0062] B2. Establish interaction between Matlab and Mathematical through NETLink;

[0063] B3, using Legendre polynomials as orthogonal basis functions;

[0064] B4, only one element 0 T Initialize sampling point ξ i ;

[0065] B5. According to the obtained sampling point ξ i Compute the corresponding orthogonal polynomial basis function φ i (ξ i );

[0066] B6, at the obtained sampling point ξ i Based on this, the corresponding system response y(ξ i );

[0067] B7. Calculate the polynomial coefficient c i ;

[0068] B8. According to the polynomial coefficient c i , and calculate the approximation error;

[0069] B9, determine whether the error satisfies the control parameter ∈; if the error does not satisfy the control parameter ∈, return to step S44, and calculate the error according to the polynomial coefficient c i Update the sampling points according to the change of i +1(ξ)=0;

[0070] B10. If the error satisfies the control parameter ∈, the proxy model y(ξ i )=φ i (ξ i )c i .

[0071] Furthermore, the step S4 comprises:

[0072] S41. Establishment of a proxy model for the upper boundary of the resonant cavity parameter space of a bidirectional CLLC resonant converter

[0073] Using the adaptive polynomial approximation method, a proxy model of the upper boundary of the parameter space taking into account all the constraints in step 2 is established in the G2V mode and the V2G mode respectively; the explicit polynomial expressions of the proxy model of the upper boundary of the parameter space in the G2V mode and the V2G mode are denoted as f up_G2V (C r ,L r ), f up_V2G (C r ,L r );

[0074] S42. Establish a proxy model for the lower boundary of the resonant cavity parameter space of the bidirectional CLLC resonant converter

[0075] Using the adaptive polynomial approximation method, a proxy model of the lower boundary of the parameter space taking into account all the constraints in step 2 is established in the G2V mode and the V2G mode respectively; the explicit polynomial expressions of the proxy model of the lower boundary of the parameter space in the G2V mode and the V2G mode are denoted as f low_G2V (C r ,L r ), f low_V2G (C r ,L r );

[0076] S43, establish parameter space and total power loss P loss Proxy Model

[0077] The parameter space and the total power loss P are established in G2V mode and V2G mode respectively using the adaptive polynomial approximation method. loss The proxy model of G2V mode and V2G mode is used to compare the parameter space and the total power loss P loss The explicit polynomial expressions of the surrogate model are denoted as f Ploss_G2V (C r ,L r ,L m ) and f Ploss_V2G (C r ,L r ,L m).

[0078] Furthermore, the step S5 comprises:

[0079] The three parameters of the resonant cavity are designed within the parameter space so that the bidirectional CLLC resonant converter can achieve the comprehensive minimum value of the total power loss in the G2V mode and the V2G mode. The parameter optimization design is summarized as follows:

[0080]

[0081] The Pareto optimal trade-off solution is obtained through the NSGA-II algorithm, and then the optimal resonance parameter solution is obtained.

[0082] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0083] Based on the time domain numerical analysis method and the adaptive polynomial approximation method, under the working conditions of the maximum output power and the minimum input voltage of the CLLC converter, the present invention establishes a proxy model of the constrained closed parameter space and the total power loss of the CLLC converter in the G2V mode and the V2G mode respectively, and at the same time establishes a proxy model of the upper and lower boundaries of the constrained closed parameter space, and takes the upper and lower boundaries of the resonant cavity parameter space and the comprehensive minimum value of the total power loss in the G2V mode and the V2G mode as the optimization target, uses the NSGA-II algorithm to perform multi-objective optimization and solve, and then obtains the optimal resonant parameter scheme to ensure the bidirectional high-efficiency operation of the CLLC converter, with a peak efficiency of 95.8%; this scheme considers more comprehensive parameter constraints, takes the upper and lower boundaries of the resonant cavity parameter space and considers more comprehensive total power loss as the optimization targets within the bidirectional wide voltage operating range, so that the optimal resonant parameter scheme has a more balanced performance; through the proxy model established based on the adaptive polynomial approximation theory to perform multi-objective optimization and solve, the complexity of the calculation is effectively reduced, the number of iterations is reduced, and the computing resources are saved. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a CLLC resonant converter topology.

[0085] Figure 2 Equivalent circuit diagram of the basic operating mode of the CLLC resonant converter, where (a) P mode; (b) N mode; (c) O mode.

[0086] Figure 3 The closed parameter space considering the working modal constraints in G2V mode and V2G mode, where (a) G2V mode; (b) V2G mode.

[0087] Figure 4The closed parameter space considering the operating modal constraints and ZVS implementation constraints, where (a) G2V mode; (b) V2G mode.

[0088] Figure 5 The closed parameter space considering the operating mode constraints, ZVS implementation constraints and switching frequency constraints, where (a) G2V mode; (b) V2G mode.

[0089] Figure 6 It is a closed parameter space that takes into account the operating mode constraints, ZVS implementation constraints, switching frequency constraints and resonant capacitor voltage stress constraints, where (a) G2V mode; (b) V2G mode.

[0090] Figure 7 Graph showing the relationship between total power loss and resonance parameters, where (a) is the G2V mode and (b) is the V2G mode.

[0091] Figure 8 Proxy models of the upper surface of the parameter space and their error distribution, where (a) the upper surface of the parameter space taking into account all constraints in the G2V mode; (b) the upper surface of the parameter space taking into account all constraints in the V2G mode; (c) the proxy model of the upper surface of the parameter space in the G2V mode; (d) the proxy model of the upper surface of the parameter space in the V2G mode; (e) the error distribution between the proxy model of the upper surface of the parameter space in the G2V mode and the time-domain numerical analysis method; (f) the error distribution between the proxy model of the upper surface of the parameter space in the V2G mode and the time-domain numerical analysis method.

[0092] Fig. 9 Proxy models of the lower surface of the parameter space and their error distribution, where (a) the lower surface of the parameter space taking into account all constraints in the G2V mode; (b) the lower surface of the parameter space taking into account all constraints in the V2G mode; (c) the proxy model of the lower surface of the parameter space in the G2V mode; (d) the proxy model of the lower surface of the parameter space in the V2G mode; (e) the error distribution between the proxy model of the lower surface of the parameter space in the G2V mode and the time-domain numerical analysis method; (f) the error distribution between the proxy model of the lower surface of the parameter space in the V2G mode and the time-domain numerical analysis method.

[0093] Fig.10 Proxy models for the relationship between total power loss and resonant parameters and their error distribution, including (a) proxy model for the relationship between total power loss and resonant parameters in G2V mode; (b) proxy model for the relationship between total power loss and resonant parameters in V2G mode; (c) error distribution between the proxy model for the relationship between total power loss and resonant parameters in G2V mode and the time domain numerical analysis method; (d) error distribution between the proxy model for the relationship between total power loss and resonant parameters in V2G mode and the time domain numerical analysis method.

[0094] Fig.11 Schematic diagram of the Pareto optimal trade-off solution.

[0095] Fig.12 Comparison of the total power loss variation range within a wide voltage range between the FHA method and this design method, where (a) is the G2V mode; (b) is the V2G mode.

[0096] Fig.13 Graph showing the system efficiency variation over a wide voltage range, including (a) G2V mode and (b) V2G mode. DETAILED DESCRIPTION

[0097] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention, so as to have a further understanding of the concept of the present invention, the technical problems solved, the technical features constituting the technical solution and the technical effects brought about.

[0098] The present invention proposes a multi-objective parameter optimization design method for a bidirectional CLLC resonant converter based on adaptive polynomial approximation theory. Firstly, based on the time domain numerical analysis method, under the worst working condition of PO mode, the working mode constraint, switching frequency constraint, soft switching constraint and resonant capacitor voltage stress constraint are taken into account. The resonant cavity excitation inductance L is established in G2V mode and V2G mode respectively. m , resonant inductor L r and resonant capacitor C r The closed parameter space of the CLLC resonant converter in G2V mode and V2G mode is established respectively, and this is used as the optimization target of this parameter design; based on the adaptive polynomial approximation theory, a proxy model of the parameter space and the optimization target is established, and the parameter space and the optimization target are fitted to obtain an explicit expression; the NSGA-II algorithm is selected for multi-objective optimization solution, and the performance of the resonant parameters designed by the traditional FHA design method is compared. The experimental prototype of the 1000W / 400V bidirectional CLLC resonant converter is constructed to verify the effectiveness and rationality of the design method. The peak efficiency of the bidirectional operation of the CLLC converter is 95.8%. The specific implementation process is as follows:

[0099] 1. Determine the design range of the resonant cavity parameters;

[0100] The main working conditions of the CLLC resonant converter are shown in Table 1. In order to reduce the switching frequency variation range, the CLLC resonant converter is designed to have a symmetrical working range in both the G2V mode and the V2G mode. Therefore, the transformer ratio is designed to be 1;

[0101] Table 1 Main operating conditions of CLLC resonant converter

[0102]

[0103] In order to analyze the resonant cavity parameter L r1 , L r2 , L m , C r1 and C r2 The influence on the working mode and form a closed parameter space, select L r1 , L r2 , C r1 and C r2 As an independent variable, L m As the dependent variable, since at the resonant frequency, L r1 and C r1 The equivalent impedance is zero, and the main loss of the converter depends on the excitation inductance; it should be noted that since the transformer ratio is equal to 1, L r1 =L r2 , C r1 =C r2 In addition, the present invention sets the range of the resonance parameter to L r =L r1 =L r2 =25~100μH,C r =C r1 =C r2 =20~80nF, and L r and C r The iteration step sizes are set to 5μH and 5nF respectively. r1 , L r2 , C r1 , C r2 and L m The relationship between is five-dimensional, but L r1 =L r2 , C r1 =C r2 , in order to facilitate the subsequent analysis, L r1 and L r2 Unified with L r Indicates that C r1 and C r2 Unified with C r Therefore, the five-dimensional relationship is transformed into a three-dimensional relationship, and then the three-parameter space of the resonant cavity can be obtained.

[0104] 2. Establishment of the cavity closure parameter space of the bidirectional CLLC converter taking into account comprehensive constraints based on the time domain numerical analysis method

[0105] like Figure 1 As shown in the figure, the topology of the bidirectional CLLC resonant converter is given. The resonant inductor L r1 , L r2 , Excitation inductance Lm and resonant capacitor C r1 , C r2 To form a resonant cavity; in order to achieve the symmetry between the G2V mode and the V2G mode, the secondary resonance parameters are converted to the primary side, which is expressed as:

[0106]

[0107] Among them, L rp , L rs , C rp and C rs are the resonant inductance and capacitance of the primary and secondary sides respectively, and N is the transformer ratio.

[0108] like Figure 2 As shown in the figure, based on different working conditions, the CLLC resonant converter can be divided into three basic working modes in one switching cycle: P (positive clamping) mode, N (negative clamping) mode, and O (intermittent) mode. When the circuit works in P mode, the resonant inductor L r1 and resonant capacitor C r1 Resonance, resonant cavity output voltage v cd NV o Clamp; When the circuit works in N mode, the resonant inductor L r1 and resonant capacitor C r1 Resonance, resonant cavity output voltage v cd NV o Clamping; when the circuit works in O mode, the excitation inductance L m , resonant inductor L r1 and resonant capacitor C r1 In ternary resonance, there is no energy exchange between input and output. Taking the basic mode P as an example, the circuit state equation can be described as follows:

[0109]

[0110] Among them, i Lr1P 、i Lr2P 、v Cr1P and v Cr2P are the resonant current and resonant capacitor voltage of the primary and secondary sides in P mode, i LmP is the excitation current in P mode.

[0111] By using Laplace transform and inverse Laplace transform for formula (2), the normalized time domain expressions of P-mode resonant current and resonant capacitor voltage are as follows:

[0112]

[0113] Where k = L r1 / L m , k1 =(k / k+2) 1 / 2 , P 1 , P 2 , P 3 and P 4 are all unknown quantities, and they are only related to the initial state of the resonant circuit. M is the voltage gain of the resonant cavity, and M = NV o / V in .

[0114] The reference values ​​of impedance, voltage, current, and switching frequency are as follows:

[0115]

[0116] From formula (3), we can see that the frequency response of the resonant circuit has not only the resonant frequency f r , and an additional frequency k 1 Therefore, compared with the traditional FHA design method, the time domain model can more accurately describe the working state of the resonant converter. Similarly, the normalized time domain expressions of the N-mode resonant current and resonant capacitor voltage are as follows:

[0117]

[0118] Among them, N 1 、N 2 、N 3 and N 4 are all unknown quantities, and they are only related to the initial state of the resonant circuit. Comparing formula (3) and formula (5), it can be seen that the only difference is that the signs of the resonant cavity voltage gain M are opposite, because when the circuit works in the N mode, the resonant cavity output voltage v cd NV o Clamp.

[0119] Mode O is different from mode P or N. Its resonant circuit is a typical LC series resonant network. Therefore, the resonant current is equal to the excitation current. Similarly, the normalized time domain expressions of the O mode resonant current and the resonant capacitor voltage are as follows:

[0120]

[0121] Among them, k 2 =(k / k+1) 1 / 2 , O 1 and O 2 are all unknown quantities, and they only depend on the initial state of the resonant circuit.

[0122] In a half-switching cycle, the combination of different basic modes constitutes various working modes of the CLLC resonant converter, and its main working modes include: PO, PON, PN, NP, NOP and OPO. The present invention selects the CLLC resonant converter to work in the PO mode for parameter optimization design, because the circuit working in the PO mode can easily achieve ZVS and has lower reactive power loss. In addition, the voltage gain in the PO mode increases monotonically with the decrease of the switching frequency, which ensures the control stability in the closed-loop design. Moreover, compared with the other working modes mentioned above, the numerical calculation complexity of the PO mode is greatly reduced because it only involves 2 basic modes in a half-switching cycle.

[0123] Since the resonant inductor current i Lr1 and i Lr2 , resonant capacitor voltage v Cr1 and v Cr2 And the magnetizing inductor current i Lm It is symmetrical in the positive and negative half switching cycles, so only the positive half switching cycle needs to be analyzed to obtain the operating characteristics of the resonant converter.

[0124] When the CLLC resonant converter transfers from one operating mode to another, the resonant current and the resonant capacitor voltage cannot change suddenly, so the continuity condition of the resonant current and the resonant capacitor voltage can be expressed as:

[0125]

[0126] Among them, Δt x It is the time experienced by the first mode in the working mode, that is, the time experienced by the P mode.

[0127] Due to the symmetry of the CLLC resonant converter, within half a switching cycle, i Lr1 、i Lr2 、v Cr1 , and v Cr2 The initial value of is opposite to the final value, so the symmetry condition of the resonant current and the resonant capacitor voltage can be described as:

[0128]

[0129] When the CLLC resonant converter works in O mode, there is no energy exchange between the primary and secondary sides, that is, the output current is intermittent, and the secondary diode is only turned on when the converter works in P mode. Therefore, the output current I o It can be expressed as:

[0130]

[0131] Among them, f n =f s / fr is the normalized operating frequency, I outn =I o / I base is the normalized output current. Substitute formula (3-4) and formula (6) into formula (7-9), and use V o 、V in ,I o and N as known quantities, the corresponding operating frequency f is obtained by solving 8 transcendental equations s and the corresponding resonant current and voltage variables, including: P 1 , P 2 , P 3 , P 4 , O 1 , O 2 and Δt x .

[0132] When the operating frequency f s Greater than the resonant frequency f r When , the CLLC resonant converter prefers to work in NP mode.

[0133] Similarly, the symmetry and continuity conditions of the resonant current and resonant capacitor voltage of the CLLC resonant converter in NP mode can be described as:

[0134]

[0135] Compared with the PO mode, when the CLLC resonant converter operates in the NP mode, the secondary diode is turned on not only during the P mode, but also during the N mode. Therefore, the output current can be derived as:

[0136]

[0137] Substitute formula (5) into formula (10-11), and use V o 、V in ,I o and N as known quantities, the corresponding operating frequency f is obtained by solving 10 transcendental equations s and the corresponding resonant current and voltage variables, including: P 1 , P 2 , P 3 , P 4 、N 1 、N 2 、N 3 、N 4 and Δt x .

[0138] Based on the above time domain numerical analysis and calculation method, combined with the comprehensive performance of the CLLC resonant converter, its physical model was established, and the resonant circuit working mode, soft switching, switching frequency, and resonant capacitor voltage stress were used as constraints to determine the resonant cavity L in the G2V mode and V2G mode. m , L r and C r Closed parameter space.

[0139] 1) Working mode constraints

[0140] When the CLLC resonant converter operates at minimum input voltage and maximum output power, it is very easy to enter the PON mode, which is undesirable for the following reasons:

[0141] (1) The gain-frequency curve of the PON mode is non-monotonic near the peak gain operating point, which may lead to control instability. Since pulse frequency modulation is usually used to control LLC resonant converters, in which the voltage gain increases with the decrease of switching frequency, once the slope of the gain-frequency curve changes, the gain will increase with the increase of switching frequency, and the output voltage will be adjusted in the opposite direction, which will cause the PFM controller to malfunction. (2) The PON mode may also cause the circuit to operate in a hard switching state, which reduces the conversion efficiency. In addition, since the current of the primary switch tube when it is turned on in the PON mode is usually very small, a large dead time is required to completely discharge the junction capacitance of the switch tube and achieve ZVS, which also reduces the conversion efficiency. Therefore, the operating conditions of maximum output power and minimum input voltage can be regarded as the worst operating conditions. In order to avoid the problem of zero switching at the input voltage V in And the output power P o When the PON mode appears during the change, the PO mode should be guaranteed to operate under the worst working condition;

[0142] According to formula (6), when the resonant converter operates in PO mode, the time domain expression of the excitation inductor voltage in the O mode stage can be derived as follows:

[0143] v LmO (t) = L m *(-k 2 O 1 sin(k 2 t)-k 2 2 (O 2 -1)cos(k 2 t)) (12)

[0144] Then, the resonant cavity output voltage v cd The time domain expression in the O mode stage can be derived as:

[0145] v cdO(t) = V LmO (t)-V Cr2O (t)(13)

[0146] With the output power P o The increase and output power P o The CLLC resonant converter will enter the PON mode from the PO mode, and within half a switching cycle, v cdO The final value will become lower than -NV o Therefore, the boundary condition between the PON mode and the PO mode can be expressed as:

[0147] v cdO (T s / 2-Δt x )<-NV O (14)

[0148] With the output power P o The decrease of input voltage V in As the CLLC resonant converter operates in the PO mode, the CLLC resonant converter will enter the OPO mode from the PO mode. However, when the CLLC resonant converter operates in the OPO mode, the effective value of the resonant current will be too high, which will lead to high reactive power loss and low conversion efficiency. In order to avoid the converter operating in the OPO mode, the boundary conditions between the OPO mode and the PO mode are analyzed. According to formula (3), when the LLC resonant converter operates in the PO mode, the v of the mode P stage LmP The initial value of can be expressed as:

[0149] v LmP (t) = L m (Mk 1 2 cos(k 1 t)+k 1 2 (1-P 1 +P 2 )cos(k 1 t))(15)

[0150] Then, the resonant cavity output voltage v cd The time domain expression in the P mode stage can be derived as:

[0151] v cdP (t) = V LmP (t)-V Cr2P (t)(16)

[0152] When v cdP (0)Below NV oWhen , the CLLC resonant converter will enter the OPO mode from the PO mode, so the boundary condition between the OPO mode and the PO mode can be expressed as:

[0153] v cdP (0)<NV O (17)

[0154] The four independent variables L r1 , L r2 , C r1 and C r2 Substitute into formulas (3-4) and (6-9) to solve for the resonant current and voltage variables O 1 , O 2 , P 1 , P 2 , the time Δt experienced by the P mode x and the switching period T s , and then substitute it into the boundary conditions given in formulas (12 to 17) to solve the corresponding dependent variable L m ,Therefore, the closed parameter space considering the working modal constraints in G2V mode and V2G mode is established successfully respectively;

[0155] Figure 3 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o =1000W) with the resonant cavity L considering the working mode constraint r , L m and C r The closed parameter space of Figure 3 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o =1000W) with the resonant cavity L considering the working mode constraint r , L m and C r The closed parameter space of Figure 3 As shown, the upper surface is the boundary between the PON mode and the PO mode, and the lower surface is the boundary between the PO mode and the OPO mode.

[0156] 2) Soft switching constraints

[0157] In order to ensure that the primary side ZVS can be achieved, the resonant current should be able to completely discharge the junction capacitance of the switch tube within the dead time at the initial moment. Therefore, the ZVS realization condition can be expressed as:

[0158]

[0159] Among them, I ZVS_min is the minimum resonant current to achieve ZVS on the primary side, t dead is the dead time between the gate level signals of the two main switches, C eq is the equivalent output capacitance of the switch tube, V in is the input voltage, i Lr1P is the primary resonant current of the bidirectional CLLC resonant converter in the P working mode. The present invention sets C eq =1200pF, t dead =200ns. Similarly, the independent variable L r1 , L r2 , C r1 and C r2 Substitute into formulas (3-4) and (6-9) to solve for the initial value of the resonant current I m , put it into formula (18), and the corresponding dependent variable L can be determined m ;

[0160] The CLLC resonant converter is very likely to lose ZVS operation when operating at maximum output power and minimum input voltage. This condition is considered the worst condition for achieving ZVS. Figure 4 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o =1000W) and considering the ZVS constraint resonant cavity L r , L m and C r The closed parameter space of Figure 4 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o =1000W) and considering the ZVS constraint resonant cavity L r , L m and C r The closed parameter space of the upper surface is the ZVS implementation constraint on the left, and the PO / PON working mode constraint on the right. Figure 4 Note that the surface of the boundary PO / PON disappears because the surface constrained by the ZVS implementation is lower than the surface of the boundary PO / PON.

[0161] 3) Switching frequency constraints

[0162] In order to ensure the power density, the present invention limits the minimum switching frequency to 70kHz. r1 , L r2 , C r1 and C r2Substitute into formulas (3-4) and (6-9) to solve for the switching frequency f s , and according to the minimum switching frequency limit of 70kHz, the corresponding dependent variable L can be determined m ;

[0163] Since the switching frequency f s With the output power P o The decrease of input voltage V in increases with the increase of the switching frequency, so the minimum switching frequency f s Appearing at maximum output power and minimum input voltage, this can be considered as the worst case of switching frequency limitation. Figure 5 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o =1000W) with switching frequency constraints in mind for the resonant cavity L r , L m and C r The closed parameter space of Figure 5 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o =1000W) with switching frequency constraints in mind for the resonant cavity L r , L m and C r The left side of the upper surface is the ZVS implementation constraint, while the right side of the upper surface is the minimum switching frequency constraint.

[0164] 4) Resonant capacitor voltage stress constraint

[0165] The resonant capacitor is a key component in the LLC resonant converter. Therefore, when designing the resonant capacitor, the maximum voltage stress of the resonant capacitor should be considered; this paper selects a resonant capacitor with a peak withstand voltage of 630V;

[0166] The voltage of the primary and secondary resonant capacitors of the CLLC resonant converter is symmetrical between each positive and negative half-switching cycle. Therefore, according to formula (1), the maximum voltage stress V of the primary and secondary resonant capacitors when the CLLC resonant converter works in PO mode can be derived: Cr1_MAX 、V Cr2_MAX for:

[0167]

[0168] Similarly, let the independent variable L r1 , L r2 , C r1 and C r2Substitute into formulas (3-4) and (6-9) to solve for the resonant current and resonant voltage variables P 1 , P 2 , P 3 and Δt x , put it into formula (19), and according to the limitation that the maximum voltage stress of the resonant capacitor is 630V, the corresponding dependent variable L can be determined m ;

[0169] Since V Cr_MAX With the output power P o increases with the increase of the input voltage V in decreases and increases, so V Cr_MAX The maximum value of appears at the maximum output power and minimum input voltage, which can be considered as V Cr_MAX Restricted worst case conditions. Figure 6 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o =1000W) and the resonant cavity L considering the voltage stress constraint of the resonant capacitor r , L m and C r The closed parameter space of Figure 6 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o =1000W) and the resonant cavity L considering the voltage stress constraint of the resonant capacitor r , L m and C r The closed parameter space of the PO / OPO boundary surface and the primary resonant capacitor voltage stress constraint surface are very close, so the lower surface is composed of these two surfaces. In addition, since the ZVS implementation constraint surface and the secondary resonant capacitor voltage stress constraint surface are very close, the left side of the upper surface is composed of these two surfaces.

[0170] Figure 6 That is, a closed parameter space taking into account constraints such as working mode, switching frequency, ZVS implementation, and resonant capacitor voltage stress is established in the G2V mode and V2G mode of the bidirectional CLLC resonant converter.

[0171] 3. Establishment of the total power loss model of bidirectional CLLC resonant converter based on time domain numerical analysis method

[0172] In the bidirectional CLLC resonant converter, although soft switching is achieved, the total power loss P loss It cannot be ignored, including the switch conduction loss PS_on , switch tube turn-off loss P S_off , Transformer core loss P T_Fe and transformer copper loss P T_Cu Therefore, the total power loss P loss can be described as:

[0173] P loss =P S_on +P S_off +P T_Fe +P T_Cu (20)

[0174] 1) Switching tube conduction loss P S_on

[0175] Conduction loss P S_on Mainly composed of the effective value of the primary resonant current I r_rms and the effective value of the secondary current I S_rms And the switch tube on resistance R d_on Decision, which can be expressed as:

[0176]

[0177] Among them, the present invention sets R d_on =0.08Ω.

[0178] 2) Switching tube turn-off loss P S_off

[0179] Switching tube turn-off loss P S_off By shutting off the current i off Calculation, assuming that the excitation current flowing through the switch tube changes linearly from the peak value i to Lm_end When it decreases to 0, the current i off The expression is:

[0180]

[0181] During the shutdown process, the switch tube shutdown voltage v off Derived from formula (22):

[0182]

[0183] Therefore, the switch turn-off loss P S_off It can be deduced as:

[0184]

[0185] 3) Transformer core loss P T_Fe

[0186] The transformer core loss can be obtained according to the Steinmetz formula:

[0187] P T_Fe =C m f s α B β (25)

[0188] Among them, C m , α, β are empirical parameters related to the core, and B is the magnetic flux density of the core, which can be expressed as:

[0189]

[0190] Among them, V o is the voltage across the transformer coil, N s is the number of turns of the transformer secondary winding, A m is the effective area of ​​the core cross section;

[0191] The present invention uses PQ50 / 50-3C95 as the transformer core. According to the data sheet provided by Ferroxcube, C m =2.253×10 -8 , α=1.793, β=2.834, A m =328mm 2 .

[0192] 4) Transformer copper loss P T_Cu

[0193] Transformer copper loss P T_Cu Mainly composed of the effective value of the primary resonant current I r_rms And the transformer primary equivalent AC resistance R T_ac Decision, which can be expressed as:

[0194] P T_Cu =I r_rms 2 R T_ac (27)

[0195] The power loss model of the bidirectional CLLC resonant converter of the present invention is established; the parameter space L r , L m , C r Substitute into formulas (3-4) and (6-9) to solve for the resonant current and resonant voltage variables, and then substitute into formulas (20-27) to solve for the corresponding total power loss P loss However, L r , L m , C r and I r_rms The relationship between is four-dimensional and cannot be visualized. In order to present the image, L mFixed to 200μH, then select L r and C r As an independent variable, P loss as the dependent variable; Figure 7 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o =1000W) under the relationship between total power loss and resonance parameters, Figure 7 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o =1000W) under the total power loss and the relationship between the resonance parameters; Figure 7 As shown, the total power loss P loss With L r and C r increases with the increase of .

[0196] 4. Establishing agent model based on adaptive polynomial approximation theory

[0197] The polynomial approximation method establishes a proxy model based on the polynomial interpolation method. It takes the input random variables as independent variables and uses the linear combination of orthogonal polynomial basis functions to approximate the functional relationship between the input and output random variables. Then, the moment and probability density of the output variable are quickly calculated through the polynomial approximation function. Therefore, the polynomial approximation method has high calculation accuracy and can accurately approximate the functional relationship between the original input and output variables through the polynomial function.

[0198] The following is an analysis of the APA method of one-dimensional input random variables: In the probability space, there is a sufficiently stable black box system model: y = g(x), where x is the independent variable, g(x) is the black box system for x, and y is the system response. Convert y = g(x) to:

[0199]

[0200] Among them, φ i (ξ) is an orthogonal polynomial basis function, c i (i=0,1,2...n) are polynomial coefficients, ξ is the input random variable, and p is the polynomial expansion order. Therefore, the proxy model can be established by determining the orthogonal polynomial basis function and calculating the polynomial coefficients, and formula (28) can be converted into a matrix form:

[0201]

[0202] Among them, ξ i(i=0,1,2,...,n) is the sampling point of the random input variable ξ. Each sampling point ξ i Each corresponds to a system response y(ξ i ), when the orthogonal polynomial basis function φ i When (ξ) is also determined, the polynomial coefficient c i It can be solved by formula (29). Therefore, the core solution of polynomial approximation theory includes two parts: 1. Orthogonal polynomial basis function φ i (ξ) selection; 2. Sampling point ξ i choice.

[0203] 1. Orthogonal polynomial basis function φ i Choice of (ξ)

[0204] In order to handle a wider range of random input variables, Askey generalized some common sets of orthogonal polynomial basis functions, as shown in Table 2;

[0205] Table 2 Correspondence between random variable types and orthogonal polynomial basis functions

[0206]

[0207] The relationship between the selected optimization target and the resonance parameters and the relationship between the resonance parameters in the parameter space can be regarded as uniform distribution. Therefore, the present invention selects Legendre polynomials as orthogonal polynomial basis functions, which can be expressed as:

[0208]

[0209] 2. Sampling point ξ i Choice

[0210] In formula (29), the sampling point ξ i ,0≤i≤n should be φ i+1 (ξ)=0, due to φ i+1 (ξ) is an orthogonal polynomial, so φ can be easily solved using open source software i+1 (ξ)=0;

[0211] Polynomial approximation theory is reliable in determining sampling points, but as the dimension of the input variables increases, the required sampling points increase exponentially. Therefore, the key to making polynomial approximation theory practical is to reduce the number of sampling points. A feasible way to reduce the sampling cost is to reduce the number of orthogonal polynomial basis functions by discarding some unnecessary orthogonal polynomial basis functions. Therefore, polynomial approximation theory introduces adaptability to determine orthogonal polynomial basis functions. The basic idea is to add decoupling terms, low-order coupling terms, and high-order coupling terms to the orthogonal polynomial basis functions in sequence. The inspiration comes from the assumption that the main coupling terms in practical problems are all low-order coupling terms. Each time a new term is added to the orthogonal polynomial basis function, the proxy model is updated, the model increment is calculated, and compared with the user-defined error control parameter ∈ to determine whether the model needs further update;

[0212] C r1 , C r2 , L r1 and L r2 Decision L m is the essence of parameter space, so C r1 , C r2 , L r1 and L r2 and L m The proxy model between can be solved using the adaptive polynomial approximation (APA) method. The core theory of this method is to adaptively sample and construct a polynomial as a proxy model to predict the output by setting the error precision, fitting the relationship between input and output, and obtaining an explicit expression. In addition, this theory has been proven to be true: if the relationship between input and output meets certain smoothness requirements, the most accurate polynomial can be constructed using a set of deterministic sampling points. The solution process specifically includes:

[0213] B1. Set the error control parameter ∈;

[0214] B2. Establish interaction between Matlab and Mathematical through NETLink;

[0215] B3, using Legendre polynomials as orthogonal basis functions;

[0216] B4, only one element 0 T Initialize sampling point ξ i ;

[0217] B5. According to the obtained sampling point ξ i Compute the corresponding orthogonal polynomial basis function φ i (ξ i );

[0218] B6, at the obtained sampling point ξ i Based on this, the corresponding system response y(ξ i );

[0219] B7. Calculate the polynomial coefficient c i ;

[0220] B8. According to the polynomial coefficient c i , and calculate the approximation error;

[0221] B9, determine whether the error satisfies the control parameter ∈; if the error does not satisfy the control parameter ∈, return to step S44, and calculate the error according to the polynomial coefficient c i Update the sampling points according to the change of i +1(ξ)=0;

[0222] B10. If the error satisfies the control parameter ∈, the proxy model y(ξ i )=φ i (ξ i )c i .

[0223] 1) Establish a proxy model for the upper boundary of the resonant cavity parameter space of the bidirectional CLLC resonant converter

[0224] Using the adaptive polynomial approximation method, a proxy model of the upper boundary of the parameter space taking into account all the constraints in step 2 is established in the G2V mode and the V2G mode respectively; the explicit polynomial expressions of the proxy model of the upper boundary of the parameter space in the G2V mode and the V2G mode are denoted as f up_G2V (C r ,L r ), f up_V2G (C r ,L r );

[0225] Figure 8 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o = 1000W) and the upper surface of the parameter space after taking into account all constraints, Figure 8 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o = 1000W) and taking into account all constraints, the upper surface of the parameter space is formed. It is obvious that the dependent variable L m With the independent variable L r and Cr The Legendre polynomials are chosen as orthogonal basis functions because they change uniformly with the change of . Figure 8 In (c) and (d), the proxy models of the upper surface of the parameter space of the G2V mode and the V2G mode are established, and their explicit expressions are recorded as f up_G2V (C r ,L r ) and f up_V2G (C r ,L r ); Figure 8 The red dots in (c) and (d) are the results of the numerical calculation method, which are the sample points of the APA method. The yellow surface is the predicted value of the proxy model. It can be seen that the predicted results are very consistent with the numerical calculation results. In order to further verify the effectiveness and accuracy of the proxy model, 1000 random test points are selected to calculate the error distribution between the time domain numerical analysis method and the proxy model, as shown in Figure 1. Figure 8 As shown in (e) and (f), the accuracy of the proxy model is effectively verified.

[0226] 2) Establish a proxy model for the lower boundary of the resonant cavity parameter space of the bidirectional CLLC resonant converter

[0227] Using the adaptive polynomial approximation method, a proxy model of the lower boundary of the parameter space taking into account all the constraints in step 2 is established in the G2V mode and the V2G mode respectively; the explicit polynomial expressions of the proxy model of the lower boundary of the parameter space in the G2V mode and the V2G mode are denoted as f low_G2V (C r ,L r ), f low_V2G (C r ,L r );

[0228] Fig. 9 (a) shows the worst case of PO mode in G2V mode (V in =400V, V o =450V, P o =1000W) and the lower surface of the parameter space after taking all constraints into account, Fig. 9 (b) shows the worst case of PO mode in V2G mode (V in =250V, V o =400V, P o = 1000W) and taking into account all constraints, the lower surface of the parameter space is formed. It is obvious that the dependent variable L m With the independent variable L r and C r , so Legendre polynomials are chosen as orthogonal basis functions. Fig. 9In (c) and (d), the proxy models of the lower surface of the parameter space of the G2V mode and the V2G mode are established, and their explicit expressions are recorded as f low_G2V (C r ,L r ) and f low_V2G (C r ,L r ); Fig. 9 The red dots in (c) and (d) are the results of the numerical calculation method, which are the sample points of the APA method. The yellow surface is the predicted value of the proxy model. It can be seen that the predicted results are very consistent with the numerical calculation results. In order to further verify the effectiveness and accuracy of the proxy model, 1000 random test points are selected to calculate the error distribution between the time domain numerical analysis method and the proxy model, as shown in Figure 2. Fig. 9 As shown in (e) and (f), the accuracy of the proxy model is effectively verified.

[0229] 3) Establish parameter space and total power loss P loss Proxy Model

[0230] The parameter space and the total power loss P are established in G2V mode and V2G mode respectively using the adaptive polynomial approximation method. loss The proxy model of G2V mode and V2G mode is used to compare the parameter space and the total power loss P loss The explicit polynomial expressions of the surrogate model are denoted as f Ploss_G2V (C r ,L r ,L m ) and f Ploss_V2G (C r ,L r ,L m );

[0231] from Figure 7 It can be seen that the total power loss of the optimization target changes evenly with the change of the resonance parameters. Therefore, the APA method uses Legendre polynomials as orthogonal basis functions and then establishes the optimization target P loss and the resonance parameter L r , C r and L m The proxy model of the relationship between them is expressed as f Ploss_G2V (C r ,L r ,L m ) and f Ploss_V2G (C r ,L r ,L m ); In order to intuitively display the approximation performance, L m is fixed at 100μH, and L is selected r and Cr As an independent variable, P loss As the dependent variable, Fig.10 (a) and (b) are the proxy models of the relationship between total loss and resonance parameters established in G2V mode and V2G mode respectively. The red dots are the results of the numerical calculation method, which are used as sample points of the APA method. The yellow surface is the predicted value of the proxy model. It can be seen that the predicted results are very consistent with the numerical calculation results. In order to further verify the effectiveness and accuracy of the proxy model, 1000 random test points are selected to calculate the error distribution between the time domain numerical analysis method and the proxy model, as shown in Figure 2. Fig.10 As shown in (c) and (d), the accuracy of the proxy model is effectively verified.

[0232] 5. Use NSGA-II algorithm to perform multi-objective optimization and obtain the optimal parameter solution.

[0233] According to the above proxy model, the three parameters of the resonant cavity are designed within the parameter space so that the bidirectional CLLC resonant converter can achieve the comprehensive minimum value of the total power loss in the G2V mode and the V2G mode. The parameter optimization design is summarized as formula (31), which can be regarded as a multi-objective optimization problem.

[0234]

[0235] The NSGA-II algorithm is used to solve the above multi-objective optimization problem. (31) is substituted into the PlatEMO platform of Matlab to realize multi-objective optimization. The Pareto optimal trade-off solution is obtained according to the comprehensive minimum value of the total power loss of the G2V mode and the V2G mode, as shown in Fig.11 As shown;

[0236] like Fig.11 As shown in the figure, the total power loss of G2V mode and V2G mode at all candidate points is very close, where P loss_G2V =14.08W, P loss_V2G =14.26W, the corresponding resonance parameters are determined as: C r =C r1 =C r2 =38nF, L r =L r1 =L r2 =48uH, L m =214uH;

[0237] In addition, the G2V mode (V in =400V, V o =450V, P o =1000W) under the initial value of resonant current I m =4.9A, higher than the minimum ZVS current I in G2V mode ZVS_min_G2V=4.8A; V2G mode (V in =250V, V o =400V, P o =1000W) under the initial value of resonant current I m =4.09A, higher than the minimum ZVS current I in G2V mode ZVS_min_V2G =3A; in G2V mode (V in =400V, V o =450V, P o =1000W) and V2G mode (V in =250V, V o =400V, P o =1000W), the minimum switching frequencies are calculated to be 100kHz and 72kHz, both of which are higher than 70kHz; the maximum value of the primary resonant capacitor voltage V Cr1_MAX In G2V mode (V in =400V, V o =450V, P o =1000W) and V2G mode (V in =250V, V o =400V, P o =1000W) are calculated as 244V and 405V respectively, both lower than 630V; the maximum value of the secondary resonant capacitor voltage V Cr2_MAX In G2V mode (V in =400V, V o =450V, P o =1000W) and V2G mode (V in =250V, V o =400V, P o =1000W), which are calculated to be 148V and 229V respectively, both lower than 630V; therefore, the selected parameter scheme meets the constraints of all design parameters of the present invention in both G2V mode and V2G mode.

[0238] 6. Experimental verification and analysis

[0239] The present invention constructs a 1000W / 250V~450V CLLC resonant converter experimental prototype to verify the theoretical comparative analysis results. Table 3 gives the power device models of the experimental prototype;

[0240] Table 3 Power device models of the bidirectional CLLC resonant converter experimental prototype

[0241]

[0242] like Fig.12As shown in the figure, the total power loss of the CLLC resonant converter designed by the design method proposed in the present invention is significantly lower than that of the FHA design method in both the G2V mode and the V2G mode, which effectively verifies the rationality and effectiveness of the parameter optimization design of the present invention;

[0243] In the wide output voltage range of 250V~450V, Fig.13 (a) shows the G2V mode (V in =400V and P o =1000W), the efficiency change curve of the CLLC resonant converter system designed by the design method proposed in the present invention shows that the peak efficiency appears at V o =400V, the CLLC resonant converter operates at the resonant frequency point, and its maximum efficiency is 95.8%;

[0244] In the wide input voltage range of 250V~450V, Fig.13 (b) shows the V2G mode (V o =250V and P o =1000W), the efficiency change curve of the CLLC resonant converter system designed by the design method proposed in the present invention shows that the peak efficiency appears at V in =400V, the CLLC resonant converter works at the resonant frequency point, and its maximum efficiency is 95.8%. Therefore, the resonant cavity parameters designed by the parameter optimization design method proposed in the present invention can ensure the bidirectional high-efficiency operation of the CLLC resonant converter.

[0245] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive, characterized in that: The following steps are involved: Step S1, determining the design range of the resonant cavity parameters; Step S2: Based on the time domain numerical analysis method, under the working conditions of maximum output power and minimum input voltage of the bidirectional CLLC resonant converter, taking into account the working mode constraint, soft switching constraint, switching frequency constraint and resonant capacitor voltage stress constraint, the excitation inductance L is established in the G2V mode and V2G mode respectively. m , resonant inductor L r and resonant capacitor C r The closed parameter space of Step S3: Based on the time domain numerical analysis method, under the working conditions of the maximum output power and minimum input voltage of the bidirectional CLLC resonant converter, taking into account the switch tube conduction loss P S_on , switch tube turn-off loss P S_off , Transformer core loss P T_Fe and transformer copper loss P T_Cu The total power loss P loss ; Step S4: Use the adaptive polynomial approximation method to establish a proxy model of the parameter space, and use the adaptive polynomial approximation method to establish the parameter space and the total power loss P loss The proxy model; Step S5: Perform multi-objective optimization using the NSGA-II algorithm to obtain the optimal parameter solution.

2. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 1, characterized in that: The step S1 comprises: S11, set the primary resonant inductance L r1 Equal to the secondary resonant inductance L r2 , and unified by the resonant inductor L r Indicates; primary resonant capacitor C r1 Equal to the secondary side resonant capacitor C r2 , and unified by the resonant capacitor C r express; S12, set the resonant inductance L r , resonant capacitor C r The value range and iteration step size of S13, select the resonant inductor L r , resonant capacitor C r As an independent variable, the excitation inductance L m as the dependent variable.

3. The parameter optimization method of a bidirectional CLLC resonant converter based on data drive according to claim 1, characterized in that: The working mode constraint in step S2 is: A1. Select the CLLC resonant converter to work in PO working mode for parameter optimization design; A2, the upper boundary is the boundary between the PO working mode and the PON working mode; A3. The lower boundary is the boundary between the PO working mode and the OPO working mode.

4. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 1, characterized in that: The soft switch constraint in step S2 is: Flowing through the magnetizing inductance L m The initial value of the resonant current I m It is necessary to fully discharge the junction capacitance of the switch tube within the dead time, so the specific conditions for achieving soft switching ZVS are: Among them, I ZVS_min is the minimum resonant current to achieve ZVS on the primary side, t dead is the dead time between the gate level signals of the two main switches, C eq is the equivalent output capacitance of the switch tube, V in is the input voltage, i Lr1P It is the primary resonant current of the bidirectional CLLC resonant converter in P working mode.

5. The parameter optimization method of a bidirectional CLLC resonant converter based on data drive according to claim 1, characterized in that: The switching frequency constraint in step S2 is: The switching frequency at the maximum output power and minimum input voltage is set as the minimum switching frequency.

6. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 1, characterized in that: The voltage stress constraint of the resonant capacitor in step S2 is: When the CLLC resonant converter works in PO mode, the maximum voltage stress of the primary and secondary resonant capacitors is: Among them, V Cr1_MAX is the maximum voltage stress of the primary resonant capacitor, V Cr2_MAX is the maximum voltage stress of the secondary resonant capacitor, v Cr1P (t) is the normalized time domain expression of the primary resonant capacitor voltage in P mode, v Cr2P (t) is the normalized time domain expression of the secondary resonant capacitor voltage in P mode, Δt x It is the time that the bidirectional CLLC resonant converter operates in P mode.

7. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 1, characterized in that: The step S3 comprises: C1. Calculate the conduction loss of the switch tube P S_on The effective value of the primary resonant current I r_rms , the effective value of the secondary current I S_rms And the switch tube on resistance R d_on Calculate the switch conduction loss P S_on : Among them, Δt x is the time that the bidirectional CLLC resonant converter works in P mode, i Lr1P is the primary resonant current of the bidirectional CLLC resonant converter in P working mode, i Lr1O is the primary resonant current of the bidirectional CLLC resonant converter in the O working mode, i Lr2P is the secondary resonant current of the bidirectional CLLC resonant converter in P working mode, T s is the switching cycle; C2. Calculate the switch tube turn-off loss P S_off Calculate the switch off current i off , the switch off current i off The expression is as follows: Among them, i Lm_end is the linear peak value of the excitation current of the switch tube during the dead time, t dead is the dead time between the gate level signals of the two main switches, C eq is the equivalent output capacitance of the switch tube, O1 and O2 are the coefficient constants of the resonant current and resonant voltage in the PO working mode of the bidirectional CLLC resonant converter, k = L r1 / L m , k2=(k / k+1) 1 / 2 , f n is the normalized operating frequency; Calculate the switch off voltage v off , switch off voltage v off The expression is as follows: The switch turns off the current i off and the switch off voltage v off Calculate the switch turn-off loss P S_off , the formula is as follows: Among them, f s is the operating frequency; C3. Calculate the transformer core loss P T_Fe Calculate the transformer core loss P using the Steinmetz formula T_Fe : P T_Fe =C m f s α B β Among them, C m , α, β are empirical parameters related to the magnetic core, f s is the operating frequency, B is the magnetic flux density of the core; The magnetic flux density B of the core is: Among them, V o is the voltage across the transformer coil, N s is the number of turns of the transformer secondary winding, A m is the effective area of ​​the core cross section; C4. Calculate the transformer copper loss P T_Cu The effective value of the primary resonant current I r_rms And the transformer primary equivalent AC resistance R T_ac Calculate the transformer copper loss P T_Cu : P T_Cu =I r_rms 2 R T_ac C5. Calculate the total power loss P loss Total power loss P loss Including the switch conduction loss P S_on , switch tube turn-off loss P S_off , Transformer core loss P T_Fe and transformer copper loss P T_Cu , the calculation formula is as follows: P loss =P S_on +P S_off +P T_Fe +P T_Cu 。 8. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 1, characterized in that: In step S4, the proxy model is established by using an adaptive polynomial approximation method, including the following steps: B1. Set the error control parameter ∈; B2. Establish interaction between Matlab and Mathematical through NETLink; B3, using Legendre polynomials as orthogonal basis functions; B4, only one element 0 T Initialize sampling point ξ i ; B5. According to the obtained sampling point ξ i Compute the corresponding orthogonal polynomial basis function ψ i (ξ i ); B6, at the obtained sampling point ξ i Based on this, the corresponding system response y(ξ i ); B7. Calculate the polynomial coefficient c i ; B8. According to the polynomial coefficient c i , and calculate the approximation error; B9, determine whether the error satisfies the control parameter ε; if the error does not satisfy the control parameter ε, return to step S44, and calculate the error according to the polynomial coefficient c. i Update the sampling points according to the change of i +1(ξ)=0; B10. If the error satisfies the control parameter ∈, the proxy model y(ξ i )=φ i (ξ i )c i .

9. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 8, characterized in that: The step S4 comprises: S41. Establishment of a proxy model for the upper boundary of the resonant cavity parameter space of a bidirectional CLLC resonant converter Using the adaptive polynomial approximation method, a proxy model of the upper boundary of the parameter space taking into account all the constraints in step 2 is established in the G2V mode and the V2G mode respectively; the explicit polynomial expressions of the proxy model of the upper boundary of the parameter space in the G2V mode and the V2G mode are denoted as f up_G2V (C r ,L r ), f up_V2G (C r ,L r ); S42. Establish a proxy model for the lower boundary of the resonant cavity parameter space of the bidirectional CLLC resonant converter Using the adaptive polynomial approximation method, a proxy model of the lower boundary of the parameter space taking into account all the constraints in step 2 is established in the G2V mode and the V2G mode respectively; the explicit polynomial expressions of the proxy model of the lower boundary of the parameter space in the G2V mode and the V2G mode are denoted as f low_G2V (C r ,L r ), f low_V2G (C r ,L r ); S43, establish parameter space and total power loss P loss Proxy Model The parameter space and the total power loss P are established in G2V mode and V2G mode respectively using the adaptive polynomial approximation method. loss The proxy model of G2V mode and V2G mode is used to compare the parameter space and the total power loss P loss The explicit polynomial expressions of the surrogate model are denoted as f Ploss_G2V (C r ,L r ,L m ) and f Ploss_V2G (C r ,L r ,L m ).

10. A parameter optimization method for a bidirectional CLLC resonant converter based on data drive as claimed in claim 9, characterized in that: The step S5 comprises: The three parameters of the resonant cavity are designed within the parameter space so that the bidirectional CLLC resonant converter can achieve the comprehensive minimum value of the total power loss in the G2V mode and the V2G mode. The parameter optimization design is summarized as follows: The Pareto optimal trade-off solution is obtained through the NSGA-II algorithm, and then the optimal resonance parameter solution is obtained.

Images