Analytic modeling method of fractional order resonant converter

Abstract

The invention discloses an analytical modeling method for a fractional order resonant converter, and belongs to the technical field of power generation, power transformation or power distribution. The specific process of the method comprises the steps that an analytical expression of excitation inductive current in a binary resonance stage is obtained through fractional order definition, then multi-element resonance current is subjected to approximate constant processing, and resonant capacitor voltage increment in the multi-element resonance stage is obtained through the expression of the excitation inductive current; analyzing a resonant capacitor voltage initial and final state relational expression of the converter in a binary resonance stage by using a superposition theorem; and substituting the obtained resonant capacitor voltage increment into the resonant capacitor voltage initial and final state relational expression to obtain a voltage gain analytical expression of the fractional-order resonant converter in a multi-element resonant working mode. According to the method, the analytical solution can be obtained without solving the high-order fractional order differential equation set, the obtained result is accurate, the influence of the order on the voltage gain can be reflected, the method has good engineering significance, and new flexibility is provided for the design of the fractional order converter.

Description

Technical Field

[0001] The present invention relates to modeling and analysis technology of fractional-order isolated resonant converters, and in particular proposes an accurate analytical modeling method of fractional-order resonant converters, which belongs to the technical field of power generation, power transformation or power distribution. Background Art

[0002] With the continuous development of power electronics, compared with traditional DC-DC converters, isolated DC-DC resonant converters have been widely used in electric vehicles, photovoltaic inverters, aerospace, data centers and other fields in recent years due to their high efficiency, high frequency and safety. However, due to the existence of resonant units, resonant converters often have the problems of difficult modeling, high degree of model nonlinearity and difficulty in obtaining analytical solutions.

[0003] In recent years, research on the modeling of inductors and capacitors has shown that ideal integer-order inductors and capacitors do not exist. The converter model established with fractional-order inductors and capacitors is more accurate than the integer-order model and can better reflect the characteristics of the converter. The fractional-order isolated resonant converter achieves more flexible and efficient energy conversion by introducing fractional-order components, such as fractional-order inductors and fractional-order capacitors. Fractional-order circuit theory expands the traditional integer-order circuit model, allowing more precise adjustment of frequency response, amplitude-frequency characteristics, and phase shift, thereby providing greater flexibility in design, and is expected to play an important role in future efficient energy conversion and sustainable development. However, expanding the resonant unit to fractional order will greatly enhance the nonlinearity of the circuit, making the originally difficult modeling even more difficult.

[0004] Existing resonant converter modeling techniques usually ignore the multi-resonance link, which can reduce the difficulty of modeling. For some LLC converters where the multi-resonance working mode accounts for a large proportion of the switching cycle, when the traditional modeling technology that ignores the inductor and capacitor orders is used for the resonant converter, the constructed model cannot accurately capture the characteristics of the converter in different working modes, affecting the accuracy of modeling, and the designed resonant converter is unstable in practical applications. At the same time, the resonant converter model established by ignoring high-frequency resonance factors may lead to the inability to effectively optimize the performance of the converter, and the voltage / current stress and fault prediction caused by the multi-resonance are insufficient, further affecting the robustness of the designed resonant converter.

[0005] In summary, the existing technology still lacks fractional-order modeling technology for resonant converters containing multiple resonant links. Summary of the invention

[0006] In view of the shortcomings of the above-mentioned background technology, the purpose of the present invention is to fill the gap in the theoretical analysis and modeling of the existing fractional-order isolated resonant converter, and to provide an accurate analytical modeling method for a fractional-order resonant converter, which can avoid solving a high-order fractional differential equation system and reduce the nonlinearity of the system, thereby obtaining an analytical expression for the working modal gain with multi-resonance, thereby achieving the purpose of the invention of improving the output stability and accuracy of the resonant converter.

[0007] To achieve the above purpose, the technical solution provided by the present invention is:

[0008] An accurate analytical modeling method for a fractional-order resonant converter comprises the following steps:

[0009] S1. Write the fractional differential equation of the excitation inductance when the converter is in the binary resonance stage, and solve the analytical expression of the excitation current;

[0010] S2, the resonant current of the converter in the multi-resonant mode is approximately constant, and the resonant capacitor voltage increment in the multi-resonant stage is calculated using the analytical expression of the excitation current calculated in S1;

[0011] S3. According to the superposition theorem of the circuit, the positive half-cycle and negative half-cycle of the binary resonance link oscillation are analyzed respectively, and the initial and final state relationship expressions of the positive and negative half-cycle resonant capacitor voltages in the binary resonance stage are obtained;

[0012] S4. Combining the resonant capacitor voltage increment in the multi-resonance stage calculated by S2 and the initial and final state relationship expressions of the positive and negative half-cycle resonant capacitor voltages in the binary resonance stage obtained by S3, the voltage gain expression of the fractional-order resonant converter in the multi-resonance mode is obtained.

[0013] Furthermore, in S1, a fractional-order differential equation is established for the excitation inductance of the fractional-order isolated resonant converter in the binary resonance stage:

[0014]

[0015] Where U Lm 、i m and L m are the voltage, current and inductance of the fractional-order excitation inductance respectively, γ is the order of the fractional-order excitation inductance, defined as: 0<γ≤1, U o is the converter output voltage equivalent to the resonant cavity on the secondary side. Further, the fractional-order Caputo definition is used to solve equation (1) to obtain the analytical time-domain expression of the excitation inductance:

[0016]

[0017] In the formula, i mPn (t) is the fractional excitation current at time t, Imp0 is the initial value of the magnetizing inductor current, and Γ(·) is the gamma function.

[0018] Furthermore, in S2, the increment of the resonant capacitor voltage in the multi-resonance stage is further calculated using formula (2). Since the inductance of the excitation inductance is often greater than the inductance of the resonant inductance, the resonance period is very large in the multi-resonance stage in which the excitation inductance participates. Therefore, it is approximately considered that the resonant current is unchanged in this stage. The end of binary resonance is the beginning of multi-resonance, so the value of the multi-resonance current is the peak value of the binary resonance excitation current, and its value is:

[0019]

[0020] Where, T r is the fractional-order resonant period, defined as follows:

[0021]

[0022] Among them, α and β are the orders of fractional-order resonant inductance and fractional-order resonant capacitance respectively, L r and C r They are the inductance of the resonant inductor and the capacitance of the resonant capacitor respectively.

[0023] In the multi-resonance stage, the resonant capacitor is I mp Constant current charging, the resonant capacitor voltage continues to increase, and the resonant capacitor voltage increment in the ternary stage is defined as δu, whose value is:

[0024]

[0025] Where, T s is the switching cycle.

[0026] Furthermore, in S3, the superposition theorem analysis is performed on the positive and negative half-cycle resonant capacitor voltages of the oscillation link of the binary resonant link.

[0027] The voltage equivalent to the resonant cavity of the rectifier and inverter sides of the converter is different for the positive and negative half cycles. Assume that the equivalent excitation of the positive half cycle is k1U in -k2U o , the equivalent excitation of the negative half cycle is k3U in -k4U o The resonant capacitor voltage response is divided into two parts: zero input response and zero state response. The two responses are calculated and superimposed to obtain the capacitor voltage response of this binary resonant link. The specific process is as follows:

[0028] S3.1. Solve for the zero input response of the resonant capacitor voltage:

[0029] The zero input response of the resonant capacitor voltage includes the fractional resonant capacitor C rThe initial voltage and fractional-order resonant inductance L r The initial current of each of them acts separately and then superimposes the response. Assuming that the resonant capacitor voltage at the end of the binary resonance positive half cycle is U1, and the resonant capacitor voltage at the end of the binary resonance negative half cycle is U2, then the binary resonance positive half cycle fractional order resonant capacitor C r The initial voltage of the binary resonant positive half-cycle fractional-order resonant capacitor is U2-δu, and the response of the initial voltage of the binary resonant positive half-cycle fractional-order resonant capacitor alone is -(U2-δu); the binary resonant positive half-cycle fractional-order resonant capacitor C r The initial voltage is U1+δu, and the binary resonant negative half-cycle fractional-order resonant capacitor C r The response of the initial voltage alone is -(U1+δu). According to the symmetry, the fractional-order resonant inductor L r The initial current is the opposite of the final current, which is -I mp , fractional-order resonant capacitor C r The response of the initial voltage alone and the response of the initial current of the fractional-order resonant inductor Lr alone are both 0.

[0030] S3.2. Solve the zero-state response of the resonant capacitor voltage:

[0031] The zero-state response of the resonant capacitor voltage is the positive and negative half-cycle equivalent excitation to L with zero initial current and zero initial voltage after ignoring the initial value. r and C r The response of the binary resonant circuit. Taking the binary resonant positive half-cycle excitation as an example, k1U in -k2U o Acting on a binary resonant circuit with an initial value of 0, T r / 2, the fractional-order resonant inductor L r The current is 0, the fractional resonant capacitor C r The voltage is 2(k1U in -k2U o ). Similarly, the zero-state response of the resonant capacitor voltage in the negative half cycle of binary resonance is 2(k3U in -k4U o )

[0032] S3.3, the resonant capacitor voltage is the superposition of the zero input response in S3.1 and the zero state response in S3.2:

[0033] At the final state of the binary resonance in the positive half cycle, time t p , the resonant capacitor voltage relationship in the positive half cycle is: U c (t p )=-(U2-δu)+2(k1U in -k2U o )=U1. At the final state of the binary resonance in the negative half cycle, tN , the resonant capacitor voltage relationship in the positive half cycle is: U c (t n )=-(U1+δu)+2(k3U in -k4U o )=U2. So far, the initial and final state relationship of the positive and negative half cycles of the binary resonance stage of the resonant capacitor voltage is obtained.

[0034] Further, in step S4, the resonant capacitor voltage increment (5) of step S2 and step S3 and the initial and final state relationship expressions of the resonant capacitor voltage are solved simultaneously, and the equation group is as follows:

[0035]

[0036] Where k1, k2, k3, and k4 are constants, and their specific values ​​are determined by different types of fractional-order resonant converters. k1 = 1, k2 = n, k3 = -1, k4 = -n, T r The binary resonance period is defined by equation (4). After simplifying the equation group in equation (6), the gain expression is as follows:

[0037]

[0038] In formula (4), T r Substituting this into the equation, we can get the intuitive gain expression of the fractional-order isolated resonant converter in this working mode:

[0039]

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] (1) The present invention extends the modeling of traditional constant-order resonant converters to fractional orders, solves the voltage gain expression of fractional-order resonant converters containing multiple resonant stages, and can qualitatively and quantitatively analyze the influence of fractional-order orders and conventional parameters on the converter, providing new flexibility for the design of resonant converters.

[0042] (2) In the modeling of fractional-order multi-element resonant links with strong nonlinearity, the present invention simplifies the multi-element resonant links by approximating constant multi-element resonant currents and combines them with binary resonant links. In the modeling process, only the fractional-order differential equations of the excitation inductance need to be solved. While there is no need to calculate the fractional-order higher-order differential equations, the calculation of the second-order fractional differential equations is also avoided. This simplifies the modeling workload during use, reduces the nonlinearity of the modeling results, makes the optimization algorithm in the design process more effective, can more accurately predict the converter performance, improve the design efficiency, and optimize the converter's key performance indicators such as efficiency and response time.

[0043] (3) The analytical modeling method proposed in the present invention comprehensively considers the influence of resonance and nonlinear effects on the voltage gain of the resonant converter. The obtained voltage gain is more in line with the actual working conditions of the converter. By using a voltage gain expression that is more in line with the actual inductor and capacitor, more precise voltage gain control can be provided, thereby improving the output stability and accuracy of the converter and meeting the requirements of precision power supply. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] FIG. 1( a ) is a circuit topology diagram of a fractional-order isolated resonant converter according to an embodiment of the present invention.

[0045] FIG1( b ) is a waveform diagram of the fractional-order isolated resonant converter in an embodiment of the present invention in a working mode containing multiple resonant links.

[0046] Figure 2 The figure is a working mode waveform diagram of the fractional-order isolated resonant converter after simplifying the multi-resonant link in the embodiment of the present invention.

[0047] Figure 3 The present invention is a flowchart of the steps of the analytical modeling method of the fractional-order isolated resonant converter.

[0048] FIG. 4( a ) is an equivalent circuit diagram of the fractional-order isolated resonant converter in the binary resonance positive half-cycle stage according to an embodiment of the present invention.

[0049] FIG4( b ) is an equivalent circuit diagram of the fractional-order isolated resonant converter in the negative half-cycle stage of binary resonance according to an embodiment of the present invention.

[0050] FIG. 5( a ) is a voltage gain-frequency curve diagram of the converter under different resistance loads in an embodiment of the present invention.

[0051] FIG. 5( b ) is a curve diagram of voltage gain-inductance order α of the converter under different resonant capacitor orders β in an embodiment of the present invention.

[0052] FIG5( c ) is a voltage gain-inductance order β curve diagram of the converter under different resonant inductance orders α in an embodiment of the present invention.

[0053] Description of the symbols in the figure: V in is the input DC voltage, Q1, Q2, Q3, Q4 are the first to fourth switch tubes, C r is the fractional-order resonant capacitor, L r is the fractional-order resonant inductor, L m is the fractional-order magnetizing inductance, i r is the resonant cavity current, i s is the output current on the rectifier side, D s1 -D s4 The first to fourth rectifier diodes, C o is the output capacitance, Vo is the output voltage, R c is the load resistance, t p is the end time of the binary resonance stage, t r is the end time of the three-element resonance stage, δu is the voltage increment of the resonant capacitor in the three-element resonance stage, I mp is the peak value of binary resonant excitation current amplitude. DETAILED DESCRIPTION

[0054] The present invention is further described in detail below in conjunction with embodiments and drawings, but the implementation method of the present invention is not limited thereto.

[0055] As shown in FIG. 1( a ), the fractional-order resonant converter of this embodiment is a fractional-order full-bridge LLC converter. The primary inverter side of the converter adopts a full-bridge structure consisting of a first switch tube Q1, a second switch tube Q2, a third switch tube Q3, and a fourth switch tube Q4. The rectifier side of the converter adopts first to fourth rectifier diodes D s1 -D s4 The full-bridge rectifier circuit is composed of the first switch tube Q1 and the fourth switch tube Q4, the second switch tube Q2 and the third switch tube Q3, the upper and lower switch tubes of the bridge arm are complementary, and the duty cycle is 0.5. Therefore, the midpoint of the full bridge outputs a frequency of the switching frequency and an amplitude of U in , a square wave with a duty cycle of 0.5. The converter resonant cavity contains a fractional-order resonant inductor L r , fractional-order resonant capacitor C r , fractional-order excitation inductance L m , the orders of the resonant inductor, resonant capacitor, and magnetizing inductor are α, β, and γ respectively, and the transformer primary-to-secondary turns ratio is n, so the output voltage equivalent to the primary side is nV o .

[0056] As shown in FIG. 1( b ), the working modal waveform of the fractional-order full-bridge LLC converter of this embodiment working in the under-resonance PO mode is shown. The two phases of this working mode are the binary resonance phase and the P phase (0, t p ) and ternary resonance stage O stage (t p , t r ). In the binary resonance stage (0, t p ), the excitation inductance voltage u m Clamping, excitation current i m Linear increase, the resonant inductor and the resonant capacitor are in a binary resonance state, and the resonant current i r First it increases and then decreases, and this pattern continues until the resonant current i r and the excitation current i m equal; in the three-element resonance stage (t p , t r), the secondary rectifier diode is turned off, the output circuit is disconnected from the resonant circuit, and the excitation inductor voltage u m No longer clamped by voltage, the magnetizing inductor performs a three-element resonance with the resonant capacitor and the resonant inductor.

[0057] like Figure 3 As shown, the analytical modeling method of the fractional-order resonant converter provided in this embodiment includes S1 to S4.

[0058] S1. Analyze the working mode of the fractional-order resonant converter with multi-resonant links, write the fractional-order differential equation of the excitation inductance when the converter is in the binary resonance stage, and solve the analytical expression of the excitation current:

[0059]

[0060] In formula (1), U Lm 、i m and L m are the voltage, current and inductance of the fractional-order excitation inductance respectively, γ is the order of the fractional-order excitation inductance, defined as: 0<γ≤1, U o is the converter output voltage equivalent to the resonant cavity on the secondary side.

[0061] Furthermore, the fractional-order Caputo definition is used to solve equation (1) to obtain the analytical time-domain expression of the excitation current:

[0062]

[0063] In formula (2), i mPn (t) is the fractional excitation current at time t, I mp0 is the initial value of the excitation current, Γ(·) is the gamma function.

[0064] S2, the resonant current of the fractional-order LLC converter under the multi-resonant mode is approximately constant, and the resonant capacitor voltage increment in the multi-resonant stage is calculated using the fractional-order excitation current solved by S1:

[0065] In actual LLC applications, in order to obtain a wider input voltage and output voltage, the excitation inductor L m The inductance value is often greater than the resonant inductance L r The inductance is more than three times that of the original value. The three-element resonance period is much longer than the two-element resonance period. Therefore, the resonant current in the three-element resonance stage is approximately constant, such as Figure 2 As shown. Formula (2) is used to further calculate the increment of the resonant capacitor voltage in the three-element resonance stage. The end time of the binary resonance is the beginning time of the multi-element resonance, so the value of the three-element resonance current is the peak value I of the binary resonance excitation current. mp , whose value is:

[0066]

[0067] In formula (3), T r is the fractional-order resonant period, defined as follows:

[0068]

[0069] In formula (4), α and β are the orders of fractional-order resonant inductance and fractional-order resonant capacitance respectively, L r and C r They are the inductance of the fractional-order resonant inductor and the capacitance of the fractional-order resonant capacitor respectively.

[0070] In the three-element resonance stage, the resonant capacitor is I mp Constant current charging, resonant capacitor voltage u c The voltage increment of the resonant capacitor in the three-element resonance stage is defined as δu, such as Figure 2 As shown, its value is:

[0071]

[0072] In formula (5), T s is the switching period, Γ(·) is the gamma function.

[0073] S3. Analyze the working principle of the binary resonance stage of the converter. According to the superposition theorem of the circuit, analyze the positive half-cycle and negative half-cycle of the binary resonance link oscillation respectively, and obtain the initial and final state relationship expression of the resonant capacitor voltage:

[0074] The positive and negative half-cycles of the fractional-order full-bridge LLC are symmetrical, so the solution process of the negative half-cycle can be simplified in this step, and the calculation can be further simplified. The equivalent circuits of the fractional-order isolated resonant converter in the positive half-cycle stage and the negative half-cycle stage of binary resonance are shown in Figure 4(a) and Figure 4(b). The voltage equivalent to the resonant cavity of the rectifier and inverter sides of the converter is different in the positive and negative half-cycles. Assume that the equivalent excitation of the positive half-cycle is k1U in -k2U o , the equivalent excitation of the negative half cycle is k3U in -k4U o , the specific values ​​of k1, k2, k3, and k4 are determined by different types of fractional-order resonant converters. As shown in Figure 4(a), the equivalent excitation of the positive half-cycle P phase is U in -nU o , which can be defined by the converter type, namely k1 = 1, k2 = n, k3 = -1, k4 = -n. The resonant capacitor voltage response is divided into two parts: zero input response and zero state response. The two responses are calculated and superimposed to obtain the resonant capacitor voltage response of this binary resonant link. The specific process is as follows:

[0075] S3.1. Solve for the zero input response of the resonant capacitor voltage:

[0076] The zero input response of the resonant capacitor voltage includes the fractional resonant capacitor C r The initial voltage and fractional-order resonant inductance L r The initial current of each of them acts separately and then superimposes the response. Assuming that the resonant capacitor voltage at the end of the binary resonance positive half cycle is U1, and the resonant capacitor voltage at the end of the binary resonance negative half cycle is U2, then the binary resonance positive half cycle fractional order resonant capacitor C r The initial voltage of the binary resonant positive half-cycle fractional-order resonant capacitor is U2-δu, and the response of the initial voltage of the binary resonant positive half-cycle fractional-order resonant capacitor alone is -(U2-δu); the binary resonant positive half-cycle fractional-order resonant capacitor C r The initial voltage is U1+δu, and the binary resonant negative half-cycle fractional-order resonant capacitor C r The response of the initial voltage alone is -(U1+δu); according to the symmetry, the fractional-order resonant inductor L r The initial current is the opposite of the final current, which is -I mp ; Fractional-order resonant capacitor C r The response of the initial voltage alone and the response of the initial current of the fractional-order resonant inductor Lr alone are both 0.

[0077] S3.2. Solve the zero-state response of the resonant capacitor voltage:

[0078] The zero-state response of the resonant capacitor voltage is the positive and negative half-cycle equivalent excitation to L with zero initial current and zero initial voltage after ignoring the initial value. r and C r The response of the binary resonant circuit. Taking the binary resonant positive half-cycle excitation as an example, U in -nU o Acting on a binary resonant circuit with an initial value of 0, T r / 2, the fractional-order resonant inductor L r The current is 0, the fractional resonant capacitor C r The voltage is 2(U in -nU o ). Similarly, according to the topological symmetry, the zero-state response of the resonant capacitor voltage in the negative half-cycle of the binary resonance is 2(nU o -U in ).

[0079] S3.3, the resonant capacitor voltage is the superposition of the zero input response in S3.1 and the zero state response in S3.2:

[0080] At the final state time t of the binary resonance positive half cycle p , the relationship between the resonant capacitor voltage in the positive half cycle of binary resonance is: U c(t p )=-(U2-δu)+2(U in -nU o )=U1. At the final state of the negative half cycle of binary resonance, t n According to the symmetry, the relationship between the resonant capacitor voltage in the negative half cycle of binary resonance is: U c (t n )=-(U1+δu)+2(-U in +nU o )=U2. So far, the initial and final state relationship between the positive and negative half-cycle resonant capacitor voltages in the binary resonance stage is obtained.

[0081] S4, combining the resonant capacitor voltage increment calculated in the multi-resonance stage in step S2 and the initial and final state relationship expression of the resonant capacitor voltage in the binary resonance stage obtained in step S3, obtain the voltage gain expression of the fractional-order resonant converter in the multi-resonance mode:

[0082] The expressions of the initial and final states of the resonant capacitor voltage increment in the three-element resonance stage and the resonant capacitor voltage in the two-element resonance stage shown in equation (5) are solved together, and the equation group is as follows:

[0083]

[0084] In formula (6), T r is the binary resonance period, that is, the fractional resonance period defined by equation (4). After simplifying the equation group in equation (6), the gain expression is as follows:

[0085]

[0086] The voltage gain frequency curve and voltage gain order curve obtained by the method of the present invention are compared with those obtained by SIMULINK circuit simulation, as shown in Figure 5(a), Figure 5(b), and Figure 5(c). It can be found from the figures that the method of the present invention can accurately calculate the voltage gain and reflect the influence of the order on the voltage gain, thus indicating that the method of the present invention is effective.

[0087] This embodiment also provides a method for optimizing the performance of a resonant converter, which is implemented by the above analytical modeling method.

[0088] This embodiment also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program that runs on the processor, and the processor executes the steps of the above-mentioned analytical modeling method when running the computer program.

[0089] This embodiment also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run, the steps of the above-mentioned analytical modeling method are executed.

[0090] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the purpose of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. An analytical modeling method for a fractional-order resonant converter, characterized in that: The steps include: S1. Solve the analytical expression of the excitation current according to the fractional differential equation of the excitation inductance in the binary resonance stage; S2, the resonant current in the approximately constant multi-resonant stage, the resonant capacitor voltage increment in the multi-resonant stage is calculated using the analytical expression of the excitation current solved by S1; S3, obtaining the initial and final state relationship of the resonant capacitor voltage in the positive and negative half-cycles during the binary resonance stage; S4. Combining the resonant capacitor voltage increment in the multi-resonance stage calculated by S2 and the initial and final state relationship of the positive and negative half-cycle resonant capacitor voltage in the binary resonance stage obtained by S3, obtain the voltage gain expression of the fractional-order resonant converter in the multi-resonance mode.

2. The analytical modeling method of a fractional-order resonant converter according to claim 1, characterized in that: The analytical expression of the excitation current solved by S1 is: The analytical time domain expression of the excitation current is: Among them, U Lm 、i m and L m are the voltage, current and inductance of the fractional-order excitation inductor respectively, γ is the order of the fractional-order excitation inductor, 0<γ≤1, U o is the converter output voltage equivalent to the resonant cavity from the secondary side, i mPn (t) is the fractional excitation current at time t, I mp0 is the initial value of the excitation current, Γ(·) is the gamma function.

3. The analytical modeling method of a fractional-order resonant converter according to claim 2, characterized in that: When the resonant converter is an LLC topology, the resonant converter contains a binary resonant mode and a ternary resonant mode. The specific method of the resonant current in the S2 approximate constant multi-resonant stage is: let the value of the ternary resonant current be the peak value of the binary resonant excitation current, Among them, I mp is the peak value of binary resonant excitation current, T r is the fractional-order resonance period, α and β are the orders of fractional-order resonant inductance and fractional-order resonant capacitance respectively, L r and C r They are the inductance of the fractional-order resonant inductor and the capacitance of the fractional-order resonant capacitor respectively.

4. The analytical modeling method of a fractional-order resonant converter according to claim 3, characterized in that: The resonant capacitor voltage increment calculated by S2 using the analytical expression of the excitation current solved by S1 in the multi-resonance stage is: Among them, δu is the resonant capacitor voltage increment in the three-element resonance stage, T s is the switching cycle.

5. The analytical modeling method of a fractional-order resonant converter according to claim 4, characterized in that: The specific method of S3 for obtaining the initial-final state relationship between the positive and negative half-cycle resonant capacitor voltages in the binary resonance stage is as follows: respectively solving the zero input response and the zero state response of the positive and negative half-cycle resonant capacitor voltages in the binary resonance stage, and respectively superimposing the zero input response and the zero state response of the resonant capacitor voltage in the positive and negative half-cycles of the binary resonance stage to obtain the initial-final state relationship between the positive and negative half-cycle resonant capacitor voltages in the binary resonance stage.

6. The analytical modeling method of a fractional-order resonant converter according to claim 5, characterized in that: The initial and final state relationship of the resonant capacitor voltage in the positive half-cycle of the binary resonance stage is obtained as U c (t p )=-(U2-δu)+2(k1U in -k2U o )=U1, the initial and final state relationship of the negative half-cycle resonant capacitor voltage in the binary resonance stage is obtained as U c (t n )=-(U1+δu)+2(k3U in -k4U o )=U2,where U c (t p ) is the final state time t of the positive half cycle in the binary resonance stage p The resonant capacitor voltage, U c (t n ) is the final state time t of the negative half cycle in the binary resonance stage n The resonant capacitor voltage at the end of the positive half cycle of the binary resonance stage is U1, and the resonant capacitor voltage at the end of the negative half cycle of the binary resonance stage is U2. in , U o are the input voltage and output voltage of the resonant converter respectively, k1=1, k2=n, k3=-1, k4=-n, and n is the turns ratio of the transformer in the resonant converter.

7. The analytical modeling method of a fractional-order resonant converter according to claim 6, characterized in that: The specific method of S4 is: combine the resonant capacitor voltage increment in the ternary resonance stage calculated by S2 and the initial and final state relationship of the resonant capacitor voltage in the positive and negative half-cycles in the binary resonance stage obtained by S3 to obtain the equation group: Simplify the equations to obtain the voltage gain expression of the fractional-order resonant converter in the multi-resonant mode:

8. A method for optimizing the performance of a resonant converter, characterized in that: This is achieved by the analytical modeling method described in any one of claims 1 to 7.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program that runs on the processor, and the processor executes the steps of the analytical modeling method according to claim 1 when running the computer program.

10. A computer-readable storage medium having a computer program stored thereon, wherein the computer program executes the steps of the analytical modeling method according to claim 1 when the computer program is executed.

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