Hybrid small signal modeling method for cascaded power supply

Abstract

The invention discloses a hybrid small signal modeling method for a cascaded power supply, and relates to the technical field of modeling, a pre-stage circuit of the cascaded power supply adopts a half-bridge Buck-Boost and CLLC bidirectional converter topology, and a post-stage circuit adopts a three-phase interleaving Buck topology. According to the mixed small signal modeling method, a generalized average method is adopted for a preceding-stage CLLC topology to establish a converter mathematical model, a state space average method is adopted for a half-bridge Buck-Boost converter and a backward-stage three-phase staggered Buck converter to establish a mathematical model, and a modular combination method is adopted to establish an overall mathematical model of a cascade system. The overall behavior of the cascade power supply can be better described; according to the technical scheme, a simple, convenient and accurate modeling method is provided for a multi-switching-frequency circuit containing a plurality of converters, the modeling analysis requirement of a cascade power supply with various types of internal modules, complex connection and various topologies is met, and an important research background and tool are provided for system optimization and performance analysis.

Description

Technical Field

[0001] The present application relates to the technical field of modeling, and in particular to a mixed small signal modeling method for a cascade power supply. Background Art

[0002] Cascade power supply is a common power supply technology with high conversion efficiency. By adding an additional intermediate voltage level, cascade power supply technology can avoid the converter working in an extremely low duty cycle state and reduce the peak current of the inductor component in the circuit. Generally, the multi-stage conversion efficiency and energy density of cascade power supply are higher than those of single-stage power supply. Since the cascade power supply contains a variety of power modules, such as resonant converters, MMC converters, Buck / Boost converters, etc., in order to ensure the stability of the converter voltage or power output in each power module or follow the given output, a high dynamic performance control strategy should be designed. Establishing a mathematical model of the system is an important part of controller design. At the same time, considering the complex connection relationship between these modules, in order to deeply study the dynamic characteristics and optimization design of the cascade power supply inside and outside, it is necessary to establish an accurate whole machine model. For DC / DC converters, the state space average method has the advantages of simplicity and mature technology; however, when the system is a high-order system, it is very difficult to accurately solve the state space equation within the switching cycle. In order to overcome the limitations of cycle average modeling and improve the model accuracy, the time period system modeling method that can consider the system frequency coupling effect has begun to receive attention.

[0003] In the prior art, there are three general modeling methods applicable to time periodic systems: Generalized Averaging Modeling (GAM) / Dynamic Phasor Modeling (DPM) modeling method, Harmonic Linearization (HL) modeling method and Harmonic State Space (HSS) / Harmonic Transfer Function (HTF) modeling method. The GAM / DPM method is based on the principle of harmonic balance. Each state variable is transformed into a different frequency space for modeling through Fourier transform. The resulting model is a multi-input and multi-output time-invariant model, which can effectively characterize the nonlinear behavior of the system and any order harmonic information. However, as the number of harmonic orders considered increases, the model derivation becomes more and more complicated. Singular perturbation, DC sequence decomposition and other methods can be used to reduce the complexity of the model. The essence of the HL method belongs to the description function method, which can be directly applied to nonlinear periodic models without averaging processing, and the single-input single-output linear time-invariant (SISO-LTI) model is obtained. Since the modeling process only considers the dominant frequency coupling component, when the sideband frequency coupling component cannot be ignored (such as asymmetric controller, unbalanced power grid, weak power grid, etc.), there is a large deviation between the obtained model and the actual system.

[0004] Patent document CN116680897A discloses a frequency domain steady-state modeling method and device for a dual active bridge converter, which is mainly used to solve the inaccurate technical problems of power transfer, effective value of inductor current and zero voltage switching performance in the prior art. Patent document CN111027269A discloses a two-stage DC / DC converter modeling method based on a harmonic equivalent circuit, which is mainly aimed at a circuit with a single switching frequency containing a single converter, and is modeled using a harmonic state space. Traditional modeling methods are mainly aimed at circuits with a single switching frequency of a single converter. The internal modules of cascade power supply circuits with multiple topologies are various and complex in connection. Traditional modeling methods cannot meet the modeling requirements of cascade power supplies with multiple topologies. The deviations generated by modeling are large, which is not conducive to subsequent analysis and calculation. Therefore, how to simply and accurately model circuits with multiple switching frequencies containing multiple converters is still a problem that needs to be solved urgently. Summary of the invention

[0005] The purpose of this application is to provide a simple and accurate modeling method for cascade power supplies. This method adopts classification modeling and modular combination methods, which can better describe the overall behavior of the cascade power supply and provide important research background and tools for system optimization and performance analysis.

[0006] The technical solution of the present application is to provide a mixed small signal modeling method for a cascade power supply, wherein the front stage of the cascade power supply includes a half-bridge Buck-Boost converter and a CLLC bidirectional converter, and the rear stage of the cascade power supply includes a three-phase interleaved parallel Buck converter. The method includes:

[0007] Step 1, defining the switching function of the CLLC bidirectional converter, establishing an average state equation of the first state variable, performing Fourier series expansion on the first state variable and bringing it into the switching function, establishing a linearized first state space equation, and deriving a corresponding first small signal model according to the first state space equation;

[0008] Step 2, determining the working stage of the half-bridge Buck-Boost converter according to the operating state of the switching element, averaging the second state variable of each working stage within one switching cycle, establishing a second state space equation, and deriving the corresponding second small signal model according to the second state space equation;

[0009] Step 3, define a switch description function of the three-phase staggered parallel Buck converter, determine the working stage of each phase according to the switch description function, average the third state variables of different working stages of each phase within a switching cycle, establish a third state space equation, and derive the corresponding third small signal model according to the third state space equation;

[0010] Step 4, making the variables of the connection part of the front-stage circuit and the rear-stage circuit of the cascaded power supply equal, combining the first state space equation, the second state space equation and the third state space equation to form a mixed small signal model of the entire cascaded power supply.

[0011] Furthermore, step 1 specifically includes:

[0012] Step 1.1, using switching functions s1 and s2 to represent the voltage output of the forward bridge arm and the reverse bridge arm in the CLLC bidirectional converter, respectively, where s1 is the switching function of the forward bridge arm and s2 is the switching function of the reverse bridge arm;

[0013] Step 1.2, establish the average state equation of the first state variable in the CLLC bidirectional converter, perform Fourier series expansion on the first state variable and bring it into the switching function, expand the Fourier series of the first state variable at the first harmonic, and obtain the generalized average expression of each first state variable;

[0014] Step 1.3, based on the generalized average expressions of the first state variables of the CLLC converter, construct the corresponding first small signal model.

[0015] Furthermore, step 1.2 specifically includes: replacing the actual value of the first state variable in the CLLC bidirectional converter circuit with the average value thereof in a switching cycle for modeling, and obtaining a linear time-invariant average state equation:

[0016]

[0017] Where x(t) represents the first state variable in the linear time-varying equation, <x> k (t) represents the average value of the linear time-invariant first state variable, k is the harmonic order, ω s is the first harmonic angular frequency, and τ is a periodic variable, T is the switching period of the CLLC bidirectional converter, t is a time variable, and j is a complex unit;

[0018] Perform Fourier series leaf expansion on the first state variable in the equation to calculate the DC quantity part and the first harmonic component part. When the DC quantity is taken, k = 0, and when the first harmonic component is taken, k = ± 1. The expression is as follows:

[0019]

[0020] Substitute the switching function into the product of the first state variable and the switching function using the zero-order and first-order Fourier series. The product of the first state variable and the switching function is:

[0021] <xy> 0＝ <x> 0 <y>0+2(<x 1R ><y 1R >+<x 1I ><y 1I >)

[0022] <xy> 1R ＝ <x> 0 <y> 1R + <x> 1R <y> 0

[0023] <xy> 1I ＝ <x> 0 <y> 1I + <y> 1I <y>0

[0024] Where x represents the first state variable, y represents the input value of the switching function, y is s1 when the forward bridge arm is working, y is s2 when the reverse bridge arm is working, <·> represents the average value, <·>0 represents the DC term, <·> 1R represents the real part of the fundamental term, <·> 1I The imaginary part of the fundamental term;

[0025] The CLLC bidirectional converter has two inductors L 11 , two inductors L 12 , two capacitors C 11 , two capacitors C 12 , L 11 The current is i1, L 12 The current is i2, C 11 The voltage of C is v1, 12 The voltage is v2, and the first state variables i1, i2, v1, v2 are expanded at the first harmonic to obtain the generalized average expression:

[0026]

[0027] v o_CLLC =(2 <s2> 1R <i2> 1R +2 <s2> 1I <i2> 1I )R L

[0028] In the formula, R1 is the power supply side resistance, R2 is the load side resistance, V dc is the input side DC voltage, L m is the mutual inductance of the transformer in the CLLC converter, a represents the coefficient of each harmonic component in the Fourier series, n is the turns ratio of the high-frequency transformer, R L is the load resistance, v o_CLLC is the output voltage of the CLLC converter.

[0029] Furthermore, the first small signal model of the CLLC converter in step 1.3 is:

[0030]

[0031] Among them, X is the first state variable u is the input variable of the CLLC converter v in_CLLC is the input voltage of the CLLC converter, is the state variable of the coupling capacitor voltage, is the input current of the CLLC converter, A CLLC , B CLLC , C CLLC , D CLLC is the system matrix.

[0032] Furthermore, step 2 specifically includes:

[0033] Step 2.1, in one switching cycle, the working process of the half-bridge Buck-Boost converter is divided into a switch-on phase and a switch-off phase, the second state variables of the two phases are averaged, and the average second state variables are used to replace the instantaneous value to obtain the second state space equation in the entire switching cycle;

[0034] The half-bridge Buck-Boost converter includes capacitors C0 and L0. In a switching cycle, the switch element in the circuit is alternately turned on and off. When the switch element is turned on, the inductor L0 starts to store energy, and the current flows through the inductor L0 and the capacitor C0 through the switch. When the switch element is turned off, the inductor L0 releases energy and provides energy to the load and the capacitor C0. The working process of the half-bridge Buck-Boost converter is divided into the switch-on stage and the switch-off stage. The average second state variable is used to approximate the instantaneous value, and the second state space equation is listed:

[0035]

[0036] Among them, V dc is the input voltage of the half-bridge Buck-Boost converter, Ts is the switching period, <·> Ts Represents the average value in a switching cycle, i L is the current of inductor L0, V o is the DC component of the output voltage of the half-bridge Buck-Boost converter, i o is the output current of the half-bridge Buck-Boost converter, v o is the output voltage of the half-bridge Buck-Boost converter, d0 is the duty cycle of the half-bridge Buck-Boost converter;

[0037] Step 2.2, based on the second state space equation of the half-bridge Buck-Boost converter, construct a corresponding second small signal model;

[0038] The average second state variable is decomposed into the sum of the DC component and the AC small signal component. At the same time, the control quantity containing the AC component is decomposed and the decomposed quantity is brought into the second state space equation:

[0039]

[0040] in, is the AC small signal component of the output voltage, V o is the DC component of the output voltage, is the AC small signal component of the inductor current, I is the DC component of the inductor current, is the small AC signal component of the duty cycle, is the AC small signal component of the output current, D0 is the average value of the duty cycle, is the AC small signal component of the input voltage;

[0041] Eliminate the DC component in the second state-space equation and ignore the high-order small signal components and Linearizing the equations, we get the AC small signal equations:

[0042]

[0043] The AC small signal equations are organized into the form of space state equations to obtain the third small signal model of the half-bridge Buck-Boost:

[0044]

[0045] Where X is the second state variable u is the input Y is the output A Buck_Boost , B Buck_Boost , C Buck_Boost , D Buck_Boost is the system matrix.

[0046] Furthermore, step 3 specifically includes:

[0047] Step 3.1, use the switch description function to represent the on and off states of the bridge arm of the three-phase interleaved parallel Buck converter, and define the switch description function of the on and off logic of the z-th phase switch as S z , when S z When S is equal to 1, the upper bridge arm is turned on and the lower bridge arm is turned off. z When it is equal to 0, the upper bridge arm is turned off and the lower bridge arm is turned on, z = 1, 2, 3;

[0048] Step 3.2, according to the switch description function, the working process of each phase is divided into a switch-on phase and a switch-off phase, the third state variables of the two phases of each phase are averaged, and the average third state variables are used to replace the instantaneous value to obtain the third state space equation in the entire switching cycle;

[0049] Step 3.3, according to the third state space equation of the three-phase interleaved parallel Buck converter, establish the corresponding third small signal model.

[0050] Further, step 3.2 specifically includes: each phase of the three-phase staggered parallel Buck converter includes inductors L1, L2, and L3 respectively, and the output end includes a capacitor C1. In a switching cycle, the working process of each phase is divided into a switch-on phase and a switch-off phase. The average third state variable is used to approximate the instantaneous value, and the third state space equation is listed:

[0051]

[0052] Among them, i L1 is the current of the inductor in the first phase Buck converter circuit, i L2 is the current of the inductor in the second phase Buck converter circuit, i L3 is the inductor current in the third-phase Buck converter circuit, U in is the input voltage, U o is the output voltage, D1 is the duty cycle of the switch on time in the first phase Buck converter circuit, D2 is the duty cycle of the switch on time in the second phase Buck converter circuit, D3 is the duty cycle of the switch on time in the third phase Buck converter circuit, T S Represents one switching cycle.

[0053] Furthermore, step 3.3 specifically includes: decomposing the average third state variable into the sum of the DC component and the AC small signal component, and decomposing other control quantities containing AC components, bringing the decomposed quantities into the third state space equation, making the input and output DC quantities correspondingly equal, eliminating the DC component, and ignoring the high-order small signal components, and obtaining the AC small signal equation group:

[0054]

[0055] in, is the small AC signal component of the inductor current in the first phase Buck converter circuit, is the small AC signal component of the inductor current in the second-phase Buck converter circuit, is the small AC signal component of the inductor current in the third-phase Buck converter circuit, is the AC small signal component of the output voltage, is the AC small signal component of the input voltage, is the AC small signal component of the duty cycle in the first phase Buck converter circuit, is the AC small signal component of the duty cycle in the second-phase Buck converter circuit, is the AC small signal component of the duty cycle in the third-phase Buck converter circuit, and R is the load resistance of the three-phase interleaved parallel Buck converter;

[0056] The AC small signal equations are organized into the form of space state equations, and the third small signal model of the three-phase interleaved parallel Buck converter is obtained:

[0057]

[0058] Among them, X is the third state variable u is the input Y is the output Let M = R c Cs+1,R c is the equivalent series resistance of the capacitor, s is the complex frequency variable, A Buck , B Buck , C Buck , D Buck is the system matrix.

[0059] Further, step 4 specifically includes: setting the output of the half-bridge Buck-Boost converter equal to the input of the CLLC bidirectional converter, setting the output of the CLLC bidirectional converter equal to the input of the three-phase interleaved parallel Buck converter to obtain:

[0060]

[0061] The first state space equation, the second state space equation and the third state space equation are combined and the expressions are combined to obtain the mixed small signal model of the cascade power supply as a whole:

[0062]

[0063] Among them, X is the state variable of the cascade power supply as a whole u is the input variable A, B, C, and D are the system matrices of the cascade power supply.

[0064] The beneficial effects of this application are:

[0065] The technical solution in the present application is applicable to circuits with multiple switching frequencies containing multiple converters. Different modeling methods are used for circuit topologies with different characteristics in the converter. For example, the generalized averaging method is used to establish the mathematical model of the converter for the front-stage CLLC topology, and the state space averaging method is used to establish the mathematical model for the half-bridge circuit and the rear-stage three-phase interleaved parallel Buck converter. In addition, a modular combination method is used to combine the mathematical models of each circuit topology to achieve the establishment of an overall mathematical model of the cascade system.

[0066] In a circuit with multiple switching frequencies of multiple converters, there are many types of modules and the connections are complex. Traditional modeling methods tend to use more complex mathematical models to improve the accuracy and applicability of the model. The modeling method used for overall circuit modeling is single, which cannot meet the modeling and analysis requirements of cascade power supplies containing multiple topologies. It will also increase the difficulty of calculation, reduce the adaptability of the model, and make subsequent experimental verification more difficult. Compared with the traditional modeling method, the technical solution in this application can better cope with such complex circuits by using different methods to establish models in modules according to the characteristics of the circuit topology. The overall model of the circuit established can be compatible with each other and take into account both accuracy and simplicity, reducing the difficulty of calculation, improving the adaptability of the model, and making subsequent experimental verification easier. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A schematic diagram of a CLLC equivalent circuit model in a cascade power supply according to an embodiment of the present application;

[0068] Figure 2 This is a schematic diagram of a half-bridge Buck-Boost equivalent circuit in a cascade power supply according to an embodiment of the present application;

[0069] Figure 3 This is a schematic diagram of a three-phase staggered parallel Buck working mode decomposition in a cascade power supply according to an embodiment of the present application;

[0070] Figure 4 A schematic diagram of a three-phase staggered parallel Buck equivalent circuit in a cascade power supply according to an embodiment of the present application;

[0071] Figure 5 This is a schematic diagram of an equivalent circuit of a cascaded power supply according to an embodiment of the present application;

[0072] Figure 6 A simulation comparison diagram of a mixed small signal model of a cascade power supply as a whole and an actual switch circuit after input voltage disturbance in one embodiment of the present application;

[0073] Figure 7 This is a simulation comparison diagram of the overall mixed small signal model of the cascade power supply of one embodiment of the present application and the actual switching circuit after the input power jump. DETAILED DESCRIPTION

[0074] In order to more clearly understand the above-mentioned purposes, features and advantages of the present application, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0075] In the following description, many specific details are elaborated to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present application is not limited to the specific embodiments disclosed below.

[0076] In this embodiment, the cascade power supply includes a front-stage circuit and a rear-stage circuit. The front-stage circuit is composed of a half-bridge converter topology and a CLLC bidirectional converter topology, and the rear-stage circuit is composed of a three-phase interleaved parallel Buck converter topology.

[0077] The half-bridge converter circuit constitutes a non-isolated bidirectional Buck-Boost circuit, i.e., a half-bridge Buck-Boost converter. This converter circuit is a voltage regulation circuit that allows the voltage to be stepped up or down when the input voltage is higher or lower than the output voltage. The non-isolated bidirectional Buck-Boost circuit adopts dual-loop control of the voltage outer loop and the current inner loop. Both the voltage loop and the current loop adopt PI control, i.e., proportional integral control. Among them, the purpose of PI control is to maintain the stability of the output voltage, the proportional term is responsible for rapid response, and the integral term is responsible for eliminating steady-state errors. The current inner loop and the voltage outer loop work together to achieve precise control of the output voltage and current, ensuring the stability and rapid dynamic response of the system.

[0078] The CLLC bidirectional converter is a resonant converter that works at a resonant frequency and makes full use of the resonant characteristics of circuit elements (resonance refers to the state where the energy exchange between the inductor and capacitor elements in the circuit reaches the maximum) to improve efficiency and simplify control. At the resonant frequency, the energy transfer between the inductor and capacitor elements is more effective, reducing energy loss. The CLLC converter system exhibits more linear characteristics near the resonant frequency, making it easier to achieve efficient energy conversion. Its control is relatively simple, and it has the advantages of high efficiency, low switching loss, and less electromagnetic interference.

[0079] In the three-phase interleaved parallel Buck converter, three Buck converters work in parallel with phase staggered mode, each Buck converter is responsible for one phase, the upper and lower bridge arms of each bridge arm of the three phases are complementary turned on (complementary conduction means that when the upper bridge arm is turned on, the lower bridge arm is turned off, and vice versa, when the lower bridge arm is turned on, the upper bridge arm is turned off), and the switching action phases of the adjacent two phases differ by 120°. Multi-phase parallel connection and phase staggering help reduce the pulsation of the output current (i.e., reduce the fluctuation or ripple contained in the output current) and improve the stability and efficiency of the system.

[0080] The prior art tends to adopt more complex mathematical models to improve the accuracy and applicability of the models, while the hybrid modeling method described in the present invention adopts different modeling methods for different circuit topology characteristics in the converter. The modeling methods include generalized state averaging and state space averaging. The obtained mathematical models are compatible with each other and take into account both accuracy and simplicity.

[0081] like Figures 1 to 5 As shown, this embodiment provides a mixed small signal modeling method for a cascade power supply, including:

[0082] Step 1, define the switching function of the CLLC bidirectional converter, use the generalized average modeling method to establish the average state equation of the first state variable, perform Fourier series expansion on the first state variable and bring it into the switching function, establish the linearized first state space equation of the CLLC bidirectional converter, and derive the corresponding third small signal model based on the first state space equation.

[0083] In this embodiment, the generalized average modeling method is applicable to converter topologies with periodic operating characteristics, dominated by harmonics and which can be described by average values ​​in steady state. The CLLC converter operates at a resonant frequency and has a high switching frequency and is periodic. These characteristics meet the assumptions of the generalized average modeling method. Modeling using the generalized average modeling method can convert complex nonlinear time-varying systems into linear time-invariant systems, simplifying the process of modeling, analysis and control strategy design.

[0084] Step 1.1, using switching functions s1 and s2 to represent the voltage output of the forward bridge arm and the reverse bridge arm in the CLLC bidirectional converter respectively;

[0085] The CLLC bidirectional converter is equipped with energy storage elements inductance and capacitance. The inductance is L 11 , L 12 , the capacitance is C 11 , C 12 , L 11 and C 11 Distributed on the primary side of the CLLC converter ( Figure 1 Center left), L 12 and C 12 Distributed on the secondary side of the CLLC bidirectional converter ( Figure 1 The CLLC bidirectional converter includes two bridge arms, the forward bridge arm and the reverse bridge arm. Both bridge arms are controlled by switches. When the bridge arms are working, energy is transferred between the input and the output. When the CLLC bidirectional converter is in the forward working state, electric energy flows from the power supply to the load. At this time, the forward bridge arm works. In this state, the output corresponds to the switching function s1. In the reverse working state, the load feeds back power to the power supply. At this time, the reverse bridge arm works. In this state, the output corresponds to the switching function s2. The forward bridge arm contains the capacitor C of the primary side. 11 , the primary inductance L 11 , the secondary capacitor C 12 and the secondary side inductor and component L 12 , the reverse bridge arm contains a symmetrical primary capacitor C 11 , the primary inductance L 11 , the secondary capacitor C 12 and the secondary inductor L 12 The energy storage element on the primary side and the energy storage element on the secondary side (the energy storage elements are capacitors and inductors) form a resonant circuit, in which energy is transferred between the inductor and the capacitor in a resonant manner.

[0086] The switching function s1 of the forward bridge arm and the switching function s2 of the reverse bridge arm are:

[0087]

[0088] Among them, s1(t) is the switching function of the forward bridge arm, s2(t) is the switching function of the reverse bridge arm, d is the duty cycle in the CLLC bidirectional converter, T is the switching period of the CLLC bidirectional converter, t is the time variable, when the switching function is 1, the switch tube in the circuit is in the on state, when the switching function is -1, the switch tube in the circuit is in the off state.

[0089] Step 1.2, establish the average state equation of the first state variable in the CLLC bidirectional converter, expand the first state variable in Fourier series and bring it into the switching function, expand the Fourier series of the first state variable at the first harmonic, and obtain the generalized average expression of each first state variable.

[0090] The CLLC bidirectional converter works in the switching state, and the circuit structure also changes with the switching of the switching state. Modeling is difficult. To simplify the analysis, the switching process is ignored, and the average value of each variable in the CLLC bidirectional converter circuit is obtained within a switching cycle. The average value is used to replace the actual value for modeling, and the relationship between the average variables is established in the form of a state space equation. The linear time-invariant average state equation is established, and its expression is:

[0091]

[0092] Where x(t) is the first state variable in the linear time-varying equation, <x> k (t) represents the average value of the linear time-invariant first state variable, k is the harmonic order, ω s is the first harmonic angular frequency, and τ is a periodic variable and j is a complex unit.

[0093] The generalized average method uses Fourier series to fit the system state, which can convert the nonlinear time-varying state space equation of the CLLC converter into a linear time-invariant state space equation. In the calculation process using the generalized average method, the nonlinear square wave waveform voltage in the switching state is approximately equivalent to a linear sine wave waveform voltage. Since the CLLC bidirectional converter operates at the resonant frequency, the resonant frequency is designed to be the frequency of the main harmonic component, which helps to limit the energy transfer to this specific harmonic component, so that the CLLC bidirectional converter can more effectively utilize the harmonic components when working and achieve efficient energy transfer. The first harmonic component is the basic frequency component, and limiting the energy transfer to only be related to the first harmonic component helps to reduce harmonic distortion. Therefore, assuming that the energy transfer of the CLLC bidirectional converter is only related to the first harmonic component, the analysis of the CLLC bidirectional converter is simpler.

[0094] In this embodiment, the first state variable of the CLLC bidirectional converter includes the capacitor voltage and the inductor current, that is, L 11 The current i1, L 12 The current i2, C 11 The voltage v1, C 12 The voltage v2 is obtained by performing Fourier series expansion on the first state variable in the equation, calculating the DC quantity part and the first harmonic component part. When the DC quantity is taken, k = 0, and when the first harmonic component is taken, k = ±1, and a linear time-invariant state space equation is obtained.

[0095] The expression for the Fourier series expansion of the first state variable is as follows:

[0096]

[0097] The periodic change of the switch state will affect the expression of the first state variable. When performing Fourier series expansion, the switch function needs to be taken into account. Since only the DC part and the first harmonic component are calculated, the zero-order and first-order Fourier series are used to express the product of the first state variable and the switch function. Substituting the switch function, the product of the first state variable and the switch function is:

[0098] <xy> 0＝ <x> 0 <y>0+2(<x 1R ><y 1R >+<x 1I ><y 1I >)

[0099] <xy> 1R ＝ <x> 0 <y> 1R + <x> 1R <y> 0

[0100] <xy> 1I ＝ <x> 0 <y> 1I + <x> 1I <y>0

[0101] Where x represents the first state variable, y represents the input value of the switching function, the switching function includes s2 and s1, when the forward bridge arm is working, y is s1, when the reverse bridge arm is working, y is s2, <·> represents the average value, <·>0 represents the DC term, <·> 1R represents the real part of the fundamental term, <·> 1I The imaginary part of the fundamental wave term. The real part of the fundamental wave term usually corresponds to the fundamental frequency of the signal, indicating the amplitude of the fundamental frequency component in the Fourier series. The imaginary part is usually used to describe the phase information of the fundamental wave term, that is, the offset of the fundamental frequency component relative to time.

[0102] Since the input voltage of the CLLC converter and the voltage across the capacitor on the output side are both DC terms, the input voltage v is ignored. in_CLLC and the output voltage v o_CLLC The DC average value is taken for the first harmonic component. There are two inductors L in the CLLC bidirectional converter. 11 (included in both bridge arms and symmetrical), two inductors L 12 , two capacitors C 11 , two capacitors C 12 , L 11 The current is i1, L 12 The current is i2, C 11 The voltage of C is v1, 12 The voltage is v2, and the Fourier series of the first state variables i1, i2, v1, and v2 are expanded at the first harmonic. The product of the above first state variables and the switching function is substituted to obtain the generalized average expression of each first state variable, and the mathematical model of the CLLC converter is established.

[0103] Expand the four groups of variables i1, i2, v1, and v2 at the first harmonic to obtain the generalized average expression:

[0104]

[0105]

[0106] v o_CLLC =(2 <s2> 1R <i2> 1R +2 <s2> 1I <i2> 1I )R L

[0107] In the formula, R1 is the power supply side resistance, R2 is the load side resistance, V dc The DC voltage on the input side is , n is the turns ratio of the high-frequency transformer, a is the coefficient of the harmonic component in the Fourier series (coefficient related to system parameters), L m is the mutual inductance of the transformer in the CLLC converter, R L is the load resistance, v o_CLLC is the output voltage of the CLLC converter.

[0108] Step 1.3, based on the generalized average expressions of the first state variables of the CLLC converter (ie, the first state space equation), a corresponding first small signal model is established, and a corresponding equivalent circuit model is constructed.

[0109] Without considering the disturbance of frequency and duty cycle, only considering the disturbance of input voltage and output voltage, the first small signal model of CLLC converter in open-loop working mode is obtained:

[0110]

[0111] The output end of the CLLC converter also includes a coupling capacitor C f , X is the first state variable u is the input variable of the CLLC converter v in_CLLC is the input voltage of the CLLC converter, is the state variable of the coupling capacitor voltage, is the input current of the CLLC converter, A CLLC , B CLLC , C CLLC , D CLLC is the system matrix, which can be expressed as follows:

[0112]

[0113] C=[2s 1R 2s 1I 0 0 0 0 0 0 0]

[0114] D=[0 0]

[0115] The small signal model is obtained by linearizing the state space equations of the system. The state space equations describe the dynamic behavior of the system, the evolution of the state variables of the inductor current and capacitor voltage, and the state variables are affected by the switch state. The small signal model is a linear representation of the system and is used to analyze the small signal response of the system near the steady-state operating point (small signal response refers to the response of the system to small input changes, which is used to evaluate the stability and performance of the system to small disturbances).

[0116] like Figure 1 As shown, based on the generalized average expression of the CLLC converter, an equivalent circuit model is constructed in the circuit simulation software on the computer platform (Multisim, LTspice, PSIM simulation software can be used). Specifically, a circuit file is created in the circuit simulation software, a blank circuit board is selected, capacitors, inductors, resistors and switch elements are added to the blank circuit board, a voltage source is added to the power supply side, and each element is connected according to the topological structure and connection relationship of the CLLC converter. The parameter value of each element is set according to the parameters of each item of the generalized average expression of the CLLC converter to form a complete equivalent circuit model of the CLLC converter. Figure 1 In the circuit, a capacitor C is set 11 , C 12 , C f , inductance L 11 , L 12 , L m , load resistance R L and voltage source, the input voltage is marked as V in-CLLC , the output voltage on the load side is marked as v o-CLLC , V o is the output voltage DC term, the input current is marked as i1, including the current i passing through the reverse bridge arm 1s and the current i passing through the positive bridge arm 1c , the load side current is marked as i2, including the current i passing through the reverse bridge arm 2s and the current i passing through the positive bridge arm 2c , the voltage corresponding to C1 in the forward bridge arm is v 1s , the voltage corresponding to C2 is v 1s , the voltage corresponding to C1 in the reverse bridge arm is v 1c , the voltage corresponding to C2 is v 1c .

[0117] Step 2, use the state space averaging method to establish the second state space equation of the half-bridge circuit topology, determine the working stage of the half-bridge Buck-Boost converter according to the operating state of the switching element, average the second state variables of each working stage within a switching cycle, and establish the second state space equation, and derive the corresponding small signal model based on the second state space equation.

[0118] In this embodiment, the state space averaging method is particularly suitable for converter topologies with periodic operation, high switching frequency and linear approximation characteristics. The non-isolated bidirectional Buck-Boost circuit operates in a high-frequency switching mode, which meets the assumptions of the state space averaging method. The state space averaging method can accurately describe the dynamic behavior of the bidirectional Buck-Boost circuit in different operating modes.

[0119] Step 2.1, divide the working process of the half-bridge Buck-Boost converter into a switch-on stage and a switch-off stage in one switching cycle, average the second state variables of these two stages, use the average second state variable to replace the instantaneous value, and obtain the second state space equation in the entire switching cycle.

[0120] The half-bridge Buck-Boost converter includes capacitor C0 and inductor L0. In a switching cycle, the switching elements in the circuit will be alternately turned on and off. This alternating operation will cause the current and voltage of the inductor and capacitor to change in two different states. When the switching element is turned on, the inductor L0 starts to store energy, and the current flows through the inductor L0 and capacitor C0 through the switch. When the switching element is turned off, the inductor L3 releases energy and provides energy to the load and capacitor C0. The working process of the half-bridge Buck-Boost converter can be divided into two stages: the switch-on stage and the switch-off stage. The working states of the switching elements are different in different stages. For the two stages, the average second state variable is used to approximate the instantaneous value, and the state equation is listed:

[0121]

[0122] Among them, V dc is the input voltage of the half-bridge Buck-Boost converter, Ts is the switching period of the half-bridge Buck-Boost converter, <·> Ts Represents the average value in a switching cycle, i L is the current of inductor L0, V o is the DC component of the output voltage of the half-bridge Buck-Boost converter, i o is the output current of the half-bridge Buck-Boost converter, d0 is the duty cycle of the half-bridge Buck-Boost converter, v o is the output voltage of the half-bridge Buck-Boost converter, <d0> Ts represents the switch off time, is the AC small signal component of the output current, represents the rate of change of capacitor voltage, is the rate of change of the inductor current.

[0123] Step 2.2, based on the second state space equation of the half-bridge Buck-Boost converter, construct the corresponding second small signal model and the corresponding equivalent circuit model.

[0124] The average second state variable is decomposed into the sum of the DC component and the AC small signal component. At the same time, the control variable containing the AC component is decomposed to obtain the following expression:

[0125]

[0126] in, is the AC small signal component of the output voltage, V o is the DC component of the output voltage, is the AC small signal component of the inductor current, I is the DC component of the inductor current, It is the small AC signal component of the duty cycle, and D0 is the average value of the duty cycle, that is, the steady-state value.

[0127] Substituting the decomposed expression of the average second state variable into the second state space equation (i.e., substituting the decomposed quantity into it), the state space average mathematical model of the half-bridge Buck-Boost converter is obtained, and the expression is as follows:

[0128]

[0129] in, is the AC small signal component of the input voltage, It is the small AC signal component of the output current.

[0130] Make the corresponding DC quantities equal and eliminate the DC component in the above state space average mathematical model expression:

[0131]

[0132] Ignore high-order small signal components and Linearizing the equations, we get the AC small signal equations:

[0133]

[0134] The above AC small signal equations are organized into the form of space state equations to obtain the state space average mathematical model of the half-bridge Buck-Boost:

[0135]

[0136] Where X is the second state variable u is the input Y is the output A Buck_Boost , B Buck_Boost , C Buck_Boost , D Buck_Boost is the system matrix, which can be expressed as follows:

[0137]

[0138] C Buck-Boost =[D0 0], D Buck-Boost =[0 0]

[0139] Among them, R1 is the load resistance in the half-bridge Buck-Boost converter, L0 is the value of the inductor in the half-bridge Buck-Boost converter, and C0 is the value of the capacitor in the half-bridge Buck-Boost converter.

[0140] like Figure 2 As shown, an equivalent circuit model is constructed in the circuit simulation software on the computer platform based on the second state space equation of the half-bridge Buck-Boost converter. Specifically, a circuit file is created in the circuit simulation software, a blank circuit board is selected, capacitors, inductors, resistors and switch elements are added to the blank circuit board, and each element is connected according to the topological structure and connection relationship of the half-bridge Buck-Boost converter. The parameter value of each element is set according to the parameters of each item in the second state space equation of the half-bridge Buck-Boost converter to form a complete equivalent circuit model of the half-bridge Buck-Boost converter. Figure 2 In the circuit, capacitor C0, inductor L0, load resistor R1 and voltage source are set up, and the input voltage is marked as V dc , the output voltage is marked as u c ,u c The DC term is marked as U c .

[0141] Step 3, define the switch description function of the three-phase staggered parallel Buck converter, determine the working stage of each phase according to the switch description function, average the third state variables of different working stages of each phase within a switching cycle, establish the third state space equation, and derive the corresponding third small signal model according to the third state space equation.

[0142] In this embodiment, the switch of each phase of the three-phase interleaved parallel Buck converter operates in a high-frequency mode, which also meets the assumptions of the state-space averaging method. The state-space averaging method can linearize the dynamic behavior of each phase and provide a simplified overall model for easy analysis and design.

[0143] Step 3.1, use the switch description function to represent the on and off states of the bridge arm of the three-phase staggered parallel Buck converter, and define the switch description function of the on and off logic of the z-th phase switch as:

[0144]

[0145] Among them, when S z When it is equal to 1, it means that the upper bridge arm is turned on and the lower bridge arm is turned off. z When it is equal to 0, it means that the upper bridge arm is turned off and the lower bridge arm is turned on. z represents the label of the phase in the three-phase interleaved parallel Buck converter, z=1, 2, 3.

[0146] Step 3.2, according to the switch description function, the working process of each phase is divided into a switch-on phase and a switch-off phase, the third state variables of the two phases of each phase are averaged, and the average third state variables are used to replace the instantaneous value to obtain the third state space equation in the entire switching cycle;

[0147] Inductors are set in each item of the three-phase interleaved parallel Buck converter, namely L1, L2 and L3, and capacitor C1 is set at the output end. In one switching cycle, the working process of each phase is divided into the switch-on stage and the switch-off stage for calculation. When the switch is on, the inductor obtains energy from the input voltage and the inductor current increases. When the switch is off, the inductor provides energy to the output capacitor and the load, and the inductor current decreases. The average third state variable is used to approximate the instantaneous value, and the third state space equation is listed for the third state variables in the two stages of each phase:

[0148]

[0149] Among them, i L1 is the current of the inductor in the first phase Buck converter circuit, i L2 is the current of the inductor in the second phase Buck converter circuit, i L3 is the inductor current in the third-phase Buck converter circuit, U in is the input voltage, U o is the output voltage, D1 is the duty cycle of the switch on time in the first phase Buck converter circuit, D2 is the duty cycle of the switch on time in the second phase Buck converter circuit, D3 is the duty cycle of the switch on time in the third phase Buck converter circuit, T S Represents a switching cycle, and t is the time variable.

[0150] Step 3.3, according to the third state space equation of the three-phase interleaved parallel Buck converter, establish the corresponding third small signal model and construct the corresponding equivalent circuit model.

[0151] The average third state variable is decomposed into the sum of the DC component and the AC small signal component. At the same time, other control variables containing AC components in the above formula (including the input voltage U in , output voltage U o ) is decomposed, and the decomposed quantity is brought into the third state space equation, and the corresponding DC quantities of the input and output are made equal. The DC component of the third state space equation of the three-phase staggered parallel Buck converter is eliminated, and the high-order small signal components are ignored. The third state space equation is linearized to obtain the AC small signal equation group:

[0152]

[0153] in, is the small AC signal component of the inductor current in the first phase Buck converter circuit, is the small AC signal component of the inductor current in the second-phase Buck converter circuit, is the small AC signal component of the inductor current in the third-phase Buck converter circuit, is the AC small signal component of the output voltage, is the AC small signal component of the input voltage, is the AC small signal component of the duty cycle in the first phase Buck converter circuit, is the AC small signal component of the duty cycle in the second-phase Buck converter circuit, is the AC small signal component of the duty cycle in the third-phase Buck converter circuit, and R is the load resistance of the three-phase interleaved parallel Buck converter.

[0154] The AC small signal equations are organized into the form of space state equations, and the third small signal model of the three-phase interleaved parallel Buck converter is obtained:

[0155]

[0156] Among them, X is the third state variable u is the input Y is the output Let M = R c Cs+1,R c is the equivalent series resistance of the capacitor, s is a complex frequency variable (used to describe the behavior of the system in the frequency domain), A Buck , B Buck , C Buck , C Buck is the system matrix, which can be expressed as follows:

[0157]

[0158] like Figure 4 As shown, an equivalent circuit model is constructed on a computer platform according to the third state space equation of the three-phase interleaved parallel Buck converter. Specifically, a circuit file is created in the circuit simulation software, a blank circuit board is selected, capacitors, inductors, resistors and transformers are added to the blank circuit board, and various components are connected according to the topological structure and connection relationship of the three-phase interleaved parallel Buck converter. The parameter value of each component is set according to the parameters of each item in the third state space equation of the three-phase interleaved parallel Buck converter to form a complete equivalent circuit model of the three-phase interleaved parallel Buck converter. Figure 4 In the circuit, capacitor C1, inductors L1, L2, L3, load resistor R, and capacitor series equivalent resistor R are set. c , transformers and voltage sources.

[0159] Step 4, making the variables of the connection part of the front-stage circuit and the rear-stage circuit of the cascaded power supply equal, combining the first state space equation, the second state space equation and the third state space equation to form a mixed small signal model of the entire cascaded power supply.

[0160] The front stage of the cascade power supply includes a half-bridge Buck-Boost converter and a CLLC bidirectional converter, the rear stage of the cascade power supply is a three-phase interleaved parallel Buck converter, the output of the half-bridge Buck-Boost converter is connected to the input of the CLLC bidirectional converter, the output of the CLLC bidirectional converter is connected to the input of the three-phase interleaved parallel Buck converter, according to the variable expressions obtained from step 1 to step 3, the output of the half-bridge Buck-Boost converter is equal to the input of the CLLC bidirectional converter, the output of the CLLC bidirectional converter is equal to the input of the three-phase interleaved parallel Buck converter, and all state space equations are combined to obtain the overall mixed small signal model of the cascade power supply;

[0161] Let the variables of the corresponding connected parts in the cascade power supply be equal, that is:

[0162]

[0163] By combining the expressions, we get the overall mixed small signal model of the cascade power supply:

[0164]

[0165] Among them, X is the state variable of the cascade power supply as a whole u is the input variable A, B, C, and D are system matrices of cascaded power supplies, which are expressed as follows:

[0166]

[0167] C=[C Buck-boost C CLLC C Buck ],D=[D Buck-boost D CLLC D Buck ]

[0168] like Figure 5 As shown in the figure, the equivalent circuit model of the half-bridge Buck-Boost converter, the equivalent circuit model of the CLLC converter and the equivalent circuit model of the three-phase interleaved parallel Buck converter are combined to obtain the overall equivalent circuit diagram of the cascade power supply. Figure 5 The input voltage of the CLLC converter is multiplied by It is used to convert the DC input voltage into an equivalent AC voltage during the analysis process.

[0169] In this embodiment, the method of the present invention is used to establish an equivalent circuit model of a cascade power supply, and the time domain simulation results of the mixed small signal model of the cascade power supply as a whole are compared with the actual switching circuit to verify the modeling accuracy.

[0170] Taking the simulated output voltage as the detection content, the same input voltage disturbance and power jump are added to the established cascade power supply overall equivalent circuit model and the actual switching circuit on the computer platform, and the response waveforms of the output voltage and input inductor current are measured respectively. When the steady-state value error, response time and corresponding overshoot error of the two are less than 5%, the modeling is considered to be reasonable and has high accuracy.

[0171] A certain disturbance is applied to the input voltage to simulate the impact of changes in input voltage on the circuit, such as Figure 6 As shown in the figure, after the input voltage is disturbed, the mixed small signal model of the cascade power supply and the output response waveform of the actual switching circuit are recorded and compared. out_switch is the voltage of the actual switching circuit, V out_mode is the voltage of the actual switching circuit, 20ms / div means that on the horizontal axis (time axis) of the simulation diagram, each scale corresponds to 20 milliseconds, and the response waveform generated by the mixed small signal model of the cascade power supply is basically consistent with the response waveform generated by the actual switching circuit (ignoring the subharmonic components generated by the switching element under non-ideal conditions), indicating that the established mixed small signal model is reasonable and accurate. Figure 7 As shown, the same power jump is added to the hybrid small signal model of the cascade power supply and the actual switching circuit, and the full load of 300kW (kilowatts) suddenly changes to half load 150kW, that is, the maximum power operating state (300kW) is quickly reduced to half the power (150kW). Comparing the response waveforms of the two outputs, the response waveforms of the hybrid small signal model of the cascade power supply and the actual switching circuit are basically overlapped, indicating that the equivalent circuit model can more accurately reflect the behavior of the actual switching circuit. The blue waveform in the figure represents the waveform of the hybrid small signal model of the cascade power supply (that is, the waveform of the equivalent circuit established using the method of the present application), and the red waveform represents the waveform of the actual switching circuit.

[0172] Compare the steady-state value error (steady-state value refers to the output value that stabilizes after a period of time after the input disturbance), response time (the time required from the input disturbance to reach the steady-state value) and corresponding overshoot error (overshoot refers to the maximum amplitude of the output response exceeding the steady-state value) of the mixed small signal model of the cascade power supply and the actual switching circuit, read and compare the deviation between the final steady-state value of the simulation waveform and the expected steady-state value, and calculate the percentage of the steady-state value error; add time marks on the simulation waveform when the disturbance occurs and when the output reaches the steady-state value through the measurement tool in the software, calculate the difference between these two time points, and get the response time; find the peak value of the output response on the simulation waveform and calculate the difference between the peak value and the steady-state value, calculate the percentage form of the difference, that is, overshoot = (peak value - steady-state value) / steady-state value * 100%, and get the corresponding overshoot error. The steady-state value error, response time and corresponding overshoot error of the mixed small signal model of the cascade power supply and the actual switching circuit are all much less than 5%.

[0173] The steps in this application can be adjusted in order, combined, and deleted according to actual needs.

[0174] The units in the device of the present application can be combined, divided and deleted according to actual needs.

[0175] Although the present application is disclosed in detail with reference to the accompanying drawings, it should be understood that these descriptions are merely exemplary and are not intended to limit the application of the present application. The scope of protection of the present application is defined by the appended claims and may include various modifications, alterations and equivalents made to the invention without departing from the scope and spirit of the present application. < / s2> < / i2> < / s2> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / xy> < / x> < / s2> < / i2> < / s2> < / y> < / y> < / y> < / x> < / xy> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / xy> < / x>

Claims

1. A mixed small signal modeling method for a cascade power supply, wherein the front stage of the cascade power supply includes a half-bridge Buck-Boost converter and a CLLC bidirectional converter, and the rear stage of the cascade power supply includes a three-phase interleaved parallel Buck converter, characterized in that: The mixed small signal modeling method for cascaded power supply includes: Step 1, defining the switching function of the CLLC bidirectional converter, establishing an average state equation of the first state variable, performing Fourier series expansion on the first state variable and bringing it into the switching function, establishing a linearized first state space equation, and deriving a corresponding first small signal model according to the first state space equation; Step 2, determining the working stage of the half-bridge Buck-Boost converter according to the operating state of the switching element, averaging the second state variable of each working stage within one switching cycle, establishing a second state space equation, and deriving the corresponding second small signal model according to the second state space equation; Step 3, define a switch description function of the three-phase staggered parallel Buck converter, determine the working stage of each phase according to the switch description function, average the third state variables of different working stages of each phase within a switching cycle, establish a third state space equation, and derive the corresponding third small signal model according to the third state space equation; Step 4, making the variables of the connection part of the front-stage circuit and the rear-stage circuit of the cascaded power supply equal, combining the first state space equation, the second state space equation and the third state space equation to form a mixed small signal model of the entire cascaded power supply.

2. The mixed small signal modeling method for cascaded power supply according to claim 1, characterized in that: The step 1 specifically includes: Step 1.1, using switching functions s1 and s2 to represent the voltage output of the forward bridge arm and the reverse bridge arm in the CLLC bidirectional converter, respectively, where s1 is the switching function of the forward bridge arm and s2 is the switching function of the reverse bridge arm; Step 1.2, establish the average state equation of the first state variable in the CLLC bidirectional converter, perform Fourier series expansion on the first state variable and bring it into the switching function, expand the Fourier series of the first state variable at the first harmonic, and obtain the generalized average expression of each first state variable; Step 1.3, based on the generalized average expressions of the first state variables of the CLLC converter, construct the corresponding first small signal model.

3. The mixed small signal modeling method for cascaded power supply according to claim 2, characterized in that: The step 1.2 specifically includes: replacing the actual value of the first state variable in the CLLC bidirectional converter circuit with the average value thereof in a switching cycle to perform modeling, and obtain a linear time-invariant average state equation: Where x(t) represents the first state variable in the linear time-varying equation, <x> k (t) represents the average value of the linear time-invariant first state variable, k is the harmonic order, ω s is the first harmonic angular frequency, and τ is a periodic variable, T is the switching period of the CLLC bidirectional converter, t is a time variable, and j is a complex unit;< / x> Perform Fourier series leaf expansion on the first state variable in the equation to calculate the DC quantity part and the first harmonic component part. When the DC quantity is taken, k = 0, and when the first harmonic component is taken, k = ± 1. The expression is as follows: Substitute the switching function into the product of the first state variable and the switching function using the zero-order and first-order Fourier series. The product of the first state variable and the switching function is: <xy> 0＝ <x> 0 <y>0+2(<x 1R ><y 1R >+<x 1I ><y 1I >)< / y> < / x> < / xy> <xy> 1R ＝ <x> 0 <y> 1R + <x> 1R (y)0< / x> < / y> < / x> < / xy> <xy> 1I ＝ <x> 0 <y> 1I + <x> 1I <y> 0< / y> < / x> < / y> < / x> < / xy> Where x represents the first state variable, y represents the input value of the switching function, y is s1 when the forward bridge arm is working, y is s2 when the reverse bridge arm is working, <·> represents the average value, <·>0 represents the DC term, <·> 1R represents the real part of the fundamental term, <·> 1I The imaginary part of the fundamental term; The CLLC bidirectional converter has two inductors L 11 , two inductors L 12 , two capacitors C 11 , two capacitors C 12 , L 11 The current is i1, L 12 The current is i2, C 11 The voltage of C is v1, 12 The voltage is v2, and the first state variables i1, i2, v1, v2 are expanded at the first harmonic to obtain the generalized average expression: v o_CLLC ＝(2 <s2> 1R <i2> 1R +2 <s2> 1I <i2> 1I )R L < / i2> < / s2> < / i2> < / s2> In the formula, R1 is the power supply side resistance, R2 is the load side resistance, V dc is the input side DC voltage, L m is the mutual inductance of the transformer in the CLLC converter, a represents the coefficient of each harmonic component in the Fourier series, n is the turns ratio of the high-frequency transformer, R L is the load resistance, v o_CLLC is the output voltage of the CLLC converter.

4. The mixed small signal modeling method for cascaded power supply according to claim 3, characterized in that: The first small signal model of the CLLC converter in step 1.3 is: Among them, X is the first state variable u is the input variable of the CLLC converter v in_CLLC is the input voltage of the CLLC converter, is the state variable of the coupling capacitor voltage, is the input current of the CLLC converter, A CLLC , B CLLC , C CLLC , D CLLC is the system matrix.

5. The mixed small signal modeling method for cascaded power supply according to claim 4, characterized in that: The step 2 specifically includes: Step 2.1, in one switching cycle, the working process of the half-bridge Buck-Boost converter is divided into a switch-on phase and a switch-off phase, the second state variables of the two phases are averaged, and the average second state variables are used to replace the instantaneous value to obtain the second state space equation in the entire switching cycle; The half-bridge Buck-Boost converter includes capacitors C0 and L0. In a switching cycle, the switch element in the circuit is alternately turned on and off. When the switch element is turned on, the inductor L0 starts to store energy, and the current flows through the inductor L0 and the capacitor C0 through the switch. When the switch element is turned off, the inductor L0 releases energy and provides energy to the load and the capacitor C0. The working process of the half-bridge Buck-Boost converter is divided into the switch-on stage and the switch-off stage. The average second state variable is used to approximate the instantaneous value, and the second state space equation is listed: Among them, V dc is the input voltage of the half-bridge Buck-Boost converter, Ts is the switching period, <·> Ts Represents the average value in a switching cycle, i L is the current of inductor L0, V o is the DC component of the output voltage of the half-bridge Buck-Boost converter, i o is the output current of the half-bridge Buck-Boost converter, v o is the output voltage of the half-bridge Buck-Boost converter, d0 is the duty cycle of the half-bridge Buck-Boost converter; Step 2.2, based on the second state space equation of the half-bridge Buck-Boost converter, construct a corresponding second small signal model; The average second state variable is decomposed into the sum of the DC component and the AC small signal component. At the same time, the control quantity containing the AC component is decomposed and the decomposed quantity is brought into the second state space equation: in, is the AC small signal component of the output voltage, V o is the DC component of the output voltage, is the AC small signal component of the inductor current, I is the DC component of the inductor current, is the small AC signal component of the duty cycle, is the AC small signal component of the output current, D0 is the average value of the duty cycle, is the AC small signal component of the input voltage; Eliminate the DC component in the second state-space equation and ignore the high-order small signal components and Linearizing the equations, we get the AC small signal equations: The AC small signal equations are organized into the form of space state equations to obtain the third small signal model of the half-bridge Buck-Boost: Where X is the second state variable u is the input Y is the output A Buck_Boost , B Buck_Boost , C Buck_Boost , D Buck_Boost is the system matrix.

6. The mixed small signal modeling method for cascaded power supply according to claim 5, characterized in that: The step 3 specifically includes: Step 3.1, use the switch description function to represent the on and off states of the bridge arm of the three-phase staggered parallel Buck converter, and define the switch description function of the on and off logic of the z-th phase switch as S z , when S z When S is equal to 1, the upper bridge arm is turned on and the lower bridge arm is turned off. z When it is equal to 0, the upper bridge arm is turned off and the lower bridge arm is turned on, z = 1, 2, 3; Step 3.2, according to the switch description function, the working process of each phase is divided into a switch-on phase and a switch-off phase, the third state variables of the two phases of each phase are averaged, and the average third state variables are used to replace the instantaneous value to obtain the third state space equation in the entire switching cycle; Step 3.3, according to the third state space equation of the three-phase interleaved parallel Buck converter, establish the corresponding third small signal model.

7. The mixed small signal modeling method for cascaded power supply according to claim 6, characterized in that: The step 3.2 specifically includes: each phase of the three-phase staggered parallel Buck converter includes inductors L1, L2, and L3 respectively, and the output end includes a capacitor C1. In a switching cycle, the working process of each phase is divided into a switch-on phase and a switch-off phase. The average third state variable is used to approximate the instantaneous value, and the third state space equation is listed as follows: Among them, i L1 is the current of the inductor in the first phase Buck converter circuit, i L2 is the current of the inductor in the second phase Buck converter circuit, i L3 is the inductor current in the third-phase Buck converter circuit, U in is the input voltage, U o is the output voltage, D1 is the duty cycle of the switch on time in the first phase Buck converter circuit, D2 is the duty cycle of the switch on time in the second phase Buck converter circuit, D3 is the duty cycle of the switch on time in the third phase Buck converter circuit, T S Represents one switching cycle.

8. The mixed small signal modeling method for cascaded power supply according to claim 7, characterized in that: The step 3.3 specifically includes: decomposing the average third state variable into the sum of the DC component and the AC small signal component, and decomposing other control quantities containing AC components, bringing the decomposed quantities into the third state space equation, making the input and output DC quantities correspondingly equal, eliminating the DC component, and ignoring the high-order small signal components, to obtain the AC small signal equation group: in, is the small AC signal component of the inductor current in the first phase Buck converter circuit, is the small AC signal component of the inductor current in the second-phase Buck converter circuit, is the small AC signal component of the inductor current in the third-phase Buck converter circuit, is the AC small signal component of the output voltage, is the AC small signal component of the input voltage, is the AC small signal component of the duty cycle in the first phase Buck converter circuit, is the AC small signal component of the duty cycle in the second-phase Buck converter circuit, is the AC small signal component of the duty cycle in the third-phase Buck converter circuit, and R is the load resistance of the three-phase interleaved parallel Buck converter; The AC small signal equations are organized into the form of space state equations, and the third small signal model of the three-phase interleaved parallel Buck converter is obtained: Among them, X is the third state variable u is the input Y is the output Let M = R c Cs+1,R c is the equivalent series resistance of the capacitor, s is the complex frequency variable, A Buck , B Buck , D Buck , D Buck is the system matrix.

9. The mixed small signal modeling method for cascaded power supply according to claim 8, characterized in that: The step 4 specifically includes: setting the output of the half-bridge Buck-Boost converter equal to the input of the CLLC bidirectional converter, setting the output of the CLLC bidirectional converter equal to the input of the three-phase interleaved parallel Buck converter to obtain: The first state space equation, the second state space equation and the third state space equation are combined and the expressions are combined to obtain the mixed small signal model of the cascade power supply as a whole: Among them, X is the state variable of the cascade power supply as a whole u is the input variable A, B, C, and D are the system matrices of the cascade power supply.

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