A hybrid small-signal modeling method for cascaded power supplies

Abstract

The application discloses a hybrid small-signal modeling method for a cascaded power supply, relates to the technical field of modeling, and adopts a half-bridge Buck-Boost plus CLLC bidirectional converter topology for a front-stage circuit of the cascaded power supply and adopts a three-phase interleaved parallel Buck topology for a rear-stage circuit; the hybrid small-signal modeling method adopts a generalized average method to establish a mathematical model of the converter for the front-stage CLLC topology, adopts a state space average method to establish mathematical models of the half-bridge Buck-Boost and the rear-stage three-phase interleaved Buck converter, and adopts a modular combination method to establish an overall mathematical model of the cascaded system, so that the overall behavior of the cascaded power supply can be better described; the technical scheme in the application provides a simple and accurate modeling method for a circuit with multiple converters and multiple switching frequencies, meets the modeling and analysis requirements of the cascaded power supply with various internal modules, complex connection and multiple topologies, and provides an important research background and tool for system optimization and performance analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of modeling, in particular to a hybrid small-signal modeling method for a cascaded power supply. BACKGROUND

[0002] The cascaded power supply is a common and high-conversion-efficiency power supply technology. The cascaded power supply technology can avoid the working state of the converter at an extremely low duty cycle and reduce the peak current of the inductance element in the circuit by additionally increasing the intermediate voltage level. Usually, the multi-stage conversion efficiency and energy density of the cascaded power supply are higher than those of the single-stage power supply. Since the cascaded power supply internally contains various power modules, such as resonant converters, MMC converters, Buck / Boost converters, etc., in order to ensure that the voltage or power output of the converter in each power module is stable or follows the given output, a high dynamic performance control strategy should be designed. Establishing a mathematical model of the system is an important link in the design of the controller. At the same time, considering the complex connection relationship between these modules, in order to deeply study the dynamic characteristics and optimize the design of the internal and external of the cascaded power supply, an accurate whole machine model needs to be established. For the DC / DC converter, the state-space averaging 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 period. In order to overcome the limitations of the periodic average modeling and improve the model accuracy, the time-periodic system modeling method which can consider the frequency coupling effect of the system has begun to attract attention.

[0003] In the prior art, there are three general modeling methods applicable to time-periodic systems: a generalized averaging modeling (GAM) / dynamic phasor modeling (DPM) method, a harmonic linearization (HL) method, and a harmonic state space (HSS) / harmonic transfer function (HTF) method. The GAM / DPM method is based on the harmonic balance principle, and each state variable is transformed into different frequency spaces for modeling through Fourier transform, and the obtained model is a multiple-input multiple-output time-invariant model, which can effectively represent the nonlinear behavior of the system and the harmonic information of any order. However, as the considered harmonic order increases, the model derivation becomes more complex, and methods such as singular perturbation and direct sequence decomposition can be used to reduce the model complexity. The HL method essentially belongs to the description function method, which can be directly applied to nonlinear periodic models without averaging processing, and the obtained model is a single-input single-output linear time-invariant (SISO-LTI) model. Since the modeling process only considers the dominant frequency coupling component, when the sideband frequency coupling component cannot be ignored (such as asymmetric controllers, unbalanced power grids, and weak power grids), there is a large deviation between the obtained model and the actual system.

[0004] The patent document CN116680897A discloses a dual active bridge converter frequency domain steady-state modeling method and device, which is mainly used to solve the inaccurate technical problems of power transmission, inductance current effective value and zero voltage switching performance in the prior art. The patent document CN111027269A discloses a two-stage DC / DC converter modeling method based on a harmonic equivalent circuit, which is mainly aimed at a single-switch-frequency circuit containing a single converter and uses harmonic state space for modeling. Traditional modeling methods are mainly aimed at single-switch-frequency circuits containing a single converter, and the internal modules of a cascaded power supply circuit of multiple topologies are various and complex in connection. Traditional modeling methods cannot meet the modeling requirements of cascaded power supplies containing multiple topologies, and the modeling deviation is large, which is not conducive to subsequent analysis and calculation. Therefore, for a multiple-switch-frequency circuit containing multiple converters, how to simply and accurately model is still a problem to be solved. SUMMARY

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

[0006] The technical scheme of the application is as follows: a hybrid small-signal modeling method for a cascade power supply is provided, the front stage of the cascade power supply comprises a half-bridge Buck-Boost converter and a CLLC bidirectional converter, the rear stage of the cascade power supply comprises a three-phase interleaved Buck converter, and the method comprises the following steps:

[0007] Step 1, defining the switching function of the CLLC bidirectional converter, establishing the average state equation of the first state variable, Fourier series expansion is carried out on the first state variable and the switching function is brought in, the linearized first state space equation is established, and the corresponding first small-signal model is derived 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 in a switching cycle, and establishing the second state space equation, and deriving the corresponding second small-signal model according to the second state space equation;

[0009] Step 3, defining the switching description function of the three-phase interleaved Buck converter, determining the working stage of each phase according to the switching description function, averaging the third state variable of each phase in different working stages in a switching cycle, establishing the third state space equation, and deriving the corresponding third small-signal model according to the third state space equation;

[0010] Step 4, equating the variables of the connection part of the front stage circuit and the rear stage circuit of the cascade power supply, merging the first state space equation, the second state space equation and the third state space equation, and forming the hybrid small-signal model of the whole cascade power supply.

[0011] Further, step 1 specifically comprises:

[0012] Step 1.1, the switching functions s1 and s2 are used to represent the voltage output conditions of the forward bridge arm and the reverse bridge arm in the CLLC bidirectional converter respectively, wherein 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, the average state equation of the first state variable in the CLLC bidirectional converter is established, the Fourier series expansion is carried out on the first state variable and the switching function is brought in, the Fourier series of the first state variable is expanded at the first harmonic, and the generalized average expression of each first state variable is obtained;

[0014] Step 1.3, based on the generalized average expression of each first state variable of the CLLC converter, the corresponding first small-signal model is constructed.

[0015] Further, step 1.2 specifically comprises: modeling the first state variable in the CLLC bidirectional converter circuit with its average value instead of its actual value in a switching cycle to obtain a linear time-invariant average state equation:

[0016]

[0017] wherein 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 number, 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 number unit;

[0018] The first state variable in the equation is expanded by Fourier series, the direct current part and the first harmonic component part are calculated, k=0 is taken for the direct current, and k=±1 is taken for the first harmonic component, and the expression is as follows:

[0019]

[0020] The switching function is brought in, the product of the first state variable and the switching function is expressed by using the zero-order and first-order Fourier series, and the product of the first state variable and the switching function is as follows:

[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 + <x> 1I <y>0

[0024] where x represents the first state variable, y represents the switching function value, y is s1 when the forward bridge arm works, y is s2 when the reverse bridge arm works, <·> represents the average value, <·>0 represents the direct current term, <·> 1R represents the real part of the fundamental wave term, <·> 1I represents the imaginary part of the fundamental wave term;

[0025] Two inductors L 11 , L 12 , two capacitors C 11 , C 12 are arranged in the CLLC bidirectional converter, the current of L 11 is i1, the current of L 12 is i2, the voltage of C 11 is v1, and the voltage of C 12 is v2, the first state variable i1, i2, v1 and 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] wherein r1 is the power 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] Further, the first small signal model of the CLLC converter in step 1.3 is:

[0030]

[0031] wherein 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] Further, step 2 specifically comprises:

[0033] Step 2.1, dividing the working process of the half-bridge Buck-Boost converter into the switch-on stage and the switch-off stage within a switching period, averaging the second state variables in the two stages, using the average second state variable to replace the instantaneous value, and obtaining the second state space equation in the whole switching period;

[0034] The half-bridge Buck-Boost converter comprises a capacitor C0 and an inductor L0. Within a switching period, the switching elements in the circuit are alternately turned on and turned off. When the switching element is turned on, the inductor L0 starts to store energy, and the current flows through the inductor L0 and the capacitor C0. When the switching element is turned off, the inductor L0 releases energy, providing 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] wherein 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 period, i L is the current of the 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 ratio 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 the 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, and the control quantity containing the AC component is also decomposed, and the decomposed quantity is brought into the second state space equation:

[0039]

[0040] wherein, 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 AC small signal component of the duty ratio, is the AC small signal component of the output current, D0 is the average value of the duty ratio, is the AC small signal component of the input voltage;

[0041] Eliminate the DC component in the second state space equation, ignore the high-order small signal component and Linearize the equation to obtain the AC small signal equation group:

[0042]

[0043] Arrange the AC small signal equation group into the form of the space state equation to obtain the third small signal model of the half-bridge Buck-Boost:

[0044]

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

[0046] Further, step 3 specifically comprises:

[0047] Step 3.1, the on and off states of the three-phase interleaved parallel Buck converter bridge arm are represented by using the switch description function, and the switch description function of the on and off logic of the zth phase switch tube is defined as S z When S z is equal to 1, the upper bridge arm is on and the lower bridge arm is off, when S z is equal to 0, the upper bridge arm is off and the lower bridge arm is 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 stage and a switch off stage, the third state variable of each phase in the two stages is averaged, and the average third state variable is used to replace the instantaneous value to obtain the third state space equation in the whole switching period.

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

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

[0051]

[0052] Wherein, 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 current of the inductor in the third phase Buck converter circuit, U in is the input voltage, U o is the output voltage, D1 is the duty ratio of the switch on time in the first phase Buck converter circuit, D2 is the duty ratio of the switch on time in the second phase Buck converter circuit, D3 is the duty ratio of the switch on time in the third phase Buck converter circuit, and T S represents a switching period.

[0053] Further, the step 3.3 specifically comprises: decomposing the average third state variable into the sum of a direct current component and an alternating current small signal component, while decomposing other control quantities containing alternating current components, bringing the decomposed quantities into the third state space equation, making the direct current components of the input and output corresponding equal, eliminating the direct current components, and ignoring high-order small signal components, to obtain an alternating current small signal equation group:

[0054]

[0055] wherein, is an alternating current small signal component of the inductor current in the first phase Buck converter circuit, is an alternating current small signal component of the inductor current in the second phase Buck converter circuit, is an alternating current small signal component of the inductor current in the third phase Buck converter circuit, is an alternating current small signal component of the output voltage, is an alternating current small signal component of the input voltage, is an alternating current small signal component of the duty ratio in the first phase Buck converter circuit, is an alternating current small signal component of the duty ratio in the second phase Buck converter circuit, is an alternating current small signal component of the duty ratio in the third phase Buck converter circuit, and R is a load resistance of the three-phase interleaved parallel Buck converter.

[0056] The alternating current small signal equation group is arranged in the form of a spatial state equation to obtain a third small signal model of the three-phase interleaved parallel Buck converter:

[0057]

[0058] wherein, X is a third state variable u is an input quantity Y is an output quantity Let N=R c Cs+1, R c is an equivalent series resistance of the capacitor, and s is a complex frequency variable, A Buck , B Buck , C Buck , D Buck are system matrices.

[0059] Further, the step 4 specifically comprises: making the output of the half-bridge Buck-Boost converter equal to the input of the CLLC bidirectional converter, and making 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 solved to obtain a hybrid small signal model of the overall cascaded power supply:

[0062]

[0063] wherein X is a state variable of the overall cascaded power supply u is an input variable A, B, C and D are system matrices of the cascaded power supply.

[0064] The application has the following beneficial effects:

[0065] The technical solution in the application is suitable for a multi-switch frequency circuit with multiple converters, different modeling methods are adopted for circuit topologies with different characteristics in the converters, such as adopting a generalized average method to establish a mathematical model of the converter for a front-stage CLLC topology, adopting a state space average method to establish a mathematical model for a half-bridge circuit and a rear-stage three-phase interleaved parallel Buck converter, and adopting a modular combination method to solve the mathematical models of each circuit topology to realize the establishment of an overall mathematical model of the cascaded system.

[0066] In the multi-switch frequency circuit with multiple converters, there are various modules and complex connections, the traditional modeling method tends to adopt a more complex mathematical model to improve the accuracy and applicability of the model, the modeling method used when the circuit is modeled as a whole is single, cannot meet the modeling and analysis requirements of the cascaded power supply containing multiple topologies, and also increases the calculation difficulty, reduces the model adaptability, and it is also difficult to verify the subsequent experiments. Compared with the traditional modeling method, the technical solution in the application can better cope with such a complex circuit by establishing a model 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 the accuracy and simplicity, reduce the calculation difficulty, improve the model adaptability, and make the subsequent experimental verification easier. BRIEF DESCRIPTION OF DRAWINGS

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

[0068] Figure 2 A half-bridge Buck-Boost equivalent circuit schematic diagram in a cascaded power supply of an embodiment of the application;

[0069] Figure 3 A three-phase interleaved parallel Buck working mode decomposition schematic diagram in a cascaded power supply of an embodiment of the application;

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

[0071] Figure 5 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 cascaded power supply according to an embodiment of the present application and an actual switching circuit after input voltage disturbance;

[0073] Figure 7 A simulation comparison diagram of a mixed small signal model of a cascaded power supply according to an embodiment of the present application and an actual switching circuit after 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 will be further described in detail below in combination with the drawings and specific embodiments. 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 set forth in order to provide a thorough understanding of the present application, however, the present application can also be implemented in other ways different from those described herein, therefore, the scope of protection of the present application is not limited by the specific embodiments disclosed below.

[0076] In the present embodiment, the cascaded power supply includes a front-stage circuit and a rear-stage circuit, the front-stage circuit is constituted by a half-bridge converter topology and a CLLC bidirectional converter topology, and the rear-stage circuit is constituted by 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, the converter circuit is a voltage regulating circuit, allowing to realize boost or buck function when the input voltage is higher or lower than the output voltage, the non-isolated bidirectional Buck-Boost circuit adopts double-loop control of voltage outer loop and current inner loop, and 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 fast response, and the integral term is responsible for eliminating steady-state error, the current inner loop and the voltage outer loop work cooperatively to realize accurate control of the output voltage and current, and ensure the stability and fast dynamic response of the system.

[0078] The CLLC bidirectional converter is a resonant converter, which works at a resonant frequency, fully utilizes the resonant characteristics of the circuit elements (resonance refers to the state that the energy exchange between the inductance and capacitance elements in the circuit reaches the maximum) to improve the efficiency and simplify the control, at the resonant frequency, the energy transfer between the inductance and capacitance elements is more effective, and the energy loss is reduced. The CLLC converter system exhibits more linear characteristics near the resonant frequency, and it is easier to achieve efficient energy conversion, and its control is relatively simple, with the advantages of high efficiency, low switching loss and small electromagnetic interference.

[0079] In the three-phase interleaved parallel Buck converter, three Buck converters work in parallel by phase staggering, and each Buck converter is responsible for one phase. The upper and lower bridge arms of the three-phase bridge arms are complementary conduction (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). The switching actions of adjacent two phases are 120° out of phase. Multi-phase parallel and phase staggering help to reduce the ripple of the output current (i.e. reduce the fluctuations or ripples contained in the output current), improve the stability and efficiency of the system.

[0080] The prior art tends to use more complex mathematical models to improve the accuracy and applicability of the models, and the hybrid modeling method described in the present application uses different modeling methods for different circuit topology characteristics in the converter, including generalized state averaging and state space averaging method. The obtained mathematical model is compatible with each other and takes into account accuracy and simplicity.

[0081] As shown in Figures 1 to 5 The embodiment provides a hybrid small-signal modeling method for a cascaded power supply, which comprises the following steps:

[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, expand the first state variable by the Fourier series 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 according to the first state space equation.

[0083] In the embodiment, the generalized average modeling method is suitable for converter topologies with periodic operation characteristics, harmonic dominance and average value description in steady state. The CLLC converter works at a resonant frequency and has a high switching frequency and periodicity. These characteristics meet the assumption conditions of the generalized average modeling method. The use of the generalized average modeling method can convert the complex nonlinear time-varying system into a linear time-invariant system, simplifying the modeling, analysis and control strategy design process.

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

[0085] The CLLC bidirectional converter includes energy storage components: an inductor and a capacitor. The inductor 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 (middle left), L 12 and C 12 Distributed on the secondary side of the CLLC bidirectional converter ( Figure 1 (Right side of the middle section) In a CLLC bidirectional converter, the primary side refers to the input side, i.e., the side where the power supply is input, and the secondary side refers to the output side, i.e., the side connected to the load. A CLLC bidirectional converter includes two bridge arms: a forward bridge arm and a reverse bridge arm. Both bridge arms are controlled by switches. When the bridge arms are working, energy is transferred between the input and output. In the forward operating state, electrical energy flows from the power supply to the load; the forward bridge arm is active, and the output in this state corresponds to the switching function s1. In the reverse operating state, the load feeds power back to the power supply; the reverse bridge arm is active, and the output in this state corresponds to the switching function s2. The forward bridge arm contains the primary side capacitor C. 11 The inductance L on the primary side 11 Secondary capacitor C 12 and secondary inductor and component L 12 The reverse bridge arm contains a symmetrical primary-side capacitance C. 11 The inductance L on the primary side 11 Secondary capacitor C 12 and the inductance L on the secondary side 12 The primary energy storage element and the secondary energy storage element (i.e., capacitor and inductor) form a resonant circuit, in which energy is transferred between the inductor and capacitor in a resonant manner.

[0086] The switching functions s1 and s2 of the forward bridge arm are as follows:

[0087]

[0088] Where 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, and t is the time variable. When the switching function is 1, the switch in the circuit is in the on state, and when the switching function is -1, the switch in the circuit is in the off state.

[0089] Step 1.2, the average state equation of the first state variable in the CLLC bidirectional converter is established, the Fourier series expansion of the first state variable is carried out and brought into the switching function, the Fourier series of the first state variable is expanded at the first harmonic, and the generalized average expression of each first state variable is obtained.

[0090] The CLLC bidirectional converter works in switching states, and the circuit structure also changes with the switching of the switching states, which is difficult to model. In order to simplify the analysis, the switching process is ignored, the average value of each variable in the CLLC bidirectional converter circuit is calculated in a switching period, the average value is used to replace the actual value for modeling, and the relationship between each average variable is established in the form of state space equation. The linear time-invariant average state equation is established, and its expression is:

[0091]

[0092] Among them, 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 number, 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. During the calculation process of the generalized average method, the nonlinear square wave voltage in the on-off state is approximately equivalent to the linear sinusoidal wave voltage. Since the CLLC bidirectional converter works at the resonant frequency, designing the resonant frequency as the frequency of the main harmonic component helps to limit the energy transmission to this specific harmonic component, so that the CLLC bidirectional converter can more effectively utilize the harmonic component during operation, realizing efficient energy transmission. The first harmonic component is the basic frequency component, and limiting energy transmission to only the first harmonic component helps to reduce harmonic distortion. Therefore, it is assumed that the energy transmission of the CLLC bidirectional converter is only related to the first harmonic component, which makes the analysis of the CLLC bidirectional converter more convenient.

[0094] In this embodiment, the first state variable of the CLLC bidirectional converter includes the capacitor voltage and the inductor current, that is, it includes the current i1 of L 11 , the current i2 of L 12 , the voltage v1 of C 11 , and the voltage v2 of C 12 . The Fourier series expansion is performed on the first state variable in the equation, the direct current part and the first harmonic component part are calculated, k=0 is taken for the direct current, and k=±1 is taken for the first harmonic component, to obtain the linear time-invariant state space equation.

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

[0096]

[0097] The periodic change of the on-off state will affect the expression of the first state variable. When performing Fourier series expansion, the switching function needs to be considered. Since only the direct current part and the first harmonic component part are calculated, the zero-order and first-order Fourier series are used to represent the product of the first state variable and the switching function. The product of the first state variable and the switching 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 switching function value, the switching function includes s2 and s1, when the forward bridge arm works, y is s1, when the reverse bridge arm works, y is s2, <·> represents the average value, <·>0 represents the direct current term, <·> 1R represents the real part of the fundamental term, <·> 1I the imaginary part of the fundamental term. The real part of the fundamental term usually corresponds to the basic frequency of the signal, indicating the amplitude of the fundamental frequency component in the Fourier series, and the imaginary part is usually used to describe the phase information of the fundamental 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 direct current terms, the input voltage v in_CLLC and the output voltage v o_CLLC The component at the first harmonic is taken as the direct current average. The CLLC bidirectional converter is provided with two inductors L 11 (including in two bridge arms and symmetric), two inductors L 12 , two capacitors C 11 , two capacitors C 12 , the current of L 11 is i1, the current of L 12 is i2, the voltage of C 11 is v1, and the voltage of C 12 is v2. The Fourier series of the first state variables i1, i2, v1 and v2 at the first harmonic is expanded, and the product of the above first state variables and the switching function is brought in, to obtain the generalized average expression of each first state variable, and the mathematical model of the CLLC converter is established.

[0103] The four groups of variables i1, i2, v1 and v2 are expanded 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] wherein r1 is a power supply side resistance, r2 is a load side resistance, v dc is an input side DC voltage, n is a high frequency transformer turns ratio, a represents a coefficient of harmonic components in Fourier series (a coefficient related to system parameters), L m is mutual inductance of transformer in CLLC converter, R L is load resistance, v o_CLLC is output voltage of CLLC converter.

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

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

[0110]

[0111] wherein the output end of the CLLC converter further comprises a coupling capacitor C f , X is a first state variable u is an input variable of the CLLC converter v in_CLLC is an input voltage of the CLLC converter, is a state variable of coupling capacitor voltage, is an input current of the CLLC converter, A CLLC , B CLLC , C CLLC , D CLLC is a system matrix, and is respectively 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 the capacitor voltage, which are affected by the switching states. The small-signal model is a linearized representation of the system, which is used to analyze the small-signal response of the system (small-signal response refers to the response of the system to small-amplitude input changes, which is used to evaluate the stability and performance of the system to small-amplitude disturbances) near the steady-state operating point.

[0116] As shown in Figure 1 , 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 switching elements are added to the blank circuit board, a voltage source is added to the power supply side, each element is connected according to the topological structure and connection relationship of the CLLC converter, and the parameter values of each element are set according to the parameters of each term of the generalized average expression of the CLLC converter, to form a complete equivalent circuit model of the CLLC converter. As shown in Figure 1 , capacitors C 11 , C 12 , C f , inductors L 11 , L 12 , L m , load resistor R L and voltage source are arranged in the circuit, the input voltage is marked as V in-CLLC , the output voltage on the load side is marked as v o-CLLC , V o in the figure is the DC term of the output voltage, the input side current is marked as i1, including the current i 1s through the reverse bridge arm and the current i 1c through the forward bridge arm, the load side current is marked as i2, including the current i 2s through the reverse bridge arm and the current i 2c through the forward bridge arm, 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 , and the voltage corresponding to C2 is v 1c .

[0117] Step 2, the second state space equation of the half-bridge circuit topology is established by using the state space averaging method, the working stage of the half-bridge Buck-Boost converter is determined according to the operating state of the switching element, the second state variable of each working stage is averaged in a switching cycle, and the second state space equation is established, and the corresponding small signal model is derived according to 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 works in high-frequency switching mode, which meets the assumption conditions of the state space averaging method, and the state space averaging method can accurately describe the dynamic behavior of the bidirectional Buck-Boost circuit in different working modes.

[0119] Step 2.1, the working process of the half-bridge Buck-Boost converter is divided into switch-on stage and switch-off stage in a switching cycle, the second state variable of the two stages is averaged, and the average second state variable is used instead of the instantaneous value to obtain the second state space equation in the whole switching cycle.

[0120] The half-bridge Buck-Boost converter includes a capacitor C0 and an inductor L0. In a switching cycle, the switching elements in the circuit will be turned on and off alternately, which 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 the capacitor C0. When the switching element is turned off, the inductor L3 releases energy, providing energy to the load and the capacitor C0. The working process of the half-bridge Buck-Boost converter can be divided into two stages: switch-on stage and switch-off stage. The working state of the switching element is different in different stages. The average second state variable is used to approximate the instantaneous value for the two stages, and the state equation is listed as follows:

[0121]

[0122] Where, V dc is the input voltage of the half-bridge Buck-Boost converter, Ts is the switching cycle of the half-bridge Buck-Boost converter, Ts represents the average value in a switching cycle, i L is the current of the 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 ratio 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. It is the small-signal AC component of the output current. Represents the rate of change of capacitor voltage. This represents the rate of change of 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 a DC component and an AC small-signal component. Simultaneously, the control quantity containing the AC component is decomposed, resulting in the following expression:

[0125]

[0126] in, V is the small-signal AC component of the output voltage. o This represents the DC component of the output voltage. Let I be the small-signal AC component of the inductor current, and let I be the DC component of the inductor current. D0 is the small-signal component of the duty cycle, and D0 is the average value of the duty cycle, i.e., 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 quantities), we obtain the state space average mathematical model of the half-bridge Buck-Boost converter, as shown below:

[0128]

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

[0130] To make the DC components equal, eliminate the DC component in the above state-space average mathematical model expression:

[0131]

[0132] Ignore higher-order small-signal components and Linearizing the equations, we obtain the AC small-signal equation system:

[0133]

[0134] The above set of small-signal equations is rearranged into a space-state equation form, yielding the state-space average mathematical model of the half-bridge Buck-Boost converter:

[0135]

[0136] Where X is the second state variable. u is the input value Y is the output quantity. A Buck_Boost B Buck_Boost C Buck_Boost D Buck_Boost The system matrix is ​​represented by the following formulas:

[0137]

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

[0139] Where R1 is the load resistor in the half-bridge Buck-Boost converter, L0 is the inductor value in the half-bridge Buck-Boost converter, and C0 is the capacitor value in the half-bridge Buck-Boost converter.

[0140] like Figure 2 As shown, an equivalent circuit model is constructed in circuit simulation software on a 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, and capacitors, inductors, resistors, and switching components are added to the blank circuit board. The components are connected according to the topology and connection relationships of the half-bridge Buck-Boost converter. The parameter values ​​of each component are set according to the parameters of each term in the second state-space equation of the half-bridge Buck-Boost converter, forming a complete equivalent circuit model of the half-bridge Buck-Boost converter. Figure 2 The circuit includes a capacitor C0, an inductor L0, a load resistor R1, and a voltage source. The input voltage is labeled V. dc The output voltage is marked as u c u c The DC term is labeled U c .

[0141] Step 3: Define the switching description function of the three-phase interleaved parallel Buck converter, determine the operating stage of each phase based on the switching description function, average the third state variables of different operating stages of each phase within one switching cycle, establish the third state space equation, and derive the corresponding third small signal model based on the third state space equation.

[0142] In this embodiment, the switches of each phase of the three-phase interleaved Buck converter work in high-frequency mode, which also meets the assumption conditions of the state-space averaging method. The state-space averaging method can linearize the dynamic behavior of each phase, provide a simplified overall model, and facilitate analysis and design.

[0143] Step 3.1: The on and off states of the bridge arm of the three-phase interleaved Buck converter are represented by the switching description function. The switching description function of the on and off logic of the zth phase switch is defined as:

[0144]

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

[0146] Step 3.2: According to the switching description function, the working process of each phase is divided into switch-on and switch-off stages. The third state variable of each phase in the two stages is averaged, and the average third state variable is used to replace the instantaneous value to obtain the third state space equation in the entire switching period.

[0147] In each term of the three-phase interleaved Buck converter, an inductor is set, which is L1, L2, and L3 respectively. A capacitor C1 is set at the output end. In a switching period, the working process of each phase is divided into switch-on and switch-off stages 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 variable in the two stages of each phase:

[0148]

[0149] Where, 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 current of the inductor in the third phase Buck converter circuit, U in is the input voltage, U o is the output voltage, D1 is the duty ratio of the switch-on time in the first phase Buck converter circuit, D2 is the duty ratio of the switch-on time in the second phase Buck converter circuit, D3 is the duty ratio of the switch-on time in the third phase Buck converter circuit, T S represents a switching period, 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, the corresponding third small signal model is established, and the corresponding equivalent circuit model is constructed.

[0151] The average third state variable is decomposed into the sum of the DC component and the AC small signal component, and other control quantities (including input voltage U in , output voltage U o ) containing AC components in the above formula are decomposed, the decomposed quantities are brought into the third state space equation, the DC components of the input and output are made to correspond to each other, the DC components of the third state space equation of the three-phase interleaved parallel Buck converter are eliminated, and the high-order small signal components are ignored, so that the third state space equation is linearized, and the AC small signal equation group is obtained:

[0152]

[0153] Among them, is the AC small signal component of the inductor current in the first phase Buck converter circuit, is the AC small signal component of the inductor current in the second phase Buck converter circuit, is the AC small 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 ratio in the first phase Buck converter circuit, is the AC small signal component of the duty ratio in the second phase Buck converter circuit, is the AC small signal component of the duty ratio 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 equation group is arranged in the form of a spatial state equation to obtain the third small signal model of the three-phase interleaved parallel Buck converter:

[0155]

[0156] Among them, X is the third state variable u is the input quantity Y is the output quantity 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 D Buck is the system matrix, and is expressed as follows:

[0157]

[0158] As shown in Figure 4 , an equivalent circuit model is built 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 a circuit simulation software, a blank circuit board is selected, capacitors, inductors, resistors and transformers are added to the blank circuit board, each component is 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 term in the third state space equation of the three-phase interleaved parallel Buck converter, and a complete equivalent circuit model of the three-phase interleaved parallel Buck converter is formed. As shown in Figure 4 , capacitors C1, inductors L1, L2 and L3, a load resistor R, a capacitor series equivalent resistor R c , a transformer and a voltage source are arranged in the circuit.

[0159] Step 4: Equate the variables of the connection part of the front-stage circuit and the rear-stage circuit of the cascaded power supply, combine the first state space equation, the second state space equation and the third state space equation, and form a mixed small signal model of the whole cascaded power supply.

[0160] The front-stage of the cascaded power supply includes a half-bridge Buck-Boost converter and a CLLC bidirectional converter, and the rear-stage of the cascaded 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, and the output of the CLLC bidirectional converter is connected to the input of the three-phase interleaved parallel Buck converter. According to the variable expression obtained in steps 1 to 3, the output of the half-bridge Buck-Boost converter is equal to the input of the CLLC bidirectional converter, and the output of the CLLC bidirectional converter is equal to the input of the three-phase interleaved parallel Buck converter. All state space equations are combined to obtain a mixed small signal model of the whole cascaded power supply;

[0161] Equate the variables corresponding to the connection part in the cascaded power supply, that is:

[0162]

[0163] The simultaneous expressions are obtained to obtain a whole mixed small signal model of the cascaded power supply:

[0164]

[0165] wherein X is a state variable of the whole cascaded power supply u is an input variable A, B, C, D are system matrixes of the cascaded power supply, respectively represented as follows:

[0166]

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

[0168] As Figure 5 shown, 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 Buck converter are combined to obtain the overall equivalent circuit diagram of the cascaded power supply, Figure 5 in which the input voltage of the CLLC converter is multiplied by in order to convert the DC input voltage into an equivalent AC voltage in the analysis process.

[0169] In this embodiment, the equivalent circuit model of the cascaded power supply is established by using the method of the present application, and the results of the time-domain simulation of the overall hybrid small-signal model of the cascaded power supply are compared with the actual switching circuit to verify the modeling accuracy.

[0170] The simulation output voltage is taken as the detection content, the established overall equivalent circuit model of the cascaded power supply and the actual switching circuit are added with the same input voltage disturbance and power jump on the computer platform, and the response waveforms of the output voltage and the input inductor current are measured respectively, when the steady-state value error and the response time, the corresponding overshoot error are all less than 5%, it is considered that the modeling is reasonable and has high accuracy.

[0171] A certain disturbance is applied to the input voltage to simulate the influence of the change of the input voltage on the circuit, as shown in Figure 6 After the input voltage disturbance, the output response waveforms of the hybrid small-signal model of the cascaded power supply and the actual switching circuit are recorded and compared, V out_switch is the voltage of the actual switching circuit, V out_mode is the voltage of the actual switching circuit, and 20 ms / div indicates that each scale on the horizontal axis (time axis) of the simulation diagram corresponds to 20 milliseconds. The response waveforms generated by the hybrid small-signal model of the cascaded power supply and the response waveforms generated by the actual switching circuit are basically coincident (ignoring the sub-harmonic components generated by the switching elements in the non-ideal case), which indicates that the established hybrid small-signal model is reasonable and has accuracy. As Figure 7 As shown, the same power jump is added to the hybrid small-signal model of the cascaded power supply and the actual switching circuit, and the full load 300kW (kilowatt) is suddenly changed to half load 150kW, that is, the maximum power operating state (300kW) is rapidly reduced to half power (150kW). The response waveforms of the two are compared. The response waveforms of the hybrid small-signal model of the cascaded power supply and the actual switching circuit are basically coincident, which shows 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 cascaded power supply (that is, the waveform of the equivalent circuit established by the method of the application), and the red waveform represents the waveform of the actual switching circuit.

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

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

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

[0175] Although the application is disclosed in detail with reference to the drawings, it should be understood that the description is only exemplary and is not intended to limit the application. The scope of protection of the application is defined by the appended claims, and can include various modifications, improvements and equivalent solutions made to the application without departing from the scope and spirit of the application. < / s2> < / i2> < / s2> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / xy> < / x> < / s2> < / i2> < / s2> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / y> < / x> < / xy> < / y> < / x> < / xy> < / x>

Claims

1. A hybrid small-signal modeling method for a cascaded power supply, wherein a front stage of the cascaded power supply comprises a half-bridge Buck-Boost converter and a CLLL bidirectional converter, and a rear stage of the cascaded power supply comprises a three-phase interleaved Buck converter, characterized in that, The hybrid small-signal modeling method for the cascaded power supply comprises the following steps: Step 1, defining the switching function of the CLLC bidirectional converter, establishing the average state equation of the first state variable, Fourier series expansion of the first state variable and the switching function, establishing the linearized first state space equation, and deriving the 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 a switching cycle, and establishing the second state space equation, and deriving the corresponding second small-signal model according to the second state space equation; Step 3, defining the switching description function of the three-phase interleaved Buck converter, determining the working stage of each phase according to the switching description function, averaging the third state variable of each phase in different working stages within a switching cycle, establishing the third state space equation, and deriving the corresponding third small-signal model according to the third state space equation; Step 4, equating the variables of the connection part of the cascaded power supply front-end circuit and the rear-end circuit, merging the first state space equation, the second state space equation and the third state space equation, and forming the hybrid small-signal model of the whole cascaded power supply.

2. The hybrid small-signal modeling method for a cascaded type power supply according to claim 1, wherein, The step 1 specifically comprises: Step 1.1, using the switching functions s1 and s2 to represent the voltage output conditions of the forward bridge arm and the reverse bridge arm in the CLLC bidirectional converter respectively, wherein s1 is the switching function of the forward bridge arm, and s2 is the switching function of the reverse bridge arm; Step 1.2, establishing the average state equation of the first state variable in the CLLC bidirectional converter, Fourier series expansion of the first state variable and the switching function, Fourier series expansion of the first state variable at the first harmonic, and obtaining the generalized average expression of each first state variable; Step 1.3, based on the generalized average expression of each first state variable of the CLLC converter, constructing the corresponding first small-signal model.

3. The hybrid small-signal modeling method for a cascaded type power supply according to claim 2, wherein, The step 1.2 specifically comprises: replacing the actual value of the first state variable in the CLLC bidirectional converter circuit with its average value within a switching cycle to obtain a linear time-invariant average state equation: where x(t) represents a first state variable in a linear time-varying equation, <x> k (t) represents the average value of the linear time-invariant first state variable, k is the harmonic number, 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> Fourier series expansion of the first state variable in the equation, calculation of the direct current part and the first harmonic component part, taking k=0 for the direct current part and k=±1 for the first harmonic component, and the expression is as follows: The switching function is brought in, and the product of the first state variable and the switching function is represented by zero-order and first-order Fourier series, and the product of the first state variable and the switching function is as follows: <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< / y> < / 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 switching function input value, 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 direct current 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 L 12 Two capacitors C 11 C 12 L 11 The current is i1, L 12 The current is i2, C 11 The voltage is v1, C 12 Given a voltage of v2, expanding the first state variables i1, i2, v1, and v2 at the first harmonic yields the generalized average expression: v o_CLLC ＝(2 <s2> 1R <i2> 1R +2 <s2> 1I <i2> 1I )R L < / i2> < / s2> < / i2> < / s2> wherein r1 is a power supply side resistance, r2 is a load side resistance, v dc is an input side DC voltage, L m is a mutual inductance of a transformer in a CLLC converter, a represents a coefficient of each harmonic component in a Fourier series, n is a turn ratio of a high frequency transformer, R L is a load resistance, v o_CLLC is an output voltage of the CLLC converter.

4. The hybrid small-signal modeling method for a cascaded type power supply according to claim 3, wherein, The first small-signal model of the CLLC converter in the step 1.3 is: where 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 hybrid small-signal modeling method for a cascaded type power supply according to claim 4, wherein, The step 2 specifically comprises: Step 2.1, dividing the working process of the half-bridge Buck-Boost converter into a switching-on stage and a switching-off stage within a switching cycle, averaging the second state variable of the two stages, using the average second state variable to replace the instantaneous value, and obtaining the second state space equation within the whole switching cycle; The half-bridge Buck-Boost converter comprises a capacitor C0 and an inductor L0, in a switching cycle, the switching elements in the circuit are alternately turned on and turned off, when the switching element is turned on, the inductor L0 starts to store energy, the current flows through the inductor L0 and the capacitor C0, when the switching 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 a switching-on stage and a switching-off stage, the average second state variable is used to approximate the instantaneous value, and the second state space equation is listed: wherein V dc is the input voltage of the half-bridge Buck-Boost converter, Ts is the switching period, Ts represents the average value in one switching period, i L is the current of the 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, a corresponding second small signal model is constructed; The average second state variable is decomposed into the sum of a direct current component and an alternating current small signal component, and the control quantity containing the alternating current component is also decomposed, and the decomposed quantity is brought into the second state space equation: wherein V is the ac small signal component of the output voltage, o V is the dc component of the output voltage, I is the dc component of the inductor current, is the ac small 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, ignore the high order small signal component and Linearize the equation, get the AC small signal equation group: The alternating current small signal equation set is arranged in the form of a spatial state equation, and the third small signal model of the half-bridge Buck-Boost is obtained: where X is a second state variable u is an input Y is an output A Buck_Boost , B Buck_Boost , C Buck_Boost , D Buck_Boost is a system matrix.

6. The hybrid small-signal modeling method for a cascaded type power supply according to claim 5, wherein, The step 3 specifically comprises: Step 3.1, the on and off states of the three-phase interleaved parallel Buck converter bridge arm are represented by using the switching description function, the switching description function of the on and off logic of the zth phase switch tube is defined as S z When S z is equal to 1, the upper bridge arm is on and the lower bridge arm is off, when S z is equal to 0, the upper bridge arm is off and the lower bridge arm is on, z = 1, 2, 3; Step 3.2, according to the switching description function, the working process of each phase is divided into a switching-on stage and a switching-off stage, the third state variable of each phase in the two stages is averaged, and the average third state variable is used to replace the instantaneous value, and the third state space equation in the whole switching cycle is obtained; Step 3.3, according to the third state space equation of the three-phase interleaved parallel Buck converter, a corresponding third small signal model is established.

7. The hybrid small-signal modeling method for a cascaded type power supply according to claim 6, wherein, The step 3.2 specifically comprises: the three-phase interleaved parallel Buck converter comprises inductors L1, L2 and L3 in each phase, and an output capacitor C1, in a switching cycle, the working process of each phase is divided into a switching-on stage and a switching-off stage, and the average third state variable is used to approximate the instantaneous value, and the third state space equation is listed: where i L1 is the current in the inductor of the first phase Buck converter circuit, i L2 is the current in the inductor of the second phase Buck converter circuit, i L3 is the current in the inductor of the third phase Buck converter circuit, U in is the input voltage, U o is the output voltage, Di is the duty cycle of the switch on time in the first phase Buck converter circuit, D2is the duty cycle of the switch on time in the second phase Buck converter circuit, D3is the duty cycle of the switch on time in the third phase Buck converter circuit, T S represents one switching period.

8. The hybrid small-signal modeling method for a cascaded type power supply according to claim 7, wherein, The step 3.3 specifically comprises: the average third state variable is decomposed into the sum of a direct current component and an alternating current small signal component, and other control quantities containing the alternating current component are also decomposed, the decomposed quantity is brought into the third state space equation, the direct current components of the input and the output are made to correspond to each other, the direct current components are eliminated, and high-order small signal components are ignored, and an alternating current small signal equation set is obtained: wherein, is an ac small-signal component of the inductor current in the first phase Buck converter circuit, is an ac small-signal component of the inductor current in the second phase Buck converter circuit, is an ac small-signal component of the inductor current in the third phase Buck converter circuit, is an ac small-signal component of the output voltage, is an ac small-signal component of the input voltage, is an ac small-signal component of the duty cycle in the first phase Buck converter circuit, is an ac small-signal component of the duty cycle in the second phase Buck converter circuit, is an ac small-signal component of the duty cycle in the third phase Buck converter circuit, R is a load resistance of the three-phase interleaved parallel Buck converter; The alternating current small signal equation set is arranged in the form of a spatial state equation, and the third small signal model of the three-phase interleaved parallel Buck converter is obtained: where X is a third state variable u is an input quantity Y is an output quantity Let M = R c Cs+1, R c is the equivalent series resistance of the capacitor, s is a complex frequency variable, A Buck , B Buck , C Buck , D Buck is a system matrix.

9. The hybrid small-signal modeling method for a cascaded type power supply according to claim 8, wherein, The step 4 specifically comprises: the output of the half-bridge Buck-Boost converter is equal to the input of the CLLC bidirectional converter, and the output of the CLLC bidirectional converter is equal to the input of the three-phase interleaved parallel Buck converter, so that: The first state space equation, the second state space equation and the third state space equation are combined, and the expressions are solved, so that the hybrid small signal model of the whole cascaded power supply is obtained: Wherein, X is the state variable of the cascade power supply as a whole u is the input variable A, B, C, D are system matrices of the cascade power supply.

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