A multi-frequency modeling method for PWM power converter switching ripple estimation and application

Abstract

The application belongs to the technical field of PWM power converter modeling, and discloses a multi-frequency modeling method and application for PWM power converter switch ripple estimation, which comprises the following steps: (1) constructing the mapping principle between the time-domain state variables and the frequency-domain state variables of the PWM power converter, and simultaneously constructing the mapping principle between the time-domain switch function and the frequency-domain switch function of the PWM power converter; (2) establishing the mapping rule between the time domain and the frequency domain of the state variable / input variable and the switch function product term of the PWM power converter system; and (3) converting the time-domain state space model of the PWM power converter system into a multi-frequency model based on the obtained mapping rule. The application improves the solving efficiency of the model.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of PWM power converter modeling, and more particularly, to a multi-frequency modeling method and application for PWM power converter switching ripple estimation. BACKGROUND

[0002] Pulse width modulation (PWM) power converters have been widely applied in renewable energy integration, motor drive and other power electronic system application scenarios. In these application scenarios, simulation models are very necessary for analyzing the transient characteristics of PWM power converters. Detailed models can characterize each switching action of the PWM power converter, thereby producing very accurate simulation results, but the model simulation step is limited by the switching period of the PWM power converter, so the simulation of such models is very time-consuming, mainly reflected in scenarios such as long simulation time of the system or the need for online parameter tuning for repeated simulation. In addition, the detailed model of the PWM power converter system is a time-varying system without steady-state equilibrium point, thus being not conducive to the design of the controller.

[0003] The simulation model based on the state space average (SSA) method can reduce the calculation time of the model by averaging the state variables of the system within one switching period to replace the switching function of the controlled PWM power converter. SSA is a common power electronic converter modeling method, and it is also conducive to the design of the controller. However, the simulation speedup of the SSA model of the PWM power converter system is at the expense of the accuracy of the model, which is reflected in the fact that the SSA model cannot characterize the ripple characteristics caused by the switching of the PWM power converter. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a multi-frequency modeling method and application for PWM power converter switching ripple estimation, which aims to solve the problem that the existing SSA model cannot characterize the ripple characteristics caused by the switching of the PWM power converter.

[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, a multi-frequency modeling method for PWM power converter switching ripple estimation is provided, which comprises the following steps:

[0006] Step one, constructing the mapping principle between the time-domain state variables and the frequency-domain state variables of the PWM power converter, and constructing the mapping principle between the time-domain switching function and the frequency-domain switching function of the PWM power converter;

[0007] Step 2: Establish the mapping rules between the time domain and frequency domain of the state variables / input variables and the product terms of the switching function of the PWM power converter system;

[0008] Step 3: Based on the circuit topology of the PWM power converter system, the mapping principle between the time-domain state variables and frequency-domain state variables of the PWM power converter system, the mapping rule between the time-domain switching function and frequency-domain switching function of the PWM power converter, and the mapping rule between the time-domain and frequency-domain of the product terms of the state variables / input variables and the switching function of the PWM power converter system, the time-domain state-space model of the PWM power converter system is converted into a multi-frequency model, i.e., an invariant state-space model.

[0009] Furthermore, the state variable x(t) is represented by a vector of length 2N+1, consisting of the coefficients of the cosine and sine terms of each Fourier series:

[0010]

[0011] The state variable x(t) can be approximated as:

[0012] x(t)≈C(t)x(3)

[0013] in:

[0014]

[0015] Equation (3) gives the algebraic relationship between the time domain and frequency domain of the state variable x(t).

[0016] Furthermore, the derivative of the time-domain state variable is obtained by simultaneously differentiating both sides of equation (3). Mapping rules in the frequency domain:

[0017]

[0018] in, The item is calculated as follows:

[0019]

[0020] Where Ω is a sparse matrix of (2N+1)×(2N+1):

[0021]

[0022] Furthermore, equation (5) can be written as:

[0023]

[0024] Equation (8) gives the derivative of the time-domain state variable. and frequency domain state variable derivatives the algebraic relationship between the time domain and the frequency domain of the switching function of the PWM power converter.

[0025] Further, when establishing the mapping rule between the time domain and the frequency domain of the switching function of the PWM power converter, the discrete Fourier transform of the PWM switching function is needed first, and then according to the amplitude spectrum of the switching function and the type of the PWM power converter, the important frequency components of the state variables are determined; and then according to the selected important frequency components, the coefficients of different frequency components in the Fourier expression of the PWM switching function are calculated.

[0026] Further, the important frequency f DC / DC of the PWM signal of the DC / DC type power converter should satisfy the following relationship:

[0027] f DC / DC = rf sw (9)

[0028] Wherein: r is an integer, indicating the multiple of f sw ;

[0029] The important frequency f DC / AC of the PWM signal of the DC / AC type power converter should satisfy the following relationship:

[0030] f DC / AC = rf sw ±sf m (10)

[0031] Wherein: r is a positive integer, and s is a natural number or an integer.

[0032] Further, the Fourier expansion of the switching function q(t) of the PWM power converter is represented as:

[0033]

[0034] Wherein, respectively represent the cosine term and the sine term coefficient of each order Fourier series of the switching function q(t); the switching function q(t) is also represented by a vector with a length of 2N+1 composed of the cosine term and the sine term coefficient of each order Fourier series:

[0035]

[0036] The switching function q(t) is approximately represented as:

[0037] q(t)≈C(t)q(13)

[0038] The formula (13) gives the algebraic relationship between the time domain and the frequency domain of the switching function of the PWM power converter.

[0039] Further, each order Fourier series term of the switching function q(t) is represented as:

[0040]

[0041] In formula (23), J

[0042]

[0043] wherein J s (x) is the first kind of Bessel function of order s, and φ m is the phase of the modulated wave signal, and φ sw is the phase of the carrier wave signal.

[0044] The application further provides a transient characteristic analysis method of a PWM power converter, which uses the model constructed by the multi-frequency modeling method for PWM power converter switching ripple estimation to analyze the transient characteristics of the PWM power converter to be analyzed.

[0045] The application further provides a multi-frequency modeling system for PWM power converter switching ripple estimation, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the multi-frequency modeling method for PWM power converter switching ripple estimation.

[0046] The application further provides a computer readable storage medium, which stores machine executable instructions, the machine executable instructions, when called and executed by a processor, cause the processor to implement the multi-frequency modeling method for PWM power converter switching ripple estimation or the transient characteristic analysis method of the PWM power converter.

[0047] Overall, compared with the prior art, the multi-frequency modeling method for PWM power converter switching ripple estimation and the application provided by the application mainly have the following beneficial effects:

[0048] 1. Based on the circuit topology of the PWM power converter system, the mapping principle between the time domain state variables and the frequency domain state variables of the PWM power converter system, the mapping rule between the time domain switching function and the frequency domain switching function of the PWM power converter, and the mapping rule between the time domain and the frequency domain of the state variable / input variable and the switching function product term of the PWM power converter system, the time domain state space model of the PWM power converter system is converted into a multi-frequency model, namely a time-invariant state space model; compared with the detailed model, the solving efficiency of the model is improved, and the steady state characteristics and the switching ripple of the PWM power converter system can be represented.

[0049] 2. Fourier series based on state variables can represent the steady-state characteristics and switching ripples of PWM power converter systems, and adaptively select a set of important frequencies for different types of power converter systems, thereby improving the computational accuracy of the model of the PWM power converter. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 (a), (b), (c) in are the switching function spectrum diagrams of two types of PWM power converters, respectively;

[0051] Figure 2 is a flowchart of the important frequency selection scheme in the multi-frequency model of the PWM power converter;

[0052] Figure 3 is a schematic diagram of PWM signal generation of a DC / DC type power converter;

[0053] Figure 4 is a schematic diagram of PWM signal generation of a DC / AC type power converter;

[0054] Figure 5 is a DCDC-BOOST boost circuit topology diagram;

[0055] Figure 6 is a PWM single-phase full-bridge inverter circuit topology diagram;

[0056] Figure 7 is a comparison diagram of voltage waveforms of the load resistor of the DCDC-BOOST boost circuit under different simulation models;

[0057] Figure 8 is a comparison diagram of inductor current waveforms of the single-phase full-bridge inverter circuit under different simulation models;

[0058] Figure 9 is a normalized CPU computing time consumption statistical diagram of the embodiment 1 of the present application and the embodiment 2 of the present application under three simulation models. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0060] The application provides a multi-frequency modeling method for PWM power converter switch ripple estimation, which is based on Fourier basis expression of state variables, converts time domain state variables to different frequency domain components for multi-frequency modeling, establishes mapping principles from time domain to multi-frequency domain, and proposes important frequency domain selection methods for different types of PWM power converters. The model constructed by the method can effectively estimate the ripple characteristics caused by the switching of the PWM power converter, and can provide faster simulation speed compared with the detailed simulation model of the PWM power converter.

[0061] The method mainly comprises the following steps:

[0062] Step one, the mapping principles between the time domain state variables and the frequency domain state variables of the PWM power converter are constructed, and the mapping principles between the time domain switching function and the frequency domain switching function of the PWM power converter are constructed.

[0063] Step one comprises the following sub-steps:

[0064] Step S1, the mapping rules between the time domain and the frequency domain of the state variables of the PWM power converter system are constructed.

[0065] The Fourier expansion of the instantaneous value x(t) of the state variable of a PWM converter system can be expressed as:

[0066]

[0067] wherein, respectively represent the cosine term and the sine term coefficients of each order Fourier series of the state variable x(t), and ω is the natural frequency of the system, for a DC / DC type power converter, the natural frequency of the system only depends on the frequency of the carrier signal; for a DC / AC type power converter, the natural frequency of the system depends on the frequency of the carrier signal, the frequency of the modulation signal and the corresponding sideband frequency. In the time domain, although the waveform of the state variable x(t) changes with time, the coefficients of each order of the Fourier expansion of the state variable x(t) are constant in the steady state. Assuming that the waveform of the state variable x(t) can be approximated by the Fourier expansion of the first N orders (the unselected harmonic components can be ignored), the state variable x(t) can be represented by a vector with a length of 2N+1 composed of the cosine term and the sine term coefficients of each order Fourier series:

[0068]

[0069] The state variable x(t) can be approximately expressed as:

[0070] x(t)≈C(t)x(3)

[0071] wherein,

[0072]

[0073] Equation (3) gives the algebraic relationship between the time domain and frequency domain of the state variable x(t). In addition, the derivative of the time domain state variable The mapping rule in the frequency domain, the derivative of both sides of equation (3) can be obtained:

[0074]

[0075] Where, The term can be calculated as:

[0076]

[0077] Where, Ω is a (2N+1) x (2N+1) sparse matrix:

[0078]

[0079] Further, equation (5) can be written as:

[0080]

[0081] Equation (8) gives the algebraic relationship between the time domain state variable derivative and the frequency domain state variable derivative .

[0082] At this point, the specific implementation steps of step S1 have been completed.

[0083] Step S2, the mapping rule between the time domain and frequency domain of the switching function of the PWM power converter is established. Wherein, step S2 includes two sub-steps S2.1 and S2.2, wherein S2.1 step needs to perform discrete Fourier transform on the PWM switching function, and then according to the amplitude spectrum of the switching function and the type of the PWM power converter, the frequency domain component of the state variable which needs to be analyzed is determined. The specific implementation steps are as follows:

[0084] First, the discrete Fourier transform needs to be performed on the switching function of the controlled PWM power converter to obtain its frequency domain distribution. For example, the carrier signal frequency of a PWM signal is f sw = 10000 Hz, Figure 1 The frequency spectrum of the PWM signal of the DC / DC type power converter generated by the duty cycle of 0.6 and the PWM signal of the DC / AC type power converter generated by the modulation wave m(t) = 0.8sin(100πt) are shown in the following two figures.

[0085] According to Figure 1 It can be seen that the frequency domain distribution of the PWM signal of the DC / DC type power converter is mainly concentrated in the direct current and carrier frequency fsw The important frequency f of the PWM signal in a DC / DC power converter is an integer multiple of [a certain value]. DC / DC The following relationship should be satisfied:

[0086] f DC / DC =rf sw (9)

[0087] Where: r is an integer, representing f sw Multiples of.

[0088] The frequency domain distribution of the PWM signal in a DC / AC power converter is quite complex. Besides being concentrated in the fundamental frequency, the modulation frequency f m and carrier signal frequency f sw Above, they are also concentrated in f sw and its integer multiples of the sideband frequency f sideband Above. The important frequency f of the PWM signal in a DC / AC power converter. DC / AC The following relationship should be satisfied:

[0089] f DC / AC =rf sw ±sf m (10)

[0090] Where: r is a positive integer, s is a natural number or integer (related to single-phase / three-phase DC / AC converters; the state-space model of a three-phase inverter system exhibits switching function cancellation, therefore the switching frequency and its integer multiples are not considered), according to Figure 2 It can be concluded that when r±s is even, the sideband frequency f sideband The corresponding amplitudes are relatively low (e.g., 9950Hz, 10050Hz, 20000Hz, 19900Hz, 20100Hz), therefore, the responses at these frequencies can be ignored.

[0091] For equations (9) and (10), since the amplitude of the switching function spectrum decays rapidly with increasing frequency, a relative error reference range ε ​​for the multi-frequency model can be introduced when actually selecting parameters r and s. The order of the multi-frequency model is increased sequentially, and when the relative error of the model... The set relative error reference range has been reached, that is... In this case, the parameters r and s can be determined. Considering the computational complexity of the model, r should not exceed 20, and the value of s should be within the range of 5 times the sideband frequency.

[0092] Figure 2 A scheme for selecting important frequencies of the switching function of a PWM power converter is presented.

[0093] S2.2 Step Calculate the coefficients of the Fourier series of the PWM switching function q(t) according to the important frequency components selected in S2.1. The detailed steps are as follows:

[0094] The Fourier expansion of the switching function q(t) of the PWM power converter can be expressed as:

[0095]

[0096] wherein, respectively represent the cosine term and the sine term coefficients of the Fourier series of the switching function q(t). Similar to equation (2), the switching function q(t) can also be represented by a vector of length 2N+1 composed of the cosine term and the sine term coefficients of the Fourier series of the switching function q(t):

[0097]

[0098] The switching function q(t) can be approximately expressed as:

[0099] q(t)≈C(t)q(13)

[0100] Equation (13) gives the algebraic relationship between the time domain and the frequency domain of the switching function of the PWM power converter; then, the corresponding Fourier series coefficients need to be calculated according to the important frequency components selected in S2.1.

[0101] The DC / DC type power converter generates the switching function q(t) by comparing the duty cycle d(t) and the carrier signal, and outputs 1 when the duty cycle signal is greater than the carrier signal; otherwise, it outputs 0.

[0102] Considering the equivalent triangular carrier signal, as shown in Figure 3 , the Fourier series terms of the switching function q(t) can be calculated as:

[0103]

[0104] wherein, t h ,t l respectively represent the rising edge time and the falling edge time within a carrier cycle. Assuming that the duty cycle d(t) changes slowly, i.e., it can be approximated as a constant d0 within a carrier cycle, we can obtain:

[0105]

[0106] Substituting equation (17) and equation (18) into equation (14), (15), (16), we can obtain:

[0107] q0=d0 (19)

[0108]

[0109] Equation (19), Equation (20), Equation (21) give the important frequency f DC / DC the coefficients of the corresponding Fourier series.

[0110] DC / AC type power converter is to generate the switching function q(t) by comparing the modulation wave signal m(t) and the carrier signal, when the modulation wave signal is greater than the carrier signal, output 1; otherwise, output 0. Assuming that the modulation signal m(t) of the DC / AC type power converter is a sine waveform without high-order harmonics, therefore, the modulation signal can be expressed as:

[0111]

[0112] In the formula, is the cosine term and the sine term coefficient of the Fourier series of the modulation signal m(t), considering the isosceles triangle carrier signal, as shown in Figure 4 f m = f sw , that is, the modulation wave signal changes very slowly compared with the carrier signal, according to the sine PWM modulation related theory, the Fourier series term of the switching function q(t) is expressed as:

[0113]

[0114] In Equation (23):

[0115]

[0116] Where, J s (x) is the first kind of Bessel function with order s, φ m is the phase of the modulation wave signal, φ sw is the phase of the carrier signal. When ω sw / ω m ≥ 10, Equation (24) has high accuracy.

[0117] Equation (24) gives the important frequency f DC / AC the coefficients of the corresponding Fourier series.

[0118] So far, the specific implementation steps of step S2 have been completed.

[0119] Step two, establish the mapping rule between the time domain and the frequency domain of the product term of the state variable / input variable and the switching function of the PWM power converter system.

[0120] The product of the state variable x(t) and the switching function q(t) in the time domain state space model of the PWM power converter system can be written as:

[0121] g = q(t)x(t) = C(t)g (25)

[0122] where the vector g is composed of the coefficients of the cosine and sine terms of its Fourier series of each order:

[0123]

[0124] The coefficients of the vector g in equation (26) are obtained by multiplying equation (1) and equation (11), applying trigonometric identities, and extracting the higher order components. For example, for a second order model with N = 2, the vector g can be expressed as:

[0125]

[0126] Equation (27) can be further written as:

[0127] g = Qx (28)

[0128] where Q is a (2N + 1) x (2N + 1) matrix. For a second order model with N = 2, the matrix Q can be expressed as:

[0129]

[0130] Substituting equation (28) into equation (25) gives:

[0131] g = q(t)x(t) = C(t)(Qx) (30)

[0132] Equation (30) gives the algebraic relationship between the time domain and frequency domain of the product of the state variables and the switching functions of the PWM power converter system.

[0133] For an input variable u(t) containing only the DC component u DC , the product of the switching function and the input variable can be expressed as:

[0134] q(t)u(t) = C(t)(qu DC ) (31)

[0135] If the input variable u(t) contains other higher harmonic components, the algebraic relationship between the time domain and frequency domain can be derived by analogy with the derivation of the product of the state variables and the switching functions:

[0136] q(t)u(t) = C(t)(Qu) (32)

[0137] In equation (32):

[0138] Step three, the time-domain state space model of the PWM power converter system is converted into a multi-frequency model, i.e. a time-invariant state space model, based on the circuit topology of the PWM power converter system, the mapping principle between the time-domain state variables and the frequency-domain state variables of the PWM power converter system, the mapping rule between the time-domain switching function and the frequency-domain switching function of the PWM power converter, and the mapping rule between the time-domain and the frequency-domain of the state variable / input variable and the switching function product term of the PWM power converter system.

[0139] In combination with Table 1, the application is further described in detail below in combination with two specific embodiments.

[0140] Table 1 Mapping principle from time-domain state space model to multi-frequency model

[0141]

[0142] Embodiment 1: DCDC-BOOST step-up converter circuit

[0143] The topology structure of the DCDC-BOOST step-up converter circuit is shown in Figure 5 . In the continuous conduction mode, the circuit has two states: the first state is that the switching function q(t) of the control switch S is 1, at which time the diode D is reverse-biased and cut off; the second state is that the switching function q(t) of the control switch S is 0, at which time the diode D is forward-biased and turned on. Assuming that all devices of the circuit are ideal elements, i.e. without considering the effects of the forward-biased voltage and reverse-recovery current of the diode and the stray parameters of the switch, the state variable is selected as i L , the following time-domain state space model can be listed:

[0144]

[0145] According to the frequency selection scheme of Figure 2 , it is assumed that the important frequency components of the power converter system are direct current, one and two times the carrier signal frequency (high-order harmonic frequencies are not considered for the moment), i.e. f DC / DC ={0,f sw ,2f sw}, and the mapping rule of Table 1 is applied to formula (33), and the multi-frequency model of this embodiment 1 is obtained:

[0146]

[0147] In formula 34, the order N of the multi-frequency model is 2, the matrices Ω and Q are both 5×5 matrices, and u=[V DC 0 0 0 0] T .

[0148] Embodiment 2: PWM single-phase full-bridge inverter circuit

[0149] The circuit topology of the PWM single-phase full-bridge inverter with LC filter and variable load resistance is shown in FIG. 2, which only considers the forward commutation process and the reverse commutation process of the full-bridge inverter, and ignores the stray parameters of the devices, such as the forward conduction voltage and the reverse recovery current of the diode. By selecting i and v as state variables, the following time-domain state space model can be listed: Figure 6

[0150] In formula (35), when Q1 is on and Q2 is off, q + (t) = 1, and vice versa, q + (t) = 0; when Q3 is on and Q4 is off, q - (t) = 1, and vice versa, q - (t) = 0; considering that q + (t) and q - (t) are complementary, formula (35) can be simplified as:

[0151]

[0152] According to the frequency selection scheme of

[0153] , it is assumed that the important frequency components are selected as: Figure 2 f DC / AC = {f m , f sw - 2f m , f sw , f sw + 2f m} (36)

[0154] By applying the mapping rules in Table 1 to formula (35), the multi-frequency model of this embodiment 2 can be obtained:

[0155]

[0156] In formula (37), the order N of the multi-frequency model is 4, and the matrix Ω is an 8x8 matrix.

[0157] It can be concluded that the model obtained by the multi-frequency modeling method proposed in the present application can represent the ripple caused by switching of the PWM power converter, greatly improving the calculation accuracy of the SSA model; from

[0158] It can be concluded that the model obtained by the multi-frequency modeling method proposed in the present application has obvious improvement in calculation efficiency compared with the detailed model. Figure 7 Figure 8 Figure 9

[0159] ​​​The application further provides a transient characteristic analysis method of the PWM power converter, which uses the model constructed by the multi-frequency modeling method for PWM power converter switch ripple estimation to analyze the transient characteristics of the PWM power converter to be analyzed.

[0160] The application further provides a multi-frequency modeling system for PWM power converter switch ripple estimation, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the multi-frequency modeling method for PWM power converter switch ripple estimation.

[0161] The application further provides a computer readable storage medium, which stores machine executable instructions, the machine executable instructions, when called and executed by a processor, make the processor realize the multi-frequency modeling method for PWM power converter switch ripple estimation or the transient characteristic analysis method of the PWM power converter.

[0162] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the application, and is not used to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A multi-frequency modeling method for PWM power converter switching ripple estimation, characterized in that, The method comprises the following steps: Step one, based on Fourier series, mapping principles between time-domain state variables and frequency-domain state variables of the PWM power converter are constructed, and mapping principles between time-domain switching functions and frequency-domain switching functions of the PWM power converter are constructed; Step two, mapping rules between time domain and frequency domain of state variable / input variable and switching function product items of the PWM power converter system are established; Step three, based on the circuit topology of the PWM power converter system, the mapping principles between time-domain state variables and frequency-domain state variables of the PWM power converter system, the mapping principles between time-domain switching functions and frequency-domain switching functions of the PWM power converter, and the mapping rules between time domain and frequency domain of state variable / input variable and switching function product items of the PWM power converter system, the time-domain state space model of the PWM power converter system is converted into a multi-frequency model, i.e. a time-invariant state space model; When establishing the mapping rules between time domain and frequency domain of the switching functions of the PWM power converter, the Fourier transform of the PWM switching function is first performed, and then according to the amplitude spectrum of the switching function and the type of the PWM power converter, the important frequency components of the state variables are determined; and then according to the selected important frequency components, the coefficients of different frequency components in the Fourier expression of the PWM switching function are calculated.

2. The multi-frequency modeling approach for PWM power converter switching ripple estimation of claim 1, wherein: State variable The vector of length 2N+1 consisting of the cosine and sine coefficients of the Fourier series of each order is denoted by: The vector of length 2N+1 consisting of the cosine and sine coefficients of the Fourier series of each order is denoted by: (2) State variable Approximately expressed as: (3) Wherein: (4) Equation (3) gives the algebraic relationship between the time and frequency domains of the state variable x.

3. The multi-frequency modeling approach for PWM power converter switching ripple estimation of claim 2, wherein: The derivative of the time-domain state variable is obtained by simultaneously differentiating both sides of equation (3) Mapping principle in frequency domain: (5) wherein The term is calculated as: (6) wherein is a sparse matrix: (7) Further, equation (5) is written as: (8) Equation (8) gives the algebraic relationship between the time-domain state variable derivative and the frequency-domain state variable derivative ​ 4. The multi-frequency modeling approach for PWM power converter switching ripple estimation of claim 1, wherein: Significant frequency of pwm signal of dc / dc type power converter The following relation should be satisfied: (9) wherein: is an integer representing a multiple of 2. Significant frequency of pwm signal of dc / ac type power converter The following relation should be satisfied: (10) wherein: is a positive integer, is a natural number or an integer.

5. The multi-frequency modeling approach for PWM power converter switching ripple estimation of claim 1, wherein: Switching function for pwm power converters The Fourier expansion of the function f(x) is given by (11) where the cosine and sine coefficients of the Fourier series of order respectively, of the switching function ; the switching function is likewise represented by a vector of length consisting of the cosine and sine coefficients of the Fourier series of order (12) Switching function is approximately expressed as: (13) Equation (13) gives the algebraic relationship between the time domain and the frequency domain of the switching function of the PWM power converter.

6. The multi-frequency modeling approach for PWM power converter switching ripple estimation of claim 5, wherein: Switching function The Fourier series terms of order n are represented as: (23) In equation (23): (24) wherein is a first kind Bessel function of order , is a phase of the modulated wave signal, is a phase of the carrier wave signal.

7. A method of analyzing the transient behavior of a PWM power converter, characterized by: The analysis method uses the model constructed by the multi-frequency modeling method for PWM power converter switching ripple estimation according to any one of claims 1-6 to analyze the transient characteristics of the PWM power converter to be analyzed.

8. A multi-frequency modeling system oriented to PWM power converter switching ripple estimation, characterized by: The system comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the multi-frequency modeling method for PWM power converter switching ripple estimation according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that: The computer readable storage medium stores machine executable instructions, and when the machine executable instructions are called and executed by the processor, the machine executable instructions cause the processor to implement the multi-frequency modeling method for PWM power converter switching ripple estimation according to any one of claims 1-6 or the transient characteristic analysis method of the PWM power converter according to claim 7.

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