Generalized steady-state analysis model construction method for IBDC topology and modulation strategy analysis

Abstract

The invention relates to a generalized steady-state analysis model construction method for IBDC topology and modulation strategy analysis, and belongs to the field of converter modeling. The method comprises the following steps: generating a corresponding equivalent circuit according to electrical parameters among devices of the IBDC circuit structure; according to the impedance characteristics of the passive networks, each passive network is represented through an impedance network in a unified form; according to the electrical characteristics of the ports of the switching networks, each switching network is represented through an analytic expression in a unified form; according to an equivalent circuit and a circuit analysis theory of the IBDC, analytical expressions of voltage, current and transmission power are calculated, so that a generalized steady-state analysis model of the IBDC is constructed. According to the method, the bottleneck that a traditional model is limited to specific topology or modulation is broken through, analytic expressions of voltage, current and transmission power can be rapidly solved, and high-reliability topology type selection, parameter optimization and modulation strategy decision support is provided for scenes such as electric vehicle charging and energy storage systems.

Description

Technical Field

[0001] The present invention belongs to the field of converter modeling and relates to a method for constructing a generalized steady-state analysis model for analyzing various isolated bidirectional DC-DC converter (IBDC) topologies and modulation strategies. Background Art

[0002] IBDC plays a vital role in modern power systems. Due to its bidirectional power flow, soft switching capability and electrical isolation characteristics, it is widely used in electric vehicles, energy storage systems and smart grids.

[0003] Bidirectional power flow is one of IBDC's most notable features. Compared to traditional unidirectional DC converters, IBDC can transfer energy in both directions between two DC circuits, which gives it unparalleled flexibility and efficiency in systems requiring energy feedback or regeneration. For example, in electric vehicles, the motor is not only an output source of driving power, but also acts as a generator during braking, converting kinetic energy into electrical energy and feeding it back into the battery. Soft switching technology is another key feature of IBDC, which greatly improves the efficiency and reliability of the converter. By introducing a transformer between the primary and secondary circuits, IBDC can achieve energy transmission between different voltage levels while ensuring physical isolation between the two circuits. This design significantly improves system safety, especially in application scenarios involving high-voltage operation.

[0004] However, as a typical multivariable, nonlinear, and strongly coupled system, the complexity of IBDC makes most existing analytical models lacking in versatility, accuracy, and solution speed, urgently requiring further research and improvement. On the one hand, many models are only applicable to specific circuit topologies or modulation strategies. However, in actual applications, circuit topologies and modulation strategies vary, resulting in the models being unable to adapt well to new application requirements. On the other hand, existing models often use simplifying assumptions when dealing with complex circuits, which may overlook some key details and reduce the accuracy of the analysis results. Therefore, it is particularly important to construct a generalized steady-state analysis model that can cover various IBDC topologies, adapt to multiple modulation strategies, and possess flexible parameter configuration, high computational speed, accuracy, and versatility. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for constructing a generalized steady-state analysis model for IBDC topology and modulation strategy analysis. The generalized steady-state analysis model constructed by this method can cover various IBDC topologies, adapt to multiple modulation strategies, and has flexible parameter configuration, high calculation speed, high precision and versatility.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for constructing a generalized steady-state analysis model for IBDC topology and modulation strategy analysis, the method comprising:

[0008] S1. Generate a corresponding equivalent circuit based on the electrical parameters between the components of the IBDC circuit structure;

[0009] S2. Based on the impedance characteristics of the passive network, each passive network is represented by a unified impedance network;

[0010] S3. Based on the electrical characteristics of the ports of the switch network, each switch network is represented by a unified analytical expression;

[0011] S4. Based on the equivalent circuit and circuit analysis theory of IBDC, the analytical expressions of voltage, current and transmission power are calculated to construct a generalized steady-state analysis model of IBDC.

[0012] Furthermore, in step S1, the IBDC circuit structure is first converted into a generalized topology structure, which includes input and output ports, and the input and output ports are coupled through a passive network and a switch network; the switch network includes a primary-side switch network at the input port and a secondary-side switch network at the output port; the passive network includes a primary-side resonant network, a secondary-side resonant network and a high-frequency transformer between the two resonant networks; and then an equivalent circuit model is generated based on the generalized topology structure.

[0013] Generating an equivalent circuit model according to the generalized topology includes defining the primary side switching network as a voltage source V p (t), the secondary side switching network is simplified to a voltage source V s (t), and define the equivalent currents of the primary and secondary side switching networks as i p (t) and i s (t); the impedance of the primary side switching network is expressed as Z 11 and Z 12 , the impedance of the secondary side switching network is expressed as Z 21 and Z 22 In this generalized topology, the impedance is mainly composed of reactance, so the primary side switch network reactance X 11 and X 12 and the secondary side switching network reactance X 21 and X 22 ; The equivalent circuit model is expressed as:

[0014]

[0015] Furthermore, in step S2, according to the impedance characteristics of the passive network, each passive network is represented by an impedance network of a unified form, and the impedance network includes two horizontal resonant branches and three vertical resonant branches; the horizontal resonant branch reactance values ​​and vertical resonant branch reactance values ​​corresponding to different passive networks are different; if a resonant device is missing in a resonant branch, the corresponding horizontal resonant branch reactance value is 0, and the vertical resonant branch reactance value tends to infinity.

[0016] Furthermore, in step S3, the switch network is represented by a unified analytical expression based on the electrical characteristics of the switch network ports, including: using a multi-level pulse waveform to represent the AC link voltage of the switch network, and obtaining a unified analytical expression of the switch network through discrete Fourier transform:

[0017]

[0018] Where V p (t) and V s (t) represents the AC link voltage of the primary-side switching network and the secondary-side switching network, respectively. α1, β1, α2, and β2 represent the internal phase shift angles. N represents the transformer turns ratio and the coil turns ratio. ω S represents the angular frequency, and n represents the harmonic number.

[0019] Furthermore, in step S4, based on the IBDC equivalent circuit model, the analytical expression of the switch network, and the impedance network, the KCL and KVL laws are used to calculate the voltage and current vector expressions of the primary-side switch network. Based on the voltage and current vector expressions of the primary-side switch network, the analytical expression of the IBDC transmission power within one switching cycle is obtained. The process is as follows:

[0020] After describing the specific passive network circuit topology in a unified form as an impedance network, the impedance network is decomposed into two independent sub-circuits corresponding to the primary side and the secondary side according to the circuit superposition principle, wherein the primary side independent sub-circuit includes a primary side voltage source, two horizontal resonant branches and two vertical resonant branches, and the secondary side independent sub-circuit includes a secondary side voltage source, two horizontal resonant branches and two vertical resonant branches;

[0021] According to the discrete Fourier transform expression of the AC link voltage and the total impedance of the primary and secondary side switching networks, the primary side current i is obtained: p (t) and the secondary side current i s (t); Based on the specific passive network circuit topology, the impedance of each resonant branch in the impedance network is known. Therefore, the current expression of each resonant branch is obtained by solving the KCL and KVL laws:

[0022]

[0023] Where A p 、B p 、A S 、B S is the corresponding coefficient:

[0024]

[0025] The primary side voltage and current vector expressions obtained based on the discrete Fourier transform expression of the primary side voltage and the primary side current expression are:

[0026]

[0027] Where, Denote the primary side voltage vector and current vector respectively; according to the primary side voltage and current vector, the IBDC transmission power within one switching cycle is obtained:

[0028]

[0029] Where, represents the external phase shift angle between the primary and secondary sides; V p,rms , I p,rms Represent the effective values ​​of primary side voltage and current respectively; Indicates voltage V p (t) and current i p (t) is the phase angle between them.

[0030] The beneficial effects of the present invention are:

[0031] (1) The present invention clarifies the rationality of the unified form of the modeling method by using the conductance matrix to represent the mathematical relationship between the port current and the port voltage and the primary and secondary side reactances. By uniformly describing the passive network in the form of impedance and the switching network in the form of multi-level pulse waveforms, the versatility of the modeling method is clarified, breaking through the bottleneck of the traditional model being limited to a specific topology or modulation, and supporting diversified topologies such as full-bridge, half-bridge, CLLC, and multi-strategy adaptation such as phase shift and pulse width modulation.

[0032] (2) Based on frequency domain harmonic expansion analysis and circuit superposition theorem, the model described in the present invention can quickly solve the analytical expressions of voltage, current and transmission power. The calculation speed is more than 5 times faster than that of traditional numerical simulation. At the same time, the accuracy is controllable and the error is less than 3%. It provides high-reliability topology selection, parameter optimization and modulation strategy decision support for scenarios such as electric vehicle charging and energy storage systems.

[0033] (3) The present invention can uniformly model and quickly analyze the steady-state characteristics of circuits under different IBDC topologies and their control modulation strategies. It has strong versatility and high computational efficiency, and can effectively support engineering applications such as circuit topology selection, parameter design, and performance evaluation. It is suitable for system design and optimization in various bidirectional energy conversion scenarios.

[0034] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0036] Figure 1 This is a logic block diagram of a comprehensive optimization modulation method according to an embodiment of the present invention:

[0037] Figure 2 It is a generalized block diagram of the IBDC network structure;

[0038] Figure 3 It is the two-port equivalent circuit diagram of the IBDC network structure;

[0039] Figure 4 It is a unified schematic diagram of the passive network;

[0040] Figure 5 It is a schematic diagram of the superposition of two independent sub-circuits based on the circuit superposition principle;

[0041] Figure 6 It is a unified schematic diagram of the switching network;

[0042] Figure 7 (a) is a schematic diagram showing the changes of the resonant inductor current and resonant capacitor voltage with the switching frequency;

[0043] Figure 7 (b) is a schematic diagram showing the variation of transmission power with switching frequency;

[0044] Figure 8 This is a schematic diagram of the overlay of calculated test values ​​and experimental test values ​​of the capacitor voltage and inductor current values ​​over time under the switching frequency of 150 kHz and the 0.4π phase shift angle working mode. DETAILED DESCRIPTION

[0045] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0046] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0047] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0048] This embodiment provides a method for constructing a generalized steady-state analysis model for IBDC topology and modulation strategy analysis. Figure 1 As shown, the method includes the following steps:

[0049] S1. Generate a corresponding equivalent circuit based on the electrical parameters between the components of the IBDC circuit structure.

[0050] The generalized topology of IBDC consists of two ports, namely the input port (the voltage amplitude of this port is V1) and the output port (the voltage amplitude of this port is V2), which are coupled through a passive network and a corresponding switch network, as shown in Figure 2 The passive network consists of two resonant networks and a high-frequency transformer with an N:1 turns ratio, used for storing and transmitting electrical energy. The input and output ports correspond to the primary and secondary switching networks, respectively. Each of these networks consists of an inverter and a rectifier circuit, controlling the switching sequence to achieve electrical energy conversion.

[0051] like Figure 3The two-port equivalent circuit of the generalized topology is shown, where the primary-side switching network is defined as a voltage source V p (t), the secondary side switching network is simplified to a voltage source V s (t); and define the equivalent currents of the primary and secondary side switching networks as i p (t) and i s (t), the impedance of the primary side switching network is expressed as Z 11 and Z 12 , the impedance of the secondary side switching network is expressed as Z 21 and Z 22 , impedance Z ij Mainly consider the reactance X kl , then the primary side reactance X 11 and X 12 , secondary side reactance X 21 and X 22 .

[0052] The conductance matrix of IBDC uses a reactance matrix or impedance matrix to represent the relationship between the port current and the port voltage, as shown in the following formula:

[0053]

[0054] Among them, v p (t), v s (t) represents the voltage on the primary side and the secondary side respectively, i p (t), i s (t) represents the current on the primary side and the secondary side respectively.

[0055] S2. According to the impedance characteristics of the passive network, various passive networks are represented by a unified impedance network.

[0056] like Figure 4 As shown, each passive network is described uniformly in the form of an impedance network. By analyzing the circuit structure of the resonant cavity of different passive networks, it can be found that its form is the first vertical resonant branch jX v1 Become the first current loop, and then the first horizontal resonant branch jX in parallel with it h1 Then through the second vertical resonant branch jX v2 A second current loop is formed, which is connected to the second vertical resonant branch jX v2 The second horizontal resonant branch jX in parallel h2 and a third vertical resonant branch jX connected in series with the second horizontal resonant branch v3 A third current loop is formed. In general, when the passive network is described uniformly as an impedance network, it can be divided into three vertical resonant branches and two horizontal resonant branches.

[0057] Therefore, the impedance network includes horizontal and vertical resonant branches, and the reactance value of the horizontal resonant branch is expressed as X hi , the vertical resonant branch reactance value is expressed as X vi . The horizontal resonant branch reactance value X corresponding to different passive networks hi And the vertical resonant branch reactance value X vi are different; if the branch lacks resonant devices such as capacitors and inductors, the corresponding horizontal resonant branch reactance value X hi =0, or vertical resonant branch reactance value X vi →∞. Taking the L-type topology resonant network as an example, in the impedance network corresponding to the L topology, the horizontal resonant branch reactance is X h1 =nωL,X h2 =0, because there is no inductance and capacitance in the vertical direction, so its X v1 →∞,X v2 →∞.

[0058] Combine Figure 4 As shown in Figure 2, since the unified form of different passive networks is described in the form of an impedance network, and the network branch reactance and the primary and secondary side reactances can be converted through mathematical calculations, the unified form of different passive networks can be decomposed into two independent sub-circuits corresponding to the primary side and the secondary side respectively based on the circuit superposition theorem, and then solved, including X 11 、X 12 、X 21 、X 22 、X h1 、X h2 、X v1 、X v2 、X v3 .

[0059] After solving, the relationship between the reactance matrix elements of each branch and the second-order matrix of the sodium conductivity is as follows:

[0060]

[0061] S3. According to the electrical characteristics of the switch network ports, various switch networks are represented by a unified analytical expression.

[0062] Since the switching network is realized by using different circuit topologies (full bridge, half bridge and three-level bridge, etc.) and parallel connection of devices, there are different modulation strategies (phase shift modulation, pulse width modulation with variable duty cycle, etc.). However, according to the gate drive signal and AC link voltage waveform, it can be seen that the AC link voltage of the switching network is a multi-level pulse waveform, such as Figure 6 As shown, the switching network can be uniformly described using multi-level pulse waveforms. Figure 6 In, V i represents the voltage amplitude, α iand β i Indicates the internal phase shift angle, by setting V i , α i and β i The values ​​of are different to distinguish different switching networks.

[0063] AC link voltage V across the primary and secondary side switching networks p (t) and V s (t) is derived from the discrete Fourier transform as follows:

[0064]

[0065] Where, ω s =2πf s represents the angular frequency, f s represents the switching frequency, V1 represents the amplitude of the input port voltage, α1 and β1 represent the internal phase shift angle of the primary side, V2 represents the amplitude of the output port voltage, α2 and β2 represent the internal phase shift angle of the secondary side, It represents the external phase shift angle between the primary and secondary voltages. n represents the harmonic order, and N represents the transformer turns ratio.

[0066] S4. Based on the equivalent circuit and circuit analysis theory of IBDC, the analytical expressions of voltage, current, and transmission power are calculated to obtain the generalized steady-state analysis model of IBDC, including the following:

[0067] After describing the specific passive network circuit topology in a unified form as an impedance network according to step S2, Figure 4 and Figure 5 Determine the impedance values ​​of the different passive network circuits on each branch. Based on Kirchhoff's voltage law, Kirchhoff's current law, equivalent circuit solution ideas, and circuit analysis theory, the primary and secondary currents and the current expressions of each branch can be solved.

[0068] Specifically, according to Figure 4 After determining the impedance of each branch in a unified form, follow Figure 5 Decompose it into two equivalent subcircuits. For the first vertical branch, its voltage is equal to the primary side voltage in parallel. Since the impedance of this branch can be known according to step S2 after the components are determined, the current of this branch can be calculated as i according to the circuit analysis expression between current, voltage and impedance. v1 (t). The same is true for other branches. For example, we can select a suitable loop for the subcircuit according to Kirchhoff’s voltage expression, and select a suitable node for the subcircuit according to Kirchhoff’s current law so that the algebraic sum of the current flowing in and out is 0, thus making the current of other branches such as the two horizontal branches i h1 (t) and i h2(t) is solved. According to this method, the branch currents of different passive network circuit topologies are successfully solved, and the process of solving the branch current is completed. According to the expression of the AC link voltage after Fourier transformation obtained by S3, V p (t) and V s (t), substitute the total impedance obtained; then according to Figure 5 The influence of the primary side voltage and secondary side voltage of the two sub-circuits on the primary side current and secondary side current respectively can finally solve i p (t) and i s (t), so we can get V p 、i p The vector expression of is obtained, and finally the transmission power of IBDC in one switching cycle is solved.

[0069] The above calculation process is expressed by the following formula:

[0070] According to the expression V after Fourier transformation of the AC link voltage obtained in step S3, p (t) and V s (t), substitute the total impedance obtained; then according to Figure 5 The influence of the primary side voltage and secondary side voltage of the two sub-circuits on the primary side current and secondary side current respectively, i p (t) and i s (t) The results are:

[0071]

[0072] Among them, A p 、B p 、A S and B S is the following constant:

[0073]

[0074] For the primary side vertical resonant branch jX v1 For example, its voltage is equal to the primary side voltage in parallel, and the impedance of the branch is known. Therefore, according to the circuit analysis expression between current, voltage, and impedance, the current of the branch can be calculated as i v1 (t). The same is true for other resonant branches. v1 (t), i v2 (t), i v3 (t), i h1 (t) and i h2 The expression of (t):

[0075]

[0076] Among them, A v1 、Av2 、B v3 are the corresponding constants, as shown below:

[0077]

[0078] Among them, i v1 (t), i v2 (t), i v3 (t) represents the current of the vertical resonant branch, i h1 (t), i h2 (t) represents the current in the horizontal resonant branch.

[0079] The primary side voltage and current vector expressions obtained based on the discrete Fourier transform expression of the primary side voltage and the primary side current expression are:

[0080]

[0081] in, Represent the primary side voltage vector and current vector respectively.

[0082] The result of the IBDC transmission power in one switching cycle obtained from the vector expression of the primary side voltage and current is:

[0083]

[0084] Where, represents the external phase shift angle between the primary and secondary sides; V p,rms , I p,rms Represent the effective values ​​of primary side voltage and current respectively. Indicates voltage V p (t) and current i p (t) is the phase angle between them.

[0085] Figure 7 (a) and Figure 7 (b) shows the curves of the resonant inductor current value, the resonant capacitor voltage value and the transmission power value as a function of the switching frequency. It can be seen that the calculation results obtained by the generalized steady-state analysis model described in this embodiment are basically consistent with the actual experimental test results. Figure 7 (a) and Figure 7 In (b), the solid line is the simulation calculation result of the model described in this embodiment, and the dotted line is the experimental test result.

[0086] Figure 8The figure shows the numerical curves of the resonant inductor current value and the resonant capacitor voltage value changing with time. It can be seen that the calculation results of the model proposed in this embodiment are basically consistent with the actual experimental test results. The red lower triangle is the simulation calculation result of this model, and the blue solid line is the experimental test result. Only at certain switching moments does the experimental waveform oscillate, resulting in poor waveform overlap. This is due to parameter measurement errors and parasitic parameters of the experimental platform, which lead to inconsistencies between the resonant parameters of the model and the experiment, ultimately causing the resonant frequency calculated by the model to be slightly lower than the resonant frequency of the experimental waveform.

[0087] Furthermore, the computation time of the model described in this embodiment was compared with that of commercial simulation software. All simulation tools used a discrete-time fixed-step solver with the same circuit configuration and relative error. The comparison results are shown in the table below. It can be seen that the generalized steady-state analysis model proposed in this embodiment, due to its analytical expression, is more than 100 times faster than the simulation software.

[0088] Table 1

[0089]

[0090] In summary, the present invention establishes a generalized steady-state analysis model through two-port network theory and harmonic impedance superposition, improving its versatility. This model is applicable to all passive and switching networks of all orders and can describe most topologies and dual-active modulation methods. Furthermore, the model provides analytical expressions, resulting in fast solution speeds. Furthermore, the use of frequency-domain extended harmonic analysis allows for adjustable computational accuracy. Furthermore, the model maintains a certain level of accuracy, accurately calculating how resonant current, voltage, and transmitted power change with switching frequency and phase shift angle.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for constructing a generalized steady-state analysis model for IBDC topology and modulation strategy analysis, characterized in that: The method includes: S1. Generate a corresponding equivalent circuit based on the electrical parameters between the components of the IBDC circuit structure; S2. Based on the impedance characteristics of the passive network, each passive network is represented by a unified impedance network; S3. Based on the electrical characteristics of the ports of the switch network, each switch network is represented by a unified analytical expression; S4. Based on the equivalent circuit and circuit analysis theory of IBDC, the analytical expressions of voltage, current and transmission power are calculated to construct a generalized steady-state analysis model of IBDC.

2. The method according to claim 1, characterized in that In step S1, the IBDC circuit structure is first converted into a generalized topology structure, which includes input and output ports, and the input and output ports are coupled through a passive network and a switch network; the switch network includes a primary-side switch network at the input port and a secondary-side switch network at the output port; the passive network includes a primary-side resonant network, a secondary-side resonant network and a high-frequency transformer between the two resonant networks; and then an equivalent circuit model is generated based on the generalized topology structure.

3. The method according to claim 2, characterized in that Generating an equivalent circuit model according to the generalized topology includes defining the primary side switching network as a voltage source V p (t), the secondary side switching network is simplified to a voltage source V s (t), and define the equivalent currents of the primary and secondary side switching networks as i p (t) and i s (t); the impedance of the primary side switching network is expressed as Z 11 and Z 12 , the impedance of the secondary side switching network is expressed as Z 21 and Z 22 In this generalized topology, the impedance is mainly composed of reactance, so the primary side switch network reactance X 11 and X 12 and the secondary side switching network reactance X 21 and X 22 ; The equivalent circuit model is expressed as:

4. The method according to claim 3, characterized in that According to the impedance characteristics of the passive network, each passive network is represented by an impedance network of a unified form, and the impedance network includes two horizontal resonant branches and three vertical resonant branches. The reactance values ​​of the horizontal resonant branches and the reactance values ​​of the vertical resonant branches corresponding to different passive networks are different. If a resonant device is missing in a resonant branch, the reactance value of the corresponding horizontal resonant branch is 0, and the reactance value of the vertical resonant branch tends to infinity.

5. The method according to claim 4, characterized in that According to the electrical characteristics of the switch network ports, the switch network is represented by a unified analytical expression. A multi-level pulse waveform is used to represent the AC link voltage of the switch network. After discrete Fourier transform, a unified analytical expression of the switch network is obtained: Where V p (t) and V s (t) represents the AC link voltage of the primary-side switching network and the secondary-side switching network, respectively. α1, β1, α2, and β2 represent the internal phase shift angles. N represents the transformer turns ratio. ω S represents the angular frequency, and n represents the harmonic number.

6. The method according to claim 5, characterized in that According to the IBDC equivalent circuit model, the analytical expression of the switching network and the impedance network, the KCL and KVL laws are used to calculate the voltage and current vector expressions of the primary-side switching network. Based on the voltage and current vector expressions of the primary-side switching network, the analytical expression of the IBDC transmission power within one switching cycle is obtained.

7. The method according to claim 6, characterized in that After describing the specific passive network circuit topology in a unified form as an impedance network, the impedance network is decomposed into two independent sub-circuits corresponding to the primary side and the secondary side according to the circuit superposition principle, wherein the primary side independent sub-circuit includes a primary side voltage source, two horizontal resonant branches and two vertical resonant branches, and the secondary side independent sub-circuit includes a secondary side voltage source, two horizontal resonant branches and two vertical resonant branches; According to the discrete Fourier transform expression of the AC link voltage and the total impedance of the primary and secondary side switching networks, the primary side current i is obtained: p (t) and the secondary side current i s (t); Based on the specific passive network circuit topology, the impedance of each resonant branch in the impedance network is known. Therefore, the current expression of each resonant branch is obtained by solving the KCL and KVL laws: Where A p 、B p 、A S 、B S is the corresponding coefficient: The primary side voltage and current vector expressions obtained based on the discrete Fourier transform expression of the primary side voltage and the primary side current expression are: Where, Denote the primary side voltage vector and current vector respectively; according to the primary side voltage and current vector, the IBDC transmission power within one switching cycle is obtained: Where, represents the external phase shift angle between the primary and secondary sides; V p,rms , I p,rms Represent the effective values ​​of primary side voltage and current respectively; Indicates voltage V p (t) and current i p (t) is the phase angle between them.

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