DC-DC converter construction method based on graph theory

Abstract

The invention discloses a graph theory-based DC-DC converter construction method. The method comprises the following steps of calculating a feasible solution of an electrical connection state of a DC-DC converter in two modes according to a provided voltage gain expression and an inductance number; converting the feasible solution into an initial circuit diagram of two modes; screening out the condition that the two modal circuit diagrams are not matched; combining the initial circuit diagrams of the two modes to obtain a DC-DC converter without a diode and a switching tube direction; determining the directions of a diode and a switch tube, generating a directional diode and a directional switch tube in the DC-DC converter without the direction of the diode and the direction of the switch tube, and obtaining a new circuit diagram; and screening out circuits which do not meet the electrical characteristics to obtain a final DC-DC converter circuit. According to the invention, the number of switching tubes and diodes in the designed DC-DC converter is reduced through a graph theory method, the control strategy is simplified, and the stability of the converter is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of DC-DC converter topology construction, and particularly relates to a method for constructing a DC-DC converter based on graph theory. Background Art

[0002] With the rapid development of the power electronics field and its in-depth application in various fields, traditional DC-DC converters can no longer meet the current needs. Therefore, it is extremely urgent to construct new DC-DC converters. However, the construction of current DC-DC converters highly depends on manual experience. Such a construction method not only has low efficiency, requires a large amount of labor costs, but also is difficult to guarantee the reliability of the constructed DC-DC converter.

[0003] Although there are already some methods for constructing DC-DC converters, they all have their own defects. For example, for the automatic construction method of DC-DC converters based on loop matrices, this method calculates the two-mode loop matrix using the flux balance design method, and then adds a switching tube to each of the two unique branches in mode 1. Select two non-adjacent nodes and connect a diode in parallel until the number of diodes is the same as that of the switching tubes. Open the switching tubes and short-circuit the diodes, and compare the obtained loop matrix with the given mode 2 loop matrix. If they are the same, record it as the corresponding branch-node relationship matrix, and finally output a non-redundant and normally working DC-DC converter. However, the converter constructed by this method contains two switching tubes and two diodes. Using a larger number of switching tubes and diodes will not only increase the cost, but also make the control strategy complex. Summary of the Invention

[0004] In order to overcome the defects and deficiencies existing in the prior art, the present invention provides a method for constructing a DC-DC converter based on graph theory. The present invention reduces the number of switching tubes and diodes in the designed DC-DC converter through the method of graph theory, thereby reducing the production cost, simplifying the control strategy, and ensuring the stability of the converter.

[0005] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for constructing a DC-DC converter based on graph theory, including the following steps:

[0007] Calculate the feasible solutions of the electrical connection states of the DC-DC converter in mode 1 and mode 2 according to the provided voltage gain expression and the number of inductors;

[0008] Convert the feasible solutions into the initial circuit diagrams of mode 1 and mode 2;

[0009] Screen out the cases where the circuit diagrams of mode 1 and mode 2 do not match;

[0010] Combine the initial circuit diagram of Mode 1 and the initial circuit diagram of Mode 2. Add the branch where the diode is located in the initial circuit of Mode 1. Obtain the connection nodes at both ends of the diode according to the expression form of the solution in Mode 2. Connect the diode in the initial circuit diagram of Mode 1 to obtain a DC-DC converter without the directions of the diode and the switching transistor.

[0011] Determine the directions of the diode and the switching transistor. Generate a diode and a switching transistor with directions in the DC-DC converter without the directions of the diode and the switching transistor to obtain a new circuit diagram.

[0012] Screen out the circuits that do not meet the electrical characteristics to obtain the final DC-DC converter circuit.

[0013] As a preferred technical solution, the calculation steps of the feasible solution include:

[0014] List all the volt-second balance characteristic equations of the inductors, calculate the voltage gain function with parameters, compare it with the input voltage gain expression to obtain a system of equations, and obtain all the feasible solutions of the parameters through the exhaustive method. Exclude the redundant solutions and invalid solutions to obtain the final feasible solution.

[0015] As a preferred technical solution, determine the voltage gain expression as:

[0016]

[0017] where V c2 represents the voltage value of capacitor C2, V s represents the voltage value of the input power supply, and D represents the duty cycle of the switching transistor.

[0018] Assume that the designed DC-DC converter has two inductors. List the volt-second balance characteristic equations of inductor L1 and inductor L2 as:

[0019] ∫v L1 dt = D(α 10 V s + α 11 V C1 + α 12 V C2 ) + D′(β 10 V s + β 11 V C1 + β 12 V C2 ) = 0

[0020] ∫v L2 dt = D(α 20 V S + α 21 V C1 + α22 V C2 ) + D′(β 20 V s + β 21 V C1 + β 22 V C2 ) = 0

[0021] Among them, v L1 , v L2 represent the voltage values of inductor L1 and inductor L2 respectively, D represents the duty cycle, D′ = 1 - D, V s , V c1 , V c2 represent the voltage values of the voltage source, capacitor C1, and capacitor C2 respectively. Let Vs = V c0 , α mn = 0 indicates that capacitor n does not exist in the loop of inductor m in mode 1, α mn = 1 indicates that capacitor n exists in the loop of inductor m in mode 1 and has the same polarity direction as inductor m, α mn = -1 indicates that capacitor n exists in the loop of inductor m in mode 1 and has the opposite polarity direction to inductor m, β mn = 0 indicates that capacitor n does not exist in the loop of inductor m in mode 2, β mn = 1 indicates that capacitor n exists in the loop of inductor m in mode 2 and has the same polarity direction as inductor m, β mn = -1 indicates that capacitor n exists in the loop of inductor m in mode 2 and has the opposite polarity direction to inductor m, m = 1, 2, n = 0, 1, 2;

[0022] According to the volt - second balance characteristic equations of inductor L1 and inductor L2, the voltage gain function is solved by simultaneous equations:

[0023]

[0024] Among them,

[0025] M0 = β 22 β 11 - β 12 β 21 ;

[0026] M1 = (α 22 β 11 - α 21 β 12 ) + (α 11 β 22 - α 12 β 21 ) - 2(β 22 β 11 - β 12 β 21 );

[0027] M2 = (α1α 11 -α 12 α 21 ) + (α 21 β 21 -α 22 β 11 ) + (α 12 β 21 -α 11 β 22 ) + (β 11 β 22 -β 22 β 12 );

[0028] N0 = β 21 β 10 -β 11 β 20 ;

[0029] N1 = (α 21 β 10 -α 20 β 11 ) + (α 10 β 21 -α 11 β 20 ) - 2(β 21 β 10 -β 11 β 20 );

[0030] N2 = (α 10 α 21 -α 11 α 20 ) + (α 20 β 11 -α 21 β 10 ) + (α 11 β 20 -α 10 β 21 ) + (β 21 β 10 -β 11 β 20 )

[0031] List equations by comparing the coefficients of the two voltage gain expressions, and calculate all the initial solutions using the exhaustive method.

[0032] As a preferred technical solution, after excluding redundant solutions and invalid solutions, the final feasible solutions are obtained, specifically including:

[0033] The redundant solutions include the solutions for the cases where the inductor polarity is reversed, the inductor numbers are interchanged, and the capacitor polarity outside the output capacitor is reversed;

[0034] The invalid solutions include the solutions for the cases that do not conform to the basic principles of graph theory.

[0035] As a preferred technical solution, the feasible solutions are expressed as:

[0036] [α i0 ,α 11 ,α 12 ,α 20 ,α 21 ,α 22 ,β 10 ,β 11 ,β 12 ,β 20 ,β 21 ,β 22

[0037] =[1,0,0,0,-1,1,1,-1,0,0,0,1]

[0038] Among them, the parameters α and β respectively represent the connection conditions of the circuit diagrams in Mode 1 and Mode 2. The first subscript represents the information of which inductor forms a loop for this solution, and the second subscript represents the connection relationship of which capacitor in the inductor loop. The value of the parameter being 0 indicates that the component corresponding to this parameter is not in the corresponding inductor loop, and the value of the parameter being 1 or -1 indicates that the component corresponding to the parameter is in the corresponding inductor loop, in the same or opposite direction as the positive direction of the inductor.

[0039] As a preferred technical solution, the feasible solutions are transformed into the initial circuit diagrams in Mode 1 and Mode 2, specifically including:

[0040] According to whether the parameters of the same component in each inductor loop in the feasible solution are all non-zero, the common part of the inductor loops is obtained. If the product value of the two is 0, the corresponding capacitor is not in the common part of the inductor loop; if the product value of the two is not 0, the corresponding capacitor is in the common part of the inductor loop;

[0041] Place the inductor L1 in Mode 1 and the components unique to its loop on the left branch of the L1 loop, and place the common components of inductor L1 and inductor L2 on the right branch of the L1 loop. Use the branch where the common component is located as the left branch of the L2 loop, and place the components unique to the L2 loop on the right branch of the L2 loop to obtain the initial circuit diagram of Mode 1;

[0042] ​Place the components specific to the inductor L1 and its circuit in Mode 2 on the left branch, and place the common components of inductors L1 and L2 on the right branch of the circuit diagram. Use the branch where the common components are located as the left branch of the inductor L2 circuit, and place the specific components of the inductor L2 circuit on the right branch of the L2 circuit to obtain the initial circuit diagram of Mode 2.

[0043] As a preferred technical solution, screen out the cases where the circuit diagrams of Mode 1 and Mode 2 do not match, specifically including:

[0044] Check whether there are unused components in the circuit diagram of Mode 1. If there are, keep the result; if not, proceed to the next screening step.

[0045] Check whether the components remaining after removing the common components of inductors L1 and L2 in Mode 1 are the same as the components used in Mode 2. If they are the same, proceed to the next screening step; if they are different, screen out this solution.

[0046] Put the specific components of the inductor L1 circuit in Mode 1 into a list, denoted as List 11 , and put the specific components of the inductor L2 circuit in Mode 1 into a list, denoted as List 12 ;

[0047] Put the specific components of the inductor L1 circuit in Mode 2 into a list, denoted as List 21 , and put the specific components of the inductor L2 circuit in Mode 2 into a list, denoted as List 22 ;

[0048] Extract the lists in List 11 and List 12 that contain only one element. If the list corresponding to the inductor in the list of Mode 2 contains the elements in Mode 1, keep it; otherwise, screen it out.

[0049] As a preferred technical solution, combine the initial circuit diagram of Mode 1 and the initial circuit diagram of Mode 2, specifically including:

[0050] Obtain the connection conditions corresponding to the two endpoints of the branch where the diode is located in the Mode 2 circuit diagram, and record the components connected to each endpoint.

[0051] According to the corresponding connection relationship, add the branch where the diode is located to the circuit diagram of Mode 1. During the process of adding the branch where the diode is located, swap the positions of the components on one branch to obtain the nodes that satisfy the connection relationship of the diode branch endpoints in Mode 2. After obtaining the corresponding nodes, add the branch where the diode is located in the initial circuit of Mode 2.

[0052] As a preferred technical solution, determine the directions of the diode and the switch tube, specifically including:

[0053] Determine the direction of the diode according to the following principles:

[0054] For the inductor and the switch tube that belong to the same specific branch or the common branch of a certain loop as the power supply, their directions are the same as that of the power supply;

[0055] The currents of inductor L1 and inductor L2 remain in the same direction in two modes, and the currents of capacitor C1 remain in opposite directions in two modes;

[0056] Avoid short - circuit of the power supply through the switch tube or the diode.

[0057] As a preferred technical solution, screen out the circuits that do not meet the electrical characteristics to obtain the final DC - DC converter circuit, specifically including:

[0058] Open - circuit the diode to obtain the equivalent circuit of Mode 1, calculate the potentials of the nodes at both ends of the diode. If there is a positive potential difference, the diode conducts simultaneously with the switch tube in Mode 1, and screen out this circuit.

[0059] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0060] (1) Through the technical solution of adding the switch tube on the common branch of the inductor loop when adding the switch tube, the present invention solves the problem in the prior art that the switch tube is added on a non - common branch, increasing the number of components, and achieves the technical effects of reducing the number of switch tubes and diodes, reducing costs, and simplifying control.

[0061] (2) By the technical solution of determining the connection nodes according to the feasible solutions of Mode 2 when adding the diode, the present invention solves the technical problem that the original method randomly selects nodes for connection and then screens, resulting in excessive computing power consumption, and achieves the technical effects of simplifying the screening process and improving the construction efficiency.

[0062] (3) By realizing the construction of the converter from the perspective of graph theory, the present invention solves the technical problems of narrow application range and small number of constructed structures in the original construction method, and achieves the technical effects of a complete theory and an increased number of constructed structures.

[0063] (4) By designing an algorithm to directly compare the solutions of Mode 1 and Mode 2, the present invention solves the technical problem that the prior art requires multiple complex judgments on whether the solutions of the two are compatible, and achieves the technical effect of only one step to screen out the feasible solutions that do not meet the requirements, thus simplifying the design process. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic flow chart of the DC - DC converter construction method based on graph theory of the present invention;

[0065] Figure 2 Schematic diagram of the circuit structure of modes 1 and 2 of the DC-DC converter of the present invention;

[0066] Figure 3 Schematic diagram of the circuit of mode 1 of the DC-DC converter of the present invention after ignoring the switching tube;

[0067] Figure 4 Initial circuit schematic diagram of mode 1 of the DC-DC converter of the present invention;

[0068] Figure 5 Schematic diagram of the circuit of mode 2 of the DC-DC converter of the present invention after ignoring the diode;

[0069] Figure 6 Initial circuit schematic diagram of mode 2 of the DC-DC converter of the present invention;

[0070] Figure 7 Circuit diagram of the branch where the diode is located in mode 2 of the DC-DC converter of the present invention after adding mode 1;

[0071] Figure 8 Schematic diagram of the circuit of the DC-DC converter of the present invention. Detailed implementation manner

[0072] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0073] As Figure 1 shown, this embodiment provides a method for constructing a DC-DC converter based on graph theory, including the following steps:

[0074] S1: Calculate the feasible solutions of the electrical connection states in two modes of the DC-DC converter according to the provided voltage gain expression and the number of inductors. Among them, mode 1 represents the situation where the switching tube in the DC-DC converter is short-circuited and the diode is open-circuited, and mode 2 represents the situation where the switching tube in the DC-DC converter is open-circuited and the diode is short-circuited. After excluding redundant solutions and invalid solutions, effective solutions are obtained. Among them, redundant solutions mainly exclude the situations where the inductor polarity is reversed, the inductor numbers are interchanged, and the polarity of the capacitors other than the output capacitor is reversed; invalid solutions mainly exclude the situations that do not conform to the basic principles of graph theory.

[0075] In this embodiment, the method for calculating the feasible solutions is as follows: list the volt-second balance characteristic equations of all inductors, then calculate the voltage gain function with parameters and compare it with the input voltage gain expression to obtain a system of equations. The values of the parameters α and β in the volt-second balance characteristic equations can only be selected from [-1, 0, 1], so all feasible solutions of the parameters can be obtained by the exhaustive method.

[0076] In this embodiment, the voltage gain expression is determined as follows:

[0077]

[0078] where V c2 represents the output voltage, i.e., the voltage value of capacitor C2, V s represents the voltage value of the input power supply, and D represents the duty cycle of the switching transistor, that is, within one switching cycle, the ratio of the conduction time of the switching transistor to the entire cycle time.

[0079] Let the designed DC-DC converter have two inductors, and then list the volt-second balance characteristic equations of inductor L1 and inductor L2:

[0080] ∫v bL dt = D(α 10 V s + α 11 V C1 + α 12 V C2 ) + D′(β 10 V s + β 11 V C1 + β 12 V C2 ) = 0

[0081] ∫v L2 dt = D(α 20 V s + α 21 V C1 + α 22 V C2 ) + D′(β 20 V s + β 21 V C1 + β 22 V C2 ) = 0

[0082] where v L1 and v L2 represent the voltage values of inductor L1 and L2 respectively, D represents the duty cycle, D′ = 1 - D, V s , V c1 , and V c2 represent the voltage values of the voltage source, capacitor C1, and V2 respectively. The voltage source is equivalent to capacitor C0, i.e., V s = V c0 . Then α mn = 0 indicates that capacitor n does not exist in the loop of inductor m in mode 1, and α mn= 1 indicates that in Mode 1, capacitor n exists in the loop of inductor m and has the same polarity direction as inductor m, α mn = -1 indicates that in Mode 1, capacitor n exists in the loop of inductor m and has the opposite polarity direction to inductor m. β mn = 0 indicates that in Mode 2, capacitor n does not exist in the loop of inductor m, β mn = 1 indicates that in Mode 2, capacitor n exists in the loop of inductor m and has the same polarity direction as inductor m, β mn = -1 indicates that in Mode 2, capacitor n exists in the loop of inductor m and has the opposite polarity direction to inductor m.

[0083] Based on the volt - second balance characteristic equations of inductor L1 and inductor L2, the voltage gain function is solved by simultaneous equations:

[0084]

[0085] Among them,

[0086] M0 = β 22 β 11 -β 12 β 21 ;

[0087] M1=(α 22 β 11 -α 21 β 12 )+(α 11 β 22 -α 12 β 21 )-2(β 22 β 11 -β 12 β 21 );

[0088] M2=(α1α 11 -α 12 α 21 )+(α 21 β 21 -α 22 β 11 )+(α 12 β 21 -α 11 β 22 )+(β 11 β 22 -β 22 β 12 );

[0089] N0 = β 21 β 10 -β 11 β 20 ;

[0090] N1 = (α 21 β 10 -α 20 β 11 ) + (α 10 β 21 -α 11 β 20 ) - 2(β 21 β 10 -β 11 β 20 );

[0091] N2 = (α 10 α 21 -α 11 α 20 ) + (α 20 β 11 -α 21 β 10 ) + (α 11 β 20 -α 10 β 21 ) + (β 21 β 10 -β 11 β 20 );

[0092] Compare the coefficients of the two voltage gain expressions and list the equations. Since the unknowns can only be -1, 0, 1, an exhaustive method is used here to calculate all the initial solutions.

[0093] Subsequently, the feasible solutions are obtained after excluding redundant solutions and invalid solutions.

[0094] In this embodiment, the case where the inductor polarity is reversed in the redundant solution is that the polarity of inductor L1 is reversed, which means that the directions of all other components in the L1 loop are all taken as the opposite numbers, that is, [α 10 , α 11 , α 12 , β 10 , β 11 , β 12 = -[α 10 , α 11 , α 12 , β 10 , β 11 , β 12 , the polarity of inductor L2 is reversed, that is, the directions of all other components in the L2 loop are all taken as the opposite numbers, that is, [α 20 , α 21 , α 22 , β 20 , β 21 , β 22 = -[α 20 , α21 , α 22 , β 20 , β 21 , β 22 ; The case where the inductor numbers are swapped is that the numbers of inductors L1 and L2 are swapped, that is, the solutions of the two inductors are permuted with each other, i.e., [α 10 , α 11 , α 12 , β 10 , β 11 , β 12 = [α 20 , α 21 , α 22 , β 20 , β 21 , β 22 . The capacitors in the converter are C1 and C2, and the output capacitor is C2. Therefore, the case where the capacitor polarities are reversed is that the polarity of capacitor C1 is reversed, that is, all the solutions corresponding to C1 are taken as the opposite numbers, i.e., [α 11 , α 21 , β 11 , β 21 = -[α 11 , α 21 , β 11 , β 21 . The circuit diagrams of the redundant solutions are all the same, so they need to be excluded.

[0095] The invalid solutions mainly exclude the solutions that do not conform to the basic principles of graph theory. For example, in this embodiment, if the situations of [α 10 , α 11 = [1, 1], [α 20 , α 21 = [1, -1] occur, this means that in mode 1, the directions of the power supply V s in inductor L1 and capacitor C1 are the same, but the directions of the power supply V s in inductor L2 and capacitor C1 are opposite, which makes the directed graphs formed by the two inductor loops unable to be combined. Such a situation must be screened out. Based on this, an algorithm can be designed to exclude this situation. In this embodiment, for the two-inductor DC-DC converter, the exclusion method is: in mode 1 or mode 2, the parameters corresponding to each inductor element are regarded as a vector respectively. If the maximum dimension of the vectors in the vector group is 1, it must be valid; if the maximum dimension of the vectors in the vector group is 2, it is valid when the inner product of the two vectors is not 0; if the maximum dimension of the vectors in the vector group is n (n ≥ 3), it is valid only when the absolute value of the inner product of the vector group is equal to n.

[0096] Here, the feasible solutions are selected as follows:

[0097] [α 10 , α 11 , α12 , α 20 , α 21 , α 22 , β 10 , β 11 , β 12 , β 20 , β 21 , β 22 =

[0098] [1, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 1];

[0099] S2: Convert the feasible solution into the initial circuit diagrams of Mode 1 and Mode 2. The initial circuit diagram in Mode 1 is the case where the switching tube is conducting, the diode is open, the branch where the switching tube is located is retained, and the branch where the diode is located is cut off; the initial circuit diagram in Mode 2 is the case where the switching tube is open, the diode is conducting, the branch where the switching tube is located is cut off, and the branch where the diode is located is retained.

[0100] In this embodiment, the components included in each inductor loop are obtained according to the equation solved in step S1. From S1, it can be seen that for the feasible solution [α 10 , α 11 , α 12 , α 20 , α 21 , α 22 , β 10 , β 11 , β 12 , β 20 , β 21 , β 22 , the parameters α and β respectively represent the connection conditions of the circuit diagrams in Mode 1 and Mode 2. The first subscript indicates the information of which inductor forms the loop for this solution. For example, the first subscript 1 of α1 indicates the connection condition of inductor L1 in Mode 1; the first subscript 1 of β1 indicates the connection condition of inductor L1 in Mode 2. The second subscript indicates which capacitor (here V sThe connection relationship in the inductance loop is regarded as C0). A parameter value of 0 indicates that the component corresponding to the parameter is not in the corresponding inductance loop. A parameter value of 1 or -1 indicates that the component corresponding to the parameter is in the corresponding inductance loop, in the same or opposite direction as the loop direction. Subsequently, based on whether the parameters for the same component in each inductance loop in the feasible solution are all non-zero, that is, whether the product value of the two is non-zero, the common part of the inductance loops is obtained. If the product value of the two is 0, the corresponding capacitor is not in the common part of the inductance loop; if the product value of the two is non-zero, the corresponding capacitor is in the common part of the inductance loop. Subsequently, a circuit diagram of the inductor in mode 1 is made. The inductor L1 and the components unique to its loop are placed on the left branch of the L1 loop. The common components of inductor L1 and inductor L2 are placed on the right branch of the L1 loop. Based on the common branch, the loop of inductor L2 is made, that is, the branch where the common component is located is used as the left branch of the L2 loop, and the components unique to the L2 loop are placed on the right branch of the L2 loop. The complete initial circuit diagram of mode 1 is obtained, and the final circuit diagram structure is as Figure 2 shown. Similarly for mode 2, the inductor L1 and the components unique to its loop are placed on the left branch, the common components of L1 and L2 are placed on the right branch of the circuit diagram, the branch where the common component is located is used as the left branch of the L2 loop, and the components unique to the L2 loop are placed on the right branch of the L2 loop to obtain the complete initial circuit diagram of mode 2.

[0101] Taking the feasible solution as an example, the solution corresponding to inductor L1 in mode 1, that is, the solution with the subscript of parameter α being 1, is [α 10 , α 11 , α 12 = [1, 0, 0]. Knowing that the components corresponding to [α 10 , α 11 , α 12 are [V s , C1, C2] respectively, and only α 10 ≠ 0 among them, so the component connected to inductor L1 in mode 1 is V S . The feasible solution corresponding to inductor L2 is [α 20 , α 21 , α 22 = [0, -1, 1], where α 21 , α 22 ≠ 0, so the components connected to inductor L2 are C1 and C2. In the solutions of the two, α 10 α 20 = 0, α 11 α 21 = 0, α 13 α 23= 0, so it can be known that there are no common components in the inductor L1 loop and the L2 loop in Mode 1. Therefore, their common branch is a wire. Place the power supply Vs on the branch where the left inductor L1 is located, and place the capacitors C1 and C2 on the branch where the right inductor L2 is located. Draw the initial circuit diagram of Mode 1 without the switching tubes as shown in Figure 3 shown. Subsequently, add a non-directional switching tube to the common branch, and finally obtain the initial circuit diagram of Mode 1 as shown in Figure 4 shown. After obtaining the circuit diagram, label each node on the circuit diagram sequentially with integers starting from 1.

[0102] The solution corresponding to the inductor L1 in Mode 2, that is, the solution with the subscript of parameter β being 1, is [β 10 , β 11 , β 12 =

[0103] [1, -1, 0]. Knowing that the components corresponding to [β 10 , β 11 , β 12 are [V s , C1, C2] respectively, and all solutions are not zero. Therefore, the components connected to the inductor L1 in Mode 2 are V S , C1, and C2. The feasible solution corresponding to the inductor L2 is [β 20 , β 21 , β 22 = [0, 0, 1], where β 22 ≠ 0. Therefore, the component connected to the inductor L2 is C2. In the solutions of both, β 10 β 20 = 0, β 11 β 21 = 0, β 12 β 22 = 0. So it can be known that there are no common components in the inductor L1 loop and the L2 loop in Mode 2. Draw the initial circuit diagram of Mode 2 without the diodes as shown in Figure 5 shown. Subsequently, add a non-directional diode to the common branch, and finally obtain the initial circuit diagram of Mode 2 as shown in Figure 6 shown. After obtaining the circuit diagram, label each node on the circuit diagram sequentially with integers starting from 1.

[0104] S3: Screen out the cases where the circuit diagram of Mode 1 does not match that of Mode 2. The non - matching cases mean that the circuit diagram of Mode 2 cannot be obtained by adding diodes to the circuit diagram of Mode 1. For a 2 - inductor DC - DC converter, in the first step, check whether there are unused components in the circuit diagram of Mode 1. If there are, keep the result; if not, proceed to the next screening step. In the second step, check whether the components remaining after removing the common components of inductors L1 and L2 in Mode 1 are the same as those used in Mode 2. If they are the same, proceed to the next screening step; if different, screen out this solution. In the third step, put the unique components of the inductor L1 loop in Mode 1 into a list, denoted as List 11 , put the unique components of the inductor L2 loop in Mode 1 into a list, denoted as List 12 . Put the unique components of the inductor L1 loop in Mode 2 into a list, denoted as List 21 , put the unique components of the inductor L2 loop in Mode 2 into a list, denoted as List 22 . Extract the lists in List 11 and List 12 that contain only one element. If the list corresponding to the inductor in Mode 2 contains the elements in Mode 1, keep it; otherwise, screen it out.

[0105] In this embodiment, in the first - step screening, the solution of Mode 1 is [α 10 , α 11 , α 12 , α 20 , α 21 , α 22 = [1, 0, 0, 0, - 1, 1]. According to S2, it can be known that the inductor L1 loop contains Vs, and the inductor L2 loop contains C1 and C2. Therefore, all components are in the circuit diagram of Mode 1, and proceed to the second - step screening. Inductors L1 and L2 have no common components, so after removal, the remaining components are Vs, C1, and C2. The solution of Mode 2 is [β 10 , β 11 , β 12 , β 20 , β 21 , β 22 = [1, - 1, 0, 0, 0, 1]. From step S2, it can be known that Mode 2 contains components Vs, C1, and C2. After removing the common - part components in Mode 1, the components contained in Mode 1 are the same as those in Mode 2, and proceed to the third - step screening. According to S2, the unique components of the L1 loop in Mode 1 are [Vs], and the unique components of the L2 loop are [C1, C2]. Therefore, List 11 = [Vs], List 12= [C1, C2]. The unique components of the L1 circuit in Mode 2 are [Vs, C1], and the unique component of the L2 circuit is [C2]. Thus, List 11 = [Vs, C1], List 12 = [C2]. The list with only one element in Mode 1 is List 11 = [Vs], and its element is Vs. The corresponding inductor L1 in Mode 2 corresponds to the list List 11 = [Vs, C1], which contains the element Vs, so the result is retained.

[0106] S4: Combine the initial circuit of Mode 1 and the initial circuit of Mode 2 to obtain a DC-DC converter without the directions of diodes and switching tubes. The combination method is to add the branch where the diode is located in Mode 2 to the basis of the initial circuit of Mode 1. According to the expression form of the solution of Mode 2, obtain the connection nodes at both ends of the diode, and connect the diode in the initial circuit diagram of Mode 1 to obtain the corresponding circuit diagram; The first step is to obtain the connection situation corresponding to both ends of the branch where the diode is located in the circuit diagram of Mode 2, that is, record the components connected to each end point. The second step is to add the branch where the diode is located to the circuit diagram of Mode 1 according to the corresponding connection relationship. Since the connection relationship corresponding to the inductor loop remains unchanged, the volt-second balance characteristic equation of the inductor will not change. Therefore, in the process of adding the branch where the diode is located in the second step, the positions of the components on a branch can be interchanged to match the connection relationship corresponding to the end points.

[0107] In this embodiment, from Figure 6 it is known that the two end points of the branch where the diode is located are 2, 4. The components connected to end point 2 are capacitor C1 and inductor L2; the components connected to end point 4 are power supply Vs and capacitor C2. Then find the corresponding nodes in the initial circuit of Mode 1. The positions of C1, L2, and C2 in the initial circuit of Mode 1 can be interchanged, and the positions of L1 and Vs can also be interchanged because interchanging the positions does not change the corresponding connection relationship. In the initial circuit diagram of Mode 1, the node 2 between C1 and L2 and the node 4 between Vs and C2 can be directly found. If they cannot be directly found here, the positions of the components can be exchanged to obtain the nodes that satisfy the connection relationship of the diode branch end points in Mode 2. After obtaining the corresponding nodes, as Figure 7 shown, add the branch where the diode is located in the initial circuit of Mode 2 between nodes 2 and 4.

[0108] S5: Determine the directions of the diode and the switching tube, and draw the diode and the switching tube with directions in the DC-DC converter without the directions of the diode and the switching tube to obtain a new circuit diagram;

[0109] In this embodiment, the direction of the diode is determined according to the following principle:

[0110] (1) The inductor and the switching transistor that belong to a specific branch or a common branch of the same loop as the power supply have the same direction as the power supply;

[0111] (2) The currents of inductors L1 and L2 must maintain the same direction in the two modes, and the currents of capacitor C1 must maintain the opposite direction in the two modes;

[0112] (3) Avoid short - circuiting the power supply through the switching transistor or diode;

[0113] It is stipulated that [m, n] represents that the positive direction of a component is at node m and the negative direction is at node n. As shown in, in mode 1, since the switching transistor and the power supply are in the same loop and the direction of the power supply is [4, 1], the sequence relationship of the loop with the power supply direction as positive is 4 → 1 → 3 → 4. Therefore, according to rule 1, the direction of the switching transistor is [3, 4], and it can be known that the current direction of L1 is from [1, 3]. According to rule 2, the currents of inductors L1 and L2 must maintain the same direction in mode 1. According to the direction of the switching transistor, the sequence relationship of the inductor L2 loop with the switching transistor direction as positive is 3 → 4 → 5 → 2 → 3. So the current direction of L2 is [5, 2], and the current direction of C1 is [2, 3]. According to rule 2, the currents of capacitor C1 must maintain the opposite direction in the two modes. As shown in, the current direction of C1 in mode 2 is [3, 2]. So at this time, the sequence relationship of the inductor L1 loop with capacitor C1 as the positive direction is 1 → 3 → 2 → 4 → 1, and the direction of the diode is [2, 4]. Thus, the circuit diagram shown in is obtained. Figure 4 shown, in mode 1, since the switching transistor and the power supply are in the same loop and the direction of the power supply is [4, 1], the sequence relationship of the loop with the power supply direction as positive is 4 → 1 → 3 → 4. Therefore, according to rule 1, the direction of the switching transistor is [3, 4], and it can be known that the current direction of L1 is from [1, 3]. According to rule 2, the currents of inductors L1 and L2 must maintain the same direction in mode 1. According to the direction of the switching transistor, the sequence relationship of the inductor L2 loop with the switching transistor direction as positive is 3 → 4 → 5 → 2 → 3. So the current direction of L2 is [5, 2], and the current direction of C1 is [2, 3]. According to rule 2, the currents of capacitor C1 must maintain the opposite direction in the two modes. As shown in, the current direction of C1 in mode 2 is [3, 2]. So at this time, the sequence relationship of the inductor L1 loop with capacitor C1 as the positive direction is 1 → 3 → 2 → 4 → 1, and the direction of the diode is [2, 4]. Thus, the circuit diagram shown in is obtained. Figure 6 shown, the current direction of C1 in mode 2 is [3, 2]. So at this time, the sequence relationship of the inductor L1 loop with capacitor C1 as the positive direction is 1 → 3 → 2 → 4 → 1, and the direction of the diode is [2, 4]. Thus, the circuit diagram shown in is obtained. Figure 8 shown circuit diagram.

[0114] S6: Screen out the circuits that do not meet the electrical characteristics, and finally obtain the DC - DC converter circuit that can work normally and corresponds to the effective solution.

[0115] In this embodiment, open - circuit the diode to obtain the equivalent circuit of mode 1, calculate the potentials of the nodes at both ends of the diode. If there is a positive potential difference, the diode conducts simultaneously with the switching transistor in mode 1, and screen out this circuit.

[0116] Figure 8 In, open - circuit the diode, and the calculated potential at both ends of the diode is - V c1 < 0, which meets the electrical characteristics. Therefore, this circuit is the DC - DC converter corresponding to the voltage gain expression.

[0117] The present invention designs a DC-DC converter with only one switching tube and one diode through a graph theory-based method. By means of the graph theory method, the switching tube is added to the common part of the two inductor circuits in mode 1, so that only one additional switching tube is required. According to the knowledge of graph theory, the number of switching tubes is the same as the number of diodes, so only one diode is also needed. This not only reduces the production cost by reducing the number of switching tubes and diodes, but also simplifies the control strategy of the DC-DC converter by reducing the number of switching tubes, thus ensuring the reliable operation of the DC-DC converter.

[0118] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A construction method of a DC-DC converter based on graph theory, characterized in that, Including the following steps: Calculating the feasible solutions of the electrical connection states of the DC-DC converter in Mode 1 and Mode 2 according to the provided voltage gain expression and the number of inductors; Converting the feasible solutions into the initial circuit diagrams of Mode 1 and Mode 2; Eliminating the cases where the circuit diagrams of Mode 1 and Mode 2 do not match; Combining the initial circuit diagram of Mode 1 and the initial circuit diagram of Mode 2, adding the branch where the diode is located in Mode 2 based on the initial circuit of Mode 1, obtaining the connection nodes at both ends of the diode according to the expression form of the solution in Mode 2, and connecting the diode in the initial circuit diagram of Mode 1 to obtain a DC-DC converter without the directions of the diode and the switching tube; Determining the directions of the diode and the switching tube, generating the diode and the switching tube with directions in the DC-DC converter without the directions of the diode and the switching tube to obtain a new circuit diagram; Eliminating the circuits that do not meet the electrical characteristics to obtain the final DC-DC converter circuit.

2. The method for constructing a DC-DC converter based on graph theory according to claim 1, wherein The calculation steps of the feasible solutions include: Listing the volt-second balance characteristic equations of all inductors, calculating the voltage gain function with parameters, comparing it with the input voltage gain expression to obtain a system of equations, and obtaining all the feasible solutions of the parameters by the exhaustive method. After excluding the redundant solutions and invalid solutions, the final feasible solutions are obtained.

3. The method for constructing a DC-DC converter based on graph theory according to claim 2, wherein Determining the voltage gain expression as: Among them, V c2 represents the voltage value of capacitor C2, and V s represents the voltage value of the input power supply, and D represents the duty cycle of the switching transistor; Assuming that the designed DC-DC converter has two inductors, and listing the volt-second balance characteristic equations of inductor L1 and inductor L2 as: ∫v L1 dt = D(α 10 V s + α 11 V C1 + α 12 V C2 ) + D′(β 10 V s + β 11 V C1 + β 12 V C2 ) = 0 ∫v L2 dt = D(α 20 V s + α 21 V C1 + α 22 V C2 ) + D′(β 20 V s + β 21 V C1 + β 22 V C2 ) = 0 Among them, v L1 and v L2 represent the voltage values of inductors L1 and L2 respectively, D represents the duty cycle, D′ = 1 - D, V s and V c1 and V c2 represent the voltage values of the voltage source, capacitor C1, and C2 respectively. α mn = 0 means that capacitor n does not exist in the loop of inductor m in mode 1, α mn = 1 means that capacitor n exists in the loop of inductor m in mode 1 and has the same polarity direction as inductor m, α mn = -1 means that capacitor n exists in the loop of inductor m in mode 1 and has the opposite polarity direction to inductor m. β mn = 0 means that capacitor n does not exist in the loop of inductor m in mode 2, β mn = 1 means that capacitor n exists in the loop of inductor m in mode 2 and has the same polarity direction as inductor m, β mn = -1 means that capacitor n exists in the loop of inductor m in mode 2 and has the opposite polarity direction to inductor m, m = 1, 2, n = 0, 1, 2; Solving the voltage gain function by simultaneously solving the volt-second balance characteristic equations of inductor L1 and inductor L2: Where, M0＝β 22 β 11 -β 12 β 21 ； M1＝(α 22 β 11 -α 21 β 12 )+(α 11 β 22 -α 12 β 21 )-2(β 22 β 11 -β 12 β 21 )； M2＝(α1α 11 -α 12 α 21 )+(α 21 β 21 -α 22 β 11 )+(α 12 β 21 -α 11 β 22 )+(β 11 β 22 -β 22 β 12 )； N0＝β 21 β 10 -β 11 β 20 ； N1＝(α 21 β 10 -α 20 β 11 )+(α 10 β 21 -α 11 β 20 )-2(β 21 β 10 -β 11 β 20 )； N2＝(α 10 α 21 -α 11 α 20 )+(α 20 β 11 -α 21 β 10 )+(α 11 β 20 -α 10 β 21 )+(β 21 β 10 -β 11 β 20 ) Comparing the coefficients of the two voltage gain expressions to list equations, and calculating all the initial solutions by the exhaustive method.

4. The method for constructing a DC-DC converter based on graph theory according to claim 2, wherein, After excluding the redundant solutions and invalid solutions, the final feasible solutions are obtained, specifically including: The redundant solutions include the solutions in the cases where the inductor polarities are reversed, the inductor numbers are interchanged, and the polarities of the capacitors other than the output capacitor are reversed; The invalid solutions include the solutions in the cases that do not conform to the basic principles of graph theory.

5. The method for constructing a DC-DC converter based on graph theory according to claim 1, characterized in that The feasible solutions are expressed as: [α 10 ,α 11 ,α 12 ,α 20 ,α 21 ,α 22 ,β 10 ,β 11 ,β 12 ,β 20 ,β 21 ,β 22 ] ＝[1,0,0,0,-1,1,1,-1,0,0,0,1] Where, the parameters α and β respectively represent the connection conditions of the circuit diagrams in Mode 1 and Mode 2. The first subscript represents the information of which inductor forms the loop for this solution, and the second subscript represents the connection relationship of which capacitor in the inductor loop. The value of the parameter being 0 means that the component corresponding to the parameter is not in the corresponding inductor loop, and the values of the parameter being 1 and -1 mean that the component corresponding to the parameter is in the corresponding inductor loop, the same as or opposite to the positive direction of the inductor.

6. The method for constructing a DC-DC converter based on graph theory according to claim 5, characterized in that Converting the feasible solutions into the initial circuit diagrams in Mode 1 and Mode 2, specifically including: According to whether the parameters of the same component in each inductor loop in the feasible solutions are all non-zero, obtaining the common part of the inductor loops. If the product value of the two is 0, the corresponding capacitor is not in the common part of the inductor loops. If the product value of the two is not 0, the corresponding capacitor is in the common part of the inductor loops; Place the components unique to the inductor L1 and its circuit in Mode 1 on the left branch of the L1 circuit. Place the common components of inductors L1 and L2 on the right branch of the L1 circuit. Use the branch where the common components are located as the left branch of the L2 circuit. Place the unique components of the L2 circuit on the right branch of the L2 circuit to obtain the initial circuit diagram of Mode 1. Place the components unique to the inductor L1 and its circuit in Mode 2 on the left branch. Place the common components of L1 and L2 on the right branch of the circuit diagram. Use the branch where the common components are located as the left branch of the L2 circuit. Place the unique components of the L2 circuit on the right branch of the L2 circuit to obtain the initial circuit diagram of Mode 2.

7. The method for constructing a DC-DC converter based on graph theory according to claim 1, wherein Screen out the mismatches between the circuit diagrams of Mode 1 and Mode 2, specifically including: Check if there are any unused components in the circuit diagram of Mode 1. If there are, keep the result; if not, proceed to the next screening step. Check if the components remaining after removing the common components of inductors L1 and L2 in Mode 1 are the same as the components used in Mode 2. If they are the same, proceed to the next screening step; if they are different, screen out this solution. Put the unique components of the inductor L1 circuit in mode 1 into a list, denoted as List 11 , put the unique components of the inductor L2 circuit in mode 1 into a list, denoted as List 12 ; Put the unique components of the inductor L1 circuit in mode 2 into a list, denoted as List 21 , put the unique components of the inductor L2 circuit in mode 2 into a list, denoted as List 22 ; Extract the List 11 and the List 12 containing only one element. If the list corresponding to the inductor in Mode 2 contains the elements in Mode 1, keep it; otherwise, filter it out.

8. The method for constructing a DC-DC converter based on graph theory according to claim 1, characterized in that, Combine the initial circuit diagram of Mode 1 and the initial circuit diagram of Mode 2, specifically including: Obtain the connection conditions corresponding to the two endpoints of the branch where the diode is located in the Mode 2 circuit diagram, and record the components connected to each endpoint. Add the branch where the diode is located to the circuit diagram of Mode 1 according to the corresponding connection relationship. During the process of adding the branch where the diode is located, swap the positions of the components on one branch to obtain the nodes that satisfy the connection relationship of the diode branch endpoints in Mode 2. After obtaining the corresponding nodes, add the branch where the diode is located in the initial circuit of Mode 2.

9. The method for constructing a DC-DC converter based on graph theory according to claim 1, wherein Determine the directions of the diode and the switching transistor, specifically including: Determine the direction of the diode according to the following principles: For inductors and switching transistors that belong to a unique branch or a common branch of the same circuit as the power supply, their directions are the same as the power supply. The currents of inductor L1 and inductor L2 remain in the same direction in the two modes, and the currents of capacitor C1 remain in opposite directions in the two modes. Avoid short - circuiting the power supply through the switching transistor or the diode.

10. The method for constructing a DC-DC converter based on graph theory according to claim 1, characterized in that, Screen out the circuits that do not meet the electrical characteristics to obtain the final DC - DC converter circuit, specifically including: Open - circuit the diode to obtain the equivalent circuit of Mode 1. Calculate the potentials of the nodes at both ends of the diode. If there is a positive potential difference, the diode and the switching transistor are conducting simultaneously in Mode 1, and screen out this circuit.

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