CN112163302B - Construction method of non-isomorphic graph for single-switch DC converter based on vertex prime degree - Google Patents

Abstract

The invention discloses a method for constructing a non-isomorphic graph of a single-switch DC converter based on the prime degree of vertices. The comprehensive influence of the quantity and edge type on the transformer structure is converted into the prime degree of vertices; the vertices are screened by using the filter conditions of vertices with different prime degrees, and the filters of vertices with the same prime degree but different prime degrees of adjacent vertices. Construct a new edge from the vertex; filter the edge by using the filter condition that the newly formed edge does not exist in the graph, and add the filtered edge into the graph; use the filter condition that the newly added edge is not the last edge to loop through the above process to obtain all Non-isomorphic graphs of topology. This method can be used to construct non-isomorphic graphs of all converter topologies with a given edge type and the number of each edge type, and can be applied to the topology initialization search of programmable DC converters to improve the operating efficiency of the algorithm.

Description

Construction method of non-isomorphic graph for single-switch DC converter based on vertex prime degree

technical field

The invention relates to the technical field of power electronics topology design, in particular to a method for constructing a non-isomorphic graph of a single-switch DC converter based on the vertex prime degree.

Background technique

Non-isomorphic graphs are graphs with the same structural parameters (number of vertices, edge types, and number of each edge type), but the connections of edges are different. It includes graphs with all different structures, so in mechanical design, electrical It has wide application value in network topology design, computer vision processing, pattern recognition and other fields.

The problem of non-isomorphic graphs is one of many difficult problems in graph theory. At present, most of the research is aimed at the identification methods of non-isomorphic graphs, mainly including: vertex order exchange method, vertex degree sequence method, and search-based algorithms. These methods study the judgment of graphs from different angles, and can reflect their respective advantages in the judgment process. But at the same time, there are also shortcomings, either the method can only be judged for the franchise graph, or the method is slow in judging. Moreover, the above-mentioned methods are all for discriminating non-isomorphic graphs for a given graph, and cannot realize the construction of non-isomorphic graphs. Therefore, it is necessary to propose a method for constructing non-isomorphic graphs.

Contents of the invention

The present invention aims to solve one of the technical problems in the related art at least to a certain extent.

For this reason, the object of the present invention is to propose a method for constructing a non-isomorphic graph of a single-switch DC converter based on the prime degree of a vertex, which can be used to build a single-switch non-isolated DC converter with a given edge type and the number of each edge type Non-isomorphic graphs of all topologies, and can be applied to the initialization search of programmable DC converter topologies to improve the operating efficiency of algorithms.

In order to achieve the above purpose, the embodiment of the present invention proposes a single-switch DC converter non-isomorphic graph construction method based on vertex prime degree, including the following steps: setting the vertices, edge types and each edge type of the DC converter topology graph The number of the number of vertices connected to the converter structure of the number of edges into a prime number, and generate the first table; the edge type of the vertices connected to the impact of the transformer structure into a prime number, and generate a second table; said The comprehensive influence of the first table and the second table on the structure of the converter is converted into a vertex prime number to generate a third table; the third table is screened for vertices by using the preset first condition to generate the first table The fourth sub-table and the second and fourth sub-tables; use the preset second condition to filter out the edges newly added to the graph from the edges formed by the first and fourth sub-tables and the second and fourth sub-tables, so as to generating a fifth table; using a preset third condition to cycle through the process from the first table to the fifth table to generate a sixth table of non-isomorphic graphs of all topologies of DC converters.

The method for constructing a non-isomorphic graph of a single-switch DC converter based on the prime degree of the vertex in the embodiment of the present invention realizes the construction of a topological non-isomorphic graph of a single-switch non-isolated DC converter based on the prime degree of the vertex, and the number and type of edges connected to the vertices Considering the impact of the converter structure comprehensively, the non-isomorphic graphs of all topologies of single-switch non-isolated DC converters with a given side type and the number of each side type are obtained, which is convenient for researchers to study the single-switch non-isolated DC converter New structure or summary analysis of structural performance.

In addition, the non-isomorphic graph construction method for a single-switch DC converter based on the vertex prime degree according to the above-mentioned embodiments of the present invention may also have the following additional technical features:

Further, in an embodiment of the present invention, the edge types include the case that all edge types in the converter topology are the same.

Further, in an embodiment of the present invention, the types of edges are distinguished by numbers, wherein edges of different types are numbered with different numbers; edges of the same type are numbered with the same number.

Further, in an embodiment of the present invention, the preset first condition is a filter condition for vertices with different prime degrees, and a filter condition for vertices with the same prime degree but adjacent vertices with different prime degrees.

Further, in an embodiment of the present invention, the preset second condition is a filter condition that newly formed edges do not exist in the graph.

Further, in an embodiment of the present invention, the preset third condition is a filter condition that a newly added edge is not the last edge.

Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Description of drawings

The above and/or additional aspects and advantages of the present invention will become apparent and easy to understand from the following description of the embodiments in conjunction with the accompanying drawings, wherein:

1 is a flow chart of a method for constructing a non-isomorphic graph of a single-switch DC converter based on a vertex prime degree according to an embodiment of the present invention;

Fig. 2 is a flow chart of the first condition screening of the non-isomorphic graph construction method of a single-switch DC converter based on the vertex prime degree according to an embodiment of the present invention;

Fig. 3 is a flow chart of the second conditional screening of the non-isomorphic graph construction method of a single-switch DC converter based on the vertex prime degree according to an embodiment of the present invention;

Fig. 4 is a flow chart of the third condition screening of the non-isomorphic graph construction method of the single-switch DC converter based on the vertex prime degree according to an embodiment of the present invention;

5 is a schematic diagram of the number of edges and edge types connected by vertices according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of adding edges to FIG. 5 to form two structures to generate a fifth table according to an embodiment of the present invention;

Fig. 7 is a single-switch DC converter non-isomorphic graph construction method based on the vertex prime degree according to an embodiment of the present invention. The number of types) all non-isomorphic graphs obtained by computer initialization search;

Fig. 8 is a topological diagram of a given converter according to an embodiment of the present invention, the number of vertices is 4, the edge types are switching devices, inductors, capacitors, input voltage sources, and output voltage sources, and the number of each edge type is 1, 1 , 1, 1, 1 All non-isomorphic graphs of the single-switch non-isolated DC converter topology.

Detailed ways

Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

The method for constructing a non-isomorphic graph of a single-switch DC converter based on the prime degree of a vertex according to an embodiment of the present invention will be described below with reference to the accompanying drawings.

Fig. 1 is a flowchart of a method for constructing a non-isomorphic graph of a single-switch DC converter based on the prime degree of a vertex according to an embodiment of the present invention.

As shown in Figure 1, the non-isomorphic graph construction method of the single-switch DC converter based on the vertex prime degree includes the following steps:

In step S101, vertices, edge types and the number of each edge type of the DC converter topology graph are set.

Among them, the number of vertices is the number of converter topology nodes, the edge type is the device type connected by the converter topology edge, and the number of each edge type is the number of each device type.

In one embodiment of the present invention, the edge type includes the case that the edge types in the converter topology are the same, and at this time it can be regarded as regardless of the edge type, that is, the method of the embodiment of the present invention is also applicable to constructing the edge type regardless of the edge type Non-isomorphic graphs when .

Further, in one embodiment of the present invention, edge types can be distinguished by numbers; for edges of different types, different numbers can be used; for edges of the same type, the same numbers can be used, such as numbers 1 number.

In step S102, the influence of the number of edges connected by vertices on the transformer structure is converted into prime numbers, and a first table is generated.

Wherein, the first table can be represented by Table 1.

In step S103, the influence of the edge type of the vertex connection on the transformer structure is converted into a prime number, and a second table is generated.

Wherein, the second table can be represented by Table 2.

In step S104, the comprehensive influence of the first table and the second table on the structure of the transformer is converted into a vertex prime number degree to generate a third table.

Wherein, the third table can be represented by Table 3.

In step S105, the vertex screening is performed on the third table by using the preset first condition to generate the first and fourth sub-tables and the second and fourth sub-tables.

Wherein, the first and fourth sub-tables and the second and fourth sub-tables can be represented in Table 4-1 and Table 4-2.

In an embodiment of the present invention, as shown in FIG. 2 , the preset first condition may be a filter condition for vertices with different prime degrees, and a filter condition for vertices with the same prime degree but adjacent vertices with different prime degrees.

In step S106, the edges newly added to the graph are screened out from the edges formed by the first and fourth sub-tables and the second and fourth sub-tables by using a preset second condition, so as to generate a fifth table.

Wherein, the fifth table can be represented by Table 5.

In an embodiment of the present invention, as shown in FIG. 3 , the preset second condition may be a filter condition that newly formed edges do not exist in the graph.

In step S107 , the process from the first table to the fifth table is cycled through the preset third condition to generate a sixth table of non-isomorphic graphs of all topologies of DC converters.

Wherein, the sixth table can be represented by Table 6. It can be understood that the process of looping the first table to the fifth table is a process of looping steps S102 to S106.

In an embodiment of the present invention, as shown in FIG. 4 , the preset third condition may be a filtering condition for a newly added edge that is not the last edge.

It should be noted that an isomorphic graph refers to a graph G(V,E) and a graph G ₁ (V ₁ ,E ₁ ), V is a vertex set, E is an edge set, and there is a bijective function f, V→V ₁ , so that any two connected vertices v ₁ , v ₂ ∈ V in graph G(V,E) have f(v ₁ ), f(v ₂ ) also have connections in graph G ₁ , then graph G ₁ (V ₁ ,E ₁ ) is an isomorphic graph of graph G(V,E); non-isomorphic graph means that for G(V,E) and graph G ₁ (V ₁ ,E ₁ ), graph G ₁ (V ₁ ,E ₁ ) is not an isomorphic graph of G(V,E).

Furthermore, a non-isomorphic graph construction method for a single-switch DC converter based on the vertex prime degree proposed by the embodiment of the present invention can be used to construct a single-switch non-isolated DC converter with a given edge type and the number of each edge type A non-isomorphic graph of all topologies of the device.

A method for constructing a non-isomorphic graph of a single-switch DC converter based on the vertex prime degree of the embodiment of the present invention is verified below in combination with a specific embodiment, which specifically includes:

Step 1): Set the number of vertices of the converter topology graph to 4, and the edge types are switching devices, inductors, capacitors, input voltage sources, and output voltage sources. As shown in Table A, the number of each edge type is 1, 1, 1, 1, 1, wherein Table A is a table of topology parameters of a single-switch non-isolated DC converter according to an embodiment of the present invention.

Table A

Step 2): Convert the influence of the number of edges connected by vertices on the transformer structure in Figure 5 into a prime number, and get Table 1.

Step 3) Convert the influence of the edge types connected by vertices on the transformer structure in Figure 5 into prime numbers, and get Table 2.

Step 4): Convert the comprehensive influence of Table 1 and Table 2 on the converter structure into the degree of vertex prime, and get Table 3.

Step 5): Use the first condition to filter the vertices in Table 3, firstly filter the vertices with different prime degrees, and further filter the vertices with the same prime degree and their adjacent vertices with different prime degrees, and get Table 4-1 and Table 4 -2.

Step 6): Use the second condition to select new edges from Table 4-1 and Table 4-2 in turn, filter the unused edges, and then add these edges to Figure 5 to form two structures, and generate Table 5, As shown in Figure 6.

Step 7): Using the process of looping Table 1-Table 5 with the third condition, that is, screening the newly added edge but not the last edge, Table 6 containing 30 non-isomorphic graph structures can be obtained, as shown in Table B.

Form B

The construction result table B of the topological non-isomorphic graph of the single-switch non-isolated DC converter is transformed into a non-isomorphic graph, as shown in Figure 7. By comparing the topological non-isomorphic graph of the DC converter shown in Figure 7 with the non-isomorphic graph shown in Figure 8, it can be found that a single-switch DC converter based on the vertex prime degree proposed by the embodiment of the present invention is non-isomorphic After the computer program is used to execute the composition construction method, 30 non-isomorphic diagrams can be obtained, which verifies the correctness of the non-isomorphic diagram construction method of a single-switch DC converter based on the vertex prime degree proposed by the embodiment of the present invention.

In summary, through the verification of this specific embodiment, it is proved that the proposed method for constructing a non-isomorphic graph of a single-switch DC converter based on the vertex prime degree can construct a single-switch non-isolated graph with a given edge type and the number of each edge type. Non-isomorphic graphs for all topologies of DC-DC converters.

It should be noted that the term vertex number "①, ②, ③, ④, ⑤" in the embodiment of the present invention is only used to distinguish or describe the vertex, and the term edge type number "1, 2, 3, 4, 5 " are only used to distinguish the types of edges and should not be understood as indicating or implying relative importance.

According to the method for constructing a non-isomorphic graph of a single-switch DC converter based on the prime degree of a vertex proposed in an embodiment of the present invention, the construction of a topological non-isomorphic graph of a single-switch non-isolated DC converter is realized based on the prime degree of a vertex, and the number of vertices connecting edges, Considering the impact of the side type on the converter structure comprehensively, the non-isomorphic diagrams of all the topologies of the single-switch non-isolated DC converter with a given side type and the number of each side type are obtained, which is convenient for researchers to analyze the single-switch non-isolated DC converter. A new structure of the converter or a summary analysis of the structural performance.

In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly specifying the quantity of indicated technical features. Thus, the features defined as "first" and "second" may explicitly or implicitly include at least one of these features. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the described specific features, structures, materials or characteristics may be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples and features of different embodiments or examples described in this specification without conflicting with each other.

Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention, those skilled in the art can make the above-mentioned The embodiments are subject to changes, modifications, substitutions and variations.

Claims (6)

1. A single-switch DC converter non-isomorphic graph construction method based on vertex prime degree, is characterized in that, comprises the following steps: Set the vertices, edge types and the number of each edge type of the topology graph of the DC converter; Convert the influence of the number of edges connected by the vertices on the structure of the transformer into a prime number, and generate the first table; Convert the effect of the edge type of the vertex connection on the transformer structure into a prime number, and generate a second table; converting the combined influence of the first table and the second table on the transformer structure into a vertex prime degree to generate a third table; performing vertex screening on the third table by using the preset first condition to generate the first and fourth sub-tables and the second and fourth sub-tables; Using a preset second condition to filter out the edges newly added to the graph from the edges formed by the first and fourth sub-tables and the second and fourth sub-tables to generate a fifth table; Looping through the process of the first table to the fifth table by using a preset third condition to generate a sixth table of non-isomorphic graphs of all topologies of DC converters. 2. The method according to claim 1, wherein the edge types include the case that all edge types in the converter topology are the same. 3. The method according to claim 1, wherein the edge types are distinguished by numerical numbers, wherein, for edges of different types, different numerical numbers are used; for edges of the same type, the same numerical numbers are used . 4. The method according to claim 1, wherein the preset first condition is a filter condition for vertices with different prime degrees, and a filter condition for vertices with the same prime degree but different prime degrees for adjacent vertices. 5 . The method according to claim 1 , wherein the preset second condition is a filter condition that newly formed edges do not exist in the graph. 6 . 6 . The method according to claim 1 , wherein the preset third condition is a filter condition that a newly added edge is not the last edge. 7 .

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