Equivalent circuit of magnetic coupling circuit, conversion method, and feature quantity extraction method

Abstract

The equivalent circuit of a magnetically coupled circuit is formed by the mutual inductance (M0) between the primary, secondary, and tertiary inductors. 12 M 23 M 13 The equivalent circuit of the three-phase magnetically coupled circuit is characterized in that the equivalent circuit of the magnetically coupled circuit comprises: a first impedance disposed between the positive terminal and the negative terminal of the primary side; a second impedance disposed between the positive terminal and the negative terminal of the secondary side; a third impedance disposed between the positive terminal and the negative terminal of the tertiary side; a fourth impedance disposed between the positive terminal of the primary side and the positive terminal of the secondary side; a fifth impedance disposed between the positive terminal of the secondary side and the positive terminal of the tertiary side; and a sixth impedance disposed between the positive terminal of the primary side and the positive terminal of the tertiary side.

Description

Technical Field

[0001] This disclosure relates to the equivalent circuit, transformation method, and feature extraction method of magnetically coupled circuits. Background Technology

[0002] For example, Patent Document 1 discloses an equivalent circuit for the leakage impedance of a transformer. This transformer is a four-winding transformer constructed by adding a fourth winding as a stabilizing winding to a three-phase magnetically coupled circuit with three inductive elements. Furthermore, Patent Document 1 also discloses a method for calculating the impedance of the equivalent circuit based on the leakage impedance between each of the four windings present in this four-winding transformer.

[0003] Existing technical documents

[0004] Patent documents

[0005] Patent Document 1: International Publication No. 2019 / 207640 Summary of the Invention

[0006] The problem that the invention aims to solve

[0007] When representing a circuit using a graphical structure composed of points and lines, with circuit components designated as points and wiring (wires) connecting these components designated as lines, in the aforementioned circuit containing magnetic coupling (three-phase magnetically coupled circuit), the inductive elements are connected through spatial coupling, thus there is no wiring and lines cannot be defined. Therefore, even if the three-phase magnetically coupled circuit is transformed into a graphical structure, the magnetic coupling will not be reflected in the graphical structure, resulting in information degradation when the circuit is transformed into a graphical structure.

[0008] Therefore, in order to define the three-phase magnetically coupled circuit as a graph structure while suppressing information degradation, it is desirable to replace the three-phase magnetically coupled circuit with a circuit that does not contain magnetic coupling, and to represent spatial coupling as a circuit component. However, as in the aforementioned Patent Document 1, there are known equivalent circuits of leakage impedance in circuits containing three-phase magnetically coupled circuits, but a method for replacing the three-phase magnetically coupled circuit with a circuit that does not contain magnetic coupling is not known.

[0009] This disclosure was made to solve the above-mentioned problem, and its purpose is to obtain an equivalent circuit of a three-phase magnetically coupled circuit that does not contain magnetic coupling.

[0010] Methods for solving problems

[0011] The equivalent circuit of the magnetic coupling circuit disclosed herein is an equivalent circuit of a three-phase magnetic coupling circuit formed by mutual inductance of a primary-side inductor, a secondary-side inductor, and a tertiary-side inductor. The equivalent circuit is characterized by comprising: a first impedance disposed between the positive and negative terminals of the primary side; a second impedance disposed between the positive and negative terminals of the secondary side; a third impedance disposed between the positive and negative terminals of the tertiary side; a fourth impedance disposed between the positive and negative terminals of the primary and secondary sides; a fifth impedance disposed between the positive and negative terminals of the secondary and tertiary sides; and a sixth impedance disposed between the positive and negative terminals of the primary and tertiary sides.

[0012] Furthermore, the equivalent circuit of the magnetic coupling circuit disclosed herein is an equivalent circuit of a three-phase magnetic coupling circuit formed by mutual inductance of the primary-side inductor, the secondary-side inductor, and the tertiary-side inductor. The equivalent circuit is characterized by comprising: a first impedance disposed between the positive and negative terminals of the primary side; a second impedance disposed between the positive and negative terminals of the secondary side; a third impedance disposed between the positive and negative terminals of the tertiary side; a fourth impedance disposed between the positive and negative terminals of the primary and secondary sides; a fifth impedance disposed between the negative terminals of the primary and secondary sides; a sixth impedance disposed between the positive and negative terminals of the secondary and tertiary sides; a seventh impedance disposed between the negative terminals of the secondary and tertiary sides; an eighth impedance disposed between the positive and negative terminals of the primary and tertiary sides; and a ninth impedance disposed between the negative terminals of the primary and tertiary sides.

[0013] Invention Effects

[0014] According to this disclosure, an equivalent circuit of a three-phase magnetically coupled circuit can be obtained, which does not include magnetic coupling. Attached Figure Description

[0015] Figure 1 This is a diagram illustrating an example of a three-phase magnetic coupling circuit according to Embodiment 1.

[0016] Figure 2 This is a diagram showing an example of the equivalent circuit of the three-phase magnetic coupling circuit in Embodiment 1.

[0017] Figure 3 This is a diagram showing an example of the equivalent circuit of the three-phase magnetic coupling circuit in Embodiment 1.

[0018] Figure 4 This is a schematic diagram illustrating a representative example of the structure of an existing three-phase transformer.

[0019] Figure 5 It is a summary Figure 1 The three-phase magnetic coupling circuit shown is Figure 3 The schematic diagram shows the relationship between the transformations and inverse transformations of the equivalent circuits. Figure 5 A is Figure 1 The three-phase magnetic coupling circuit shown is as follows: Figure 5 B is Figure 3 The equivalent circuit shown.

[0020] Figure 6 This refers to a circuit involving a three-phase transformer with magnetic coupling. Figure 2 The graph shows the calculation results of the equivalent circuit based on circuit simulation. Figure 6 A represents a three-phase magnetically coupled circuit with AC power supply and load resistor. Figure 6 B indicates that it has AC power supply and load resistance. Figure 2 The equivalent circuit, Figure 6 C indicates Figure 6 A and Figure 6 The frequency characteristics of the voltage across the load resistors on the secondary and tertiary sides of B.

[0021] Figure 7 It is Figure 6 B's Lb 12 Divided into Lc 12 and Lc 21 , Lb 23 Divided into Lc 23 and Lc 32 , Lb 13 Divided into Lc 13 and Lc 31 The image.

[0022] Figure 8 This refers to the case where all K1, K2, and K3, which correspond to coupling coefficients k12, k23, and k13, are different, regarding the circuit of a three-phase transformer containing magnetic coupling. Figure 2 The graph shows the calculation results of the equivalent circuit based on circuit simulation. Figure 8 A represents a three-phase magnetically coupled circuit with AC power supply and load resistor. Figure 8 B indicates that it has AC power supply and load resistance. Figure 2 The equivalent circuit, Figure 8 C indicates Figure 8 A and Figure 8 The frequency characteristics of the voltage across the load resistors on the secondary and tertiary sides of B.

[0023] Figure 9 This is a diagram illustrating an example of a three-phase magnetic coupling circuit according to Embodiment 2.

[0024] Figure 10This is a diagram illustrating an example of the diagram structure of implementation method 3.

[0025] Figure 11 This is a diagram illustrating an example of the diagram structure of implementation method 3.

[0026] Figure 12 This is a diagram representing an example of the dataset used in the classification problem of the graph neural network in Implementation 3.

[0027] Figure 13 This is a diagram, taken as an example, showing the inference accuracy of the test data when learning without considering the magnetic coupling component.

[0028] Figure 14 This is a graph showing the inference accuracy when learning data and test data are generated using the transformation method of Embodiment 3, and the type of circuit component is inferred using the test data. Detailed Implementation

[0029] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings.

[0030] Implementation method 1.

[0031] The circuit in Embodiment 1, which includes three-phase magnetic coupling (hereinafter referred to as "three-phase magnetic coupling circuit"), is a circuit spatially coupled by mutual inductance of three inductor elements (coils) that are DC-isolated and divided into a primary side, a secondary side, and a tertiary side. In Embodiment 1, as a method for transforming the three-phase magnetic coupling circuit into a graphical structure while suppressing information degradation, a method is shown to transform the magnetic coupling circuit into a graphical structure by replacing it with a three-phase equivalent circuit containing six or nine impedance elements.

[0032] The three-phase equivalent circuit shown in Embodiment 1 can be applied to any type of magnetically coupled circuit, as long as it is a circuit with magnetic coupling between three inductive elements. For example, the three-phase equivalent circuit shown in Embodiment 1 can be applied to magnetic coupling in three-phase three-wire transformers, insulation circuits, motors, compressors, or wireless power transmission, i.e., magnetically coupled circuits that transmit or receive power or signals via space or magnetic bodies. In any of these cases, the three-phase magnetically coupled circuit is a circuit structure represented by three inductive elements and the mutual inductance or coupling coefficient between these three inductive elements. In their magnetic circuits, the coupling coefficients between the inductive elements do not necessarily need to be equal, and this can be true under different circumstances. Thus, the three-phase equivalent circuit shown in Embodiment 1 is valid in all magnetic circuits regardless of application, characteristics, frequency, etc. Therefore, in Embodiment 1, the case of a three-phase magnetically coupled circuit used in a transformer is used as an example for explanation.

[0033] In a three-phase magnetic coupling circuit, it is conventional to sometimes refer to the power supply side as R, S, T, and the load side as U, V, W, or sometimes to use uppercase and lowercase letters to distinguish between the power supply and load sides. In Embodiment 1, the three-phase magnetic coupling circuit is described as consisting of six terminals: a + terminal on the primary side, a + terminal on the secondary side, a + terminal on the tertiary side, a - terminal on the primary side, a - terminal on the secondary side, and a - terminal on the tertiary side.

[0034] In three-phase magnetically coupled circuits, Y-connection or Δ-connection is widely used as a wiring method. However, Embodiment 1 shows a technique that replaces the parts in the magnetically coupled circuit that are represented by magnetic coupling with a form that does not include magnetic coupling. Therefore, the wiring method other than magnetic coupling, such as power supply or load, can be arbitrary. Thus, by changing the connections between the primary side + terminal, the secondary side + terminal, the tertiary side + terminal, the primary side - terminal, the secondary side - terminal, and the tertiary side - terminal, a Y-connection or Δ-connection can be formed, and a Y-connection or Δ-connection can also be formed according to the application.

[0035] Figure 1 This is a diagram illustrating an example of a three-phase magnetically coupled circuit. Figure 1 This diagram illustrates a representative magnetic coupling circuit in which three inductors are coupled by spatial coupling, and a portion of the AC current flowing between the terminals of the primary inductor is transferred to the secondary and tertiary inductors, generating a voltage between the terminals of the secondary and tertiary inductors.

[0036] In addition, for the sake of simplicity, in the following description, the inductor on the primary side of the three-phase magnetic coupling circuit will sometimes be referred to as "primary side", the inductor on the secondary side as "secondary side", and the inductor on the tertiary side as "tertiary side".

[0037] exist Figure 1 In the three-phase magnetically coupled circuit shown, the primary to tertiary sides are all represented as open terminals. However, for example, an AC power supply is connected between the + and - terminals of the primary side, and load resistors are connected between the + and - terminals of the secondary side and between the + and - terminals of the tertiary side, respectively. Current flows through the circuit, and through magnetic coupling, the power from the primary side propagates to the secondary and tertiary sides. Furthermore, the example of connecting an AC power supply between the terminals of the primary side was described above, but... Figure 1The magnetic coupling circuit shown is symmetrical, therefore, it operates in the same way as described above when an AC power supply is connected between the terminals on the secondary side or the terminals on the tertiary side. Furthermore, by connecting a power supply to the positive terminal on the primary side, the positive terminal on the secondary side, and the positive terminal on the tertiary side, and connecting a load to the negative terminal on the primary side, the negative terminal on the secondary side, and the negative terminal on the tertiary side, the power between the positive terminals on the primary side, the positive terminal on the secondary side, and the positive terminal on the tertiary side can be transmitted as power between the negative terminals on the primary side, the negative terminal on the secondary side, and the negative terminal on the tertiary side.

[0038] Figure 2 It means Figure 1 The diagram shows an example of an equivalent circuit for a magnetically coupled circuit. This equivalent circuit is configured, for example, to include: a first impedance disposed between the + and - terminals on the primary side; a second impedance disposed between the + and - terminals on the secondary side; a third impedance disposed between the + and - terminals on the tertiary side; a fourth impedance disposed between the + terminals on the primary side and the + terminals on the secondary side; a fifth impedance disposed between the + terminals on the secondary side and the + terminals on the tertiary side; and a sixth impedance disposed between the + terminals on the primary side and the + terminals on the tertiary side.

[0039] in addition, Figure 3 This diagram also represents an example of the equivalent circuit of a three-phase magnetically coupled circuit. Figure 3 and Figure 2 Different, will Figure 2 The fourth impedance is divided into the fourth impedance and the fifth impedance, and... Figure 2 The 5th impedance is divided into the 6th and 7th impedances, and... Figure 2 The 6th impedance is divided into the 8th and 9th impedances. Furthermore, Figure 2 The value of the fourth impedance and Figure 3 The sum of the values ​​of the 4th and 5th impedances is equal. Figure 2 The value of the 5th impedance and Figure 3 The sum of the values ​​of the 6th and 7th impedances is equal. Figure 2 The value of the 6th impedance and Figure 3 The sum of the values ​​of the 8th and 9th impedances is equal. Thus, the segmented impedances become the same value when Kirchhoff's law of conservation of current holds. In contrast, in graph networks, graph neural networks, and other applications where Kirchhoff's law of conservation of current may not hold, since short circuits are not included, the characteristics do not change with the path.

[0040] The first impedance is a circuit component connected in parallel between the positive and negative terminals on the primary side. The second impedance is a circuit component connected in parallel between the positive and negative terminals on the secondary side. The third impedance is a circuit component connected in parallel between the positive and negative terminals on the tertiary side. The fourth impedance is a circuit component connected in series between the positive and negative terminals on the primary and secondary sides. The fifth impedance is a circuit component connected in series between the negative and negative terminals on the primary and secondary sides. The sixth impedance is a circuit component connected in series between the positive and positive terminals on the secondary and tertiary sides. The seventh impedance is a circuit component connected in series between the negative and negative terminals on the secondary and tertiary sides. The eighth impedance is a circuit component connected in series between the positive and positive terminals on the primary and tertiary sides. The ninth impedance is a circuit component connected in series between the negative and negative terminals on the primary and tertiary sides.

[0041] Magnetic coupling circuits can change polarity, for example, by changing the direction of the current, reversing the phase of the current by 180°, or reversing the winding direction of the wire forming the inductance. Therefore, the + terminal and the - terminal can also be opposite. Thus, in Embodiment 1, the + terminal and the - terminal are used to represent either end of the inductor element.

[0042] observe Figure 1 The magnetic coupling circuit shown is Figure 3 The correspondence of the equivalent circuits shown is as follows: Figure 1 The inductor on the primary side of the magnetic coupling circuit shown is... Figure 3 The first impedance in the equivalent circuit shown corresponds to, Figure 1 The inductor on the secondary side of the magnetic coupling circuit shown is... Figure 3 The second impedance in the equivalent circuit shown corresponds to, Figure 1 The inductor on the third side of the magnetic coupling circuit shown is... Figure 3 The third impedance corresponds to the equivalent circuit shown.

[0043] in addition, Figure 1 The mutual inductance between the positive terminal on the primary side and the positive terminal on the secondary side in the magnetic coupling circuit shown corresponds to Figure 3 The fourth impedance in the equivalent circuit shown. Figure 1 The mutual inductance between the primary-side terminal and the secondary-side terminal in the magnetic coupling circuit shown corresponds to Figure 3 The fifth impedance in the equivalent circuit shown. Figure 1 The mutual inductance between the positive terminal on the secondary side and the positive terminal on the tertiary side in the magnetic coupling circuit shown corresponds to Figure 3 The sixth impedance in the equivalent circuit shown.

[0044] in addition, Figure 1The mutual inductance between the secondary-side terminal and the tertiary-side terminal in the magnetic coupling circuit shown corresponds to Figure 3 The 7th impedance in the equivalent circuit shown. Figure 1 The mutual inductance between the primary-side + terminal and the tertiary-side + terminal in the magnetic coupling circuit shown corresponds to Figure 3 The 8th impedance in the equivalent circuit shown. Figure 1 The mutual inductance between the primary-side terminal and the tertiary-side terminal in the magnetic coupling circuit shown corresponds to Figure 3 The 9th impedance in the equivalent circuit shown. That is, Figure 1 The magnetic coupling circuit shown is Figure 3 The equivalent circuits shown are structurally corresponding.

[0045] Figure 4 This is a schematic diagram illustrating a typical example of a three-phase transformer. The transformer has a structure where the primary, secondary, and tertiary conductors are wound around a ring-shaped iron core. The voltage ratios on the primary to tertiary sides change depending on the number of times the conductors are wound around the core.

[0046] Furthermore, for example, when the primary side is used as the input and the secondary and tertiary sides as the outputs, by using a material with high relative permeability for the core, the magnetic flux generated by the current flowing through the primary side terminals is less likely to leak to the outside of the core. Therefore, the ratio of the power input to the primary side to the power output from the secondary and tertiary sides can be close to 1. Conversely, by using a material with low relative permittivity for the core, the power input to the primary side is less likely to be transferred to the secondary and tertiary sides. The amount of coupling between the primary, secondary, and tertiary sides, determined by the relative permittivity of the core material, the size of the core, or the construction of the core, is expressed as the coupling coefficient k.

[0047] Let the coupling coefficient between the primary and secondary sides be k1, the coupling coefficient between the secondary and tertiary sides be k2, and the coupling coefficient between the primary and tertiary sides be k3. Let the inductance of the primary side of the transformer be L1, the inductance of the secondary side be L2, the inductance of the tertiary side be L3, and the mutual inductance between the primary and secondary sides be M. 12 Let the mutual inductance between the secondary and tertiary sides be M. 23 Let the mutual inductance between the primary and tertiary sides be M. 13 When, the following equations (1) to (3) hold true between them. In addition, inductance L1, inductance L2 and inductance L3 refer to self-inductance, but in embodiment 1 they are only described as inductance.

[0048]

[0049] At this time, k1, k2, and k3 take values ​​greater than or equal to 0 and less than or equal to 1. Alternatively, when polarity is defined, k1, k2, and k3 can be set to values ​​greater than or equal to -1 and less than or equal to 1, but in Implementation 1, polarity is not limited; therefore, k1, k2, and k3 are set to values ​​greater than or equal to 0 and less than or equal to 1. In many magnetically coupled circuits containing three-phase transformers, a coupling coefficient k (k1, k2, k3) close to 1 means that power is transferred to the output side without loss, which is an ideal condition. However, there are cases where the iron core heats up due to the large magnetic flux applied to it, leading to magnetic saturation and a decrease in relative permeability, or where the iron core (magnetic body) is thermally damaged due to heating.

[0050] Therefore, methods such as using gaps in the middle of the toroidal core to prevent magnetic flux from easily passing through, or intentionally generating leakage flux by using materials with relatively low permeability in the core, are employed. In these cases, k is not 1, but is greater than 0 and less than 1. Furthermore, k also varies depending on the gap construction, the material used for the magnetic material, and the temperature of the magnetic material. Thus, ideally, k would be "1", but in practical circuits, it will not be "1", for example, such as "0.9" or "0.99". In particular, in cases such as wireless power transmission where it is difficult to use magnetic materials and where positional misalignment between inductive elements is easily caused, k becomes a small value such as "0.1". Therefore, the equivalent circuit of a magnetically coupled circuit needs to be able to represent a value of k less than 1.

[0051] Generally, the inductance on the primary side of the transformer is designated as L1, the inductance on the secondary side as L2, and the inductance on the tertiary side as L3. The current flowing through the inductor on the primary side is designated as I1, the current flowing through the inductor on the secondary side as I2, the current flowing through the inductor on the tertiary side as I3, and the mutual inductance between the primary and secondary sides is designated as M. 12 Let the mutual inductance between the secondary and tertiary sides be M. 23 Let the mutual inductance between the primary and tertiary sides be M. 13 When j is set as a complex number and ω is set as the angular frequency, the voltages v1, v2, and v3 between the terminals of the primary inductor, the secondary inductor, and the tertiary inductor are calculated using equations (4) to (6), respectively. Furthermore, in Figures 1-4 And the following Figure 5 From now on, uppercase letters V1~V3 will be used to represent voltages v1~v3.

[0052]

[0053] However, defining a new circuit construction (circuit topology) is not necessarily consistent with analytically deriving the electrical equivalent constants in the equivalent circuit of that circuit. Generally speaking, in Figure 3 In the equivalent circuit shown, it is difficult to determine the circuit constants that are electrically equivalent to an arbitrarily defined circuit. Regarding this point, the inventors of this application have discovered that... Figure 1 The three-phase magnetic coupling circuit shown and Figure 3 The equivalent circuit shown can determine the circuit constants of both sides in a manner that gives them the same electrical characteristics according to Kirchhoff's laws.

[0054] Specifically, let the complex number be j, and the angular frequency be ω (= 2π × (frequency [Hz])). Figure 1 In the magnetic coupling circuit shown, the inductance between the primary side terminals is defined as L1, the inductance between the secondary side terminals is defined as L2, the inductance between the tertiary side terminals is defined as L3, and the mutual inductance between the primary and secondary side inductances is defined as M. 12 The mutual inductance between the secondary and tertiary inductances is defined as M. 23 The mutual inductance between the primary and tertiary inductances is defined as M. 13 .

[0055] In addition, Figure 3 In the equivalent circuit shown, when the circuit constant of the first impedance is set to z1, the circuit constant of the second impedance to z2, the circuit constant of the third impedance to z3, the circuit constant of the fourth impedance to z4, the circuit constant of the fifth impedance to z5, the circuit constant of the sixth impedance to z6, the circuit constant of the seventh impedance to z7, the circuit constant of the eighth impedance to z8, and the circuit constant of the ninth impedance to z9, in Figure 1 The magnetic coupling circuit shown is Figure 3 The following equations (7) to (12) hold true regarding the circuit constants of the equivalent circuit shown. Furthermore, the sum of z4 and z5 equals the z shown in equation (10). 12 The sum of z6 and z7 is equal to the z shown in equation (11). 23 The sum of z8 and z9 is equal to the z shown in equation (12). 13 .

[0056]

[0057] Among them, the impedance values ​​of the 4th impedance z4, the 5th impedance z5, the 6th impedance z6, the 7th impedance z7, the 8th impedance z8, and the 9th impedance z9 are all determined by the sum of z4 and z5 equal to z. 12 The sum of z6 and z7 equals z 23 The sum of z8 and z9 equals z 13 It can be freely changed, and it can also have circuit constants that are negative real numbers.

[0058] In addition, Figure 2In the equivalent circuit shown, let the first impedance z1, the second impedance z2, the third impedance z3, and the fourth impedance z4 be... 12 , 5th impedance z 23 The 6th impedance z 13 When these impedances are calculated using equations (7) to (12) above.

[0059] Thus, by setting the equivalent circuit of the three-phase magnetic coupling circuit as Figure 3 The circuit configuration shown can replace a three-phase magnetically coupled circuit with a circuit that does not contain magnetic coupling. Furthermore, by transforming this equivalent circuit into a graph structure, information degradation in the three-phase magnetically coupled circuit can be suppressed while simultaneously transforming it into a graph structure. This transformed graph structure can then be used as input data for learning in a graph network or graph neural network. However, in this case, it is preferable to set the circuit constants so that the circuit constants of the 4th and 5th impedances are equal, the circuit constants of the 6th and 7th impedances are equal, and the circuit constants of the 8th and 9th impedances are equal.

[0060] This is because, unlike circuit theory, Kirchhoff's law of current conservation does not hold in graph networks or graph neural networks. Specifically, Kirchhoff's law of current conservation assumes the starting and ending points are the same circuit component, considering closed paths where the current flowing out of the component equals the current flowing into it. In contrast, in graph neural networks, only connections between two components are considered in a hidden layer. Even with additional hidden layers, the law of current conservation does not hold, as closed paths cannot be considered. Therefore, in processing graph networks or graph neural networks... Figure 3 The equivalent circuit shown is transformed into a graphical structure, for example, by setting the circuit constant of the 5th impedance to "0" and assigning the above z to the 4th impedance. 12 When processing through graph networks or graph neural networks, circuits containing conditions of short circuits on both the primary and secondary sides are processed.

[0061] In contrast, Figure 3 In the equivalent circuit shown, by setting the impedances of the 4th and 5th impedances to be equal, the impedances of the 6th and 7th impedances to be equal, and the impedances of the 8th and 9th impedances to be equal, in the processing of graph networks or graph neural networks where Kirchhoff's law of current conservation does not hold, for example when processing only one path containing the 4th or 5th impedance, no short circuit occurs between the primary and secondary sides, and the same effect is received regardless of which path is used. Therefore, it can be processed as correct circuit information based on circuit theory.

[0062] Furthermore, according to embodiment 1, contrary to the above, it is also possible to obtain from Figure 3The equivalent circuit without magnetic coupling shown is transformed into a circuit with magnetic coupling. Thus, it is possible to recover a circuit with magnetic coupling (magnetically coupled circuit) from a graph structure that has been generated or processed in a graph network or graph neural network.

[0063] Furthermore, it is difficult to calculate the mutual inductance in a magnetically coupled circuit based on actual measured data. This is because the mutual inductance in a magnetically coupled circuit is calculated as a value combined with self-inductance. Regarding this, according to Embodiment 1, it is possible to calculate based on... Figure 3 The equivalent circuit shown, which does not include magnetic coupling, calculates the circuit constants by measurement, and then inversely calculates the self-inductance or mutual inductance in the magnetically coupled circuit based on the results. Therefore, it achieves a significant effect previously unseen: making it easier to calculate the mutual inductance in magnetically coupled circuits than ever before.

[0064] Furthermore, if the mutual inductance in a magnetically coupled circuit can be calculated, the coupling coefficient or relative permeability in that circuit can also be easily calculated based on circuit theory. Therefore, circuit constants can be easily extracted from actual magnetically coupled circuits.

[0065] From Figure 3 The equivalent circuit shown is directed towards Figure 1 In the transformation of the magnetic coupling circuit shown, the complex number is set as j, the angular frequency is set as ω, the circuit constant of the first impedance is set as z1, the circuit constant of the second impedance is set as z2, the circuit constant of the third impedance is set as z3, the circuit constant of the fourth impedance is set as z4, the circuit constant of the fifth impedance is set as z5, the circuit constant of the sixth impedance is set as z6, the circuit constant of the seventh impedance is set as z7, the circuit constant of the eighth impedance is set as z8, and the circuit constant of the ninth impedance is set as z9. Here, the sum of z4 and z5 equals z 12 The sum of z6 and z7 equals z 23 The sum of z8 and z9 equals z 13 In addition, for the sake of simplicity, Z is defined as shown in equation (13) below.

[0066]

[0067] At this time, in the Figure 1 In the magnetic coupling circuit shown, the inductance between the primary side terminals is designated L1, the inductance between the secondary side terminals is designated L2, the inductance between the tertiary side terminals is designated L3, and the mutual inductance between the primary and secondary side inductances is designated M. 12 Let the mutual inductance between the secondary and tertiary inductors be M. 23 Let the mutual inductance between the primary inductor and the tertiary inductor be M. 13 When, the following equations (14) to (19) hold true between the above circuit constants.

[0068]

[0069] Figure 5 It is a summary Figure 1 The three-phase magnetic coupling circuit shown is Figure 3 A schematic diagram showing the relationship between the transformations and inverse transformations of the equivalent circuits shown. Figure 5 A is Figure 1 The three-phase magnetic coupling circuit shown is as follows: Figure 5 B is Figure 3 The equivalent circuit shown.

[0070] like Figure 5 A and Figure 5 As shown in Figure B, the three-phase magnetically coupled circuit and its equivalent circuit, which replaces the spatial coupling in the magnetically coupled circuit with circuit components, are reversibly transformed. Therefore, this reversible transformation can also be applied to transforming the magnetically coupled circuit into structures other than graphical. For example, in... Figure 5 In the equivalent circuit shown in B, a design goal is set, and the equivalent circuit is transformed using the above equations (14) to (19) into... Figure 5 The magnetic coupling circuit shown in A can determine the physical structure or material constants of the actual magnetic coupling circuit.

[0071] For example, to calculate L1, L2, L3, M 12 M 23 M 13 ,like Figure 2 As shown, there are 6 unknowns; therefore, 6 independent measurement results are sufficient. For example, measurements can be performed under three conditions: with the + and - terminals of V2 short-circuited while the + and - terminals of V3 are disconnected, and with the V3 + and - terminals short-circuited while the V3 + and - terminals of V2 are disconnected, and with the V3 + and - terminals of V3 short-circuited, the measurements can be performed under three conditions. This allows us to determine... Figure 2 The circuit constant. Furthermore, by combining the addition of circuit components such as resistors, coils, and capacitors (other than 50Ω) to the V2 terminal and measuring V2 with the + and - terminals of V3 short-circuited, the circuit constant can be improved. Figure 2 The measurement accuracy of the 1st, 2nd, 3rd, 4th, 5th, and 6th impedances is improved. Specifically, for 6 unknowns (variables), a constraint equation with more than 6 elements is established, thus becoming the optimal decision equation. Therefore, it is preferable to determine the 1st to 6th impedances as the least squares solution in the generalized inverse matrix, thereby reducing measurement errors. Based on the determined 1st to 6th impedances, L1, L2, L3, and M can be uniquely determined according to the method shown in this embodiment. 12 M 23 M13 Previously, in methods using equations (4), (5), and (6), mutual inductance M was included. 12 M 23 M 13 And it depends on the currents I1, I2, and I3. Therefore, it is necessary to determine the voltages v1, v2, and v3 and the currents I1, I2, and I3 simultaneously. However, due to the relationship between current and voltage, L1, L2, L3, and M... 12 M 23 M 13 They are interdependent, making measurement difficult. In contrast, to determine z1, z2, and z3 in equations (7), (8), (9), (10), (11), and (12), L1, L2, L3, and M are determined in equations (13), (14), (15), (16), (17), (18), and (19). 12 M 23 M 13 Since the aforementioned dependencies have been eliminated, it is possible to obtain previously unseen effects that can be calculated without special processing.

[0072] Thus, according to Embodiment 1, it is possible to combine the representation methods of the actual magnetic coupling circuit and its equivalent circuit in two different regions, allowing for various processing in the regions where each circuit excels. Therefore, Figure 5 The reversible transformation relationship shown can be used, for example, to improve efficiency in the design of magnetically coupled circuits or the structural design of transformers equipped with such magnetically coupled circuits, and can also be used when extracting mutual inductance from actual magnetically coupled circuits.

[0073] Figure 6 This illustrates the design for three-phase magnetically coupled circuits and Figure 2 The equivalent circuits shown use calculations from a circuit simulator. These calculations represent the frequency characteristics of the voltages across the load resistors on the secondary and tertiary sides when the input is set as the primary side, the output as the secondary and tertiary sides, an AC power supply is connected between the + and - terminals on the primary side, and load resistors are connected between the + and - terminals on the secondary side and between the + and - terminals on the tertiary side.

[0074] Figure 6 A shows a three-phase magnetically coupled circuit with an AC power supply and a load resistor. Figure 6 B shows a diagram with an AC power supply and a load resistor. Figure 2 The equivalent circuit, Figure 6 C shows Figure 6 A and Figure 6 The frequency characteristics of the voltage across the load resistors on the secondary and tertiary sides of B.

[0075] exist Figure 6 In A, the coupling coefficients k1 between the primary and secondary inductors, k2 between the secondary and tertiary inductors, and k3 between the primary and tertiary inductors are all set to "0.9". Additionally, in Figure 6 In A, the inductor La1 on the primary side (input) is "100μH", the inductor La2 on the secondary side (output) is "100μH", the inductor La3 on the tertiary side (output) is "10μH", the impedance Ra2 of the load resistor on the secondary side is "100Ω", and the impedance Ra3 of the load resistor on the tertiary side is "10Ω".

[0076] In addition, Figure 6 In B, it is equivalent to Figure 2 The circuit constant of z1 has an inductance Lb1 of -15.17μH, which is equivalent to Figure 2 The circuit constant of z2 has an inductance Lb2 of -15.17μH, which is equivalent to Figure 2 The circuit constant of z3 has an inductance Lb3 of "2.10μH", which is equivalent to Figure 2 z 12 The circuit constant of the inductance Lb 12 "31.11μH" is equivalent to Figure 2 z 23 The circuit constant of the inductance Lb 23 It is "9.84μH", which is equivalent to Figure 2 z 13 The circuit constant of the inductance Lb 13 The value is "9.84μH". At this time, the power supply voltage Vb on the input side, the impedance Rb2 (which serves as the load resistor on the secondary side of the output) of "100Ω", and the impedance Rb3 (which serves as the load resistor on the tertiary side of the output) of "10Ω" do not change.

[0077] In addition, Figure 6 In C, Figure 6 The voltage across the load resistor on the secondary side of the circuit shown in A is labeled V(out_a1), and the voltage across the load resistor on the tertiary side is labeled V(out_a2). Figure 6 The voltage across the load resistor on the secondary side of the circuit shown in B is labeled V(out_b1), and the voltage across the load resistor on the tertiary side is labeled V(out_b2). For example... Figure 6 As shown in Figure C, it can be seen that the frequency characteristics of the two circuits mentioned above are consistent on both the secondary and cubic sides in terms of amplitude and phase. The circuit constants can be calculated, for example, using the Python programming language (version 3.9.17).

[0078] #------Python code (start)------

[0079] `from math import sqrt` # Importing a library

[0080] L1 = 100 1e-6 # 100μH

[0081] L2 = 100 1e-6 # 100μH

[0082] L3 = 10 1e-6 # 10μH

[0083] k1=0.9# Coupling coefficient

[0084] k2=0.9# Coupling coefficient

[0085] k3=0.9# Coupling coefficient

[0086] M12 =k1 sqrt(L1) L2) #Mutual Induction

[0087] M23 =k2 sqrt(L2) L3) #Mutual Induction

[0088] M13 =k3 sqrt(L3) L1) #Mutual Induction

[0089] print("initial conditions")

[0090] print(f"L1:{L1:.3e}, L2:{L2:.3e}, L3:{L3:.3e}")

[0091] print(f"k1:{k1:.3e}, k2:{k2:.3e}, k3:{k3:.3e}")

[0092] print(f"M12:{M12:.3e}, M23:{M23:.3e}, M13:{M13:.3e}", end="\n\n")

[0093] #Forward expression (7) ~ (12)

[0094] Z = -L1 L2 L3 + L1 M23 2 + L2 M13 2 + L3 M12 2 - 2 M12 M13 M23

[0095] z1 = Z / (-L2 L3 + L2 M13 + L3 M12 - M12 M23 - M13 M23 + M23 2)

[0096] z2 = Z / (-L1 L3 + L1 M23 + L3 M12 - M12 M13 + M13 2 - M13 M23)

[0097] z3 = Z / (-L1 L2 + L1 M23 + L2 M13 + M12 2 - M12 M13 - M12 M23)

[0098] z12 = Z / (-L3 M12 + M13 M23)

[0099] z23 = Z / (-L1 M23 + M12 M13)

[0100] z13 = Z / (-L2 M13 + M12 M23)

[0101] print("Forward mutual inductance has → none")

[0102] print(f"z1:{z1:.3e}, z2:{z2:.3e}, z3:{z3:.3e}")

[0103] print(f"z12:{z12:.3e}, z23:{z23:.3e}, z13:{z13:.3e}", end="\n\n")

[0104] # Reverse equations (13) to (19)

[0105] y1, y2, y3 = 1 / z1, 1 / z2, 1 / z3

[0106] y12, y23, y13 = 1 / z12, 1 / z23, 1 / z13

[0107] Y = y1 y2 y3 + y1 y3 y23 + y1 y3 y1​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ 2) / Y

[0112] L2_inv = ((y1 + y12 + y13) (y3 + y23 + y13) - y13 2) / Y

[0113] L3_inv = ((y1 + y12 + y13) (y2 + y12 + y23) - y12 2) / Y

[0114] M12_inv = ((y3 + y23 + y13) y12 + y23 y13) / Y

[0115] M23_inv = ((y1 + y12 + y13) y23 + y12 y13) / Y

[0116] M13_inv = ((y2 + y12 + y23)<0000,​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0123] print(f"M12_inv:{M12_inv:.3e}, M23_inv:{M23_inv:.3e}, M13_inv:{M13_inv:.3e}")

[0124] #-------Python code (end)-------

[0125] When executing the above procedure, the following results were obtained.

[0126] #-------Python code output (start)-------

[0127] Initial conditions

[0128] L1:1.000e-04, L2:1.000e-04, L3:1.000e-05

[0129] k1:9.000e-01, k2:9.000e-01, k3:9.000e-01

[0130] M12:9.000e-05, M23:2.846e-05, M13:2.846e-05

[0131] Positive mutual induction exists → does not exist

[0132] z1:-1.517e-05, z2:-1.517e-05, z3:2.104e-06

[0133] z12:3.111e-05, z23:9.838e-06, z13:9.838e-06

[0134] Reverse mutual inductance: no → present

[0135] L1_inv:1.000e-04, L2_inv:1.000e-04, L3_inv:1.000e-05

[0136] k1_inv:9.000e-01, k2_inv:9.000e-01, k3_inv:9.000e-01

[0137] M12_inv:9.000e-05, M23_inv:2.846e-05, M13_inv:2.846e-05

[0138] #---------Python code output (end)---------

[0139] According to the output, L1 is equal to L1_inv, L2 is equal to L2_inv, L3 is equal to L3_inv, M12 is equal to M12_inv, M23 is equal to M23_inv, and M13 is equal to M13_inv. As a result, k1 is equal to k1_inv, k2 is equal to k2_inv, and k3 is equal to k3_inv. Therefore, the transformations of equations (7) to (12) and the inverse transformations of equations (13) to (19) are reversible. Furthermore, it can be seen that this becomes a general solution that does not depend on the power supply voltage or the load resistance.

[0140] Furthermore, such as Figure 7 As shown, even if Lb 12 Equally divided into Lc 12 and Lc 21 , Lb 23 Equally divided into Lc 23 and Lc 32 , Lb 13 Equally divided into Lc 13 and Lc 31 It also became with Figure 6 The same result as B. At this point, Figure 7 Lc1 and Figure 6 For B, Lb1 is equal to Lb2, Lc2 is equal to Lb2, Lc3 is equal to Lb3, and the load Rc2 is equal to Rb2, and Rc3 is equal to Rc2. Additionally, regarding the power supply voltage, Figure 6 A's Va Figure 6 B's Vb, Figure 7 The Vc values ​​are equal.

[0141] Therefore, Figure 2 The equivalent circuit shown is Figure 1 The three-phase magnetically coupled circuit shown is equivalent. This result is only under one condition, but it remains equivalent to the above even if the input power supply (AC power supply), coupling coefficient, or inductance value connected to the magnetically coupled circuit changes. Furthermore, the result remains the same even if the load connected to the three-phase magnetically coupled circuit is composed of a combination of active or passive circuits other than resistors. For example, as... Figure 8 As shown, K1, K2, and K3, which are equivalent to coupling coefficients k12, k23, and k13, can all be different, and the equivalent circuit remains valid even if the power supply voltage, the circuit topology of the load circuit, and the circuit constants change. Figure 8 In the diagram, z1 is "104.9μH", z2 is "-18.97μH", z3 is "4.87μH", and z 12 "18.97μH", z 23 "12.00μH", z 13The value is "-107.5μH", and resonance and anti-resonance occur at approximately 9MHz. However, it is known that the amplitude and phase are exactly the same for both the circuit with and without magnetic coupling based on this embodiment. This is as follows: Figure 6 B and Figure 7 That kind of relationship Figure 8 Lb 12 Lb 23 Lb 13 This also applies when performing a segmentation.

[0142] Furthermore, in Embodiment 1, an example of using a three-phase magnetic coupling circuit in a transformer was described. However, this magnetic coupling circuit is not limited to transformers. For example, it can be used in any circuit where three coils (inductors) are magnetically coupled through mutual inductance, such as in a motor, compressor, insulation circuit, wireless power transmission circuit, coupling between wiring based on residual inductance, or coupling between circuit components based on residual inductance.

[0143] In conventional circuit theory, it is believed that a circuit containing magnetic coupling cannot be represented by a circuit without magnetic coupling. Therefore, a circuit without magnetic coupling is represented by current, and a magnetic circuit containing magnetic coupling is represented by magnetic current. Although the circuit and the magnetic circuit are in a comparative relationship, they are generally solved as different circuits. For example, the electromotive force, current, and resistance of the circuit are compared with the magnetomotive force, magnetic current, and magnetic reluctance of the magnetic circuit. This theory assumes that the circuit and the magnetic circuit are in an orthogonal coordinate system relationship and exist completely independently without any relation. In contrast, Implementation 1 shows that there are equations (7) to (12) that transform the magnetic circuit into a circuit and equations (13) to (19) that transform the circuit into a magnetic circuit. That is, contrary to conventional circuit theory, it shows that the circuit and the magnetic circuit do not have a completely orthogonal coordinate system relationship, but have a dependency relationship according to equations (7) to (12) and equations (13) to (19) that can only be expressed by arithmetic operations, i.e., an oblique coordinate system relationship.

[0144] As described above, according to Embodiment 1, the equivalent circuit of the magnetic coupling circuit is an equivalent circuit of a three-phase magnetic coupling circuit formed by the mutual inductance of the primary-side inductor, the secondary-side inductor, and the tertiary-side inductor. It is configured to include: a first impedance disposed between the positive and negative terminals of the primary side; a second impedance disposed between the positive and negative terminals of the secondary side; a third impedance disposed between the positive and negative terminals of the tertiary side; a fourth impedance disposed between the positive and negative terminals of the primary and secondary sides; a fifth impedance disposed between the positive and negative terminals of the secondary and tertiary sides; and a sixth impedance disposed between the positive and negative terminals of the primary and tertiary sides. Therefore, in Embodiment 1, an equivalent circuit of a three-phase magnetic coupling circuit without magnetic coupling can be obtained. Furthermore, the magnetic coupling circuit can be represented as a graph structure. If the magnetic coupling circuit can be represented as a graph structure, processing in graph networks or graph neural networks can be performed.

[0145] Furthermore, according to Embodiment 1, the equivalent circuit of the magnetic coupling circuit is the equivalent circuit of a three-phase magnetic coupling circuit formed by the mutual inductance of the primary-side inductor, the secondary-side inductor, and the tertiary-side inductor. It is configured to include: a first impedance disposed between the positive terminal and the negative terminal of the primary side; a second impedance disposed between the positive terminal and the negative terminal of the secondary side; a third impedance disposed between the positive terminal and the negative terminal of the tertiary side; a fourth impedance disposed between the positive terminal of the primary side and the positive terminal of the secondary side; a fifth impedance disposed between the negative terminal of the primary side and the negative terminal of the secondary side; a sixth impedance disposed between the positive terminal of the secondary side and the positive terminal of the tertiary side; a seventh impedance disposed between the negative terminal of the secondary side and the negative terminal of the tertiary side; an eighth impedance disposed between the positive terminal of the primary side and the positive terminal of the tertiary side; and a ninth impedance disposed between the negative terminal of the primary side and the negative terminal of the tertiary side. Therefore, in Embodiment 1, an equivalent circuit of a three-phase magnetically coupled circuit that does not include magnetic coupling can be obtained. Furthermore, the magnetically coupled circuit can be represented as a graph structure; if the magnetically coupled circuit can be represented as a graph structure, then processing in graph networks or graph neural networks can be performed.

[0146] Furthermore, let the complex number be j, the angular frequency be ω, the inductance of the primary inductor in the magnetic coupling circuit be L1, the inductance of the secondary inductor in the magnetic coupling circuit be L2, the inductance of the tertiary inductor in the magnetic coupling circuit be L3, and the mutual inductance between the primary and secondary inductors be M. 12 Let the mutual inductance between the secondary and tertiary inductors be M. 23 Let the mutual inductance between the primary and tertiary inductors be M. 13Then, the first impedance z1, the second impedance z2, the third impedance z3, and the fourth impedance z4 are calculated using the above equations (7) to (12). 12 The fifth impedance z 23 and the sixth impedance z 13 Therefore, in Embodiment 1, for each of the first to sixth impedances constituting the equivalent circuit, it is possible to calculate the circuit constants that are electrically equivalent to the magnetically coupled circuit.

[0147] Furthermore, the circuit constant of the fourth impedance is equal to the circuit constant of the fifth impedance, the circuit constant of the sixth impedance is equal to the circuit constant of the seventh impedance, and the circuit constant of the eighth impedance is equal to the circuit constant of the ninth impedance. Therefore, in Embodiment 1, in graph processing such as graph neural networks where Kirchhoff's law of current conservation does not hold, processing based on the characteristics of the magnetically coupled circuit can be performed.

[0148] Furthermore, the inductance L1 of the primary side inductor of the magnetic coupling circuit, the inductance L2 of the secondary side inductor of the magnetic coupling circuit, the inductance L3 of the tertiary side inductor of the magnetic coupling circuit, and the mutual inductance M between the primary side inductor and the secondary side inductor are calculated using the above equations (13) to (19). 12 The mutual inductance M between the secondary and tertiary inductors 23 And the mutual inductance M between the primary and tertiary inductors. 13 Therefore, in Embodiment 1, the circuit constants of the magnetically coupled circuit can be calculated using the circuit constants of each of the first to ninth impedances constituting the equivalent circuit. That is, it is possible to inversely transform an equivalent circuit without magnetic coupling into a circuit containing magnetic coupling.

[0149] Furthermore, let the complex number be j, the angular frequency be ω, the inductance of the primary inductor in the magnetic coupling circuit be L1, the inductance of the secondary inductor in the magnetic coupling circuit be L2, the inductance of the tertiary inductor in the magnetic coupling circuit be L3, and the mutual inductance between the primary and secondary inductors be M. 12 Let the mutual inductance between the secondary and tertiary inductors be M. 23 Let the mutual inductance between the primary and tertiary inductors be M. 13 Then, the first impedance z1, the second impedance z2, the third impedance z3, the fourth impedance z4, the fifth impedance z5, the sixth impedance z6, the seventh impedance z7, the eighth impedance z8, and the ninth impedance z9 are calculated using the above formulas (7) to (12). The sum of z4 and z5 equals z 12 The sum of z6 and z7 equals z 23 The sum of z8 and z9 equals z 13Therefore, in Embodiment 1, for each of the first to ninth impedances constituting the equivalent circuit, it is possible to calculate the circuit constants that are electrically equivalent to the magnetically coupled circuit.

[0150] Implementation method 2.

[0151] In Embodiment 1, an equivalent circuit configured as a magnetic coupling circuit including inductance and mutual inductance on the primary to tertiary sides is described. In Embodiment 2, an equivalent circuit considering parasitic components such as residual resistance, parasitic capacitance, and residual inductance caused by the physical size or structure of the actual magnetic coupling circuit is described.

[0152] Figure 9 This is a diagram illustrating an example of a three-phase magnetic coupling circuit according to Embodiment 2. This magnetic coupling circuit is relative to... Figure 1 The magnetic coupling circuit shown has an impedance X1 connected between the positive terminal on the primary side and the positive terminal on the secondary side, an impedance X2 connected between the positive terminal on the secondary side and the positive terminal on the tertiary side, and an impedance X3 connected between the positive terminal on the primary side and the positive terminal on the tertiary side. Furthermore, there are short circuits between the negative terminals on the primary side and the negative terminals on the secondary side, between the negative terminals on the secondary side and the negative terminals on the tertiary side, and between the negative terminals on the primary side and the negative terminals on the tertiary side. Impedances X1 to X3 are considered, for example, in addition to being considered as floating capacitance (also called parasitic capacitance) generated by spatial coupling, or as a conductance component representing the degree of current leakage, as well as capacitors with a physical reality, placed between the primary and secondary sides, between the secondary and tertiary sides, and between the primary and tertiary sides to reduce electromagnetic noise. Moreover, any circuit component that can measure impedance characteristics, such as an inductor or diode, can be used.

[0153] In Embodiment 2, similarly to Embodiment 1, the circuit constants of the equivalent circuit can be determined, such that... Figure 9 The three-phase magnetic coupling circuit shown and Figure 2 The equivalent circuit shown has the same electrical characteristics according to Kirchhoff's laws.

[0154] Specifically, let the complex number be j, and the angular frequency be ω (= 2π × (frequency [Hz])). To avoid complicating the mathematical expression, we will... Figure 9 In the magnetic coupling circuit shown, the impedance value obtained by multiplying the inductance between the primary side terminals by j×ω is defined as L1; the impedance value obtained by multiplying the inductance between the secondary side terminals by j×ω is defined as L2; ​​the impedance value obtained by multiplying the inductance between the tertiary side terminals by j×ω is defined as L3; and the impedance value obtained by multiplying the mutual inductance between the primary and secondary side inductances by j×ω is defined as M. 12The impedance value obtained by multiplying the mutual inductance between the secondary and tertiary inductances by j×ω is defined as M. 23 The impedance value obtained by multiplying the mutual inductance between the primary and tertiary inductances by j×ω is defined as M. 13 In addition, Figure 9 In the magnetic coupling circuit shown, the impedance value of impedance X1 is defined as X1, the impedance value of impedance X2 is defined as X2, and the impedance value of impedance X3 is defined as X3.

[0155] In addition, to simplify the following explanation, a is defined as follows (20): 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 .

[0156]

[0157] Furthermore, to simplify the following explanation, A and b are defined as follows (21): 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 .

[0158]

[0159] Furthermore, to simplify the following explanation, c is defined as follows (22): 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33 .

[0160]

[0161] At this time, Figure 2 In the equivalent circuit shown, let the first impedance z1, the second impedance z2, the third impedance z3, and the fourth impedance z4 be... 12 , 5th impedance z 23 The circuit constant of the 6th impedance is z. 13 At that time, Figure 9The magnetic coupling circuit shown is Figure 2 The following equations (23) to (28) hold true between the circuit constants of the equivalent circuit shown.

[0162]

[0163] When the impedance between mutual inductances is considered to be insulating, X1, X2, and X3 are assumed to be sufficiently large. Therefore, in equation (20), a 11 a 22 and a 33 The a component is "1", and all other components of a are "0". Therefore, in equation (21), A is "1" and b is "0". 11 b 22 and b 33 The value of b is "1", and all other components of b are "0". As a result, in equation (22), c... 11 =L1、c 12 =M 12 c 13 =M 13 c 21 =M 12 c 22 =L2、c 23 =M 23 c 31 =M 13 c 32 =M 23 c 33 =L3, therefore, equations (23) to (28) are equal to equations (7) to (12) above.

[0164] As described above, according to Embodiment 2, the equivalent circuit of the magnetic coupling circuit is defined by the complex number j, the angular frequency ω, and the impedance value L1 (multiplied by j×ω) of the inductance of the primary inductor of the magnetic coupling circuit, the impedance value L2 (multiplied by j×ω) of the inductance of the secondary inductor of the magnetic coupling circuit, the impedance value L3 (multiplied by j×ω) of the inductance of the tertiary inductor of the magnetic coupling circuit, and the impedance value M (multiplied by j×ω) of the mutual inductance between the primary and secondary inductors. 12 Let the impedance obtained by multiplying the mutual inductance between the secondary and tertiary inductors by j×ω be M. 23 Let the impedance obtained by multiplying the mutual inductance between the primary and tertiary inductors by j×ω be M. 13Let the impedance between the positive terminal of the inductor on the primary side and the positive terminal of the inductor on the secondary side be X1, let the impedance between the positive terminal of the inductor on the secondary side and the positive terminal of the inductor on the tertiary side be X2, and let the impedance between the positive terminal of the inductor on the primary side and the positive terminal of the inductor on the tertiary side be X3. Define a as in equation (20) above. 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 Define A and b as in equation (21) above. 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 c is defined as in equation (22) above. 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33 Then, the first impedance z1, the second impedance z2, the third impedance z3, and the fourth impedance z4 are calculated using the above equations (23) to (28). 12 The fifth impedance z 23 and the sixth impedance z 13 Therefore, in Embodiment 2, in addition to the effects of Embodiment 1, even when the magnetic coupling circuit contains parasitic components, it is possible to calculate the circuit constants that are electrically equivalent to the magnetic coupling circuit for each of the first to sixth impedances constituting the equivalent circuit.

[0165] Implementation method 3.

[0166] In Embodiment 1, an equivalent circuit represented using the first to ninth impedances was described. In Embodiment 3, an example of transforming the above equivalent circuit into a graphical structure was described.

[0167] In Embodiment 3, in the equivalent circuit represented by the first to ninth impedances shown in Embodiment 1, the first impedance is set as the first node, the second impedance as the second node, the third impedance as the third node, the fourth impedance as the fourth node, the fifth impedance as the fifth node, the sixth impedance as the sixth node, the seventh impedance as the seventh node, the eighth impedance as the eighth node, and the ninth impedance as the ninth node.

[0168] Furthermore, by connecting nodes 1 and 4, 1 and 5, 1 and 8, 1 and 9, 2 and 4, 2 and 5, 2 and 6, 2 and 7, 3 and 6, 3 and 7, 3 and 8, and 3 and 9 with edges respectively, the equivalent circuit is transformed into a graph structure.

[0169] Figure 10 This is a diagram illustrating an example of the graph structure of Embodiment 3. This graph structure has nodes 1 through 9 and edges connecting these nodes. Based on this graph structure, graph-related information (hereinafter referred to as "graph information") can be obtained. The graph information may, for example, include information related to the nodes included in the graph structure and information related to the edges included in the graph structure. Additionally, the graph information may also include information indicating the connection relationships between the nodes (hereinafter referred to as "connection information") and attribute information, etc.

[0170] Connection information can be maintained, for example, as node-based text data, as follows. Here, each newline represents a different node, and semicolons (;) are used to separate nodes and edges. Furthermore, the order of the nodes and the order of edges within each node can be freely interchanged.

[0171] Node 1; Edge 1, Edge 2, Edge 11, Edge 12

[0172] Node 2; Edges 3, 4, 5, and 6

[0173] Node 3; Edges 7, 8, 9, and 10

[0174] Node 4; Edge 1, Edge 3

[0175] Node 5; Edge 2, Edge 4

[0176] Node 6; Edges 5 and 7

[0177] Node 7; Edges 6 and 8

[0178] Node 8; Edges 9 and 11

[0179] Node 9; Edges 10 and 12

[0180] Alternatively, connection information can be maintained based on edges, as shown below. In this case, each newline represents a different edge, and a semicolon (;) is used to separate nodes and edges. Furthermore, the order of nodes and the order of nodes within each edge can be freely interchanged.

[0181] Edge 1; Node 1, Node 4

[0182] Edge 2; Node 1, Node 5

[0183] Edge 3; Node 2, Node 4

[0184] Edge 4; Node 2, Node 5

[0185] Edge 5; Node 2, Node 6

[0186] Edge 6; Node 2, Node 7

[0187] Edge 7; Node 3, Node 6

[0188] Edge 8; Node 3, Node 7

[0189] Edge 9; Node 3, Node 8

[0190] Edge 10; Node 3, Node 9

[0191] Edge 11; Node 1, Node 8

[0192] Edge 12; Node 1, Node 9

[0193] Furthermore, connectivity information can be preserved not only as an adjacency matrix, but also as a combination of a connectivity matrix, an order matrix, and a Grafian matrix. In any preservation form, invertible transformations are possible; therefore, connectivity information can be preserved in any form.

[0194] In particular, adjacency matrices are suitable as input forms for graph neural networks and are therefore preferred. An adjacency matrix is ​​a square matrix of (number of nodes) × (number of nodes), where elements are 1 if there is a connection from one node to other nodes, and 0 if there is no connection. Furthermore, in nodes with self-loops, 1s are added to the diagonal elements of the corresponding node; in graphs without self-loops, all diagonal elements are 0s.

[0195] By transforming the equivalent circuit into a graph structure in this way, the magnetically coupled circuit can be processed (graph processing) through graph networks or graph neural networks. Furthermore, by inputting the graph information obtained from the graph structure into the graph neural network, the feature quantities of the magnetically coupled circuit can be extracted.

[0196] Features refer to a set of numerical values ​​in the input training or testing data that serve as clues for predicting the correct label for the training or testing data. These features can be obtained within the framework of graph neural networks. For ranking classification problems, these features can be input into a fully connected layer and output a number of values ​​equal to the number of ranks, with an activation function such as the log softmax function or softmax function used in ranking classification applied immediately before the output layer. Regression problems can be solved by fully coupling these features into the input layer and outputting them as a single numerical value. Furthermore, not only in cases with correct labels, such as ranking classification or regression problems, but also in unsupervised learning (i.e., self-supervised learning) that combines graph neural networks that extract features (like autoencoders) with deep learning that reconstructs the input data from the features, or unsupervised learning that masks node or edge attributes to predict hidden values, is possible. Thus, features are abstract numerical representations of the characteristics of the input data obtained by applying a non-linear function to the input data within a deep learning framework. Although humans cannot understand the features themselves, by combining them with a loss function (the difference between the output and the correct label) for learning, features of the input data can be captured from the data.

[0197] In addition, the extracted features can be used to perform a variety of functions, such as predicting the output voltage between the terminals of a magnetically coupled circuit or the current flowing through the wiring, predicting the frequency characteristics of the voltage or current, predicting the cost of the magnetically coupled circuit, predicting the amount or frequency characteristics of electromagnetic noise generation, predicting the heat generation of coils or transformers, capacitors, semiconductors, etc., optimizing circuit constants, predicting the number of layers or area required for mounting to semiconductors or printed circuit boards, selecting the best circuit components containing semiconductors, optimizing circuit structure, etc.

[0198] In order to achieve the above functions, the graph information obtained by transforming the equivalent circuit into a graph structure as described in Implementation 3, and the graph information as supervision data (e.g., selecting any integer from 1 to 10), regression data (e.g., calculating any real value from 0 to 1), or waveform (as time information, for example, regression data containing N columns) can be provided to the graph neural network.

[0199] For example, predicting the output signal between the terminals of a magnetically coupled circuit is waveform prediction; predicting the cost of a magnetically coupled circuit is regression prediction; predicting the amount of electromagnetic noise generated or the frequency characteristics in a magnetically coupled circuit is a waveform prediction or regression problem; predicting the heat generation of semiconductors in a magnetically coupled circuit is regression prediction; optimizing the circuit constant of a magnetically coupled circuit is regression prediction; predicting the number of semiconductor or printed circuit board layers in a magnetically coupled circuit is classification prediction; predicting the area is regression prediction; selecting circuit components containing semiconductors in a magnetically coupled circuit is classification prediction; and optimizing the circuit structure of a magnetically coupled circuit is a binary classification problem involving the presence or absence of wiring. All of the above functions can be implemented using existing methods of graph neural networks.

[0200] Furthermore, by applying autoencoders, variational autoencoders, or GANs (Generative Adversarial Networks) to graph neural networks, generative models of magnetically coupled circuits can be constructed. For example, in any learning process—supervised, unsupervised, or reinforcement learning—graph neural networks can be used to process circuits with magnetically coupled components, such as three-phase three-wire transformers, insulated circuits, electric motors, compressors, or wireless power transmission systems, which transmit or receive electricity or signals via space or magnetic bodies. This is not limited to the aforementioned circuit components; all circuit components represented by mutual inductance or coupling coefficients are considered objects, regardless of the circuit's size, type, purpose, frequency, power, or other conditions.

[0201] Figure 11 This is a diagram illustrating an example of the diagram structure of Embodiment 3. This diagram structure will... Figure 3 In the equivalent circuit shown, the positive terminal on the primary side is designated as the first terminal node, the negative terminal on the primary side is designated as the second terminal node, the positive terminal on the secondary side is designated as the third terminal node, the negative terminal on the secondary side is designated as the fourth terminal node, the positive terminal on the secondary side is designated as the fifth terminal node, and the negative terminal on the secondary side is designated as the sixth terminal node. Furthermore, the following connections are made using edges: the first terminal node is connected to the first node, the first terminal node is connected to the fourth node, the first terminal node is connected to the eighth node, the second terminal node is connected to the first node, the second terminal node is connected to the fifth node, the second terminal node is connected to the ninth node, the third terminal node is connected to the second node, the third terminal node is connected to the fourth node, the third terminal node is connected to the sixth node, the fourth terminal node is connected to the second node, the fourth terminal node is connected to the fifth node, the fourth terminal node is connected to the seventh node, the fifth terminal node is connected to the third node, the fifth terminal node is connected to the sixth node, the fifth terminal node is connected to the eighth node, the sixth terminal node is connected to the third node, the sixth terminal node is connected to the seventh node, and the sixth terminal node is connected to the ninth node.

[0202] In this circuit structure, for example, by inputting signals with phases staggered by 60 degrees to terminal nodes 1, 3, and 5, power-converted signals can be output to terminal nodes 2, 4, and 6. Alternatively, signals with phases staggered by 60 degrees can be input to terminal nodes 2, 4, and 6, and power-converted signals can be output to terminal nodes 1, 3, and 5. Furthermore, a bidirectional circuit can be constructed, for example, connecting an input circuit and a load circuit between terminal nodes 1 and 2, between terminal nodes 3 and 4, and between terminal nodes 5 and 6, and switching them using semiconductor switches, similar to regenerative braking, thereby allowing selective switching of the input circuit and the load circuit.

[0203] Furthermore, it is preferable to assign the aforementioned attribute information to each node from node 1 to node 9. While the attribute information can freely be assigned to each node, including numerical values, when processing each node as a graph, the size of the attribute information matrix (the number of rows and columns in a two-dimensional case) and the information of the elements input into each matrix should be consistent. In this case, the entire graph can be aggregated and processed via a graph network or graph neural network without relying on nodes or requiring pre-processing or post-processing, making processing easier and therefore preferred. Moreover, as long as the number of elements in the matrix is ​​equal, it is not limited to one-dimensional form; it can also be any form, such as a tensor or more of two dimensions. For example, by setting it to 1 row and N columns, it can hold N elements, making it easy to maintain tabular data, thus making it a preferred method of utilization.

[0204] The attribute information of each node at least retains the circuit constants of each impedance. In Implementation 3, the circuit constants of each impedance can take negative values. For example, the circuit constant of the first impedance is "10μH", the circuit constant of the second impedance is "-3μH", the circuit constant of the third impedance is "1μH", etc.

[0205] In particular, in graph neural networks, activation functions such as ReLU, Sigmoid, Tanh, or Softmax tend to respond to signals of real numbers between 0 and 1, or integers between 0 and 1. Therefore, it is preferable to normalize the attribute information of nodes and edges to be greater than 0 and less than 1 (e.g., in the case of ReLU) or greater than -1 and less than 1 (e.g., in the case of Tanh). However, when considering negative circuit constants such as negative resistance or negative inductance that only arise under special conditions, the attribute information of nodes is limited to a dynamic range of half the positive value when normalizing the node attribute information.

[0206] For example, when "10μH" and "20μH" are normalized using real numbers from 0 to 1, they become "0.10" and "0.11", but when normalized considering the negative components, they become "0.100" and "0.105". The difference between the two becomes smaller, which can easily lead to information degradation due to the rounding error of the computer in the processing of graph neural networks and the like.

[0207] Therefore, the attribute information corresponding to the circuit constants of each impedance can be represented by a first element indicating the positive or negative sign and a second element indicating the absolute value of each impedance. Thus, negative elements are not included in the node's attribute information, thereby preventing a reduction in the accuracy of the attribute information.

[0208] For example, when the circuit constant corresponding to node 1 is set to "10μH" and the circuit constant corresponding to node 2 is set to "-3μH", the circuit constant corresponding to node 2 is a negative real number. Therefore, the first element of the attribute information for node 2 is set to "1". On the other hand, the circuit constant corresponding to node 1 is a positive real number, so the first element of the attribute information for each node is set to "0". Furthermore, by inputting the absolute value of the circuit constant of each node into the second element of the attribute information, the attribute information for each node is as follows.

[0209] Node 1; 0, 10μH

[0210] Node 2; 1, 3μH

[0211] Therefore, since the attribute information does not contain negative elements, the information content of the attribute information will not decrease due to the reduction in dynamic range, thus suppressing the reduction in processing accuracy in the graph neural network. In particular, the circuit constant after taking the absolute value can be logarithmically normalized. Therefore, by normalizing to 0~1 or -1~1 after taking the logarithm, a circuit constant as small as 1pF will not be rounded off, which is preferred. Furthermore, for example, in circuit simulation, when the coupling coefficient k is set to 1, sometimes "0" is included in the attribute information. In this case, "0" is neither positive nor negative. Therefore, the first element representing the symbol can be set to "0" or "1", but it is preferred to set it to a positive value. This is because information such as a negative circuit constant is generated under special conditions. By setting the circuit constant to negative when it is generated under special conditions, it can be processed by graph neural networks as information with a large amount of information, such as information about a special component. When "0" is an element, it is always 0 regardless of the elements of the weight matrix of the graph neural network. Therefore, by implementing a hidden layer, 0 propagates to the surrounding nodes and does not have special information. In contrast, when assigning "1" as an element, by applying a hidden layer, elements other than 0 propagate to nodes surrounding the node with the "1" element, thus propagating specific information. Therefore, the element with "1" is preferably used for negative values ​​as specific information, and set to "0" for positive values. Furthermore, in practical magnetically coupled circuits, the coupling coefficient k will not be "1". Therefore, by inputting components infinitely close to "1", such as "0.9999", the circuit constant is transformed into a value larger than "0". Thus, the problem of reduced information content of attribute information as described above is avoided, which is preferable.

[0212] Furthermore, in equations (7) to (12) shown in Implementation 1, the coupling coefficient k being "1" is not valid. The dataset used in the evaluation described later is not real, but a circuit simulation model, so it includes the case where the coupling coefficient k is "1". However, in such cases, the coupling coefficient k is transformed to a value of "0.999" and close to "1". Even with this transformation, in a device that still has actual magnetic coupling, even if the coupling coefficient is infinitely close to "1", it will not become "1", so it is not a constraint. In addition, in equations (10) to (12), when M12, M23, and M13 are all 0, the denominator becomes 0, so z12, z23, and z13 become infinitely large, so it becomes a computer error. In a device that still has actual magnetic coupling, the conductors around the conductor through which the current flows (theoretically an infinitely large distance) also generate an induced electromotive force caused by magnetic coupling, so M12, M23, and M13 take values ​​greater than 0. Therefore, by using equations (10) to (12), when M12, M23, and M13 are all "0", by setting at least one of M12, M23, and M13 to a sufficiently small value, such as "0.000001", it is possible to prevent z12, z23, and z13 from becoming infinitely large and thus causing a computer error.

[0213] Furthermore, such as Figure 11 As shown, when using terminal nodes 1 through 6 in the equivalent circuit, the attribute information of each terminal node from 1 to 6 is preferably as follows. In this case, special effects can be obtained, especially when inputting graph information into the graph neural network.

[0214] Specifically, the attribute information of the first terminal node is assigned the arithmetic mean of the attribute information of the first, fourth, and eighth nodes; the attribute information of the second terminal node is assigned the arithmetic mean of the attribute information of the first, fifth, and ninth nodes; and the attribute information of the third terminal node is assigned the arithmetic mean of the attribute information of the second, fourth, and sixth nodes. Similarly, the attribute information of the fourth terminal node is assigned the arithmetic mean of the attribute information of the second, fifth, and seventh nodes; the attribute information of the fifth terminal node is assigned the arithmetic mean of the attribute information of the third, sixth, and eighth nodes; and the attribute information of the sixth terminal node is assigned the arithmetic mean of the attribute information of the third, seventh, and ninth nodes.

[0215] In a graph neural network, a hidden layer applies a learned weight matrix to the attribute information of its neighboring nodes and embeds it into the node's own attribute information. Initially, by assigning the attribute information of the nodes adjacent to the 1st to 6th terminal nodes to the weight matrix, the convergence of the weight matrix is ​​faster, and divergence is suppressed, preventing the processing result from falling to a minimum. This results in reduced computation time and improved computational accuracy. Furthermore, when the dataset is small, or when computation time is not limited, the attribute information of each terminal node from the 1st to the 6th terminal nodes can be set to "0", or the elements representing terminal nodes can be provided as one-hot vectors. This reduces the user's preconceived notions during learning. However, in the case of nodes with negative elements, such as the 4th to 3rd segments from the top, instead of one-hot vectors, a matrix with two elements having values ​​greater than 0 is used. Furthermore, when using the formulas shown in (23) to (28), if any one of X1, X2, or X3 has an element other than an inductive component, such as a resistive or capacitive component, z1 to z13 cannot be represented by inductance alone. Therefore, they become matrices with two or more elements in the one-hot vector having values ​​greater than 0. Thus, the matrix representing the node attributes does not necessarily have to be a one-hot vector.

[0216] Furthermore, since terminal nodes 1 through 4 are of different types from nodes 1 through 4, the positions of 0 in the matrix (one-hot vector) representing the attributes of each node must differ by at least one position. Therefore, node attributes will not mix within the graph neural network, maintaining a separable state, which is preferred. Learning can also be achieved by inputting circuit constants into the elements of the matrix that are 1, so the positions of 0 are set to be different. However, in the case where the matrix consists only of 0 or 1 (a typical one-hot vector), the positions of 0 differing by at least one position is synonymous with the positions of 1 differing.

[0217] [evaluate]

[0218] Implementation method 3 describes a method for reversibly transforming a magnetically coupled circuit into a graph structure, and conversely, transforming a graph structure back into a magnetically coupled circuit. The circuit information of the magnetically coupled circuit is preferably provided as text data containing a netlist obtained based on the equivalent circuit of the magnetically coupled circuit.

[0219] Regarding the accuracy of the transformation from a magnetically coupled circuit to a graph structure, if the netlist can be transformed into a graph structure, and then the transformed graph structure can be inversely transformed back into a netlist to reconstruct the original magnetically coupled circuit, then the transformation from a magnetically coupled circuit to a graph structure is considered to have no information degradation. However, since the transformation from a netlist to a graph structure and from a graph structure to a netlist cannot be performed reversibly, other algorithms are needed. Furthermore, as an evaluation method for the generated netlist, circuit simulation using the netlist is considered, but it is not guaranteed that the graph structure can be inversely transformed into data that can complete circuit simulation without errors, even with small information loss.

[0220] Therefore, the inventors of this application have designed the following method: without performing an inverse transformation from the graph structure to the netlist, the graph information contained in the generated graph structure is input into a graph neural network, and the transformation accuracy from the magnetically coupled circuit to the graph structure is confirmed based on the inference accuracy of the graph neural network. The graph information input to the graph neural network includes, for example, information related to the nodes contained in the graph structure and information related to the edges, and may also include the aforementioned connection information and attribute information.

[0221] In the transformation from a magnetically coupled circuit to a graph structure, if information degradation is minimal, the information required for inference by the graph neural network is more likely to remain, thus increasing inference accuracy. Conversely, if significant information degradation occurs during the transformation, the inference accuracy of the graph neural network is expected to decrease. To fairly compare Implementation 3 with existing examples, the graph neural network's structure (number of hidden layers or channels in each hidden layer), number of rounds, number of mini-batches, and optimization method remain unchanged, except for increasing the number of nodes representing impedances 4 through 9 in the equivalent circuit of the magnetically coupled circuit. Furthermore, the learning and testing data are fixed. Additionally, since graph neural networks are biased during learning due to the initial value of random numbers, averaging through 10 learning iterations mitigates this bias. The dataset uses 3,308 netlists extracted from 3,308 circuits included with Analog Devices' LTspice. 2,315 netlists (equivalent to 70%) are used as learning data, and 993 are used as testing data; the learning and testing data remain fixed.

[0222] Then, as Figure 12 As shown, a ranking classification problem was generated using seven types of circuit components. Figure 12 The diagram shows the number of circuits, the average number of nodes, the average number of edges, and the average number of node types contained in the netlist used as the dataset. Figure 12Among the circuit components, power products are the most numerous, accounting for 70% of the total. Furthermore, the learning data and test data are randomly divided into equal quantities in a way that avoids bias.

[0223] Furthermore, since the circuits contained in the dataset are small in scale, nodes 1 through 9 are used in the graph structure, while terminal nodes 1 through 6 are not used. However, when the circuit scale increases and multiple components are connected to circuit components containing magnetic coupling, it is preferable to use terminal nodes 1 through 6 in the graph structure.

[0224] [Graph Neural Network]

[0225] The graph neural network consists of a neural network with three hidden layers. Furthermore, in the algorithm for reducing inter-node information to extract features from magnetically coupled circuits, GraphSage, which boasts the highest inference accuracy under all conditions among existing algorithms, is used. In the three-layer neural network based on GraphSage and the ReLU function as the activation function, the softmax function is used as the activation function before the output layer for 7-value classification.

[0226] [Experimental Results]

[0227] exist Figure 13 In this example, for comparison, the results of learning and inference are shown without considering mutual inductance M, assuming no mutual inductance M. Learning is represented by 4,000 repetitions (epochs), where epoch represents the average of the 10 trials in the epoch with the highest inference accuracy. Figure 13 In this study, the maximum inference accuracy based on the test data was 97.20%.

[0228] in addition, Figure 14 This indicates the inference accuracy when using the graph transformation method described in Embodiment 3 to generate learning data and test data, and using the test data to infer the type of circuit component. Figure 13 Similarly, in the existing example shown, when the average of the maximum values ​​from 10 trials is calculated, the maximum inference accuracy is 97.51%, which is consistent with... Figure 13 Compared to the existing examples shown, the inference accuracy for the test data is improved by 0.31%.

[0229] Of the 3,308 sampling circuits included in LTspice, 26 are three-phase magnetically coupled circuits, representing 0.79% of the total. While this percentage is small, it confirms an improvement in inference accuracy during both learning and inference. Furthermore, the learning time using a GPU (Nvidia RTX A5000) is... Figure 13The existing example shown is 7 minutes, in Figure 14 In the implementation method 3 shown, the time was 8 minutes, and no significant difference was observed.

[0230] As described above, the transformation method of Embodiment 3 is a method of transforming the equivalent circuit of the magnetic coupling circuit described above into a graphical structure. Its characteristic is that the first impedance of the equivalent circuit is designated as the first node, the second impedance as the second node, the third impedance as the third node, the fourth impedance as the fourth node, the fifth impedance as the fifth node, the sixth impedance as the sixth node, the seventh impedance as the seventh node, and the eighth impedance as the eighth node. Let the 9th impedance of the equivalent circuit be the 9th node. Connect the 1st and 4th nodes, the 1st and 5th nodes, the 1st and 8th nodes, the 1st and 9th nodes, the 2nd and 4th nodes, the 2nd and 5th nodes, the 2nd and 6th nodes, the 2nd and 7th nodes, the 3rd and 6th nodes, the 3rd and 7th nodes, the 3rd and 8th nodes, and the 3rd and 9th nodes with edges respectively. Thus, the transformation method of Embodiment 3 can transform the equivalent circuit of the magnetically coupled circuit described above into a graph structure represented by a combination of nodes and edges.

[0231] Furthermore, let the positive terminal of the primary side of the equivalent circuit be the first terminal node, the negative terminal of the primary side of the equivalent circuit be the second terminal node, the positive terminal of the secondary side of the equivalent circuit be the third terminal node, the negative terminal of the secondary side of the equivalent circuit be the fourth terminal node, the positive terminal of the cubic side of the equivalent circuit be the fifth terminal node, and the negative terminal of the cubic side of the equivalent circuit be the sixth terminal node. Connect the first terminal node to the first node, the first terminal node to the fourth node, the first terminal node to the eighth node, the second terminal node to the first node, and the second terminal node to the eighth node, respectively, using edges to connect the first terminal node to the second terminal node. The relationships between the 5th and 6th nodes are as follows: between the 2nd and 9th terminal nodes, between the 3rd and 2nd terminal nodes, between the 3rd and 4th terminal nodes, between the 3rd and 6th terminal nodes, between the 4th and 2nd terminal nodes, between the 4th and 5th terminal nodes, between the 4th and 7th terminal nodes, between the 5th and 3rd terminal nodes, between the 5th and 6th terminal nodes, between the 5th and 8th terminal nodes, between the 6th and 3rd terminal nodes, between the 6th and 7th terminal nodes, and between the 6th and 9th terminal nodes. Thus, the transformation method of Embodiment 3 can transform the equivalent circuit of the magnetic coupling circuit described above into a graph structure represented by a combination of nodes, edges, and terminal nodes.

[0232] Furthermore, attribute information is assigned to each node from node 1 to node 9, and the attribute information of node 1 is assigned a circuit constant of the first impedance, the attribute information of node 2 is assigned a circuit constant of the second impedance, the attribute information of node 3 is assigned a circuit constant of the third impedance, the attribute information of node 4 is assigned a circuit constant of the fourth impedance, the attribute information of node 5 is assigned a circuit constant of the fifth impedance, the attribute information of node 6 is assigned a circuit constant of the sixth impedance, the attribute information of node 7 is assigned a circuit constant of the seventh impedance, the attribute information of node 8 is assigned a circuit constant of the eighth impedance, and the attribute information of node 9 is assigned a circuit constant of the ninth impedance. Thus, the transformation method of Embodiment 3 can transform the equivalent circuit of the magnetically coupled circuit described above into a graph structure represented by a combination of nodes, edges, and node attribute information.

[0233] Furthermore, the attribute information of the 1st node, the 2nd node, the 3rd node, the 4th node, the 5th node, the 6th node, the 7th node, the 8th node, and the 9th node all have at least a first element representing the positive or negative sign of the circuit constant and a second element representing the absolute value of the circuit constant. Therefore, in Embodiment 3, information degradation during the normalization of the attribute information of each of the 1st to 3rd nodes can be suppressed.

[0234] In addition, attribute information is assigned to each terminal node from the 1st to the 6th terminal node and to each node from the 1st to the 9th node. The attribute information of the 1st terminal node is assigned the arithmetic mean of the attribute information of the 1st node, the 4th node, and the 8th node. The attribute information of the 2nd terminal node is assigned the arithmetic mean of the attribute information of the 1st node, the 5th node, and the 9th node. The attribute information of the 3rd terminal node is assigned the arithmetic mean of the attribute information of the 2nd node, the 4th node, and the 6th node. The attribute information of the 4th terminal node is assigned the arithmetic mean of the attribute information of the 2nd node, the 5th node, and the 7th node. The attribute information of the 5th terminal node is assigned the arithmetic mean of the attribute information of the 3rd node, the 6th node, and the 8th node. The attribute information of the 6th terminal node is assigned the arithmetic mean of the attribute information of the 3rd node, the 7th node, and the 9th node. Therefore, in implementation method 3, the convergence of the weight matrix when processing the transformed graph structure through the graph neural network becomes faster, and the processing divergence can be suppressed, preventing the processing result from falling into a minimum value.

[0235] Furthermore, the number of attribute information elements is the same for all nodes from node 1 to node 9. Therefore, in embodiment 3, no preprocessing or post-processing is required, and graph information can be used as input data to the graph network or graph neural network, making processing easier.

[0236] Furthermore, the feature extraction method of Embodiment 3 is a method for extracting the feature quantities of a three-phase magnetically coupled circuit formed by the mutual inductance of the primary, secondary, and tertiary inductors. This method extracts the feature quantities of the magnetically coupled circuit by using the node representation information and edge representation information obtained from the graph structure obtained through the aforementioned transformation method as input information to a graph neural network. Therefore, the feature extraction method of Embodiment 3 can extract the feature quantities of a magnetically coupled circuit using the graph structure obtained from the equivalent circuit transformation of a single-phase magnetically coupled circuit.

[0237] Furthermore, the feature extraction method of Embodiment 3 is a method for extracting the feature quantities of a three-phase magnetically coupled circuit formed by the mutual inductance of the primary, secondary, and tertiary inductors. This method extracts the feature quantities of the magnetically coupled circuit by using the node representation information, edge representation information, and node attribute information obtained from the graph structure obtained through the aforementioned transformation method as input information to a graph neural network. Therefore, the feature extraction method of Embodiment 3 can extract the feature quantities of a magnetically coupled circuit using the graph structure obtained from the equivalent circuit transformation of a single-phase magnetically coupled circuit.

[0238] Furthermore, this disclosure allows for free combination of various embodiments, modification of any constituent elements of each embodiment, or omission of any constituent elements in each embodiment.

[0239] Industrial availability

[0240] This disclosure provides an equivalent circuit for a three-phase magnetically coupled circuit that does not contain magnetic coupling, and is suitable for equivalent circuits, transformation methods, and feature extraction methods for magnetically coupled circuits.

[0241] Label Explanation

[0242] L1, L2, L3, L4, L5, L6, L7, L8, L9, L 10 L 11 L 12 Inductance; M 12 M 23 M 13 : Mutual inductance; v1: Voltage between terminals of the primary inductor; v2: Voltage between terminals of the secondary inductor; v3: Voltage between terminals of the tertiary inductor; X1, X2, X3: Impedance.

Claims

1. An equivalent circuit of a magnetically coupled circuit, which is an equivalent circuit of a three-phase magnetically coupled circuit formed by the mutual inductance of a primary-side inductor, a secondary-side inductor, and a tertiary-side inductor, characterized in that, The equivalent circuit configuration of this magnetic coupling circuit includes: The first impedance is set between the positive terminal and the negative terminal on the primary side; The second impedance is set between the positive terminal and the negative terminal on the secondary side; The third impedance is provided between the positive terminal and the negative terminal on the third side; The fourth impedance is located between the positive terminal on the primary side and the positive terminal on the secondary side. The fifth impedance is provided between the positive terminal on the secondary side and the positive terminal on the tertiary side; and The sixth impedance is located between the positive terminal on the primary side and the positive terminal on the tertiary side.

2. An equivalent circuit of a magnetically coupled circuit, which is an equivalent circuit of a three-phase magnetically coupled circuit formed by the mutual inductance of primary-side inductors, secondary-side inductors, and tertiary-side inductors, characterized in that, The equivalent circuit configuration of this magnetic coupling circuit includes: The first impedance is set between the positive terminal and the negative terminal on the primary side; The second impedance is set between the positive terminal and the negative terminal on the secondary side; The third impedance is provided between the positive terminal and the negative terminal on the third side; The fourth impedance is located between the positive terminal on the primary side and the positive terminal on the secondary side. The fifth impedance is located between the - terminal on the primary side and the - terminal on the secondary side; The sixth impedance is located between the positive terminal on the secondary side and the positive terminal on the tertiary side. The 7th impedance is located between the - terminal on the secondary side and the - terminal on the tertiary side; The eighth impedance is provided between the positive terminal on the primary side and the positive terminal on the tertiary side; and The 9th impedance is located between the - terminal on the primary side and the - terminal on the tertiary side.

3. The equivalent circuit of the magnetic coupling circuit according to claim 1, characterized in that, Let the complex number be j, Let the angular frequency be ω. Let the inductance of the inductor on the primary side of the magnetic coupling circuit be L1. Let the inductance of the inductor on the secondary side of the magnetic coupling circuit be L2. Let the inductance of the inductor on the third side of the magnetic coupling circuit be L3. Let the mutual inductance between the primary-side inductor and the secondary-side inductor be M. 12 , Let the mutual inductance between the secondary-side inductor and the tertiary-side inductor be M. 23 , Let the mutual inductance between the primary-side inductor and the tertiary-side inductor be M. 13 hour, The first impedance z1, the second impedance z2, the third impedance z3, and the fourth impedance z4 are calculated using the following equations (7) to (12). 12 The fifth impedance z 23 and the sixth impedance z 13 , 。 4. The equivalent circuit of the magnetic coupling circuit according to claim 2, characterized in that, The circuit constant of the fourth impedance is equal to the circuit constant of the fifth impedance. The circuit constant of the sixth impedance is equal to the circuit constant of the seventh impedance. The circuit constant of the 8th impedance is equal to the circuit constant of the 9th impedance.

5. The equivalent circuit of the magnetic coupling circuit according to claim 3, characterized in that, The inductance L1 of the primary side inductor of the magnetic coupling circuit, the inductance L2 of the secondary side inductor of the magnetic coupling circuit, the inductance L3 of the tertiary side inductor of the magnetic coupling circuit, and the mutual inductance M between the primary side inductor and the secondary side inductor are calculated using the following equations (13) to (19). 12 The mutual inductance M between the secondary-side inductor and the tertiary-side inductor 23 And the mutual inductance M between the primary-side inductor and the tertiary-side inductor. 13 , 。 6. The equivalent circuit of the magnetic coupling circuit according to claim 1, characterized in that, Let the complex number be j, Let the angular frequency be ω. Let the impedance value obtained by multiplying the inductance of the inductor on the primary side of the magnetic coupling circuit by j×ω be L1. Let the impedance obtained by multiplying the inductance of the inductor on the secondary side of the magnetic coupling circuit by j×ω be L2. Let the impedance value obtained by multiplying the inductance of the inductor on the third side of the magnetic coupling circuit by j×ω be L3. Let the impedance value obtained by multiplying the mutual inductance of the primary-side inductor and the secondary-side inductor by j×ω be M. 12 , Let the impedance value obtained by multiplying the mutual inductance of the secondary-side inductor and the tertiary-side inductor by j×ω be M. 23 , Let the impedance obtained by multiplying the mutual inductance of the primary-side inductor and the tertiary-side inductor by j×ω be M. 13 , Let the impedance value be X1, where X1 is the impedance between the positive terminal of the inductor on the primary side and the positive terminal of the inductor on the secondary side. Let the impedance value between the positive terminal of the inductor on the secondary side and the positive terminal of the inductor on the tertiary side be X2. Let the impedance value between the positive terminal of the inductor on the primary side and the positive terminal of the inductor on the tertiary side be X3. Define a as follows (20): 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 and a 33 , Define A and b as shown in equation (21) below. 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 and b 33 , c is defined as follows (22). 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 and c 33 hour, The first impedance z1, the second impedance z2, the third impedance z3, and the fourth impedance z4 are calculated using the following equations (23) to (28). 12 The fifth impedance z 23 and the sixth impedance z 13 , 。 7. The equivalent circuit of the magnetic coupling circuit according to claim 2 or 4, characterized in that, Let the complex number be j, Let the angular frequency be ω. Let the inductance of the inductor on the primary side of the magnetic coupling circuit be L1. Let the inductance of the inductor on the secondary side of the magnetic coupling circuit be L2. Let the inductance of the inductor on the third side of the magnetic coupling circuit be L3. Let the mutual inductance between the primary-side inductor and the secondary-side inductor be M. 12 , Let the mutual inductance between the secondary-side inductor and the tertiary-side inductor be M. 23 , Let the mutual inductance between the primary-side inductor and the tertiary-side inductor be M. 13 hour, The first impedance z1, the second impedance z2, the third impedance z3, the fourth impedance z4, the fifth impedance z5, the sixth impedance z6, the seventh impedance z7, the eighth impedance z8, and the ninth impedance z9 are calculated using the following equations (7) to (12). ， The sum of z4 and z5 equals z 12 The sum of z6 and z7 equals z 23 The sum of z8 and z9 equals z 13 .

8. A transformation method for transforming the equivalent circuit of the magnetic coupling circuit of claim 2 into a graphical structure, characterized in that, Let the first impedance of the equivalent circuit be the first node. Let the second impedance of the equivalent circuit be the second node. Let the third impedance of the equivalent circuit be the third node. Let the fourth impedance of the equivalent circuit be the fourth node. Let the fifth impedance of the equivalent circuit be the fifth node. Let the sixth impedance of the equivalent circuit be the sixth node. Let the 7th impedance of the equivalent circuit be the 7th node. Let the 8th impedance of the equivalent circuit be the 8th node. Let the 9th impedance of the equivalent circuit be the 9th node. The nodes are connected by edges: the first node and the fourth node, the first node and the fifth node, the first node and the eighth node, the first node and the ninth node, the second node and the fourth node, the second node and the fifth node, the second node and the sixth node, the second node and the seventh node, the third node and the eighth node, and the third node and the ninth node.

9. The transformation method according to claim 8, characterized in that, Let the positive terminal on the primary side of the equivalent circuit be the first terminal node. Let the terminal on the primary side of the equivalent circuit be the second terminal node. Let the positive terminal on the secondary side of the equivalent circuit be the third terminal node. Let the terminal on the secondary side of the equivalent circuit be the fourth terminal node. Let the positive terminal on the third side of the equivalent circuit be the fifth terminal node. Let the terminal on the third side of the equivalent circuit be the sixth terminal node. The following terminals are connected by edges: the first terminal node and the first node, the first terminal node and the fourth node, the first terminal node and the eighth node, the second terminal node and the first node, the second terminal node and the fifth node, the second terminal node and the ninth node, the third terminal node and the second node, the third terminal node and the fourth node, the third terminal node and the sixth node, the fourth terminal node and the second node, the fourth terminal node and the fifth node, the fourth terminal node and the seventh node, the fifth terminal node and the third node, the fifth terminal node and the sixth node, the fifth terminal node and the eighth node, the sixth terminal node and the third node, the sixth terminal node and the seventh node, and the sixth terminal node and the ninth node.

10. The transformation method according to claim 8, characterized in that, Assign attribute information to each node from node 1 to node 9, and Assign the circuit constant of the first impedance to the attribute information of the first node. Assign the circuit constant of the second impedance to the attribute information of the second node. Assign the circuit constant of the third impedance to the attribute information of the third node. Assign the circuit constant of the fourth impedance to the attribute information of the fourth node. Assign the circuit constant of the fifth impedance to the attribute information of the fifth node. Assign the circuit constant of the sixth impedance to the attribute information of the sixth node. Assign the circuit constant of the 7th impedance to the attribute information of the 7th node. Assign the circuit constant of the 8th impedance to the attribute information of the 8th node. Assign the circuit constant of the 9th impedance to the attribute information of the 9th node.

11. The transformation method according to claim 10, characterized in that, The attribute information of the first node, the second node, the third node, the fourth node, the fifth node, the sixth node, the seventh node, the eighth node, and the ninth node all have at least a first element representing the positive or negative sign of the circuit constant and a second element representing the absolute value of the circuit constant.

12. The transformation method according to claim 9, characterized in that, Attribute information is assigned to each terminal node from the first terminal node to the sixth terminal node, and to each node from the first node to the ninth node. The attribute information of the first terminal node is assigned the arithmetic mean of the attribute information of the first node, the attribute information of the fourth node, and the attribute information of the eighth node. The attribute information of the second terminal node is assigned the arithmetic mean of the attribute information of the first node, the attribute information of the fifth node, and the attribute information of the ninth node. The attribute information of the third terminal node is assigned the arithmetic mean of the attribute information of the second node, the attribute information of the fourth node, and the attribute information of the sixth node. The attribute information of the fourth terminal node is assigned the arithmetic mean of the attribute information of the second node, the attribute information of the fifth node, and the attribute information of the seventh node. The attribute information of the fifth terminal node is assigned the arithmetic mean of the attribute information of the third node, the attribute information of the sixth node, and the attribute information of the eighth node. The attribute information of the sixth terminal node is assigned the arithmetic mean of the attribute information of the third node, the attribute information of the seventh node, and the attribute information of the ninth node.

13. The transformation method according to claim 9, characterized in that, Each terminal node from the first terminal node to the sixth terminal node, and each node from the first node to the ninth node, is assigned attribute information using a one-hot vector, and The positions of 0 in the attribute information of the first terminal node to the sixth terminal node are equal. The positions of 0 in the attribute information of nodes 1 through 9 are equal. The position of 0 in each attribute information of the first terminal node to the sixth terminal node is different from the position of 0 in each attribute information of the first node to the ninth node at least once.

14. The transformation method according to claim 10 or 11, characterized in that, The number of attribute information elements of all nodes from node 1 to node 9 is the same.

15. A feature quantity extraction method, comprising extracting feature quantities of a three-phase magnetically coupled circuit formed by mutual inductance of primary-side inductors, secondary-side inductors, and tertiary-side inductors, characterized in that, The information representing nodes and the information representing edges obtained from the graph structure obtained by the transformation method of claim 8 are used as input information for the graph neural network, thereby extracting the feature quantities of the magnetic coupling circuit.

16. A feature quantity extraction method, comprising extracting feature quantities of a three-phase magnetically coupled circuit formed by mutual inductance of primary-side inductors, secondary-side inductors, and tertiary-side inductors, characterized in that, The information representing nodes, the information representing edges, and the attribute information of nodes obtained from the graph structure obtained by the transformation method described in any one of claims 10 to 14 are used as input information for the graph neural network, thereby extracting the feature quantities of the magnetic coupling circuit.

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