Equivalent circuit of magnetic coupling circuit, conversion method, feature extraction method, manufacturing method of equivalent circuit of magnetic coupling circuit, manufacturing method of system, and manufacturing method of feature extraction device

Abstract

This equivalent circuit is for a three-phase magnetic coupling circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled through mutual inductances (M12, M23, M13), and is characterized by comprising: a first impedance provided between a primary-side plus terminal and a primary-side minus terminal; a second impedance provided between a secondary-side plus terminal and a secondary-side minus terminal; a third impedance provided between a tertiary-side plus terminal and a tertiary-side minus terminal; a fourth impedance provided between the primary-side plus terminal and the secondary-side plus terminal; a fifth impedance provided between the secondary-side plus terminal and the tertiary-side plus terminal; and a sixth impedance provided between the primary-side plus terminal and the tertiary-side plus terminal.

Description

Equivalent circuit, conversion method, and feature extraction method for magnetically coupled circuits

[0001] The present disclosure relates to an equivalent circuit of a magnetic coupling circuit, a conversion method, and a feature extraction method.

[0002] For example, Patent Document 1 discloses an equivalent circuit of leakage impedance in a transformer. This transformer is a four-winding transformer configured by adding a quaternary winding, which is a stabilizer winding, to a three-phase magnetically coupled circuit in which three inductance elements are magnetically coupled. Patent Document 1 also discloses a method for calculating the impedance of the equivalent circuit from the leakage impedances present between each of the four windings in this four-winding transformer.

[0003] International Publication No. 2019 / 207640

[0004] If a circuit is represented by a graph structure consisting of points and lines, with circuit components as points and the wiring (conductors) connecting the circuit components as lines, in a circuit that includes magnetic coupling like the one described above (a three-phase magnetically coupled circuit), the inductance elements are connected by spatial coupling, so there are no wirings and it is not possible to define lines.As a result, even if a three-phase magnetically coupled circuit is converted into a graph structure, the magnetic coupling is not reflected in the graph structure, and information degradation occurs when the circuit is converted into a graph structure.

[0005] Therefore, in order to define a three-phase magnetically coupled circuit as a graph structure while suppressing information degradation, it is expected that the three-phase magnetically coupled circuit will be replaced with a circuit that does not include magnetic coupling, and the spatial coupling will be expressed as a circuit component. However, while an equivalent circuit of leakage impedance in a circuit that includes a three-phase magnetically coupled circuit has been known in the past, as in Patent Document 1, a method for replacing a three-phase magnetically coupled circuit with a circuit that does not include magnetic coupling has not been known.

[0006] The present disclosure has been made to solve the above-mentioned problems, and aims to obtain an equivalent circuit of a three-phase magnetically coupled circuit that does not include magnetic coupling.

[0007] The equivalent circuit of the magnetic coupling circuit according to the present disclosure is an equivalent circuit of a three-phase magnetic coupling circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, and is characterized in that it is configured to include a first impedance provided between the primary-side + terminal and the primary-side − terminal, a second impedance provided between the secondary-side + terminal and the secondary-side − terminal, a third impedance provided between the tertiary-side + terminal and the tertiary-side − terminal, a fourth impedance provided between the primary-side + terminal and the secondary-side + terminal, a fifth impedance provided between the secondary-side + terminal and the tertiary-side + terminal, and a sixth impedance provided between the primary-side + terminal and the tertiary-side + terminal. Furthermore, the equivalent circuit of the magnetic coupling circuit according to the present disclosure is an equivalent circuit of a three-phase magnetic coupling circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, and is characterized in that it is configured to include a first impedance provided between the primary-side + terminal and the primary-side − terminal, a second impedance provided between the secondary-side + terminal and the secondary-side − terminal, a third impedance provided between the tertiary-side + terminal and the tertiary-side − terminal, a fourth impedance provided between the primary-side + terminal and the secondary-side + terminal, a fifth impedance provided between the primary-side − terminal and the secondary-side − terminal, a sixth impedance provided between the secondary-side + terminal and the tertiary-side + terminal, a seventh impedance provided between the secondary-side − terminal and the tertiary-side − terminal, an eighth impedance provided between the primary-side + terminal and the tertiary-side + terminal, and a ninth impedance provided between the primary-side − terminal and the tertiary-side − terminal.

[0008] According to the present disclosure, it is possible to obtain an equivalent circuit of a three-phase magnetically coupled circuit that does not include magnetic coupling.

[0009] 5A is a diagram showing an example of a three-phase magnetic coupling circuit according to embodiment 1; FIG. 5B is a diagram showing an example of an equivalent circuit of the three-phase magnetic coupling circuit according to embodiment 1; FIG. 5C is a diagram showing an example of the configuration of a typical conventional three-phase transformer; FIG. 5D is a schematic diagram summarizing the relationship between the conversion and inverse conversion between the three-phase magnetic coupling circuit shown in FIG. 1 and the equivalent circuit shown in FIG. 3, where FIG. 5A is the three-phase magnetic coupling circuit shown in FIG. 1, and FIG. 5B is the equivalent circuit shown in FIG. 3; FIG. 5E is a diagram showing the calculation results of a circuit simulation for a three-phase transformer circuit including magnetic coupling and the equivalent circuit shown in FIG. 2, where FIG. 6A shows a three-phase magnetic coupling circuit including an AC power supply and a load resistor, FIG. 6B shows the equivalent circuit of FIG. 2 including the AC power supply and the load resistor, and FIG. 6C shows the frequency characteristics of the voltages across the load resistors on the secondary and tertiary sides of FIGS. 6A and 6B. １２ Lc １２ and Lc ２１ Divide equally into Lb ２３ Lc ２３ and Lc ３２ Divide equally into Lb １３ Lc １３ and Lc ３１8A shows a three-phase magnetic coupling circuit including an AC power supply and a load resistor, FIG. 8B shows the equivalent circuit of FIG. 2 including an AC power supply and a load resistor, and FIG. 8C shows the frequency characteristics of the voltages across the load resistors on the secondary and tertiary sides of FIGS. 8A and 8B. FIG. 8B shows an example of a three-phase magnetic coupling circuit according to embodiment 2. FIG. 8C shows an example of a graph structure according to embodiment 3. FIG. 8D shows an example of a graph structure according to embodiment 3. FIG. 8E shows an example of a dataset used for a classification problem of the graph neural network according to embodiment 3. FIG. 8F shows, as a conventional example, the inference accuracy for test data when learning is performed without taking magnetic coupling components into consideration. FIG. 8G shows the inference accuracy when training data and test data are created using the conversion method according to embodiment 3 and the type of circuit component is inferred using the test data.

[0010] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Embodiment 1. A circuit including three-phase magnetic coupling according to embodiment 1 (hereinafter referred to as a "three-phase magnetic coupling circuit") is a circuit insulated against direct current and in which three inductance elements (coils) divided into primary, secondary, and tertiary sides are spatially coupled by mutual inductance. In embodiment 1, a method for converting this three-phase magnetic coupling circuit into a graph structure while suppressing information degradation is shown, in which the magnetic coupling circuit is replaced with a three-phase equivalent circuit including six or nine impedance elements.

[0011] The three-phase equivalent circuit shown in the first embodiment can be applied to any magnetically coupled circuit as long as it is a circuit in which three inductance elements are magnetically coupled. For example, the three-phase equivalent circuit shown in the first embodiment can be applied to magnetically coupled circuits, i.e., magnetically coupled circuits that transmit and receive power or signals via space or a magnetic material, such as three-phase, three-wire transformers, isolation circuits, electric motors, compressors, or wireless power transmission. In any of these cases, the three-phase magnetically coupled circuit has a circuit configuration represented by three inductance elements and the mutual inductance or coupling coefficient between the three inductance elements. In these magnetic circuits, the coupling coefficients between the inductance elements do not necessarily need to be equal; they can also be different. As such, the three-phase equivalent circuit shown in the first embodiment is valid for all magnetic circuits regardless of their applications, characteristics, frequencies, etc. Therefore, in the first embodiment, a case in which the three-phase magnetically coupled circuit is used in a transformer will be described as an example.

[0012] In a three-phase magnetic coupling circuit, the power supply side is customarily represented as R, S, and T, and the load side as U, V, and W, or the power supply and load sides are sometimes distinguished using uppercase and lowercase letters. In the first embodiment, the three-phase magnetic coupling circuit will be described as being configured with six terminals: a positive terminal on the primary side, a positive terminal on the secondary side, a positive terminal on the tertiary side, a negative terminal on the primary side, a negative terminal on the secondary side, and a negative terminal on the tertiary side.

[0013] In a three-phase magnetically coupled circuit, a Y connection or a Delta connection is widely used as a wiring method, but since the first embodiment shows a technique for replacing the magnetically coupled portion of a magnetically coupled circuit with a form that does not include magnetic coupling, any wiring method other than magnetic coupling, for example, a power supply or a load, can be used. Therefore, a Y connection or a Delta connection can be made by switching the connections between the + terminal on the primary side, the + terminal on the secondary side, the + terminal on the tertiary side, the - terminal on the primary side, the - terminal on the secondary side, and the - terminal on the tertiary side, and a Y connection or a Delta connection can be used depending on the application.

[0014] Fig. 1 is a diagram showing an example of a three-phase magnetically coupled circuit. Fig. 1 shows a typical magnetically coupled circuit in which three inductance elements are coupled by spatial coupling, and part of the alternating current flowing between the terminals of the primary inductance element of the three inductance elements is transmitted to the secondary and tertiary inductance elements, generating a voltage between the terminals of the secondary and tertiary inductance elements.

[0015] In the following explanation, for simplicity, the primary-side inductance element in a three-phase magnetic coupling circuit may be simply referred to as the "primary side," the secondary-side inductance element may be simply referred to as the "secondary side," and the tertiary-side inductance element may be simply referred to as the "tertiary side."

[0016] In the three-phase magnetic coupling circuit shown in Figure 1, all sides from the primary to the tertiary sides are shown as open ends. However, for example, by connecting an AC power supply between the + and - terminals on the primary side and connecting load resistors between the + and - terminals on the secondary side and between the + and - terminals on the tertiary side, current flows through the circuit, and power from the primary side is propagated to the secondary and tertiary sides by magnetic coupling. Note that while the above describes an example in which an AC power supply is connected between the primary side terminals, the magnetic coupling circuit shown in Figure 1 is symmetrical, and therefore operates in the same way when an AC power supply is connected between the secondary side terminals or the tertiary side terminals. Furthermore, by connecting power supplies to the + terminal on the primary side, the + terminal on the secondary side, and the + terminal on the tertiary side, and connecting loads to the - terminal on the primary side, the - terminal on the secondary side, and the - terminal on the tertiary side, power between the + terminal on the primary side, the + terminal on the secondary side, and the + terminal on the tertiary side can be transmitted as power between the - terminal on the primary side, the - terminal on the secondary side, and the - terminal on the tertiary side.

[0017] FIG. 2 is a diagram showing an example of an equivalent circuit of the magnetic coupling circuit shown in FIG. 1 . This equivalent circuit includes, for example, a first impedance provided between the positive and negative terminals on the primary side, a second impedance provided between the positive and negative terminals on the secondary side, a third impedance provided between the positive and negative terminals on the tertiary side, a fourth impedance provided between the positive terminal on the primary side and the positive terminal on the secondary side, a fifth impedance provided between the positive terminal on the secondary side and the positive terminal on the tertiary side, and a sixth impedance provided between the positive terminal on the primary side and the positive terminal on the tertiary side. FIG. 3 is also a diagram showing an example of an equivalent circuit of a three-phase magnetic coupling circuit. Unlike FIG. 2 , FIG. 3 divides the fourth impedance of FIG. 2 into a fourth impedance and a fifth impedance, the fifth impedance of FIG. 2 into a sixth impedance and a seventh impedance, and the sixth impedance of FIG. 2 into an eighth impedance and a ninth impedance. The value of the fourth impedance in Fig. 2 is equal to the sum of the value of the fourth impedance and the value of the fifth impedance in Fig. 3, the value of the fifth impedance in Fig. 2 is equal to the sum of the value of the sixth impedance and the value of the seventh impedance in Fig. 3, and the value of the sixth impedance in Fig. 2 is equal to the sum of the value of the eighth impedance and the value of the ninth impedance in Fig. 3. Dividing the impedance in this way results in equal values ​​when Kirchhoff's law of conservation of current holds, but in cases where Kirchhoff's law of conservation of current does not necessarily hold, such as in graph networks and graph neural networks, it has the special effect that the characteristics do not change depending on the path because no short circuit is included.

[0018] The first impedance is a circuit component connected in parallel between the positive and negative terminals of the primary side, the second impedance is a circuit component connected in parallel between the positive and negative terminals of the secondary side, the third impedance is a circuit component connected in parallel between the positive and negative terminals of the tertiary side, the fourth impedance is a circuit component connected in series between the positive terminal of the primary side and the positive terminal of the secondary side, the fifth impedance is a circuit component connected in series between the negative terminal of the primary side and the negative terminal of the secondary side, the sixth impedance is a circuit component connected in series between the positive terminal of the secondary side and the positive terminal of the tertiary side, the seventh impedance is a circuit component connected in series between the negative terminal of the secondary side and the negative terminal of the tertiary side, the eighth impedance is a circuit component connected in series between the positive terminal of the primary side and the positive terminal of the tertiary side, and the ninth impedance is a circuit component connected in series between the negative terminal of the primary side and the negative terminal of the tertiary side.

[0019] Since the polarity of the magnetic coupling circuit can be changed by, for example, changing the direction of the current, inverting the phase of the current by 180°, or reversing the winding direction of the conductor that forms the inductance, the + terminal and the - terminal may have an inverted relationship. Therefore, in the first embodiment, the + terminal and the - terminal are used to mean either end of the inductance element.

[0020] Looking at the correspondence between the magnetic coupling circuit shown in FIG. 1 and the equivalent circuit shown in FIG. 3, the inductance element on the primary side in the magnetic coupling circuit shown in FIG. 1 corresponds to the first impedance in the equivalent circuit shown in FIG. 3, the inductance element on the secondary side in the magnetic coupling circuit shown in FIG. 1 corresponds to the second impedance in the equivalent circuit shown in FIG. 3, and the inductance element on the tertiary side in the magnetic coupling circuit shown in FIG. 1 corresponds to the third impedance in the equivalent circuit shown in FIG. 3.

[0021] In addition, the mutual inductance between the + terminal on the primary side and the + terminal on the secondary side in the magnetic coupling circuit shown in FIG. 1 corresponds to the fourth impedance in the equivalent circuit shown in FIG. 3, the mutual inductance between the − terminal on the primary side and the − terminal on the secondary side in the magnetic coupling circuit shown in FIG. 1 corresponds to the fifth impedance in the equivalent circuit shown in FIG. 3, and the mutual inductance between the + terminal on the secondary side and the + terminal on the tertiary side in the magnetic coupling circuit shown in FIG. 1 corresponds to the sixth impedance in the equivalent circuit shown in FIG. 3.

[0022] Furthermore, the mutual inductance between the negative terminal on the secondary side and the negative terminal on the tertiary side in the magnetic coupling circuit shown in Fig. 1 corresponds to the seventh impedance in the equivalent circuit shown in Fig. 3, the mutual inductance between the positive terminal on the primary side and the positive terminal on the tertiary side in the magnetic coupling circuit shown in Fig. 1 corresponds to the eighth impedance in the equivalent circuit shown in Fig. 3, and the mutual inductance between the negative terminal on the primary side and the negative terminal on the tertiary side in the magnetic coupling circuit shown in Fig. 1 corresponds to the ninth impedance in the equivalent circuit shown in Fig. 3. In other words, the magnetic coupling circuit shown in Fig. 1 and the equivalent circuit shown in Fig. 3 are structurally related to each other.

[0023] Fig. 4 is a schematic diagram showing a typical configuration example of a conventional three-phase transformer. This transformer has a structure in which the primary, secondary, and tertiary conductors are wound around a single annular iron core. The ratio of the voltages from the primary to the tertiary sides changes depending on the number of times each conductor from the primary to the tertiary sides is wound around the iron core.

[0024] Furthermore, for example, if the primary side is the input and the secondary and tertiary sides are the output, using a material with a high relative magnetic permeability for the iron core makes it difficult for magnetic flux generated by current flowing through the primary terminals to leak outside the iron core, allowing the ratio of power input to the primary side to power output from the secondary and tertiary sides to approach 1. Conversely, using a material with a low relative permittivity for the iron core makes it difficult for power input to the primary side to be transmitted to the secondary and tertiary sides. The amount of coupling between the primary, secondary, and tertiary sides, which is determined by the relative permittivity of the iron core material, the dimensions of the iron core, or the structure of the iron core, is expressed as the coupling coefficient k.

[0025] The coupling coefficient between the primary and secondary sides is k １ , the coupling coefficient between the secondary and tertiary sides is k ２ , the coupling coefficient between the primary and tertiary sides is k ３ , the inductance of the primary side of the transformer is L １ , the secondary inductance is L ２ , the inductance of the tertiary side is L ３ , the mutual inductance between the primary and secondary sides is M １２ , the mutual inductance between the secondary and tertiary sides is M ２３ , the mutual inductance between the primary and tertiary sides is M １３ Then, the following relationships (1) to (3) hold between them. １ , inductance L ２ , inductance L ３ Although each of these means self-inductance, in the first embodiment, they will be simply referred to as inductance.

[0026] At this time, k １ , k ２ , and k ３ takes a value between 0 and 1. When defining the polarity, k １ , k ２ , and k ３ can be set to -1 or more and 1 or less, but in the first embodiment, the polarity does not matter, so k1, k ２ , k ３ are assumed to be between 0 and 1. In many magnetically coupled circuits including three-phase transformers, the coupling coefficient k (k １ , k ２ , and k ３ ) is close to 1, which means that power is transmitted to the output side without loss, and is therefore an ideal condition. However, when a large magnetic flux is applied to the iron core, the iron core heats up, and the heat generated can cause magnetic saturation, reducing the relative permeability, or the heat generated by the iron core can thermally destroy the iron core (magnetic material).

[0027] For this reason, methods such as creating a gap (gap) in the middle of the annular iron core to make it difficult for magnetic flux to pass through and thereby prevent magnetic saturation of the iron core, or using a material with low relative magnetic permeability for the iron core to intentionally generate leakage magnetic flux, are used. In such cases, k is not 1 but is greater than or equal to 0 and less than 1. Furthermore, k varies depending on the gap structure, the material used for the magnetic body, the temperature of the magnetic body, and other factors. Thus, while k is ideally 1, in actual circuits it is not 1, such as 0.9 or 0.99. In particular, in cases such as wireless power transmission, where it is difficult to use magnetic bodies and misalignment between inductance elements is likely, k takes a small value such as 0.1. Therefore, the equivalent circuit of a magnetic coupling circuit must be able to represent k values ​​less than 1.

[0028] Generally, the inductance of the primary side of the transformer is L １ , the secondary inductance is L ２ , the inductance of the tertiary side is L ３ , the current flowing through the primary inductance element is I １ , the current flowing through the secondary inductance element is I ２ , the current flowing through the inductance element on the tertiary side is I ３ , the mutual inductance between the primary and secondary sides is M １２ , the mutual inductance between the secondary and tertiary sides is M ２３ , the mutual inductance between the primary and tertiary sides is M １３ , j is a complex number, and ω is an angular frequency, the voltage v1 between the terminals of the primary inductance element, the voltage v2 between the terminals of the secondary inductance element, and the voltage v3 between the terminals of the tertiary inductance element are calculated by equations (4) to (6), respectively. Note that in Figures 1 to 4 and Figure 5 and subsequent figures described below, the voltages v1 to v3 are represented by capital letters V1 to V3.

[0029] However, defining a new circuit structure (circuit topology) does not necessarily equate to analytically determining the electrically equivalent constants in the equivalent circuit of this circuit, and it is generally difficult to determine circuit constants in the equivalent circuit shown in Figure 3 that are electrically equivalent to an arbitrarily defined circuit structure. In this regard, the inventors of the present application have discovered that the circuit constants of both the three-phase magnetically coupled circuit shown in Figure 1 and the equivalent circuit shown in Figure 3 can be determined so that they have the same electrical characteristics according to Kirchhoff's laws.

[0030] Specifically, assuming that the complex number is j and the angular frequency is ω (= 2π × (frequency [Hz])), the inductance between the terminals on the primary side of the magnetic coupling circuit shown in FIG. 1 is L １ , the inductance between the secondary terminals is L ２ , the inductance between the terminals on the tertiary side is L ３ , the mutual inductance between the primary inductance and the secondary inductance is M １２ , the mutual inductance between the secondary inductance and the tertiary inductance is M ２３ , the mutual inductance between the primary inductance and the tertiary inductance is M １３ It is defined as:

[0031] In the equivalent circuit shown in FIG. 3, the circuit constant of the first impedance is z １ , the circuit constant of the second impedance is z ２ , the circuit constant of the third impedance is z ３ , the circuit constant of the fourth impedance is z ４ , the circuit constant of the fifth impedance is z ５ , the circuit constant of the sixth impedance is z ６ , the circuit constant of the seventh impedance is z ７ , the circuit constant of the eighth impedance is z ８ , the circuit constant of the ninth impedance is z ９ Then, the following equations (7) to (12) hold between the circuit constants of the magnetic coupling circuit shown in FIG. 1 and the equivalent circuit shown in FIG. 3. ４ and Z ５ The sum of z shown in equation (10) １２ is equal to z６ and Z ７ The sum of z shown in equation (11) ２３ is equal to z ８ and Z ９ The sum of z shown in equation (12) １３ is equal to

[0032] However, the fourth impedance z ４ , fifth impedance z ５ , sixth impedance z ６ , the seventh impedance z ７ , the eighth impedance z ８ , and the ninth impedance z ９ The impedance values ​​of each of the ４ and Z ５ The sum of these is z １２ is equal to z ６ and Z ７ The sum of these is z ２３ is equal to z ８ and Z ９ The sum of these is z １３ may be freely changed as long as it is equal to , and may have circuit constants that are negative real numbers.

[0033] In the equivalent circuit shown in FIG. 2, the first impedance z １ , second impedance z ２ , the third impedance z ３ , the fourth impedance z １２、 Fifth impedance z ２３ , sixth impedance z １３ Then, these impedances are calculated using the above equations (7) to (12).

[0034] In this way, by configuring the equivalent circuit of the three-phase magnetic coupling circuit as shown in Figure 3, it is possible to replace the three-phase magnetic coupling circuit with a circuit that does not include magnetic coupling. Furthermore, by converting this equivalent circuit into a graph structure, it is possible to convert the magnetic coupling circuit into a graph structure while suppressing information degradation of the three-phase magnetic coupling circuit, and the converted graph structure can be used as input data for learning in a graph network or graph neural network. In this case, however, it is desirable to set the circuit constants so that the fourth impedance and the fifth impedance are equal, the circuit constants of the sixth impedance and the seventh impedance are equal, and the circuit constants of the eighth impedance and the ninth impedance are equal.

[0035] This is because, unlike circuit theory, Kirchhoff's law of conservation of current does not hold in the processing of graph networks or graph neural networks. Specifically, Kirchhoff's law of conservation of current considers a closed path in which the current flowing out of and the current flowing into a circuit component are equal, assuming that the starting point and the end point are the same circuit component, whereas a graph neural network considers only the connection between two components in one hidden layer, and even if the number of hidden layers is increased, the law of conservation of current does not hold, and a closed path cannot be considered. Therefore, the equivalent circuit shown in Figure 3 is converted into a graph structure, and, for example, among the circuit constants of the fourth impedance and the fifth impedance, the circuit constant of the fifth impedance is set to "0", and the fourth impedance is set to the above z １２ When processing is performed using a graph network or a graph neural network with the above equations, a circuit including a condition in which the primary side and the secondary side are short-circuited is processed.

[0036] In contrast to this, in the equivalent circuit shown in FIG. 3, by setting the fourth impedance and the fifth impedance to be equal, the sixth impedance and the seventh impedance to be equal, and the eighth impedance and the ninth impedance to be equal, in processing of a graph network or graph neural network in which Kirchhoff's law of conservation of current does not hold, even when processing is performed that includes only one of the paths of the fourth impedance or the fifth impedance, for example, no short circuit occurs between the primary and secondary sides, and the same effect occurs whether the path is taken, so processing can be performed as correct circuit information based on circuit theory.

[0037] Furthermore, according to the first embodiment, it is also possible to convert, conversely to the above, the equivalent circuit not including magnetic coupling shown in Fig. 3 into a circuit including magnetic coupling. This makes it possible to restore a circuit including magnetic coupling (magnetically coupled circuit) from a graph structure generated or processed by a graph network or a graph neural network.

[0038] Furthermore, it is difficult to calculate the mutual inductance in a magnetically coupled circuit from actual measurement data of the circuit. This is because the mutual inductance in the magnetically coupled circuit is calculated as a value mixed with the self-inductance. In this regard, according to the first embodiment, the circuit constants are calculated by measurement based on an equivalent circuit that does not include magnetic coupling, such as that shown in FIG. 3, and the self-inductance or mutual inductance in the magnetically coupled circuit can be calculated from the results. Therefore, an unprecedented and remarkable effect is achieved in that the mutual inductance in a magnetically coupled circuit can be calculated more easily than before.

[0039] Furthermore, if the mutual inductance in a magnetic coupling circuit can be calculated, the coupling coefficient or relative permeability in the magnetic coupling circuit can also be easily calculated based on electric circuit theory, and therefore, circuit constants can be easily extracted from an actual magnetic coupling circuit.

[0040] In the conversion from the equivalent circuit shown in FIG. 3 to the magnetic coupling circuit shown in FIG. 1, the complex number is j, the angular frequency is ω, and the circuit constant of the first impedance is z １ , the circuit constant of the second impedance is z ２ , the circuit constant of the third impedance is z ３ , the circuit constant of the fourth impedance is z ４ , the circuit constant of the fifth impedance is z ５ , the circuit constant of the sixth impedance is z ６ , the circuit constant of the seventh impedance is z ７ , the circuit constant of the eighth impedance is z ８ , the circuit constant of the ninth impedance is z ９ Here, z ４ and Z ５ The sum is z １２ is equal to z ６ and Z ７ The sum is z ２３ is equal to z ８ and Z ９ The sum is z １３ For ease of explanation, Z is defined as in the following equation (13).

[0041] At this time, the inductance between the terminals on the primary side of the magnetic coupling circuit shown in FIG. １ , the inductance between the secondary terminals is L ２ , the inductance between the terminals on the tertiary side is L ３ , the mutual inductance between the primary inductance and the secondary inductance is M １２ , the mutual inductance between the secondary inductance and the tertiary inductance is M ２３ , the mutual inductance between the primary inductance and the tertiary inductance is M １３ Then, the relationships of the following equations (14) to (19) hold between the above circuit constants.

[0042] Fig. 5 is a schematic diagram summarizing the relationship between the conversion and inverse conversion between the three-phase magnetic coupling circuit shown in Fig. 1 and the equivalent circuit shown in Fig. 3. Fig. 5A shows the three-phase magnetic coupling circuit shown in Fig. 1, and Fig. 5B shows the equivalent circuit shown in Fig. 3.

[0043] As shown in Figures 5A and 5B, there is a reversible transformation relationship between a three-phase magnetic coupling circuit and an equivalent circuit in which the spatial coupling in this magnetic coupling circuit is replaced with circuit components. Therefore, this reversible transformation relationship can be applied to applications other than converting a magnetic coupling circuit into a graph structure. For example, by setting a design target in the equivalent circuit shown in Figure 5B and converting this equivalent circuit into the magnetic coupling circuit shown in Figure 5A using the above equations (14) to (19), it is possible to determine the physical structure or material constants of the actual magnetic coupling circuit. For example, L １、 L ２、 L ３、 M １２、 M ２３、 M １３ To calculate this, six independent measurement results are required, since there are six unknowns as shown in Figure 2. For example, the circuit constants shown in Figure 2 can be determined by measuring under three conditions: when the + and - terminals of V2 are shorted, when open, and connected at 50 Ω, and when the + and - terminals of V2 are shorted, when open, and when connected at 50 Ω, and when the + and - terminals of V3 are shorted, when open, and when connected at 50 Ω, while the + and - terminals of V2 are open. Furthermore, the measurement accuracy of the first, second, third, fourth, fifth, and sixth impedances shown in Figure 2 can be improved by combining the following: attaching circuit components other than 50 Ω, such as resistors, coils, or capacitors, to the V2 terminal, or measuring V2 with the + and - terminals of V3 shorted. Specifically, since more than six constraint equations can be established for six unknowns (variables), this results in an overdetermined equation. Therefore, it is desirable to determine the first through sixth impedances as a solution to the least squares method using a generalized inverse matrix, which reduces measurement error. From the determined first impedance to sixth impedance, L is uniquely determined according to the method shown in this embodiment. １、 L ２、 L ３、 M １２、 M ２３、 M １３ Conventionally, in the method using the formulas (4), (5), and (6), the mutual inductance M １２ , M２３ , M １３ Since the voltages v1, v2, and v3 and the currents I1, I2, and I3 depend on the currents I1, I2, and I3, it is necessary to determine the voltages v1, v2, and v3 and the currents I1, I2, and I3 simultaneously. １、 L ２、 L ３、 M １２、 M ２３、 M １３ are mutually dependent and therefore difficult to measure. On the other hand, z in equations (7), (8), (9), (10), (11), and (12) １ , z ２ , z ３ and L is calculated using equations (13), (14), (15), (16), (17), (18), and (19). １、 L ２、 L ３、 M １２、 M ２３、 M １３ By defining the above, the above dependency is resolved, and therefore calculation can be performed without requiring any special processing, which is an unprecedented effect.

[0044] As described above, according to the first embodiment, by combining methods of expression in two different domains, that is, an actual magnetic coupling circuit and an equivalent circuit of the magnetic coupling circuit, it is possible to perform various processes in the domain that each circuit excels in. Therefore, the reversible transformation relationship shown in Fig. 5 not only contributes to improving the efficiency of, for example, the design of a magnetic coupling circuit or the structural design of a transformer or the like incorporating this magnetic coupling circuit, but can also be used when extracting mutual inductance from an actual magnetic coupling circuit.

[0045] Figure 6 shows the results of calculations using a circuit simulator for the three-phase magnetic coupling circuit and the equivalent circuit shown in Figure 2. The calculation results show the frequency characteristics of the voltage across the load resistance on the secondary and tertiary sides when an AC signal of 1 V is applied to the primary side and the frequency of the AC signal is changed, with the input on the primary side and the output on the secondary and tertiary sides, an AC power supply connected between the + and - terminals on the primary side, and load resistances connected between the + and - terminals on the secondary side and between the + and - terminals on the tertiary side.

[0046] FIG. 6A shows a three-phase magnetic coupling circuit including an AC power supply and a load resistance, FIG. 6B shows the equivalent circuit of FIG. 2 including an AC power supply and a load resistance, and FIG. 6C shows the frequency characteristics of the voltages across the load resistances on the secondary and tertiary sides of FIGS. 6A and 6B.

[0047] In FIG. 6A, the coupling coefficient k between the primary and secondary inductance elements １ and the coupling coefficient k between the secondary and tertiary inductance elements ２ and the coupling coefficient k between the primary and tertiary inductance elements ３ In addition, in FIG. 6A, the inductance La of the primary side, which is the input, １ is "100 μH", the inductance of the secondary side that becomes the output La ２ is "100 μH", and the inductance of the tertiary side that becomes the output is La ３ is "10 μH", the impedance of the secondary load resistance Ra ２ is "100Ω", the impedance of the tertiary load resistance Ra ３ was set to "10 Ω".

[0048] Also, in FIG. 6B, z in FIG. １ Inductance Lb corresponding to the circuit constant １ is "-15.17μH", z in Figure 2 ２ Inductance Lb corresponding to the circuit constant ２ is "-15.17μH", z in Figure 2 ３ Inductance Lb corresponding to the circuit constant ３ is "2.10 μH", z in Figure 2 １２ Inductance Lb corresponding to the circuit constant １２ is "31.11 μH", and z in Figure 2 ２３ Inductance Lb corresponding to the circuit constant ２３ is "9.84 μH", z in Figure 2 １３ Inductance Lb corresponding to the circuit constant １３ At this time, the power supply voltage of the input side power supply Vb and the impedance of the secondary side load resistance Rb ２ "100 Ω" of the output, the impedance of the load resistance on the tertiary side Rb ３The "10 Ω" does not change.

[0049] In addition, in Figure 6C, the voltage across the load resistor on the secondary side of the circuit shown in Figure 6A is represented as V(out_a1), the voltage across the load resistor on the tertiary side is represented as V(out_a2), and the voltage across the load resistor on the secondary side of the circuit shown in Figure 6B is represented as V(out_b1), and the voltage across the load resistor on the tertiary side is represented as V(out_b2). As shown in Figure 6C, it can be seen that the frequency characteristics of the above two circuits are consistent on both the secondary and tertiary sides in both amplitude and phase. Each circuit constant can be calculated as follows using the programming language Python (version 3.9.17), for example. # -------------- python code (start) ----------------------- from math import sqrt # Import libraries L1 = 100 * 1e-6 # 100μH L2 = 100 * 1e-6 # 100μH L3 = 10 * 1e-6 # 10μH k1 = 0.9 # Coupling coefficient k2 = 0.9 # Coupling coefficient k3 = 0.9 # Coupling coefficient M12 = k1 * sqrt(L1 * L2) # Mutual inductance M23 = k2 * sqrt(L2 * L3) # Mutual inductance M13 = k3 * sqrt(L3 * L1) # Mutual inductance print("Initial conditions") print(f"L1:{L1:.3e}, L2:{L2:.3e}, L3:{L3:.3e}") print(f"k1:{k1:.3e}, k2:{k2:.3e}, k3:{k3:.3e}") print(f"M12:{M12:.3e}, M23:{M23:.3e}, M13:{M13:.3e}", end="\n\n") # Forward direction, equations (7) to (12) Z = -L1*L2*L3 + L1*M23**2 + L2*M13**2 + L3*M12**2 - 2*M12*M13*M23 z1 = Z / (-L2*L3 + L2*M13 + L3*M12 - M12*M23 - M13*M23 + M23**2) z2 = Z / (-L1*L3 + L1*M23 + L3*M12 - M12*M13 + M13**2 - M13*M23) z3 = Z / (-L1*L2 + L1*M23 + L2*M13 + M12**2 - M12*M13 - M12*M23) z12 = Z / (-L3*M12 + M13*M23) z23 = Z / (-L1*M23 + M12*M13) z13 = Z / (-L2*M13 + M12*M23) print("Forward direction, mutual inductance present → absent") print(f"z1:{z1:.3e}, z2:{z2:.3e}, z3:{z3:.3e}") print(f"z12:{z12:.3e}, z23:{z23:.3e}, z13:{z13:.3e}", end="\n\n") # Reverse direction, Equations (13) - (19) y1, y2, y3 = 1 / z1, 1 / z2, 1 / z3 y12, y23, y13 = 1 / z12, 1 / z23, 1 / z13 Y = y1*y2*y3 + y1*y3*y23 + y1*y3*y12 + y2*y3*y12 \ + y3*y12*y23 + y2*y3*y13 + y3*y23*y13 + y3*y12*y13 \ + y1*y2*y23 + y1*y12*y23 + y2*y12*y23 + y2*y13*y23 \ + y1*y2*y13 + y1*y23*y13 + y1*y12*y13 + y2*y12*y13 L1_inv = ((y2 + y12 + y23) * (y3 + y23 + y13) - y23**2) / Y L2_inv = ((y1 + y12 + y13) * (y3 + y23 + y13) - y13**2) / Y L3_inv = ((y1 + y12 + y13) * (y2 + y12 + y23) - y12**2) / Y M12_inv = ((y3 + y23 + y13) * y12 + y23*y13) / Y M23_inv = ((y1 + y12 + y13) * y23 + y12*y13) / Y M13_inv = ((y2 + y12 + y23) * y13 + y12*y23) / Y k1_inv = M12_inv / (sqrt(L1_inv*L2_inv)) k2_inv = M23_inv / (sqrt(L2_inv*L3_inv)) k3_inv = M13_inv / (sqrt(L1_inv*L3_inv)) print("Reverse direction, mutual inductance from none to present") print(f"L1_inv:{L1_inv:.3e}, L2_inv:{L2_inv:.3e}, L3_inv:{L3_inv:.3e}") print(f"k1_inv:{k1_inv:.3e}, k2_inv:{k2_inv:.3e}, k3_inv:{k3_inv:.3e}") print(f"M12_inv:{M12_inv:.3e}, M23_inv:{M23_inv:.3e}, M13_inv:{M13_inv:.3e}") # -------------- python code (end) ----------------------- When you run the above program, you will get the following result. # -------------- python code output (start) ----------------------- Initial conditions L1:1.000e-04, L2:1.000e-04, L3:1.000e-05 k1:9.000e-01, k2:9.000e-01, k3:9.000e-01 M12:9.000e-05, M23:2.846e-05, M13:2.846e-05 Forward direction With mutual inductance → Without mutual inductance z1:-1.517e-05, z2:-1.517e-05, z3:2.104e-06 z12:3.111e-05, z23:9.838e-06, z13:9.838e-06 Reverse direction Mutual inductance: No → Present L1_inv:1.000e-04, L2_inv:1.000e-04, L3_inv:1.000e-05 k1_inv:9.000e-01, k2_inv:9.000e-01, k3_inv:9.000e-01 M12_inv:9.000e-05, M23_inv:2.846e-05, M13_inv:2.846e-05 # -------------- python code output (end) -----------------------.

[0050] From this output result, L1 and L1_inv, L2 and L2_inv, L3 and L3_inv, M12 and M12_inv, M23 and M23_inv, and M13 and M13_inv are equal, and as a result, k1 and k1_inv, k2 and k2_inv, and k3 and k3_inv are equal, which shows that 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 is a general solution that is not dependent on the power supply voltage or load resistance.

[0051] Furthermore, as shown in FIG. １２ Lc １２ and Lc ２１ Divide equally into Lb ２３ Lc２３ and Lc ３２ Divide equally into Lb １３ Lc １３ and Lc ３１ Dividing them equally will produce the same result as in Figure 6B. In this case, Lc1 in Figure 7 is equal to Lb1 in Figure 6B, and similarly Lc2 is equal to Lb2, Lc3 is equal to Lb3, the load Rc2 is equal to Rb2, and Rc3 is equal to Rc2. Also, with regard to the power supply voltage, Va in Figure 6A, Vb in Figure 6B, and Vc in Figure 7 are equal.

[0052] From this, it can be seen that the equivalent circuit shown in Figure 2 is equivalent to the three-phase magnetic coupling circuit shown in Figure 1. This result is based on only one condition, but even if the input power supply (AC power supply) connected to the magnetic coupling circuit, the coupling coefficient, or the inductance value changes, the equivalent circuit will be the same as above. Furthermore, this result will be the same even if the load connected to the three-phase magnetic coupling circuit is configured with something other than a resistor, for example, a combination of active and passive circuits. For example, as shown in Figure 8, K1, K2, and K3, which correspond to the coupling coefficients k12, k23, and k13, can all be different, and the equivalent circuit will hold even if the power supply voltage, the circuit topology of the load circuit, or the circuit constants change. In Figure 8, z １ is "104.9μH", z ２ is "-18.97μH", z ３ is "4.87μH", z １２ is "18.97μH", z ２３ is "12.00μH", z １３ is "-107.5 μH", and resonance and anti-resonance appear at about 9 MHz, but it can be seen that the amplitude and phase are exactly the same for the circuit including magnetic coupling and the two circuits based on this embodiment that do not include magnetic coupling. This is because, as in the relationship between FIG. 6B and FIG. 7, the Lb １２ , Lb ２３ , Lb １３ This also holds true if you divide it.

[0053] Furthermore, in the first embodiment, an example has been described in which the three-phase magnetic coupling circuit is used in a transformer. However, this magnetic coupling circuit is not limited to transformers, and may be used in any circuit, regardless of the application, in which three coils (inductors) are magnetically coupled by mutual inductance, such as an electric motor, a compressor, an insulating circuit, a wireless power transmission circuit, coupling between wires due to residual inductance, or coupling between circuit components due to residual inductance.

[0054] Conventional circuit theory has traditionally believed that a circuit with magnetic coupling cannot be expressed as a circuit without magnetic coupling. Therefore, electric circuits without magnetic coupling are expressed using current, while magnetic circuits with magnetic coupling are expressed using magnetic current. Although electric circuits and magnetic circuits are in a contrasting relationship, they are generally treated as separate circuits. For example, the electromotive force, current, and electrical resistance of an electric circuit are compared with the magnetomotive force, magnetic current, and magnetic resistance of a magnetic circuit. This theory assumes that electric circuits and magnetic circuits exist in a Cartesian coordinate system, that is, completely independent of each other. In contrast, the first embodiment demonstrates the existence of equations (7) to (12) that convert a magnetic circuit to an electric circuit and equations (13) to (19) that convert an electric circuit to a magnetic circuit. In other words, contrary to conventional circuit theory, the electric circuit and magnetic circuit do not have a completely Cartesian coordinate system relationship, but rather have a dependency relationship based on equations (7) to (12) and equations (13) to (19), which can be expressed using only four arithmetic operations, i.e., an oblique coordinate system relationship.

[0055] As described above, according to the first embodiment, the equivalent circuit of the magnetic coupling circuit is a three-phase equivalent circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, and includes a first impedance provided between the primary-side positive terminal and the primary-side negative terminal, a second impedance provided between the secondary-side positive terminal and the secondary-side negative terminal, a third impedance provided between the tertiary-side positive terminal and the tertiary-side negative terminal, a fourth impedance provided between the primary-side positive terminal and the secondary-side positive terminal, a fifth impedance provided between the secondary-side positive terminal and the tertiary-side positive terminal, and a sixth impedance provided between the primary-side positive terminal and the tertiary-side positive terminal. Thus, in the first embodiment, an equivalent circuit of the three-phase magnetic coupling circuit that does not include magnetic coupling can be obtained. Furthermore, the magnetic coupling circuit can be represented as a graph structure, and if the magnetic coupling circuit can be represented as a graph structure, processing using a graph network or a graph neural network becomes possible.

[0056] Furthermore, according to the first embodiment, the equivalent circuit of the magnetic coupling circuit is an equivalent circuit of a three-phase magnetic coupling circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, and is characterized in that it includes a first impedance provided between the primary-side + terminal and the primary-side − terminal, a second impedance provided between the secondary-side + terminal and the secondary-side − terminal, a third impedance provided between the tertiary-side + terminal and the tertiary-side − terminal, a fourth impedance provided between the primary-side + terminal and the secondary-side + terminal, a fifth impedance provided between the primary-side − terminal and the secondary-side − terminal, a sixth impedance provided between the secondary-side + terminal and the tertiary-side + terminal, a seventh impedance provided between the secondary-side − terminal and the tertiary-side − terminal, an eighth impedance provided between the primary-side + terminal and the tertiary-side + terminal, and a ninth impedance provided between the primary-side − terminal and the tertiary-side − terminal. As a result, in embodiment 1, it is possible to obtain an equivalent circuit of a three-phase magnetically coupled circuit that does not include magnetic coupling. Furthermore, the magnetically coupled circuit can be represented as a graph structure, and if the magnetically coupled circuit can be represented as a graph structure, processing in a graph network or a graph neural network becomes possible.

[0057] In addition, the complex number is j, the angular frequency is ω, and the inductance of the inductance element on the primary side of the magnetic coupling circuit is L １ , the inductance of the inductance element on the secondary side of the magnetic coupling circuit is L ２ , the inductance of the inductance element on the tertiary side of the magnetic coupling circuit is L ３ , the mutual inductance between the primary inductance element and the secondary inductance element is M １２ , the mutual inductance between the secondary inductance element and the tertiary inductance element is M ２３ , the mutual inductance between the primary inductance element and the tertiary inductance element is M １３ When this is the case, the first impedance z １ , the second impedance z ２, the third impedance z ３ , the fourth impedance z １２ , the fifth impedance z ２３ , the sixth impedance z １３ is calculated using the above formulas (7) to (12). In this way, in the first embodiment, 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 that constitute the equivalent circuit.

[0058] 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. As a result, in the first embodiment, in graph processing such as a graph neural network in which Kirchhoff's law of conservation of current does not hold, processing can be performed taking into account the characteristics of the magnetic coupling circuit.

[0059] In addition, the inductance L of the inductance element on the primary side of the magnetic coupling circuit １ , the inductance L of the secondary inductance element of the magnetic coupling circuit ２ , the inductance L of the inductance element on the tertiary side of the magnetic coupling circuit ３ , the mutual inductance M between the primary inductance element and the secondary inductance element １２ , the mutual inductance M between the secondary inductance element and the tertiary inductance element ２３ , and the mutual inductance M between the primary inductance element and the tertiary inductance element １３ is calculated using the above equations (13) to (19). As a result, in the first embodiment, the circuit constants of the magnetic coupling circuit can be calculated using the circuit constants of each of the first to ninth impedances that make up the equivalent circuit. In other words, an equivalent circuit that does not include magnetic coupling can be inversely converted into a circuit that includes magnetic coupling.

[0060] In addition, the complex number is j, the angular frequency is ω, and the inductance of the inductance element on the primary side of the magnetic coupling circuit is L １, the inductance of the inductance element on the secondary side of the magnetic coupling circuit is L ２ , the inductance of the inductance element on the tertiary side of the magnetic coupling circuit is L ３ , the mutual inductance between the primary inductance element and the secondary inductance element is M １２ , the mutual inductance between the secondary inductance element and the tertiary inductance element is M ２３ , the mutual inductance between the primary inductance element and the tertiary inductance element is M １３ When this is the case, the first impedance z １ , second impedance z ２ , the third impedance z ３ , the fourth impedance z ４ , fifth impedance z ５ , sixth impedance z ６ , the seventh impedance z ７ , the eighth impedance z ８ , and the ninth impedance z ９ is calculated using the above formulas (7) to (12), and z ４ and Z ５ The sum of these is z １２ is equal to z ６ and Z ７ The sum of these is z ２３ is equal to z ８ and Z ９ The sum of these is z １３ In this way, in the first embodiment, it is possible to calculate a circuit constant that is electrically equivalent to the magnetic coupling circuit for each of the first to ninth impedances that configure the equivalent circuit.

[0061] Embodiment 2. In embodiment 1, an equivalent circuit of a magnetic coupling circuit configured to include inductances from the primary side to the tertiary side and mutual inductance was described. In embodiment 2, an equivalent circuit will be described in consideration of parasitic components that arise due to the physical dimensions or structure of an actual magnetic coupling circuit, i.e., residual resistance, parasitic capacitance, and residual inductance.

[0062] 9 is a diagram showing an example of a three-phase magnetic coupling circuit according to embodiment 2. This magnetic coupling circuit has an impedance X between the positive terminal on the primary side and the positive terminal on the secondary side, in comparison with the magnetic coupling circuit shown in FIG. １ is connected, and an impedance X is provided between the positive terminal of the secondary side and the positive terminal of the tertiary side. ２ is connected, and an impedance X is provided between the + terminal on the primary side and the + terminal on the tertiary side. ３ In addition, the negative terminal on the primary side and the negative terminal on the secondary side, the negative terminal on the secondary side and the negative terminal on the tertiary side, and the negative terminal on the primary side and the negative terminal on the tertiary side are short-circuited. Impedance X １ ~X ３ can be considered as, for example, stray capacitance (also called parasitic capacitance) generated by spatial coupling, or a conductance component that indicates the degree of current leakage, or as a capacitor with a physical entity that is provided between the primary and secondary sides, between the secondary and tertiary sides, and between the primary and tertiary sides to reduce electromagnetic noise. Furthermore, any circuit component, such as an inductance component or diode, can be used as long as its impedance characteristics can be measured.

[0063] In the second embodiment, as in the first embodiment, the circuit constants of the equivalent circuit can be determined so that the three-phase magnetically coupled circuit shown in FIG. 9 and the equivalent circuit shown in FIG. 2 have the same electrical characteristics according to Kirchhoff's law.

[0064] Specifically, the complex number is j, the angular frequency is ω (= 2π × (frequency [Hz])), and in order to avoid the equations from becoming complicated, the impedance value obtained by multiplying the inductance between the terminals on the primary side in the magnetic coupling circuit shown in FIG. 9 by j × ω is defined as L １ The impedance value obtained by multiplying the inductance between the secondary terminals by j × ω is L ２ The impedance value obtained by multiplying the inductance between the terminals on the tertiary side by j × ω is L ３ , the impedance value obtained by multiplying the mutual inductance between the primary inductance and the secondary inductance by j × ω is M １２, the impedance value obtained by multiplying the mutual inductance between the secondary inductance and the tertiary inductance by j × ω is M ２３ , the impedance value obtained by multiplying the mutual inductance between the primary inductance and the tertiary inductance by j × ω is M １３ The impedance X in the magnetic coupling circuit shown in FIG. １ The impedance value of X １ , impedance X ２ The impedance value of X ２ , impedance X ３ The impedance value of X ３ It is defined as:

[0065] In addition, to simplify the following explanation, １１ , a １２ , a １３ , a ２１ , a ２２ , a ２３ , a ３１ , a ３２ , and a ３３ is defined as the following equation (20).

[0066] Furthermore, for the sake of simplicity, A and b １１ , b １２ , b １３ , b ２１ , b ２２ , b ２３ , b ３１ , b ３２ , and b ３３ is defined as the following equation (21).

[0067] Furthermore, for the sake of simplicity, １１ , c １２ , c １３ , c ２１ , c ２２ , c ２３ , c ３１ , c ３２ , and c ３３ is defined as the following equation (22).

[0068] At this time, in the equivalent circuit shown in FIG. 2, the first impedance z １ , second impedance z ２ , the third impedance z ３ , the fourth impedance z １２ , fifth impedance z ２３ , the circuit constant of the sixth impedance is z １３ Then, the following relationships (23) to (28) hold between the magnetic coupling circuit shown in FIG. 9 and the circuit constants of the equivalent circuit shown in FIG.

[0069] If the impedance between the mutual inductances is insulation, then X １、 X ２、 and X ３ is considered to be sufficiently large, so in equation (20), １１ , a ２２ , and a ３３ becomes "1", and all other a components become "0". Then, A in equation (21) becomes "1", and b １１ , b ２２ , and b ３３ is "1", and all other b components are "0". As a result, in equation (22), １１ =L １ , c １２ = M １２ , c １３ = M １３ , c ２１ =M １２ , c ２２ =L ２ , c ２３ =M ２３ , c ３１ =M １３ , c ３２ =M ２３ , c ３３ =L ３ Therefore, the formulas (23) to (28) are equal to the above formulas (7) to (12).

[0070] As described above, according to the second embodiment, the equivalent circuit of the magnetic coupling circuit is expressed as follows: j is a complex number, ω is an angular frequency, and L is an impedance value obtained by multiplying the inductance of the inductance element on the primary side of the magnetic coupling circuit by j×ω. １, the impedance value obtained by multiplying the inductance of the inductance element on the secondary side of the magnetic coupling circuit by j × ω is L ２ , the impedance value obtained by multiplying the inductance of the inductance element on the tertiary side of the magnetic coupling circuit by j × ω is L ３ , the impedance value obtained by multiplying the mutual inductance between the primary inductance element and the secondary inductance element by j×ω is M １２ , the impedance value obtained by multiplying the mutual inductance between the secondary inductance element and the tertiary inductance element by j×ω is M ２３ , the impedance value obtained by multiplying the mutual inductance between the primary inductance element and the tertiary inductance element by j×ω is M １３ , the impedance value of the impedance connected between the positive terminal of the primary inductance element and the positive terminal of the secondary inductance element is X １ , the impedance value of the impedance connected between the positive terminal of the secondary inductance element and the positive terminal of the tertiary inductance element is X ２ , the impedance value of the impedance connected between the positive terminal of the primary inductance element and the positive terminal of the tertiary inductance element is X ３ Let a １１ , a １２ , a １３ , a ２１ , a ２２ , a ２３ , a ３１ , a ３２ , and a ３３ is defined as in the above formula (20), and A and b １１ , b １２ , b １３ , b ２１ , b ２２ , b ２３ , b ３１ , b ３２ , and b ３３ is defined as in the above formula (21), and c １１ , c １２ , c １３ , c ２１ , c ２２ , c ２３ , c ３１ , c ３２ , and c３３ When the first impedance z is defined as in the above equation (22), １ , the second impedance z ２ , the third impedance z ３ , the fourth impedance z １２ , the fifth impedance z ２３ , the sixth impedance z １３ is calculated using the above formulas (23) to (28). As a result, in addition to the effect of the first embodiment, the second embodiment makes it possible to calculate circuit constants that are electrically equivalent to the magnetic coupling circuit for each of the first to sixth impedances that constitute the equivalent circuit, even when the magnetic coupling circuit includes a parasitic component.

[0071] Embodiment 3 In the first embodiment, an equivalent circuit expressed using the first to ninth impedances has been described. In the third embodiment, an example of converting the above equivalent circuit into a graph structure will be described.

[0072] In the third embodiment, in the equivalent circuit expressed using the first to ninth impedances shown in the first embodiment, the first impedance is the first node, the second impedance is the second node, the third impedance is the third node, the fourth impedance is the fourth node, the fifth impedance is the fifth node, the sixth impedance is the sixth node, the seventh impedance is the seventh node, the eighth impedance is the eighth node, and the ninth impedance is the ninth node.

[0073] Furthermore, the equivalent circuit is converted into a graph structure by connecting 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 sixth node, the third node and the seventh node, the third node and the eighth node, and the third node and the ninth node with edges.

[0074] FIG. 10 is a diagram showing an example of a graph structure according to the third embodiment. This graph structure has first to ninth nodes and edges connecting the nodes. From this graph structure, information about the graph (hereinafter referred to as "graph information") can be obtained. The graph information includes, for example, information about the nodes included in the graph structure and information about the edges included in the graph structure. The graph information may also include information indicating the connection relationships between the nodes (hereinafter referred to as "connection information") and attribute information.

[0075] The connection information can be stored as text data based on nodes, for example, as follows: In this case, each line break represents a different node, and ";" is used to separate nodes and edges. The order of the nodes and the order of the edges within each node can be freely changed. First node: Edge 1, Edge 2, Edge 11, Edge 12 Second node: Edge 3, Edge 4, Edge 5, Edge 6 Third node: Edge 7, Edge 8, Edge 9, Edge 10 Fourth node: Edge 1, Edge 3 Fifth node: Edge 2, Edge 4 Sixth node: Edge 5, Edge 7 Seventh node: Edge 6, Edge 8 Eighth node: Edge 9, Edge 11 Ninth node: Edge 10, Edge 12

[0076] Furthermore, connection information can also be stored, for example, based on edges, as follows. In this case, each line break represents a different edge, and ";" is used to separate nodes from edges. The order of nodes and the order of nodes within each edge can be freely changed. Edge 1: 1st node, 4th node Edge 2: 1st node, 5th node Edge 3: 2nd node, 4th node Edge 4: 2nd node, 5th node Edge 5: 2nd node, 6th node Edge 6: 2nd node, 7th node Edge 7: 3rd node, 6th node Edge 8: 3rd node, 7th node Edge 9: 3rd node, 8th node Edge 10: 3rd node, 9th node Edge 11: 1st node, 8th node Edge 12: 1st node, 9th node

[0077] The connectivity information can be stored as an adjacency matrix, an incidence matrix, or a combination of an order matrix and a graph Laplacian matrix. Since reversible conversion is possible between any of the storage formats, the connectivity information can be stored in any format.

[0078] In particular, an adjacency matrix is ​​desirable because it is suitable as an input format for graph neural networks. An adjacency matrix is ​​a square matrix (number of nodes) x (number of nodes) in which an element is 1 when a connection exists from one node to another node and an element is 0 when no connection exists. In addition, in an adjacency matrix, for a node that has a self-loop, the diagonal element of the node is 1, and in a graph that has no self-loop, all diagonal elements are 0.

[0079] By converting the equivalent circuit into a graph structure using this method, it becomes possible to process the magnetic coupling circuit using a graph network or graph neural network (graph processing). Furthermore, by inputting the graph information obtained from the graph structure into the graph neural network, feature quantities of the magnetic coupling circuit can be extracted. A feature is a group of values ​​that serve as clues for predicting the correct label of the input training or test data. These feature quantities can be acquired within the framework of a graph neural network. Classification problems can be solved by inputting these feature quantities into a fully connected layer, outputting the same number of values ​​as the number of classes, and applying an activation function used in classification, such as a log softmax function or a softmax function, immediately before the output layer. Regression problems can be solved by inputting these feature quantities into a fully connected layer and outputting a single numerical value. In addition to classification and regression problems with correct labels, it is also possible to combine a graph neural network that extracts feature quantities, such as an autoencoder, with deep learning that restores input data from feature quantities. Self-supervised learning, which involves masking node or edge attributes and predicting the hidden values, is also possible. In this way, features are a group of numbers that abstractly represent the characteristics of input data obtained by applying a nonlinear function to the input data within a deep learning framework. Although the features themselves cannot be understood by humans, by learning them in combination with a loss function that outputs the difference from the correct answer, it is possible to capture the characteristics of the input data from the data.

[0080] In addition, the extracted features can be used to realize many functions, such as predicting the output voltage between the terminals of a magnetic coupling circuit or the current value flowing in the wiring, predicting the frequency characteristics of the voltage or current, predicting the cost of a magnetic coupling circuit, predicting the amount of electromagnetic noise generated or the frequency characteristics, predicting the heat generation of coils or transformers, capacitors, semiconductors, etc., optimizing circuit constants, predicting the number of layers or area required for mounting on a semiconductor or printed circuit board, selecting optimal circuit components including semiconductors, and optimizing the circuit structure.

[0081] In this case, each of the above functions can be realized by providing the graph neural network with graph information obtained by converting the equivalent circuit into a graph structure as described in the third embodiment, and classification (e.g., selecting an integer between 1 and 10), regression data (e.g., calculating a real value between 0 and 1), or waveform (e.g., including regression data of length N as time information) that serves as teacher data for the graph information.

[0082] For example, predicting the output signal between the terminals of a magnetic coupling circuit is waveform prediction, predicting the cost of a magnetic coupling circuit is regression prediction, predicting the amount of electromagnetic noise generated or the frequency characteristics in a magnetic coupling circuit is waveform prediction or a regression problem, predicting the amount of heat generated by a semiconductor in a magnetic coupling circuit is regression prediction, optimizing the circuit constants of a magnetic coupling circuit is regression prediction, predicting the number of layers of a semiconductor or printed circuit board in a magnetic coupling circuit is classification prediction and predicting the area is regression prediction, selecting circuit components including semiconductors in a magnetic coupling circuit is classification prediction, optimizing the circuit structure of a magnetic coupling circuit is a binary classification problem of whether wiring is present or not, etc. Each of the above functions can be realized using existing techniques of graph neural networks.

[0083] Furthermore, by applying an autoencoder, a variational autoencoder, or a generative adversarial network (GAN) to a graph neural network, a generative model of a magnetically coupled circuit can be constructed. For example, a graph neural network can process circuits with circuit components that include magnetic coupling, i.e., magnetic coupling that transmits and receives power or signals through space or magnetic materials, such as a three-phase, three-wire transformer, an isolation circuit, an electric motor, a compressor, or wireless power transmission, in supervised learning, unsupervised learning, or reinforcement learning. This applies not only to the above circuit components, but also to all circuit components represented by mutual inductance or coupling coefficient within a circuit, regardless of the size, type, application, frequency, power, or other conditions of the circuit.

[0084] 11 is a diagram showing an example of a graph structure according to embodiment 3. In this graph structure, the + terminal on the primary side of the equivalent circuit shown in FIG. 3 is designated as a first terminal node, the − terminal on the primary side is designated as a second terminal node, the + terminal on the secondary side is designated as a third terminal node, the − terminal on the secondary side is designated as a fourth terminal node, the + terminal on the tertiary side is designated as a fifth terminal node, and the − terminal on the tertiary side is designated as a sixth terminal node. Then, between the first terminal node and the first node, between the first terminal node and the fourth node, between the first terminal node and the eighth node, between the second terminal node and the first node, between the second terminal node and the fifth node, between the second terminal node and the ninth node, between the third terminal node and the second node, between the third terminal node and the fourth node, between the third terminal node and the sixth node, between the fourth terminal node and the second node, between the fourth terminal node and the fifth node, between the fourth terminal node and the seventh node, between the fifth terminal node and the third node, between the fifth terminal node and the sixth node, between the fifth terminal node and the eighth node, between the sixth terminal node and the third node, between the sixth terminal node and the seventh node, and between the sixth terminal node and the ninth node are respectively connected by edges.

[0085] In this graph structure, for example, by inputting signals with a phase difference of 60 degrees to the first terminal node, the third terminal node, and the fifth terminal node, respectively, it is possible to output power-converted signals to the second terminal node, the fourth terminal node, and the sixth terminal node. Furthermore, it is also possible to input signals with a phase difference of 60 degrees to the second terminal node, the fourth terminal node, and the sixth terminal node, respectively, and output power-converted signals to the first terminal node, the third terminal node, and the fifth terminal node. Alternatively, for example, an input circuit and a load circuit may be connected between the first terminal node and the second terminal node, between the third terminal node and the fourth terminal node, and between the fifth terminal node and the sixth terminal node, and a bidirectional circuit may be configured in which the input circuit and the load circuit can be selectively switched by switching a switch such as a semiconductor, like a regenerative brake.

[0086] It is also desirable to assign the above-mentioned attribute information to each node from the first node to the ninth node. Attribute information, including numerical values, can be freely assigned to each node. However, when processing each node as a single graph, it is advisable to uniform the size of the attribute information matrix (the number of rows and columns in the two-dimensional case) and the information to be input into each matrix element. In this case, the entire graph can be processed collectively using a graph network or graph neural network without relying on the nodes and without requiring pre- or post-processing, which is desirable because it facilitates processing. Note that the matrix may be in any format, such as a one-dimensional or two- or higher-dimensional tensor format, as long as the number of elements is the same. However, for example, a one-row, N-column matrix is ​​desirable because it can hold N elements and is easy to store as tabular data.

[0087] The attribute information of each node holds at least the circuit constant of each impedance. In the third embodiment, the circuit constant of each impedance can be a negative value. For example, the circuit constant of the first impedance is "10 μH," the circuit constant of the second impedance is "-3 μH," and the circuit constant of the third impedance is "1 μH."

[0088] In particular, in graph neural networks, activation functions such as the ReLU function, Sigmoid function, Tanh function, or Softmax function are likely to respond to real numbers between 0 and 1, or integer signals between 0 and 1, and therefore it is desirable to normalize the attribute information of nodes and edges to between 0 and 1 (for example, in the case of the ReLU function), or between -1 and 1 (for example, in the case of the Tanh function). In this case, when taking into account negative circuit constants that occur only under special conditions, such as negative resistance or negative inductance, there is a problem in that the dynamic range of the node attribute information is limited to half the positive value when normalized.

[0089] For example, when "10 μH" and "20 μH" are normalized to real numbers between 0 and 1, they become "0.10" and "0.11", but when normalized taking into account negative components, they become "0.100" and "0.105", and the difference between the two becomes smaller, making it more susceptible to information degradation due to computer rounding errors in processing such as graph neural networks.

[0090] Therefore, it is advisable to express the attribute information corresponding to the circuit constant of each impedance as a first element indicating the sign (positive or negative) and a second element indicating the absolute value of each impedance. This prevents negative elements from being included in the attribute information of the node, thereby preventing a decrease in the accuracy of the attribute information.

[0091] For example, if the circuit constant corresponding to the first node is "10 μH" and the circuit constant corresponding to the second node is "-3 μH," the circuit constant corresponding to the second node will be a negative real number. Therefore, the first element of the attribute information for the second node is set to "1." On the other hand, since the circuit constant corresponding to the first node is a positive real number, the first element of the attribute information for each node is set to "0." Furthermore, by inputting the absolute value of the circuit constant for each node into the second element of the attribute information, the attribute information for each node will be, for example, as follows: First node: 0, 10 μH Second node: 1, 3 μH

[0092] This prevents negative elements from being included in the attribute information, preventing a decrease in the amount of information in the attribute information due to a reduced dynamic range and suppressing a decrease in processing accuracy in the graph neural network. In particular, since absolute circuit constants can be logarithmized, log-normalization, which involves normalizing the logarithm from 0 to 1 or -1 to 1, is desirable because it prevents small circuit constants such as 1 pF from being rounded. Note that, for example, in circuit simulations, when the coupling coefficient k is set to exactly 1, the attribute information may contain "0." In this case, since "0" is neither positive nor negative, the first element representing the sign can be either "0" or "1," but a positive value is preferable. This is because information that a circuit constant is negative occurs under special conditions, and by making the circuit constant negative when this occurs, it can be processed in a graph neural network or the like as information with a large amount of information, such as information indicating a special component. When a "0" is an element, it is always 0 regardless of the elements of the weight matrix of the graph neural network. Therefore, applying a hidden layer propagates 0 to surrounding nodes, resulting in no special information. On the other hand, if a "1" is assigned as an element, a hidden layer is applied, and elements other than "0" are propagated to nodes surrounding the node with a "1" element, thereby propagating special information. Therefore, it is desirable to use a "1" element for negative values, which are special information, and a "0" element for positive values. Furthermore, since the coupling coefficient k never becomes "1" in an actual magnetic coupling circuit, inputting a component as close to "1" as possible, such as "0.9999," converts the circuit constant to a value greater than "0," thereby avoiding the problem of a decrease in the amount of information in the attribute information described above. Furthermore, in equations (7) to (12) shown in embodiment 1, the coupling coefficient k cannot be "1." Because the dataset used in the evaluation described below is a circuit simulation model rather than a real one, there are cases where the coupling coefficient k is "1." In such cases, the coupling coefficient k was converted to "0.999," a value close to "1." Even with this conversion, in an actual device with magnetic coupling, the coupling coefficient may approach "1" but never actually become "1," so this does not constitute a constraint.Furthermore, in equations (10) to (12), if M12, M23, and M13 are all 0 at the same time, the denominator becomes 0, and z12, z23, and z13 become infinite, resulting in a computer error. In a device that also has actual magnetic coupling, induced electromotive forces due to magnetic coupling are generated in conductors around the current-carrying conductor (theoretically at an infinite distance), so M12, M23, and M13 take values ​​greater than or equal to 0. Therefore, if equations (10) to (12) are used and M12, M23, and M13 are all 0 at the same time, setting at least one of M12, M23, and M13 to a sufficiently small value, such as 0.000001, can prevent z12, z23, and z13 from becoming infinite and resulting in a computer error.

[0093] Furthermore, as shown in Figure 11, when the first to sixth terminal nodes are used in the equivalent circuit, it is desirable that the attribute information of each of the first to sixth terminal nodes be as follows: In this case, a special effect can be obtained, particularly when graph information is input to the graph neural network.

[0094] Specifically, the arithmetic mean of the attribute information of the first, fourth, and eighth nodes is assigned to the attribute information of the first terminal node, the arithmetic mean of the attribute information of the first, fifth, and ninth nodes is assigned to the attribute information of the second terminal node, and the arithmetic mean of the attribute information of the second, fourth, and sixth nodes is assigned to the attribute information of the third terminal node. Similarly, the arithmetic mean of the attribute information of the second, fifth, and seventh nodes is assigned to the attribute information of the fourth terminal node, the arithmetic mean of the attribute information of the third, sixth, and eighth nodes is assigned to the attribute information of the fifth terminal node, and the arithmetic mean of the attribute information of the third, seventh, and ninth nodes is assigned to the attribute information of the sixth terminal node.

[0095] That is, in a graph neural network, each hidden layer applies a weight matrix acquired through learning to the attribute information of adjacent nodes and embeds it in the attribute information of its own node. In this case, by initially assigning the attribute information of nodes adjacent to the first through sixth terminal nodes to the first through sixth terminal nodes, the weight matrix converges faster, processing divergence is suppressed, and processing results can be prevented from falling into a local minimum. This reduces computation time and improves computation accuracy. Furthermore, when the data set is small or there is no computation time limit, the attribute information of each terminal node from the first through sixth terminal nodes may be set to "0" or an element indicating that the node is a terminal node may be assigned as a one-hot vector. This has the effect of reducing user bias during learning. However, in the case of a node with a negative element, as in paragraph 0092, the node does not become a one-hot vector but becomes a matrix with two elements greater than zero. Furthermore, when using the equations (23) to (28), if any of X1, X2, and X3 contains an element other than inductance, such as a resistance or capacitance component, z1 to z13 cannot be expressed solely as inductance, resulting in a one-hot vector with two or more elements greater than 0. Thus, the matrix representing node attributes does not necessarily have to be a one-hot vector. Furthermore, because the first through fourth terminal nodes are different types of nodes from the first through fourth nodes, it is desirable to have at least one different zero in the matrix representing each node attribute (one-hot vector), as this prevents the node attributes from mixing and keeps them separable within the graph neural network. Learning can also be performed by inputting circuit constants into the 1 elements of the matrix, so the 0 positions are considered to be different. However, when the matrix is ​​composed only of 0s or 1s (a typical one-hot vector), having at least one different zero is equivalent to having at least one different one.

[0096] [Evaluation] Embodiment 3 shows a method for reversibly converting a magnetic coupling circuit into a graph structure and, conversely, converting from the graph structure to a magnetic coupling circuit. Circuit information of the magnetic coupling circuit is preferably provided as text data including a netlist obtained based on an equivalent circuit of the magnetic coupling circuit.

[0097] The accuracy of the conversion from a magnetic coupling circuit to a graph structure is evaluated by converting a netlist to a graph structure, then converting the converted graph structure back to a netlist, and determining that the original magnetic coupling circuit can be restored without information degradation when the magnetic coupling circuit is converted to a graph structure. However, because the conversion from a netlist to a graph structure and the conversion from a graph structure to a netlist cannot be performed reversibly, a separate algorithm must be developed. Furthermore, one method of evaluating the generated netlist is to perform a circuit simulation with the netlist, but there is no guarantee that the graph structure can be converted back to data that will allow the circuit simulation to be completed without error, even with a small loss of information.

[0098] For this reason, the inventors of the present application have devised a method in which, instead of performing a reverse conversion from the graph structure to a netlist, graph information contained in the generated graph structure is input to a graph neural network, and the accuracy of the conversion from the magnetic coupling 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 is, for example, information about the nodes and edges contained in the graph structure, and this information may include the connection information and attribute information described above.

[0099] If there is little information degradation during the conversion from the magnetic coupling circuit to a graph structure, the information necessary for inference by the graph neural network is more likely to remain, resulting in higher inference accuracy. Conversely, if there is significant information degradation during the conversion, the inference accuracy of the graph neural network is expected to be lower. To compare the third embodiment with the conventional example under fair conditions, the structure of the graph neural network (the number of hidden layers or the number of channels in each hidden layer), the number of epochs, the number of mini-batches, the optimization method, etc. were not changed, except for the addition of nodes to represent each of the fourth to ninth impedances in the equivalent circuit of the magnetic coupling circuit. Furthermore, the training data and test data were fixed. Furthermore, because the graph neural network experiences variability in learning due to the initial values ​​of the random numbers, the average was taken over 10 training runs to reduce the variability in learning. The data set used was a 3,308 netlist extracted from 3,308 circuits included in LTspice from Analog Devices, with 2,315 netlists (70%) used as training data and 993 netlists used as test data, with the training data and test data being fixed.

[0100] Then, as shown in FIG. 12, a classification problem was generated using seven types of circuit components. FIG. 12 shows the number of circuits, the average number of nodes, the average number of edges, and the average value of node types included in the netlist used as the dataset. In FIG. 12, power products are the most common type of circuit components, accounting for 70% of the total. The training data and test data were randomly divided to ensure equal numbers to prevent bias.

[0101] In addition, because the circuits included in the data set are small in circuit scale, the graph structure uses each node from the 1st node to the 9th node, but does not use each terminal node from the 1st terminal node to the 6th terminal node. However, when the circuit scale becomes large and multiple components are connected to a circuit component that includes magnetic coupling, it is preferable to use each terminal node from the 1st terminal node to the 6th terminal node in the graph structure.

[0102] [Graph Neural Network] The graph neural network was constructed as a neural network with three hidden layers. GraphSage, which achieved the highest inference accuracy under all conditions among existing algorithms, was used as the algorithm for reducing information between nodes to extract the features of the magnetic coupling circuit. A seven-value classification was performed using a three-layer neural network consisting of GraphSage and the ReLU function as an activation function, and the softmax function as an activation function before the output layer.

[0103] [Experimental Results] For comparison, Fig. 13 shows the results of learning and inference as a conventional example, assuming that mutual inductance M is not taken into account and that there is no mutual inductance M. Learning was repeated 4,000 times (epochs), and the average value of 10 trials at the epoch at which inference accuracy was highest is shown. In Fig. 13, the maximum inference accuracy for the test data was 97.20%.

[0104] 14 shows the inference accuracy when training data and test data are created using the conversion method to a graph structure described in embodiment 3, and the test data is used to infer the type of circuit component. As with the conventional example shown in Fig. 13, when the average of the maximum values ​​of 10 trials is calculated, the maximum inference accuracy is 97.51%, which is an improvement of 0.31% in the inference accuracy for the test data compared to the conventional example shown in Fig. 13.

[0105] Of the 3,308 sample circuits included in LTspice, 26 were three-phase magnetically coupled circuits, accounting for 0.79% of the total. Although this percentage is small, it was confirmed that learning and inference improved inference accuracy. The learning time using a GPU (NVIDIA RTX A5000) was 7 minutes for the conventional example shown in Figure 13 and 8 minutes for the third embodiment shown in Figure 14, with no significant difference apparent.

[0106] As described above, the conversion method according to the third embodiment is a method for converting the equivalent circuit of the above-described magnetic coupling circuit into a graph structure, and is characterized in that the first impedance of the equivalent circuit is defined as the first node, the second impedance of the equivalent circuit as the second node, the third impedance of the equivalent circuit as the third node, the fourth impedance of the equivalent circuit as the fourth node, the fifth impedance of the equivalent circuit as the fifth node, the sixth impedance of the equivalent circuit as the sixth node, the seventh impedance of the equivalent circuit as the seventh node, the eighth impedance of the equivalent circuit as the eighth node, and the ninth impedance of the equivalent circuit as the ninth node, and the first and fourth nodes, between the first and fifth nodes, between the first and eighth nodes, between the first and ninth nodes, between the second and fourth nodes, between the second and fifth nodes, between the second and sixth nodes, between the second and seventh nodes, between the third and sixth nodes, between the third and seventh nodes, between the third and eighth nodes, and between the third and ninth nodes are connected by edges, respectively. As a result, the conversion method according to the third embodiment can convert the equivalent circuit of the magnetic coupling circuit described above into a graph structure expressed by a combination of nodes and edges.

[0107] In addition, the + terminal on the primary side of the equivalent circuit is the first terminal node, the - terminal on the primary side of the equivalent circuit is the second terminal node, the + terminal on the secondary side of the equivalent circuit is the third terminal node, the - terminal on the secondary side of the equivalent circuit is the fourth terminal node, the + terminal on the tertiary side of the equivalent circuit is the fifth terminal node, and the - terminal on the tertiary side of the equivalent circuit is the sixth terminal node. The following are connections between the first terminal node and the first node, between the first terminal node and the fourth node, between the first terminal node and the eighth node, between the second terminal node and the first node, between the second terminal node and the fifth node, and between the second terminal node and the ninth node. The conversion method according to the third embodiment thereby converts the equivalent circuit of the magnetic coupling circuit described above into a graph structure represented by a combination of nodes, edges, and terminal nodes.

[0108] Furthermore, attribute information is assigned to each of the first to ninth nodes, and a circuit constant of a first impedance is assigned to the attribute information of the first node, a circuit constant of a second impedance is assigned to the attribute information of the second node, a circuit constant of a third impedance is assigned to the attribute information of the third node, a circuit constant of a fourth impedance is assigned to the attribute information of the fourth node, a circuit constant of a fifth impedance is assigned to the attribute information of the fifth node, a circuit constant of a sixth impedance is assigned to the attribute information of the sixth node, a circuit constant of a seventh impedance is assigned to the attribute information of the seventh node, a circuit constant of an eighth impedance is assigned to the attribute information of the eighth node, and a circuit constant of a ninth impedance is assigned to the attribute information of the ninth node. As a result, the conversion method according to the third embodiment can convert the equivalent circuit of the magnetic coupling circuit described above into a graph structure expressed by a combination of nodes, edges, and attribute information of the nodes.

[0109] Furthermore, the attribute information of the first node, the attribute information of the second node, the attribute information of the third node, the attribute information of the fourth node, the attribute information of the fifth node, the attribute information of the sixth node, the attribute information of the seventh node, the attribute information of the eighth node, and the attribute information of the ninth node each 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. This makes it possible to suppress information degradation when the attribute information of each node from the first node to the third node is normalized in the third embodiment.

[0110] Furthermore, attribute information is assigned to each terminal node from the first terminal node to the sixth terminal node and each node from the first node to the ninth node, and the additive average of the attribute information of the first node, the attribute information of the fourth node, and the attribute information of the eighth node is assigned to the attribute information of the first terminal node, the additive average of the attribute information of the first node, the attribute information of the fifth node, and the attribute information of the ninth node is assigned to the attribute information of the second terminal node, the additive average of the attribute information of the second node, the attribute information of the fourth node, and the attribute information of the sixth node is assigned to the attribute information of the third terminal node, the additive average of the attribute information of the second node, the attribute information of the fifth node, and the attribute information of the seventh node is assigned to the attribute information of the fourth terminal node, the additive average of the attribute information of the third node, the attribute information of the sixth node, and the eighth node is assigned to the attribute information of the fifth terminal node, and the additive average of the attribute information of the third node, the attribute information of the seventh node, and the attribute information of the ninth node is assigned to the attribute information of the sixth terminal node. As a result, in the third embodiment, when the converted graph structure is processed by a graph neural network, the convergence of the weight matrix is ​​accelerated, the divergence of the processing is suppressed, and the processing result is prevented from dropping to a minimum value.

[0111] Furthermore, the number of elements in the attribute information of all nodes from the first node to the ninth node is the same. As a result, in the third embodiment, graph information can be used as input data to a graph network or a graph neural network without requiring pre-processing or post-processing, making processing easier.

[0112] Furthermore, a feature extraction method according to a third embodiment is a method for extracting feature quantities of a three-phase magnetically coupled circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, and extracts feature quantities of the magnetically coupled circuit by using information indicating nodes and information indicating edges obtained from the graph structure obtained by the above-described conversion method as input information for a graph neural network. As a result, the feature extraction method according to the third embodiment can extract feature quantities of the magnetically coupled circuit by using the graph structure converted from the equivalent circuit of a single-phase magnetically coupled circuit.

[0113] Furthermore, a feature extraction method according to a third embodiment is a method for extracting feature quantities of a three-phase magnetically coupled circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, and extracts feature quantities of the magnetically coupled circuit by using, as input information for a graph neural network, information indicating nodes, information indicating edges, and node attribute information obtained from the graph structure obtained by the above-described conversion method. As a result, the feature extraction method according to the third embodiment can extract feature quantities of the magnetically coupled circuit by using the graph structure converted from the equivalent circuit of a single-phase magnetically coupled circuit.

[0114] In addition, the present disclosure allows for free combination of the embodiments, modification of any of the components of the embodiments, or omission of any of the components of the embodiments.

[0115] The present disclosure makes it possible to obtain an equivalent circuit of a three-phase magnetically coupled circuit that does not include magnetic coupling, and is suitable for use in an equivalent circuit, a conversion method, and a feature extraction method for a magnetically coupled circuit.

[0116] L １ , L ２ , L ３ , L ４ , L ５ , L ６ , L ７ , L ８ , L ９ , L １０, L １１ , L １２ Inductance, M １２ , M ２３ , M １３ Mutual inductance, v1: Voltage between the terminals of the primary inductance element, v2: Voltage between the terminals of the secondary inductance element, v3: Voltage between the terminals of the tertiary inductance element, X １ , X ２ , X ３ Impedance.

Claims

1. An equivalent circuit of a three-phase magnetically coupled circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, a first impedance provided between the positive terminal of the primary side and the negative terminal of the primary side; a second impedance provided between the positive terminal of the secondary side and the negative terminal of the secondary side; a third impedance provided between the tertiary side positive terminal and the tertiary side negative terminal; a fourth impedance provided between the positive terminal of the primary side and the positive terminal of the secondary side; a fifth impedance provided between the positive terminal of the secondary side and the positive terminal of the tertiary side; a sixth impedance provided between the positive terminal of the primary side and the positive terminal of the tertiary side; 1. An equivalent circuit of a magnetic coupling circuit, comprising:

2. An equivalent circuit of a three-phase magnetically coupled circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, a first impedance provided between the positive terminal of the primary side and the negative terminal of the primary side; a second impedance provided between the positive terminal of the secondary side and the negative terminal of the secondary side; a third impedance provided between the tertiary side positive terminal and the tertiary side negative terminal; a fourth impedance provided between the positive terminal of the primary side and the positive terminal of the secondary side; a fifth impedance provided between the negative terminal on the primary side and the negative terminal on the secondary side; a sixth impedance provided between the positive terminal of the secondary side and the positive terminal of the tertiary side; a seventh impedance provided between the negative terminal on the secondary side and the negative terminal on the tertiary side; an eighth impedance provided between the positive terminal of the primary side and the positive terminal of the tertiary side; a ninth impedance provided between the negative terminal on the primary side and the negative terminal on the tertiary side; 1. An equivalent circuit of a magnetic coupling circuit, comprising:

3. Let j be a complex number, Let ω be the angular frequency. The inductance of the inductance element on the primary side of the magnetic coupling circuit is L １ , The inductance of the inductance element on the secondary side of the magnetic coupling circuit is L ２ , The inductance of the inductance element on the tertiary side of the magnetic coupling circuit is L ３ , The mutual inductance between the primary inductance element and the secondary inductance element is M １２ , The mutual inductance between the secondary inductance element and the tertiary inductance element is M ２３ , The mutual inductance between the primary inductance element and the tertiary inductance element is M １３ When The first impedance z １ , the second impedance z ２ , the third impedance z ３ , the fourth impedance z １２ , the fifth impedance z ２３ , the sixth impedance z １３ is calculated using the following formulas (7) to (12):

2. An equivalent circuit of the magnetic coupling circuit according to claim 1.

4. the circuit constant of the fourth impedance is equal to the circuit constant of the fifth impedance, the sixth impedance has an equal circuit constant to the seventh impedance; The circuit constant of the eighth impedance is equal to the circuit constant of the ninth impedance.

3. An equivalent circuit of the magnetic coupling circuit according to claim 2.

5. The inductance L of the inductance element on the primary side of the magnetic coupling circuit １ , The inductance L of the secondary inductance element of the magnetic coupling circuit ２ , The inductance L of the inductance element on the tertiary side of the magnetic coupling circuit ３ , The mutual inductance M between the primary inductance element and the secondary inductance element １２ , The mutual inductance M between the secondary inductance element and the tertiary inductance element ２３ , and The mutual inductance M between the primary inductance element and the tertiary inductance element １３ is calculated using the following formulas (13) to (19):

4. An equivalent circuit of the magnetic coupling circuit according to claim 3.

6. Let j be a complex number, Let ω be the angular frequency. The impedance value obtained by multiplying the inductance of the inductance element on the primary side of the magnetic coupling circuit by j×ω is L １ , The impedance value obtained by multiplying the inductance of the inductance element on the secondary side of the magnetic coupling circuit by j×ω is L ２ , The impedance value obtained by multiplying the inductance of the inductance element on the tertiary side of the magnetic coupling circuit by j×ω is L ３ , The impedance value obtained by multiplying the mutual inductance between the primary inductance element and the secondary inductance element by j×ω is defined as M １２ , The impedance value obtained by multiplying the mutual inductance between the secondary inductance element and the tertiary inductance element by j×ω is defined as M ２３ , The impedance value obtained by multiplying the mutual inductance between the primary inductance element and the tertiary inductance element by j×ω is defined as M １３ , The impedance value of the impedance connected between the positive terminal of the primary inductance element and the positive terminal of the secondary inductance element is set to X １ , The impedance value of the impedance connected between the positive terminal of the secondary inductance element and the positive terminal of the tertiary inductance element is set to X ２ , The impedance value of the impedance connected between the positive terminal of the primary inductance element and the positive terminal of the tertiary inductance element is set to X ３ year, a １１ , a １２ , a １３ , a ２１ , a ２２ , a ２３ , a ３１ , a ３２ , and a ３３ is defined as the following equation (20): A and b １１ , b １２ , b １３ , b ２１ , b ２２ , b ２３ , b ３１ , b ３２ , and b ３３ is defined as the following equation (21): c １１ , c １２ , c １３ , c ２１ , c ２２ , c ２３ , c ３１ , c ３２ , and c ３３ When is defined as the following equation (22), The first impedance z １ , the second impedance z ２ , the third impedance z ３ , the fourth impedance z １２ , the fifth impedance z ２３ , the sixth impedance z １３ is calculated using the following equations (23) to (28):

2. An equivalent circuit of the magnetic coupling circuit according to claim 1.

7. Let j be a complex number, Let ω be the angular frequency. The inductance of the inductance element on the primary side of the magnetic coupling circuit is L １ , The inductance of the inductance element on the secondary side of the magnetic coupling circuit is L ２ , The inductance of the inductance element on the tertiary side of the magnetic coupling circuit is L ３ , The mutual inductance between the primary inductance element and the secondary inductance element is M １２ , The mutual inductance between the secondary inductance element and the tertiary inductance element is M ２３ , The mutual inductance between the primary inductance element and the tertiary inductance element is M １３ When The first impedance z １ , the second impedance z ２ , the third impedance z ３ , the fourth impedance z ４ , the fifth impedance z ５ , the sixth impedance z ６ , the seventh impedance z ７ , the eighth impedance z ８ , and the ninth impedance z ９ is calculated using the following formulas (7) to (12), z ４ and Z ５ The sum of these is z １２ is equal to z ６ and Z ７ The sum of these is z ２３ is equal to z ８ and Z ９ The sum of these is z １３ is equal to 5. An equivalent circuit of the magnetic coupling circuit according to claim 2 or 4.

8. A method for converting an equivalent circuit of a magnetic coupling circuit according to claim 2 into a graph structure, comprising the steps of: The first impedance of the equivalent circuit is a first node, The second impedance of the equivalent circuit is a second node, The third impedance of the equivalent circuit is a third node, The fourth impedance of the equivalent circuit is a fourth node, A fifth impedance of the equivalent circuit is a fifth node, A sixth impedance of the equivalent circuit is a sixth node, The seventh impedance of the equivalent circuit is a seventh node, The eighth impedance of the equivalent circuit is the eighth node, A ninth impedance of the equivalent circuit is defined as a ninth node, Between the first node and the fourth node, Between the first node and the fifth node, Between the first node and the eighth node, Between the first node and the ninth node, Between the second node and the fourth node, Between the second node and the fifth node, Between the second node and the sixth node, Between the second node and the seventh node, Between the third node and the sixth node, Between the third node and the seventh node, Between the third node and the eighth node, and A conversion method characterized by connecting the third node and the ninth node with an edge.

9. The positive terminal on the primary side of the equivalent circuit is the first terminal node, The negative terminal on the primary side of the equivalent circuit is the second terminal node, The positive terminal on the secondary side of the equivalent circuit is the third terminal node, The negative terminal on the secondary side of the equivalent circuit is the fourth terminal node, The positive terminal of the tertiary side of the equivalent circuit is the fifth terminal node, The negative terminal on the tertiary side of the equivalent circuit is set as a sixth terminal node, Between the first terminal node and the first node, Between the first terminal node and the fourth node, Between the first terminal node and the eighth node, Between the second terminal node and the first node, Between the second terminal node and the fifth node, Between the second terminal node and the ninth node, Between the third terminal node and the second node, Between the third terminal node and the fourth node, Between the third terminal node and the sixth node, Between the fourth terminal node and the second node, Between the fourth terminal node and the fifth node, Between the fourth terminal node and the seventh node, Between the fifth terminal node and the third node, Between the fifth terminal node and the sixth node, Between the fifth terminal node and the eighth node, Between the sixth terminal node and the third node, Between the sixth terminal node and the seventh node, and 9. The conversion method according to claim 8, wherein the sixth terminal node and the ninth node are connected by edges.

10. Attribute information is assigned to each of the first to ninth nodes, assigning a circuit constant of the first impedance to attribute information of the first node; assigning a circuit constant of the second impedance to attribute information of the second node; assigning a circuit constant of the third impedance to attribute information of the third node; assigning a circuit constant of the fourth impedance to attribute information of the fourth node; assigning a circuit constant of the fifth impedance to attribute information of the fifth node; assigning a circuit constant of the sixth impedance to attribute information of the sixth node; assigning a circuit constant of the seventh impedance to attribute information of the seventh node; assigning a circuit constant of the eighth impedance to attribute information of the eighth node; The circuit constant of the ninth impedance is assigned to the attribute information of the ninth node.

9. The method of claim 8.

11. The attribute information of the first node, the attribute information of the second node, the attribute information of the third node, the attribute information of the fourth node, the attribute information of the fifth node, the attribute information of the sixth node, the attribute information of the seventh node, the attribute information of the eighth node, and the attribute information of the ninth node are a first element representing at least the positive or negative sign of a circuit constant; and a second element representing the absolute value of the circuit constant.

11. The method of claim 10.

12. Attribute information is assigned to each of the first terminal node to the sixth terminal node and each of the first node to the ninth node, and assigning an arithmetic average of the attribute information of the first node, the attribute information of the fourth node, and the attribute information of the eighth node to the attribute information of the first terminal node; assigning an arithmetic average of the attribute information of the first node, the attribute information of the fifth node, and the attribute information of the ninth node to the attribute information of the second terminal node; assigning an arithmetic average of the attribute information of the second node, the attribute information of the fourth node, and the attribute information of the sixth node to the attribute information of the third terminal node; assigning an arithmetic average of the attribute information of the second node, the attribute information of the fifth node, and the attribute information of the seventh node to the attribute information of the fourth terminal node; assigning an arithmetic average of the attribute information of the third node, the attribute information of the sixth node, and the attribute information of the eighth node to the attribute information of the fifth terminal node; An 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 is assigned to the attribute information of the sixth terminal node.

10. The method of claim 9.

13. Attribute information is assigned to each of the first terminal node to the sixth terminal node and each of the first node to the ninth node by a one-hot vector, The positions of 0 in the attribute information from the first terminal node to the sixth terminal node are equal, The positions of 0 in the attribute information of each of the first node to the ninth node are equal, The position of 0 in each piece of attribute information from the first terminal node to the sixth terminal node is different from the position of 0 in each piece of attribute information from the first node to the ninth node in at least one position.

10. The method of claim 9.

14. 12. The conversion method according to claim 10, wherein the number of elements in the attribute information of all nodes from the first node to the ninth node is the same.

15. A method for extracting a feature quantity of a three-phase magnetically coupled circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, comprising: The information indicating the nodes and the information indicating the edges obtained from the graph structure obtained by the conversion method according to claim 8 is used as input information for a graph neural network, thereby extracting the feature quantity of the magnetic coupling circuit. A feature extraction method characterized by:

16. A method for extracting a feature quantity of a three-phase magnetically coupled circuit in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, comprising: The information indicating the nodes, the information indicating the edges, and the attribute information of the nodes obtained from the graph structure obtained by the conversion method according to any one of claims 10 to 13 are used as input information for a graph neural network, thereby extracting the feature quantity of the magnetic coupling circuit. A feature extraction method characterized by:

17. A method for manufacturing an equivalent circuit of the magnetic coupling circuit of claim 1, comprising: the process of arranging circuit elements having the first impedance, the second impedance, the third impedance, the fourth impedance, the fifth impedance, and the sixth impedance into a circuit; A method for manufacturing an equivalent circuit of a magnetic coupling circuit, comprising:

18. A method for manufacturing a system for performing the conversion method of claim 8, comprising: a process for generating each of the first to ninth nodes; Between the first node and the fourth node, Between the first node and the fifth node, Between the first node and the eighth node, Between the first node and the ninth node, Between the second node and the fourth node, Between the second node and the fifth node, Between the second node and the sixth node, Between the second node and the seventh node, Between the third node and the sixth node, Between the third node and the seventh node, Between the third node and the eighth node, and generating an edge connecting the third node and the ninth node; A method for manufacturing a system comprising:

19. A method for manufacturing an apparatus for extracting features of a three-phase magnetically coupled circuit, in which a primary-side inductance element, a secondary-side inductance element, and a tertiary-side inductance element are magnetically coupled by mutual inductance, by using a graph structure of the circuit including an equivalent circuit of the magnetically coupled circuit as input information for a graph neural network, comprising: a process for constructing the graph neural network; inputting the graph structure, including node and edge information, into the graph neural network; a process of configuring an output unit that outputs a feature quantity of the magnetic coupling circuit; Including, The graph structure is The graph structure is obtained by generating nodes corresponding to at least one of each element or each terminal constituting a circuit including the equivalent circuit of the magnetic coupling circuit, generating edges according to the connection relationships between the nodes, and connecting the nodes with the generated edges. A method for manufacturing a feature extraction device, comprising:

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