An inductance winding optimization method based on finite element simulation software

Abstract

The application discloses an inductance winding optimization method based on finite element simulation software, relates to the technical field of converters, and first obtains the impedance of each turn winding by using the finite element simulation software, then arranges the winding by programming, matches the impedance of each parallel winding by using winding series connection, makes the parallel winding current as evenly distributed as possible, reduces winding loss, combines the simulation tool with theoretical calculation, and can quickly and accurately find the optimal arrangement mode of the inductance winding, compared with a solving method based on a theoretical loss model, can avoid a complex theoretical solving process and has higher precision, and compared with a solving method based on the finite element simulation software alone, can save a large amount of simulation time.

Description

Technical Field

[0001] This invention relates to the field of converter technology, and in particular to an inductor winding optimization method based on finite element simulation software. Background Technology

[0002] With the continuous development of power electronics, magnetic components, as key devices in switching power supply design, have a significant impact on system efficiency and power density. Magnetic components in switching power supplies mainly include two types: inductors and transformers. The winding structure of inductors has three types: series, parallel, and series-parallel.

[0003] For series windings, although the impedance of each turn of the winding is different, the current flowing through each turn of the winding is naturally equal because the winding adopts a series structure.

[0004] Parallel windings are typically used in high-current applications. In such cases, if a single-turn winding is used, the winding loss will cause the winding to heat up rapidly when a large current flows through it, posing a risk of damage. To improve the current-carrying capacity of the winding, multiple turns can be connected in parallel. However, it is worth noting that the current sharing among parallel windings is affected by many factors, such as the skin effect, proximity effect, the distribution of the air gap, and the distribution of the windings. Moreover, the influence of these factors is mutually coupled. In particular, when there are many turns in parallel, the current sharing problem of parallel windings becomes very complex, which brings great difficulties to the design of parallel windings.

[0005] When the parallel winding design is unreasonable, there will be severe current imbalance between the windings. This current imbalance will lead to a significant increase in winding losses, which not only reduces efficiency but also increases the temperature rise, making thermal design more difficult and limiting the further improvement of the power density of the switching power supply. In extreme cases, it may even cause the current in some parallel windings to reverse, resulting in the losses of multi-turn parallel windings being even greater than the losses of single-turn windings.

[0006] For series-parallel windings, there are both series and parallel connections between the windings. For parallel windings, a reasonable design is also required to ensure that the current is as evenly distributed as possible. In addition, the windings can be connected in parallel first and then in series, or in series first and then in parallel. Under different connection methods, the current distribution between the windings is very different, which has a great impact on the winding losses.

[0007] To optimize the arrangement of inductor windings, the winding losses can be theoretically calculated, and the winding arrangement can be selected based on the lowest possible winding loss. However, winding losses include not only DC losses but also AC losses, and the AC resistance affecting the winding AC losses is influenced by factors such as the skin effect and proximity effect, making the calculation very complex. Currently, the Dowell model is commonly used, but this model has many limitations in application and its accuracy is limited. Alternatively, finite element simulation software can be used to obtain the winding losses. This method provides relatively accurate winding losses, but to obtain the optimal winding losses, it is necessary to simulate every winding arrangement. However, as the number of windings increases, the number of winding arrangement methods increases dramatically, and simulating so many winding arrangement methods will consume a lot of time. Summary of the Invention

[0008] To address the above technical problems, this invention provides an inductor winding optimization method based on finite element simulation software, comprising the following steps:

[0009] S1. Build an inductor model in finite element simulation software;

[0010] S2. Perform Fourier decomposition on the inductor current. If the inductor current is a sine wave, this step can be omitted.

[0011] S3. Inject DC, switching frequency and multiples thereof into all windings to obtain the winding impedance matrix at each frequency point;

[0012] S4. Conduct preliminary screening of the winding arrangement;

[0013] S5. For the initially selected winding arrangement, list the port voltage and current constraints, and solve for the current flowing through each turn of the winding.

[0014] S6. Filter the results calculated in step S5 and select the arrangement with the highest current sharing degree of the winding current as the optimal winding arrangement.

[0015] The technical solution further defined in this invention is:

[0016] Furthermore, in step S2, the inductor current is decomposed using Fourier transform, as shown in equation (1).

[0017] i L =i L (DC)+i L (f s )+…i L (m·f s (1)

[0018] Among them, i L Indicates inductor current, iL (DC) represents the DC component of the inductor current, i L (m·f s ) represents the m-th harmonic component of the inductor current, f s represents the switching frequency, and m represents the harmonic order.

[0019] In the aforementioned inductor winding optimization method based on finite element simulation software, the harmonic order m is set to 1 in step S2.

[0020] In the aforementioned inductor winding optimization method based on finite element simulation software, step S3 involves setting the number of windings to n·i, with the winding impedance matrix at each frequency point being Z(DC) and Z(f). s ...Z(m·f s ), where Z(DC) represents the impedance matrix at DC, Z(m·f s ) represents the impedance matrix at the m-th harmonic frequency, f s represents the switching frequency, and m represents the harmonic order.

[0021] In the aforementioned inductor winding optimization method based on finite element simulation software, step S3 involves n·i windings and an impedance matrix consisting of n·i rows and n·i columns, as shown in equation (2).

[0022]

[0023] In the impedance matrix, the real part of each element represents the resistive component, and the imaginary part represents the inductive component.

[0024] In the aforementioned inductor winding optimization method based on finite element simulation software, step S4 involves setting the number of windings to n·i, divided into i branches, with n windings connected in series in each branch, denoted as W. x1 ...W xn The current flowing through it is I x The method for preliminary screening of winding arrangement, where x = 1 to i, includes the following steps:

[0025] S4.1 Assume that the current is evenly distributed across all windings, and the current flowing through them is I, i.e., I1 = I2 = ... = I i =I, the impedance matrix is ​​set to n·i rows and n·i columns. Combining the impedance matrix, the voltage across each turn of the winding is obtained, specifically:

[0026]

[0027] Among them, U x1 ...U xn (x = 1 to i) represents the corresponding winding W x1 ...W xnThe voltage that (x=1~i) bears,

[0028] Simplifying equation (3), we get

[0029]

[0030] S4.2. Add the voltages of each group of n turns of winding to obtain the total voltage after n turns are connected in series. Define the total voltage of each series branch as: U1, U2, ... U i ;

[0031] If U1~U i If they are exactly the same, then under this arrangement, the current in each turn of the winding will be exactly the same;

[0032] If U1~U i If they are not completely identical, then under this arrangement, the currents between the turns will be unequal, and U1~U i The greater the difference, the more severe the uneven distribution of current.

[0033] Therefore, the concept of variance is introduced to measure U1 to U2. i The differences between them are used as the basis for preliminary screening of winding arrangement methods. The specific expression is as follows:

[0034]

[0035] in, For U1~U i Calculate the average value and the variance S for all winding arrangements. 2 Then, select the winding arrangement with the smallest variance, and proceed to step S5.

[0036] In the aforementioned inductor winding optimization method based on finite element simulation software, step S4 is omitted when the number of winding arrangement methods is less than 15.

[0037] In the aforementioned inductor winding optimization method based on finite element simulation software, step S5 involves setting the number of windings to n·i, divided into i branches, with each branch containing n windings connected in series, denoted as W. x1 ...W xn The current flowing through it is I x Each winding W x1 ...W xn The voltage it withstands is U x1 ...U xn x = 1 to i, impedance matrix Z(f s Let be the secondary impedance at the switching frequency, denoted as n·i rows and n·i columns. Solve for the current flowing through each turn of the winding.

[0038]

[0039] I1+I2+...I i =I (7)

[0040] U 11 +U 12 +…+U 1n =U 21 +U 22 +…+U 2n =...=U i1 +U i2 +…+U in (8)

[0041] Equations (6)-(8) represent the current sharing situation of the secondary current at the switching frequency.

[0042] In the aforementioned inductor winding optimization method based on finite element simulation software, step S5 also requires calculating the DC current sharing situation and summing up the currents to obtain the actual current of each turn of the winding.

[0043] The beneficial effects of this invention are:

[0044] First, the impedance of each turn of the winding is obtained using finite element simulation software. Then, the windings are arranged using programming. The impedance of each parallel winding is matched by connecting the windings in series, so that the current in the parallel windings is distributed as evenly as possible to reduce winding losses. By combining simulation tools with theoretical calculations, the optimal arrangement of the inductor windings can be found quickly and accurately. Compared with the solution method based on theoretical loss models, it avoids the complex theoretical solution process and has higher accuracy. Compared with the solution method based solely on finite element simulation software, it can save a lot of simulation time. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the series winding structure in this invention;

[0046] Figure 2 This is a schematic diagram of the parallel winding structure of the present invention;

[0047] Figure 3 This is a schematic diagram of the parallel-then-series winding structure of the present invention;

[0048] Figure 4 This is a schematic diagram of the series-parallel structure winding of the present invention;

[0049] Figure 5 This is a flowchart of the optimization method steps of the present invention;

[0050] Figure 6 This is a schematic diagram of the inductor winding structure when n=3 and i=2 in this invention;

[0051] Figure 7 This is a diagram showing the distribution of winding current under different winding arrangements in this invention;

[0052] Figure 8 This is a comparison chart of the winding current calculation and simulation in this invention. Detailed Implementation

[0053] like Figure 1 As shown, in a series winding structure, the current flowing through each turn of the winding is naturally equal; as Figure 2 As shown, in parallel winding structures, the spatial distribution of the windings and the distribution of air gaps have a significant impact on the impedance of each turn, and consequently affect the current distribution of each turn. During design, it is essential to ensure that the coupling between windings is as uniform as possible, and the distribution of air gaps should avoid using concentrated air gaps. Figure 3 and Figure 4 As shown, the series-parallel structure is much more complex than the series and parallel structures, and it is the most widely used. This invention mainly focuses on the optimized design of windings in the series-parallel structure.

[0054] like Figure 3 As shown, the windings can be connected in parallel first and then in series; as Figure 4 As shown, it is also possible to connect them in series first and then in parallel; Figure 3 The presented connection method involves first connecting i windings in parallel, and then connecting n parallel windings in series. At this point, to ensure that the current in each winding is equal (i.e., I1 = I2 = ... = I...),... i Therefore, it is necessary to ensure that the impedances of the i windings in each group of parallel windings are equal (i.e., Z). 11 =Z 21 =...=Z i1 Z 12 =Z 22 =...=Z i2 , ..., Z i1 =Z i2 =...=Z in However, the impedance of each winding includes not only the self-impedance of the winding itself, but also the mutual impedance with other windings, making the coupling very complex. Therefore, it is difficult to ensure that the impedances of each set of parallel windings are equal.

[0055] Figure 4 The presented connection method involves first connecting n windings in series, and then connecting these i series branches in parallel. To ensure that the current in each winding is equal (i.e., I1 = I2 = ... = I...),... i It is only necessary to ensure that the sum of the impedances of each branch winding is equal (i.e., Z). 11 +Z 12 +...+Z 1n =Z 21 +Z 22 +...+Z2n =...=Z i1 +Z i2 +...+Z in Compared to Figure 3 The structure shown, with this winding arrangement, greatly reduces the requirements for single-turn impedance matching. Therefore, when the inductor winding has both series and parallel windings, the configuration of series and parallel windings should be chosen. Figure 4 Based on the winding method shown, this invention seeks the optimal winding arrangement. Figure 4 The structure shown is a baseline, but the present invention is not limited to this structure.

[0056] This embodiment provides an inductor winding optimization method based on finite element simulation software, such as... Figure 5 As shown, it includes the following steps

[0057] S1. Build an inductor model in finite element simulation software, and the windings do not need to be combined;

[0058] S2. Perform Fourier decomposition on the inductor current, as shown in equation (1).

[0059] i L =i L (DC)+i L (f s )+…i L (m·f s (1)

[0060] Among them, i L This represents the inductor current, which is typically a triangular wave. It includes not only the DC current and the switching frequency components, but also harmonic components that are multiples of the switching frequency. L (DC) represents the DC component of the inductor current, i L (m·f s ) represents the m-th harmonic component of the inductor current, f s The value represents the switching frequency, and m represents the harmonic order. In practical applications, the value is set according to the accuracy requirements. Usually, m=1 is sufficient to meet the accuracy requirements. The larger m is, the more accurate the result, but the more complex the calculation.

[0061] S3. Inject DC, switching frequency, and multiples thereof into the n·i windings respectively to obtain the winding impedance matrix Z(DC), Z(f) at each frequency point. s ...Z(m·f s The impedance matrix has n·i rows and n·i columns, as shown in equation (2).

[0062]

[0063] In the impedance matrix, the real part of each element represents the resistive component, and the imaginary part represents the inductive component.

[0064] S4. Preliminary screening of winding arrangement methods is performed. As the number of windings increases, the number of winding arrangement methods increases dramatically. For example, a 12-turn winding distributed across 12 layers of a PCB, with one turn per layer, three turns connected in series, and then four series branches connected in parallel to form an inductor, results in a total of 15,400 winding arrangement methods. Such a large number of arrangements will significantly increase the computational load in subsequent steps. To reduce the computational load in subsequent steps, a preliminary screening of winding arrangement methods is required, including the following steps:

[0065] S4.1 For series-parallel windings, the goal is to distribute the current in all windings as evenly as possible. Assuming the current is evenly distributed and the current flowing through is I, using the impedance matrix obtained in step S3, the voltage across each turn of the winding can be calculated as follows:

[0066]

[0067] Simplifying equation (3), we get

[0068]

[0069] S4.2. Divide the n·i turns winding into i groups, each with n turns. Add the voltages of the n turns in each group to get the total voltage after the n turns are connected in series. Define the total voltage of each series branch as: U1, U2, ... U i ;

[0070] If U1~U i If they are exactly the same, then under this arrangement, the current in each turn of the winding will be exactly the same;

[0071] If U1~U i If they are not completely identical, then under this arrangement, the currents between the windings will be unequal. This is because, when the same current is applied, unequal winding voltages mean that the winding impedances are different. However, when the windings are connected in parallel, the voltage across the windings will be the same. Applying the same voltage to different impedances will produce different currents, and U1~U i The greater the difference, the more severe the uneven distribution of current.

[0072] Therefore, the concept of variance is introduced to measure U1 to U2. i The differences between them are used as the basis for preliminary screening of winding arrangement methods. The specific expression is as follows:

[0073]

[0074] in, For U1~U iCalculate the average value and the variance S for all winding arrangements. 2 Then, select the winding arrangement with the smallest variance and proceed to the next step; when there are few winding arrangement methods, consider them specifically in actual application. Generally, if there are fewer than 15, the entire step S4 is omitted.

[0075] S5. For the initially selected winding arrangement, list the port voltage and current constraints, and solve for the current flowing through each turn of the winding.

[0076]

[0077] I1+I2+...I i =I (7)

[0078] U 11 +U 12 +…+U 1n =U 21 +U 22 +…+U 2n =...=U i1 +U i2 +…+U in (8)

[0079] Equations (6)-(8) characterize the current sharing at the switching frequency; the current sharing of the DC current also needs to be calculated, where Z(DC) is the impedance matrix at the DC current obtained in step S3.

[0080]

[0081] I1+I2+...I i =I (10)

[0082] U 11 +U 12 +…+U 1n =U 21 +U 22 +…+U 2n =...=U i1 +U i2 +…+U in (11)

[0083] Equations (9)-(11) represent the current sharing of DC current; then the currents are added together to get the actual current of each turn of the winding.

[0084] S6. Filter the results calculated in step S5 and select the arrangement with the highest current sharing degree of the winding current as the optimal winding arrangement.

[0085] The optimization method proposed in this invention only requires one simulation in step 3 using finite element simulation software. All subsequent steps can be completed by programming or other means, effectively saving a significant amount of simulation time.

[0086] To verify the effectiveness of the optimization method proposed in this invention, an inductor winding with n=3 and i=2 is used as an example, such as... Figure 6 As shown, optimization is performed according to the above steps. To simplify the calculation process, it is assumed that the inductor current is a 1MHz sinusoidal component. The optimization method includes the following steps:

[0087] First, an inductor model is built in the finite element simulation software. Specifically, a 6-turn winding is distributed on a 6-layer PCB, with one turn winding on each layer. The inductor uses a single-sided air gap, and the air gap is located close to the top layer winding.

[0088] Next, the excitation current is set to a sine wave;

[0089] Then, a sinusoidal excitation with a frequency of 1MHz is injected into each of the six windings to obtain the winding impedance matrix Z6 at each frequency point; the impedance matrix has 6 rows and 6 columns, specifically as follows:

[0090]

[0091] Next, there are only 10 possible winding arrangements, as shown in Table 1.

[0092] serial number Winding arrangement serial number Winding arrangement 1 1-2-3 / / 4-5-6 6 1-3-5 / / 2-4-6 2 1-2-4 / / 3-5-6 7 1-3-6 / / 2-4-5 3 1-2-5 / / 3-4-6 8 1-4-5 / / 2-3-6 4 1-2-6 / / 3-4-5 9 1-4-6 / / 2-3-5 5 1-3-4 / / 2-5-6 10 1-5-6 / / 2-3-4

[0093] Table 1 Inductor winding arrangement

[0094] Then, based on the port voltage and current constraints, the current of each winding is calculated. The calculation results for the 10 winding arrangements are as follows: Figure 7 As shown;

[0095] Finally, based on the calculation results of the 10 winding arrangements in the previous step, it can be found that the winding structure formed by connecting 1-5-6 and 2-3-4 in series and then in parallel is the most current-equalizing. To verify the accuracy of the method, an inductor model of 1-5-6 / / 2-3-4 was built for simulation. The simulation results are as follows. Figure 8 As shown, the simulation results and the calculation results are basically the same, thus verifying the effectiveness of the proposed method.

[0096] This invention first uses finite element simulation software to obtain the impedance of each turn of the winding, and then uses programming to arrange the windings. By connecting the windings in series, the impedance of each parallel winding is matched so that the current in the parallel windings is distributed as evenly as possible to reduce winding losses. By combining simulation tools with theoretical calculations, the optimal arrangement of the inductor windings can be found quickly and accurately. Compared with the solution method based on theoretical loss models, it avoids the complex theoretical solution process and has higher accuracy. Compared with the solution method based solely on finite element simulation software, it can save a lot of simulation time.

[0097] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. An inductor winding optimization method based on finite element simulation software, characterized in that: Includes the following steps S1. Build an inductor model in finite element simulation software; S2. Perform Fourier decomposition on the inductor current. If the inductor current is a sine wave, this step can be omitted. S3. Inject DC, switching frequency, and multiples of the switching frequency into all windings to obtain the winding impedance matrix at each frequency point. S4. Perform preliminary screening of the winding arrangement; there are n·i windings, divided into i branches, with n windings connected in series in each branch, denoted as W. x1 ...W xn The current flowing through it is I x A method for preliminary screening of winding arrangement, where x = 1 to i. Includes the following steps S4.1 Assume that the current is evenly distributed across all windings, and the current flowing through them is I, i.e., I1 = I2 = ... = I i =I, the impedance matrix is ​​set to n·i rows and n·i columns. Combining the impedance matrix, the voltage across each turn of the winding can be calculated as follows: （1） Among them, U x1 ...U xn (x=1~i) represents the corresponding winding W x1 ...W xn The voltage that (x=1~i) withstands Simplifying equation (1), we get （2） S4.

2. Add the voltages of each group of n turns of winding to obtain the total voltage after n turns are connected in series. Define the total voltage of each series branch as: U1, U2, ... U i ; If U1~ U i If they are exactly the same, then under this arrangement, the current in each turn of the winding will be exactly the same; If U1~ U i If they are not completely identical, then under this arrangement, the currents between the turns will be unequal, and U1~U i The greater the difference, the more severe the uneven distribution of current. Therefore, we introduce the concept of variance to measure U1~U i The differences between them are used as the basis for preliminary screening of winding arrangement methods. The specific expression is as follows: （3） in, For U1~ U i Calculate the variance of all winding arrangements based on the average value. Then, select the winding arrangement with the smallest variance, and proceed to step S5. S5. For the initially selected winding arrangement, list the port voltage and current constraints, and solve for the current flowing through each turn of the winding. S6. Filter the results calculated in step S5 and select the arrangement with the highest current sharing degree of the winding current as the optimal winding arrangement.

2. The inductor winding optimization method based on finite element simulation software according to claim 1, characterized in that: In step S2, the inductor current is decomposed using Fourier transform, as shown in equation (4). （4） Among them, i L Indicates inductor current, i L (DC) represents the DC component of the inductor current, i L (m·f s f represents the m-th harmonic component of the inductor current at the switching frequency. s represents the switching frequency, and m represents the harmonic order.

3. The inductor winding optimization method based on finite element simulation software according to claim 2, characterized in that: In step S2, the harmonic order m is set to 1.

4. The inductor winding optimization method based on finite element simulation software according to claim 1, characterized in that: In step S3, the number of windings is set to n·i, and the winding impedance matrix at each frequency point is Z(DC), Z(f s ...Z(m·f s ), where Z(DC) represents the impedance matrix at DC, Z(m·f s ) represents the impedance matrix at the m-th harmonic frequency, f s represents the switching frequency, and m represents the harmonic order.

5. The inductor winding optimization method based on finite element simulation software according to claim 1, characterized in that: In step S3, there are n·i windings, and the impedance matrix is ​​set to n·i rows and n·i columns, as shown in equation (5). （5） In the impedance matrix, the real part of each element represents the resistive component, and the imaginary part represents the inductive component.

6. The inductor winding optimization method based on finite element simulation software according to claim 1, characterized in that: In step S4, if the number of winding arrangements is less than 15, the entire step S4 is omitted.

7. The inductor winding optimization method based on finite element simulation software according to claim 1, characterized in that: In step S5, there are n·i windings, divided into i branches, and each branch has n windings connected in series, which are W x1 ...W xn The current flowing through it is I x Each winding W x1 ...W xn The voltage it withstands is U x1 ...U xn , x=1~i, impedance matrix Z( Let be the secondary impedance at the switching frequency, and set it as follows: OK, The column is used to calculate the current flowing through each turn of the winding. （6） （7） （8） Equations (6)-(8) represent the current sharing situation of the secondary current at the switching frequency.

8. The inductor winding optimization method based on finite element simulation software according to claim 7, characterized in that: In step S5, it is also necessary to calculate the current sharing of DC current and add up the currents of each turn to obtain the actual current of each winding.

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