Double-layer coil interlayer displacement current loss optimization method based on distributed compensation
By dividing the centralized compensation capacitor into two series capacitors and building a double-layer coil equivalent circuit model, the problem of displacement current loss between the two-layer coils is solved, and the loss optimization of symmetric and asymmetric coils is achieved, and the applicability and performance improvement of symmetric and asymmetric coils is achieved. .
Patent Information
- Application Number
- CN202410996543.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-24
- Publication Date
- 2025-01-07
AI Technical Summary
The prior art is difficult to effectively reduce the interlayer displacement current (IDC) loss of the double-layer coil, especially in symmetric and asymmetric coils, and traditional methods limit the amount of wires and lack of applicability.
By dividing the centralized compensation capacitor into two series capacitors, a double-layer coil equivalent circuit model with distributed parameters is constructed, the self-inductance, mutual inductance and inter-turn capacitance of each turn of coil is calculated, and the IDC is constructed based on Ohm's law and calculus principle. Mathematical model between the loss and the inter-layer series compensation capacitor, solving the optimal value to optimize IDC loss.
It realizes the reduction of IDC losses of the double-layer coil without increasing the wire usage, and is suitable for symmetric and asymmetric coils, improving universality and system performance.
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Figure CN119272684A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of inductive wireless power transmission, and in particular to a double-layer coil loss optimization method based on distributed compensation. Background Art
[0002] Inductive wireless power transfer (IPT) technology has attracted wide attention in various fields due to its advantages such as flexibility and safety. Mutual inductance is one of the key technical indicators of the IPT system, and the power transfer performance of the system is closely related to it. Building a double-layer coil is one of the common methods to increase mutual inductance, which has been widely used in many fields such as implantable biomedical applications, consumer electronics, and domino resonator IPT systems.
[0003] Unlike single-layer coils, the losses of double-layer coils include not only the power losses caused by skin effect and proximity effect, but also IDC losses. When current flows through a double-layer coil, there is a potential difference between any two turns of coils in different layers, which will cause a displacement current to be generated in the interlayer insulating material. The power loss caused by the displacement current flowing through the interlayer insulating material is called IDC loss. So far, the power loss caused by skin effect and proximity effect has been studied in depth. However, only a small number of scholars have conducted research on the IDC loss of double-layer coils. For example, Wang Yijie and others from Harbin Institute of Technology proposed an improved compensation method for multi-layer coils. [1] , by making the winding coils follow the same order from outside to inside in each layer and using layer compensation to reduce IDC loss. However, the method proposed in the patent will limit the winding direction of each layer of coils, increase the amount of wire used, reduce the flatness of the coils, and this method is not suitable for asymmetric coils and is not universal.
[0004] [1|Wang Yijie. Harbin Institute of Technology. CN112311204B[P]. 2022-04-22 Summary of the invention
[0005] The purpose of the present invention is to propose a compensation method for reducing the interlayer displacement current (IDC) loss of a double-layer coil, which is applicable to symmetrical and asymmetrical double-layer coils. The method divides the concentrated compensation capacitor into two series capacitors: one for interlayer series compensation and the other for auxiliary compensation, so as to optimize the interlayer series compensation capacitor to improve the IDC distribution of the double-layer coil, thereby reducing the IDC loss. This method is applicable to both symmetrical and asymmetrical coils without increasing the amount of wire used, thereby improving its universality.
[0006] In order to achieve the above purpose, the present invention adopts the following technical means:
[0007] In order to achieve the purpose of accurately and simply solving the optimal value of the interlayer series compensation capacitance of the double-layer coil of the inductive wireless power transmission system, the present invention provides the following technical solutions: clarify the geometric parameters such as the number of turns, inner and outer diameters, and wire diameters of each layer of the double-layer coil, construct an equivalent circuit model of the double-layer coil with distributed parameters, and then calculate the self-inductance L of each coil turn, the mutual inductance M between any two coil turns, and the inter-turn capacitance C between two coil turns with the same inner and outer diameters in two adjacent layers of coils; combine Ohm's law and the principle of calculus to calculate the equivalent resistance R of the insulating medium between two coil turns with the same inner and outer diameters in two adjacent layers of coils. D ; Calculate the voltage difference U between any two turns of coils with the same inner and outer diameters in two adjacent layers of coils, and then construct the IDC loss P between the two adjacent layers of coils loss About interlayer series compensation capacitor C 1_2 The mathematical model of P loss_min The corresponding C 1_2 .
[0008] The general equivalent circuit model with distributed parameters is applicable to any double-layer coil (symmetrical or asymmetrical). In this model, each coil turn is taken as the research object and each coil turn is regarded as an equipotential ring. The self-inductance of each coil turn in the first layer is L 1X , the internal resistance is R L1X (X=1,…,N 1 )(This internal resistance is part of the multi-layer coil and is generally small, so it is ignored in subsequent calculations). The self-inductance of each turn of the coil in the second layer is L 2Y , the internal resistance is R L2Y .L 1X and L 2Y The inter-turn capacitance is C L1X_L2Y , the equivalent resistance of the insulation medium between turns is R L1X_L2Y , the mutual inductance between turns is M L1X_L2Y The interlayer series compensation capacitor C is connected in series between the first and second coils. 1_2 The specific connection relationship of each element in the general model of the equivalent circuit with distributed parameters is as follows: each coil turn in the two layers and the interlayer series compensation capacitor are connected in series, and the coupling capacitor and the equivalent resistance of the insulating medium between any two coil turns are connected in parallel and connected to the corresponding two coil turns.
[0009] The parameter design method with the double-layer coil IDC loss as the optimization target defines the system operating frequency as ω and the air medium magnetic permeability as μ. 0 The loop radii of the two coaxial parallel single-turn coils are R 1 and R 2 , d is the axial distance between the centers of the wire cross-sections of the two coils, D is the average diameter of the single-turn coil loop, h is the inter-turn gap between two single-turn coils with the same inner and outer diameters in adjacent layers, ε0 is the dielectric constant of the inter-turn medium, ρ is the resistivity of the dielectric, and the coupling capacitance C between the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i) , the potential difference between the i-th turn in the first layer and the (a+i)-th turn in the second layer is U L1i_L2(a+i) , the mutual inductance between the i-th turn in the first layer and the (a+i)-th turn in the second layer is M L1i_L2(a+i) , the dielectric loss tangent between the i-th turn in the first layer and the (a+i)-th turn in the second layer is tanθ 0 , the total self-inductance of the double-layer coil is L all .
[0010] The self-inductance L of a certain turn of the coil can be determined by formula (1):
[0011]
[0012] where μ 0 represents the magnetic permeability of vacuum, R represents the radius of the coil, r represents the radius of the coil wire, and ln represents the natural logarithmic function;
[0013] The mutual inductance between the two coaxial parallel single-turn coils is determined by formula (2):
[0014]
[0015] Where R 1 and R 2 Represent the radii of the two coils, d represents the axial distance between the centers of the wire cross sections of the two coils, where K(k) and E(k) are the first and second complete elliptic integrals, respectively.
[0016] The coupling capacitance C between the two single-turn coils with the same inner and outer diameters in the adjacent layers, i.e., the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i) Determined by formula (3)
[0017]
[0018] where ε 0 represents the dielectric constant of a vacuum, D represents the average diameter of a single-turn coil loop, and r 0 represents the wire diameter, δ is an angle variable used to describe the position of the integral on the circumference, and h represents the inter-turn gap between the i-th turn of the first layer coil and the a+i-th turn of the second layer coil;
[0019] The equivalent resistance of the insulating medium between the i-th turn of the first layer and the (a+i)-th turn of the second layer is determined by formula (4):
[0020]
[0021] Where R m represents the equivalent resistance of each trapezoidal body divided by the insulating medium along the radius of the coil, ρ represents the resistivity of the dielectric, and h m-1 represents the height of the trapezoidal body of the insulating medium along the radius of the coil, and Δr represents the thickness of the insulating medium along the radius of the coil;
[0022] The potential difference U between the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i) Determined by formula (5)
[0023]
[0024] It is worth noting that C1_2 is still an unknown number here. This is to construct the functional relationship between the interlayer displacement current loss Ploss and C1_2, where represents the current intensity flowing through the coil, ω represents the angular frequency, and L 1x represents the self-inductance of the xth turn of the first layer of coil, L 2y represents the self-inductance of the yth turn of the second layer coil, M L1x_L1y represents the mutual inductance between the xth turn of the first layer coil and the yth turn of the first layer coil, M L1x_L2y represents the mutual inductance between the xth turn of the first coil and the yth turn of the second coil, M L2x_L2y represents the mutual inductance between the xth turn of the second layer coil and the yth turn of the second layer coil, M L2x_L1y represents the mutual inductance between the xth turn of the second coil and the yth turn of the first coil, N 1 Represents the total number of turns of the first layer coil, N 1+b Represents the total number of turns of the first layer coil and the second layer coil; N 1+a+b d represents the total number of turns of the second layer coil, C 1_2 represents the interlayer series compensation capacitance;
[0025] The double-layer coil interlayer displacement current loss P loss Determined by formula (6):
[0026]
[0027] R loss Represents the loss resistance caused by interlayer displacement current in the double-layer coil system;
[0028] The optimal value of the interlayer series compensation capacitance of the double-layer coil is determined by formula (7):
[0029]
[0030]
[0031] Where L all Represents the total self-inductance of the double-layer coil system.
[0032] Compared with the prior art, the double-layer coil IDC loss optimization method based on distributed compensation of the present invention has the following beneficial effects:
[0033] 1. Distributed compensation method: This invention proposes a method for optimizing the interlayer displacement current (IDC) loss of a double-layer coil based on distributed compensation. By dividing the concentrated compensation capacitor into two series capacitors, namely the interlayer series compensation capacitor and the auxiliary compensation capacitor, it solves the limitation of using only a single concentrated capacitor for compensation in the traditional method. This distributed compensation method helps to improve the IDC distribution of the double-layer coil, thereby reducing the IDC loss.
[0034] 2. Applicable to various coil types: Compared with the traditional method, the method of the invention is applicable not only to symmetrical double-layer coils, but also to asymmetrical double-layer coils, regardless of whether the number of turns and inner and outer diameters of adjacent layers of coils are the same. This feature makes the method more widely applicable.
[0035] 3. Reduce the amount of wire used: This method will not increase the amount of wire used in the double-layer coil while reducing IDC loss, thereby maintaining the flatness of the coil and saving material costs.
[0036] 4. Accurate calculation and optimization: This method constructs a double-layer coil equivalent circuit model with distributed parameters, accurately calculates the self-inductance, mutual inductance and inter-turn capacitance of each turn of the coil, and combines the principles of calculus and Ohm's law to construct a mathematical model between IDC loss and inter-layer series compensation capacitance, and solves the optimal value of inter-layer series compensation capacitance corresponding to minimizing IDC loss.
[0037] 5. General model: The proposed general equivalent circuit model with distributed parameters is applicable to any symmetrical or asymmetrical double-layer coil, which improves its universality.
[0038] 6. Minimization of losses: By optimizing the interlayer series compensation capacitance, this method effectively reduces the IDC loss of the double-layer coil and improves the overall efficiency and performance of the system.
[0039] In summary, this invention patent effectively solves the problem of interlayer displacement current loss of the double-layer coil through distributed compensation methods and precise parameter design. It also has the advantages of saving materials, wide application range, and minimized loss. It is of great significance to improving the performance of the inductive wireless power transmission system. BRIEF DESCRIPTION OF THE DRAWINGS
[0040] Figure 1 Schematic diagrams of four double-layer coils applicable to the double-layer coil IDC loss optimization method based on distributed compensation proposed in the present invention;
[0041] Figure 2 An equivalent circuit diagram of a double-layer coil including distributed parameters applicable to the double-layer coil IDC loss optimization method based on distributed compensation proposed in the present invention;
[0042] Figure 3 Calculate the equivalent resistance of the IDC loss between the i-th turn of the first layer and the (a+i)-th turn of the second layer of the double-layer coil for the present invention;
[0043] Figure 4 The IDC loss of the double-layer coil of the present invention is related to the interlayer series compensation capacitor C 1_2 The curve of
[0044] Figure 5 , Figure 6 , Figure 7 This is a three-dimensional display diagram corresponding to the coil structure. DETAILED DESCRIPTION
[0045] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the embodiments described are only part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.
[0046] In practical applications, there may be four types of asymmetry in the double-layer coil, such as Figure 1 As shown. The outer diameter and inner diameter of the first layer coil are defined as d 11 and d 12 , define the inner and outer diameters of the second layer coil as d 21 and d 22 , the wire diameter is d 12 Under these conditions, a=(d 21 -d 11 ) / (2*d 12 ), b=(d 22 -d 12 ) / (2*d 12 ). Therefore, the type of double-layer coil should be determined first, and the geometric parameters such as the number of turns, inner and outer diameters, and wire diameter of each layer of the double-layer coil should be clarified to construct Figure 2 The double-layer coil with distributed parameters is shown in the figure. Then the self-inductance L of each coil turn, the mutual inductance M between any two coil turns, and the inter-turn capacitance C between two coil turns with the same inner and outer diameters in two adjacent layers of coils are calculated. When the radius of the single-turn coil loop is R and the wire radius is r, R / r<<1, and its self-inductance can be calculated using (1)
[0047]
[0048] With coil loop radius R 1 and R 2 The mutual inductance of two coaxial parallel single-turn coils can be calculated using (2), where d is the axial distance between the centers of the wire cross sections of the two coils, as Figure 3 (a) shown.
[0049]
[0050] where K(k) and E(k) are the complete elliptic integrals of the first and second kind, respectively.
[0051]
[0052] The inter-turn capacitance (coupling capacitance) C between the i-th turn in the first layer and the (a+i)-th turn in the second layer in adjacent layers can be calculated using (4): L1i_L2(a+i)
[0053]
[0054] Where D is the average diameter of the loop, h is the gap between turns, and ε 0 is the dielectric constant of the inter-turn medium, r 0 represents the line diameter, and δ is an angular variable used to describe the position of the integral on the circumference.
[0055] Combining Ohm's law and the principle of calculus, the equivalent resistance R of the insulating medium between two turns of coils with the same inner and outer diameters in two adjacent layers of coils is calculated. The dielectric between the i-th turn in the first layer and the (a+i)-th turn in the second layer is evenly divided into 2N parts along the radius of the coil. Figure 7 As shown, when Δr / r<<1, the dielectric between the two turns can be equivalent to 2N trapezoids with a height of h n , thickness is Δr, side length is l n and l n+1 (n=0,1,...,2N) As shown in the figure, hn is the length of the side l n .h n , the length of one side of the trapezoid is l n and ΔS m It can be calculated as:
[0056] Where m=n+1, 1≤m≤2N
[0057]
[0058] According to Ohm's law, R 0 =p 0 l 0 / S 0 , the equivalent resistance R of the mth (m=1, 2, ..., 2N) trapezoid m It can be expressed as:
[0059]
[0060] Where ρ is the resistivity of the dielectric. Figure 3 As shown in (c), the equivalent resistance of the IDC loss between the i-th turn of the first layer and the (a+i)-th turn of the second layer can be expressed as:
[0061]
[0062] Based on steps (1) and (2), the voltage difference U between any two turns of coils with the same inner and outer diameters in two adjacent layers of coils is calculated, and then the IDC loss P between the two adjacent layers of coils is constructed. loss About interlayer series compensation capacitor C 1_2 The mathematical model of P loss_min The corresponding C 1_2 The potential difference U between the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i) It can be calculated as:
[0063]
[0064] Where M represents the mutual inductance between the two coils, for example, M L1i_L2j represents the mutual inductance between the i-th turn in the first layer and the j-th turn in the second layer, where L L1i_L2(a+i) Represents the equivalent self-inductance between the i-th coil turn in the first layer and the (a+i)-th coil turn in the second layer.
[0065] The dielectric loss tangent tanθ between the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i)
[0066]
[0067] where ε 0 represents the dielectric constant of vacuum, r 0 Represents the wire diameter.
[0068] According to (9), the tangent of the dielectric loss angle between adjacent single-turn coils in the upper and lower layers is the same. Therefore, the IDC loss between adjacent layers of the double-layer coil can be calculated as
[0069]
[0070] Obviously, when the geometric parameters of the coil and the current flowing through the coil are determined, P loss Depends only on 1 / C 1_2 Equation (10) can be transformed into
[0071]
[0072] According to (11), when the coil and operating frequency are determined, A 1 , A 2 and A 3 Is independent of C 12 The constant, R loss Only with the interlayer capacitance C 1_2 Therefore, optimizing C 1_2 It can improve the distribution of IDC and reduce the loss of IDC. From (11), it can be seen that when the coil current is constant, P loss It is C 1_2 In order to maintain the inductive characteristic of the coil impedance (L all -1 / (ωC 1_2 )>0), C 1_2 Implementing P loss There are two possible conditions for the minimum value of Figure 4 shown.
[0073] like Figure 4 As shown in (a), when ω 2 L all >-0.5A 2 / A 1 When P loss_min =f(-0.5A 2 / A 1 );like Figure 4 As shown in (b), when ω 2 L all <-0.5A 2 / A 1 When P loss_min =f(ω 2 L all ). Therefore, design C within a certain range 1_2 It can reduce IDC loss. Figure 4 In the two cases shown, corresponding to P loss_min C 1_2 The value of can be calculated as:
[0074]
[0075] If the number of layers of the multi-layer coil is greater than two, when calculating the voltage difference U between two turns of coils with the same inner and outer diameters in two adjacent layers of coils, it is necessary to consider the induced voltage generated in each turn of coils in the two adjacent layers when the alternating current flows through the other layers of coils of the multi-layer coil.
[0076] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. A method for optimizing interlayer displacement current loss of double-layer coils based on distributed compensation, characterized in that: The following steps are involved: Clarify the geometric parameters of the double-layer coil, including the number of turns, inner and outer diameters, and wire diameter of each layer of coil; Construct a double-layer coil equivalent circuit model with distributed parameters, and then calculate the self-inductance L of each coil turn, the mutual inductance M between any two coil turns, and the inter-turn capacitance C between two coil turns with the same inner and outer diameters in two adjacent layers of coils; Combining Ohm's law and the principle of calculus, calculate the equivalent resistance R of the insulating medium between two turns of coils with the same inner and outer diameters in two adjacent layers of coils; The voltage difference U between any two turns of coils with the same inner and outer diameters located in two adjacent layers of coils is calculated by the coil self-inductance L and mutual inductance M; Then, the voltage difference U, the equivalent resistance R of the insulating medium, and the inter-turn capacitance C are used to construct the IDC loss P between two adjacent layers of coils. loss About interlayer series compensation capacitor C 1_2 The mathematical model of P loss_min The corresponding C 1_2 .
2. According to the method for optimizing the interlayer displacement current loss of a double-layer coil based on distributed compensation according to claim 1, it is characterized in that: The specific connection relationship of each component in the general model of the equivalent circuit with distributed parameters is as follows: each coil turn in the two layers and the interlayer series compensation capacitor are connected in series, and the coupling capacitor and the equivalent resistance of the insulating medium between any two coil turns are connected in parallel to each other and connected to the corresponding two coil turns.
3. The method for optimizing the interlayer displacement current loss of a double-layer coil based on distributed compensation according to claim 2 is characterized in that: The general equivalent circuit model with distributed parameters is used for any symmetrical or asymmetrical double-layer coil. In this model, each coil turn is taken as the research object and each coil turn is regarded as an equipotential ring. The self-inductance of each coil turn in the first layer is L 1X , the internal resistance is R LlX (X=1, ..., N1), the self-inductance of each turn of the coil in the second layer is L 2Y , the internal resistance is R L2Y , L 1X and L 2Y The inter-turn capacitance is C L1X_L2Y , the equivalent resistance of the insulation medium between turns is R L1X_L2Y , the mutual inductance between turns is M L1X_L2Y The interlayer series compensation capacitor C is connected in series between the first and second coils. 1_2 .
4. The method for optimizing the interlayer displacement current loss of a double-layer coil based on distributed compensation according to claim 3 is characterized in that: The self-inductance L of a certain turn of coil can be determined by formula (1): Where μ0 represents the magnetic permeability of vacuum, R represents the radius of the coil, r represents the radius of the coil wire, and ln represents the natural logarithmic function; The mutual inductance between two coaxial parallel single-turn coils is determined by equation (2): Where R1 and R2 represent the radii of the two coils, respectively, d represents the axial distance between the centers of the wire cross sections of the two coils, where K(k) and E(k) are the first and second complete elliptic integrals, respectively.
5. The method for optimizing the interlayer displacement current loss of a double-layer coil based on distributed compensation according to claim 4 is characterized in that: The coupling capacitance C between two single-turn coils with the same inner and outer diameters in adjacent layers, i.e., the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i) Determined by formula (3): Where ε0 represents the dielectric constant of vacuum, D represents the average diameter of a single-turn coil loop, r0 represents the wire diameter, δ is an angle variable used to describe the position of the integral on the circumference, and h represents the inter-turn gap between the i-th turn of the first layer coil and the a+i-th turn of the second layer coil.
6. The method for optimizing the interlayer displacement current loss of a double-layer coil based on distributed compensation according to claim 5 is characterized in that: The potential difference U between the i-th turn in the first layer and the (a+i)-th turn in the second layer L1i_L2(a+i) Determined by formula (5): Among them, represents the current intensity flowing through the coil, ω represents the angular frequency, and L 1x represents the self-inductance of the xth turn of the first layer of coil, L 2y represents the self-inductance of the yth turn of the second layer coil, M L1x_L1y represents the mutual inductance between the xth turn of the first layer coil and the yth turn of the first layer coil, M L1x_L2y represents the mutual inductance between the xth turn of the first coil and the yth turn of the second coil, M L2x_L2y represents the mutual inductance between the xth turn of the second layer coil and the yth turn of the second layer coil, M L2x_L1y represents the mutual inductance between the xth turn of the second coil and the yth turn of the first coil, N1 represents the total number of turns of the first coil, N 1+b Represents the total number of turns of the first layer coil and the second layer coil; N 1+a+b d represents the total number of turns of the second layer coil, C 1_2 Represents the interlayer series compensation capacitance.
7. The method for optimizing the interlayer displacement current loss of a double-layer coil based on distributed compensation according to claim 6 is characterized in that: The double-layer coil interlayer displacement current loss P loss Determined by formula (6) R loss Represents the loss resistance caused by interlayer displacement current in the double-layer coil system; The optimal value of the interlayer series compensation capacitance of the double-layer coil is determined by formula (7): Where L all Represents the total self-inductance of the double-layer coil system.