Power density calculation method and improvement method of non-invasive magnetic field energy harvesting system

Abstract

The present invention relates to the field of magnetic field energy harvesting technology, and specifically discloses a power density calculation method and improvement method for a non-invasive magnetic field energy harvesting system. The power density calculation method analyzes and establishes a non-invasive magnetic field energy harvesting system based on an H-type magnetic core, and provides a power density calculation method for the system, and obtains a power density expression that is closely related to the parameters of the H-type magnetic core and the parameters of the energy harvesting coil, filling the gap in the existing system model and providing theoretical support for guiding the design of a non-invasive magnetic field energy harvesting system. The power density improvement method, based on the power density expression of the non-invasive magnetic field energy harvesting system, comprehensively considers the influence of the parameters of the H-type magnetic core and the energy harvesting coil on the system power density, and proposes a power density improvement method for designing the number of coil turns, optimizing the thickness of the laminations and the length of the magnetic column, and designing the coil wire diameter, so that the power density of the system is at a higher level, avoiding the optimization system based on simulation guidance.

Description

Technical Field

[0001] This invention relates to the field of magnetic field energy harvesting technology, and in particular to a method for calculating and improving the power density of a non-invasive magnetic field energy harvesting system. Background Technology

[0002] Busbars are a crucial component of smart substations, undertaking the key functions of collecting, distributing, and transmitting electrical energy. To ensure reliable operation of the busbars, it is necessary to monitor their temperature, voltage, and current. Wireless sensors, as remote monitoring devices, play an irreplaceable role in ensuring the safe and reliable operation of the busbars. However, the batteries powering the sensors have a limited lifespan, and regular battery replacements result in significant losses in manpower and resources. Therefore, researching a novel self-powered sensor system is urgently needed.

[0003] Non-invasive magnetic field energy harvesting technology, based on Faraday's law of electromagnetic induction, converts the energy of the magnetic field generated by a current-carrying conductor into electrical energy, thereby powering sensors and other electronic devices. Non-invasive magnetic field energy harvesting systems offer advantages such as small size, simple structure, and ease of installation. However, current research on these systems is in its early stages, with few publications analyzing theoretical models, making it difficult to provide theoretical guidance for the design of practical energy harvesting devices. Therefore, establishing a theoretical model of the system is currently a research hotspot in non-invasive magnetic field energy harvesting technology. Furthermore, the output power of non-invasive magnetic field energy harvesting systems is limited by the size of the magnetic core; smaller cores result in lower output power, restricting application scenarios. Therefore, improving the system's power density is crucial for promoting the application of non-invasive magnetic field energy harvesting devices. Summary of the Invention

[0004] This invention provides a method for calculating and improving the power density of a non-intrusive magnetic field energy harvesting system. The technical problem it solves is: how to calculate the power density of a non-intrusive magnetic field energy harvesting system for a busbar and how to improve the power density of the non-intrusive magnetic field energy harvesting system by designing the parameters of the magnetic core and coil.

[0005] To address the above technical problems, this invention provides a method for calculating the power density of a non-intrusive magnetic field energy harvesting system. The non-intrusive magnetic field energy harvesting system includes a primary side, a secondary side, a power conversion module, and a resistor R. S The load, wherein the primary side includes a current of I B Self-perception as L B The busbar, the secondary side includes a self-inductance of L S The internal resistance is R S The current is I S The energy harvesting coil and the coil wound around it with an equivalent resistance of R core The H-shaped magnetic core, the power conversion module includes an input voltage of V OA full-bridge rectifier, wherein the voltage of the load is V. D The mutual inductance between the energy harvesting coil and the busbar is M; the H-shaped magnetic core includes a magnetic column with side length d and length l, and two laminates with side length b and thickness a respectively disposed at the center positions of both ends of the magnetic column, where d < b; the height of the energy harvesting coil wound on the magnetic column is d. c The corresponding number of coil turns is N, and the wire diameter and insulation layer thickness of the energy harvesting coil are d and d, respectively. w The power density calculation method includes the following steps: σ;

[0006] S1. The power conversion module and the load are both equivalent to a resistance value of R. O The equivalent load, and the H-shaped magnetic core is equivalent to a side length d and a length l. eq = 2a + b - d + l equivalent bar core;

[0007] S2. Calculate the induced voltage U across the energy harvesting coil. S :U S =ωMI B ω is the busbar current I B angular frequency;

[0008] S3. Calculate the power P on the equivalent load. O : in A = d 2 The effective cross-sectional area of ​​the energy harvesting coil is... λ is the magnetic flux density at the location of the energy harvesting coil, μ0 is the free permeability, and λ is the vertical distance from the center of the H-shaped magnetic core to the busbar. eff The effective permeability of the H-shaped magnetic core is μ. eff The relative permeability μ of the magnetic core r and l eq N is determined jointly by l and d, and N is determined by l and d. c d w R is jointly determined by , d, and σ. S The resistivity ρ and l, d of the coil material c d w , d, and σ are jointly determined;

[0009] S4. Calculate the power density D of the non-intrusive magnetic field energy harvesting system. P :D P =P O / V, V=2ab 2 +d 2 l represents the volume of the H-shaped magnetic core.

[0010] Further, in step S3, μ effSpecifically, it is expressed as follows:

[0011]

[0012] D M Let D be the demagnetizing coefficient used to measure the strength of the demagnetizing field. M By l eq d and d jointly decide.

[0013] Further, in step S3, D M Specifically, it is expressed as follows:

[0014]

[0015] intermediate variable K eq =2l eq / d, intermediate variable r eq =[1-(2 / K)] eq ) 2 ] 0.5 ;

[0016] Then μ eff Specifically, it is expressed as follows:

[0017]

[0018] Further, in step S3, N is specifically represented as:

[0019]

[0020] Further, in step S3, R S Specifically, it is expressed as follows:

[0021]

[0022] Further, in step S4, D P Specifically, it is expressed as follows:

[0023]

[0024] The intermediate variables α, β, ε, δ, γ, and κ are represented as follows:

[0025]

[0026] This invention also provides a method for improving the power density of a non-invasive magnetic field energy harvesting system, by jointly optimizing the height d of the energy harvesting coil. c The thickness 'a' of the laminate, the diameter 'd' of the magnetic post, and the diameter 'd' of the coil wire. w To improve the power density D calculated by the above power density calculation method P .

[0027] Furthermore, the coil height d is jointly optimized. c The thickness 'a' of the laminate, the diameter 'd' of the magnetic column, and the wire diameter 'd' of the energy harvesting coil w To improve the power density D calculated by the above power density calculation method P The specific steps include:

[0028] X1. Determine the power density D based on actual needs. P In the expression except d c a, d, d w Other than the parameters, we get only about d c a, d, d w The first power density function;

[0029] X2, Set a, d, d w All are constant values, thus obtaining the first power density function with respect to d. c The second power density function, in d c Within the range of values, the value of d when the second power density function reaches its maximum value. c As d c The optimal value is denoted as d. c ';

[0030] X3, set d c =d c 'and d w As a constant, the third power density function of the first power density function with respect to a and d is obtained. Within the respective ranges of a and d, the values ​​of a and d when the third power density function reaches its maximum value are taken as the optimal values ​​of a and d, and are denoted as a' and d' respectively.

[0031] X4, Set d c =d c ', a = a', d = d', thus obtaining the first power density function with respect to d w The fourth power density function, in d w Within the range of values, the value of d when the fourth power density function reaches its maximum value. w As d w The optimal values ​​are denoted as d. w ';

[0032] X5, Setting d c =d c '、a=a'、d=d'、d w =d w '.

[0033] Specifically, in step X2, d c The optimal value d c '=b.

[0034] This invention provides a method for calculating the power density of a non-intrusive magnetic field energy harvesting system. It analyzes and establishes a non-intrusive magnetic field energy harvesting system based on an H-type magnetic core, and gives a method for calculating the power density of the system. It obtains a power density expression that is closely related to the parameters of the H-type magnetic core and the parameters of the energy harvesting coil, filling the gap in existing system models and providing theoretical support for guiding the design of non-intrusive magnetic field energy harvesting systems.

[0035] This invention also provides a method for improving the power density of a non-invasive magnetic field energy harvesting system. Based on the power density expression of the non-invasive magnetic field energy harvesting system, it comprehensively considers the influence of the parameters of the H-type magnetic core and the energy harvesting coil on the system power density, and proposes a power density improvement method by designing the number of coil turns, optimizing the lamination thickness and magnetic column length, and designing the coil wire diameter, so that the power density of the system is at a high level, avoiding the need for simulation-guided system optimization. Attached Figure Description

[0036] Figure 1 This is an equivalent circuit diagram of the non-invasive magnetic field energy harvesting system provided in the embodiments of the present invention;

[0037] Figure 2 This is provided by the embodiments of the present invention. Figure 1 Simplified equivalent circuit diagram;

[0038] Figure 3 This is a schematic diagram of the demagnetization field of the non-invasive magnetic field energy harvesting system provided in the embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram of the H-shaped magnetic core and its equivalent of the non-invasive magnetic field energy harvesting system provided in this embodiment of the invention.

[0040] Figure 5 This is a schematic diagram of the energy harvesting coil arrangement of the non-invasive magnetic field energy harvesting system provided in this embodiment of the invention;

[0041] Figure 6 This is a graph showing the power density of the non-intrusive magnetic field energy harvesting system provided in this embodiment of the invention as a function of coil height.

[0042] Figure 7 This is a three-dimensional graph showing the power density of the non-invasive magnetic field energy harvesting system provided in this embodiment of the invention as a function of the lamination thickness and the diameter of the magnetic column.

[0043] Figure 8 This is a graph showing the power density of the non-intrusive magnetic field energy harvesting system provided in this embodiment of the invention as a function of the coil wire diameter. Detailed Implementation

[0044] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0045] This invention first provides a non-invasive magnetic field energy harvesting system, such as... Figure 1 As shown, the non-intrusive magnetic field energy harvesting system includes a primary side, a secondary side, an energy conversion module, and a resistor R. S The load, on the primary side, includes a current of I. B Self-perception as L B The busbar, secondary side including self-inductance L S The internal resistance is R S The current is I S The energy extraction coil (or simply coil) and the coil wound around which the energy extraction coil is equivalent to a resistance of R. core The H-type magnetic core, the power conversion module includes an input voltage of V O The full-bridge rectifier (including rectifier diodes D1-D4 and filter capacitor C) D The load voltage is V. D The mutual inductance between the energy extraction coil and the busbar is M. The power conversion module and the load can be considered together as having a resistance of R. O The equivalent load, such as Figure 2 As shown.

[0046] Figure 3 This is a schematic diagram of the demagnetizing field of a typical long straight magnetic core. The core length is L, and the side length is D. M H is the demagnetizing coefficient, N and S represent the magnetic poles of the resulting demagnetizing field, and the strength of the demagnetizing field is H. d The external magnetic field strength is H ex The magnetic field strength H inside the magnetic core in It can be represented as H in =H ex -H d .

[0047] like Figure 4 As shown, the H-type magnetic core used in this embodiment includes a magnetic column with a side length of d and a length of l, and two laminated sheets with a side length of b and a thickness, respectively disposed at the center positions of both ends of the magnetic column, where d < b. The height of the coil wound on the magnetic column (the total height of the coil and the magnetic column) is d. c The corresponding number of coil turns is N. The H-type magnetic core can be equivalently represented as a core with side length d and length l. eq = 2a+b-d+l equivalent bar core.

[0048] Figure 5This is a schematic diagram of the energy harvesting coil arrangement for this non-invasive magnetic field energy harvesting system, d w σ is the wire diameter of the energy harvesting coil, and σ is the insulation thickness of the energy harvesting coil.

[0049] According to Faraday's law of electromagnetic induction, the induced voltage U generated across the coil... S It can be represented as:

[0050] U S =ωMI B (1)

[0051] ω is the busbar current I B angular frequency.

[0052] The simplified equivalent circuit of the non-invasive magnetic field energy harvesting system is shown in the attached figure. Figure 2 As shown, the equivalent load R O Power P on O for:

[0053]

[0054] The induced voltage U across the coil S Another formula for calculation is:

[0055] U S =ωNBAμ eff (3)

[0056] μ eff Where A is the effective permeability, B is the effective cross-sectional area of ​​the coil, and C is the magnetic flux density at the location of the energy harvesting coil.

[0057] From equations (1) and (3), we can obtain the expression for mutual inductance M:

[0058]

[0059] Effective permeability μ eff It is related to the core material, structure, and size, and can be expressed as:

[0060]

[0061] μ r D is the relative permeability of the magnetic core. M This is the demagnetization coefficient.

[0062] For the attached Figure 3 The ordinary long straight magnetic core shown has a demagnetizing field inside because it is a non-closed structure. The demagnetizing coefficient D is... M It can be used to measure the strength of the demagnetizing field, and the demagnetizing coefficient is affected by the core length L and the core side length D, and has the following expression:

[0063]

[0064] Where the intermediate variable K = 2L / D, and the intermediate variable r = [1 - (2 / K)] 2 ] 0.5 .

[0065] This embodiment uses the appendix Figure 4 The H-shaped magnetic core shown is used to improve the system power density, and the H-shaped magnetic core is equivalent to a long straight magnetic core with an equivalent core length l. eq It can be represented as:

[0066] l eq =2a+b-d+l (7)

[0067] At this point, there is K. eq =2l eq / d,r eq =[1-(2 / K)] eq ) 2 ] 0.5 .

[0068] For H-type magnetic cores, K is usually used. eq >2, therefore the demagnetization coefficient D M It can be represented as:

[0069]

[0070] Substituting equation (8) into equation (5), the effective permeability μ eff for:

[0071]

[0072] The coil uses an attached Figure 5 The winding arrangement shown is wound on the magnetic pillar of an H-shaped magnetic core. The number of turns N of the coil can be calculated by the following formula:

[0073]

[0074] At this time, the coil internal resistance R S for:

[0075]

[0076] If we consider the busbar as an infinitely long straight conductor, then the magnetic field strength B at the location of the coil can be expressed as:

[0077]

[0078] λ is the vertical distance from the center of the H-type magnetic core to the busbar.

[0079] Meanwhile, the effective cross-sectional area A of the coil is equivalent to:

[0080] A = d 2(13)

[0081] The volume V of the magnetic core can be expressed as:

[0082] V = 2ab 2 +d 2 l (14)

[0083] By combining equations (2), (4), (9) to (14), the power density D of the system can be calculated. P for:

[0084]

[0085] The intermediate variables are:

[0086]

[0087] Based on the theoretical analysis of the above-mentioned non-invasive magnetic field energy harvesting system, this embodiment of the invention also provides a method for calculating the power density of a non-invasive magnetic field energy harvesting system, specifically including the following steps:

[0088] S1. Equivalently represent the power conversion module and the load together as having a resistance of R. O The equivalent load, and the equivalent of the H-type magnetic core to a side length of d and a length of l eq = 2a + b - d + l equivalent bar core;

[0089] S2. Calculate the induced voltage U across the energy harvesting coil. S :U S =ωMI B ;

[0090] S3. Calculate the power P on the equivalent load. O : in Effective permeability μ eff The number of coil turns N is calculated using equation (17), and the coil internal resistance R is calculated using equation (18). S The magnetic induction intensity B is calculated by equation (19), the effective cross-sectional area A of the coil is calculated by equation (20), and the effective cross-sectional area A of the coil is calculated by equation (21).

[0091] S4. Calculate the power density D of the non-intrusive magnetic field energy harvesting system. P :D P =P O / V, the core volume V is calculated by equation (22), and finally the power density D is obtained. P The expressions are shown in equations (23) and (24).

[0092] This power density calculation method analyzes and establishes a non-intrusive magnetic field energy harvesting system based on an H-type magnetic core, and provides a method for calculating the power density of the system. It obtains a power density expression that is closely related to the parameters of the H-type magnetic core and the parameters of the energy harvesting coil, filling the gap in existing system models and providing theoretical support for guiding the design of non-intrusive magnetic field energy harvesting systems.

[0093] Based on the power density D shown in equations (25) and (26) P In addition to the expression, this embodiment also provides a method for calculating the power density of a non-invasive magnetic field energy harvesting system, which optimizes the height d of the energy harvesting coil. c The thickness 'a' of the laminate, the diameter 'd' of the magnetic column, and the diameter 'd' of the coil wire. w To increase the calculated power density D P The specific steps include:

[0094] X1. Determine the power density D based on actual needs. P In the expression except d c a, d, d w Other than the parameters, we get only about d c a, d, d w The first power density function;

[0095] X2, Set a, d, d w All are constants, thus obtaining the first power density function with respect to d. c The second power density function, in d c Within the range of values, the value of d when the second power density function reaches its maximum value. c As d c The optimal value is denoted as d. c ';

[0096] X3, set d c =d c 'and d w As constants, the third power density function of the first power density function with respect to a and d is obtained. Within the respective ranges of a and d, the values ​​of a and d when the third power density function reaches its maximum value are taken as the optimal values ​​of a and d, and are denoted as a' and d' respectively.

[0097] X4, Set d c =d c ', a = a', d = d', thus obtaining the first power density function with respect to d w The fourth power density function, in d w Within the range of values, the value of d when the fourth power density function reaches its maximum value. w As d w The optimal values ​​are denoted as d. w ';

[0098] X5, Setting d c =d c '、a=a'、d=d'、d w =d w '.

[0099] Set busbar current I B The current is 100A, the angular frequency ω is 100π, and the free permeability μ0 is 4π×10⁻⁶. -7 The relative permeability μ of the magnetic core r The value is 30000, and the load is R. O The resistance is 1 kΩ, and the coil resistivity ρ is 1.72 × 10⁻⁶. -8 Ω·m, the coil insulation layer thickness σ is 0.00001m, and the total dimensions of the H-type magnetic core are limited to 0.03m × 0.03m × 0.04m, that is, the side length b of the laminate is 0.03m, and the total length 2a+l is 0.04m. The system optimization design process is as follows:

[0100] The equivalent core length of the H-type magnetic core is l eq for:

[0101] l eq =0.07-d

[0102] Effective permeability μ eff for:

[0103]

[0104] in:

[0105]

[0106] Calculate the number of turns N and the internal resistance R of the coil. S :

[0107]

[0108] The magnetic induction intensity B at the location of the coil is calculated to be approximately 0.0013 T, and the effective cross-sectional area A of the coil is d. 2 .

[0109] The core volume V is:

[0110] V = 0.0018a + (0.04 - 2a)d 2

[0111] Substituting the above parameters into the power density expression, we obtain the power density D. P Regarding the coil height d c The thickness of the laminate (a), the diameter of the magnetic column (d), and the diameter of the coil wire (d) w The first power density function is as follows:

[0112]

[0113] When the lamination thickness 'a', the magnetic column diameter 'd', and the coil wire diameter 'd' w When the value is constant, the power density is obtained with respect to the coil height d. c The second power density function, the function curve is shown in the attached figure. Figure 6 As shown, it can be observed that the greater the coil height, i.e., the more coil turns, the higher the system power density. When d c =b=30mm, meaning that when the coil is fully wound around the magnetic core, the system power density can reach 4.9mW / cm². 3 Compared to d c =15mm corresponds to a power density of 0.6mW / cm² 3 The improvement effect can be up to 8 times. Therefore, designing the number of coil turns can effectively improve the system power density. For a magnetic core with a limited overall size, the coil should be designed to be fully wound around the core.

[0114] When the coil is fully wound around the magnetic core, and the coil wire diameter d w When the value is constant, the power density D can be obtained. P The third power density function relating lamination thickness *a* and magnetic column diameter *d* is shown in the attached three-dimensional graph. Figure 7 As shown, it can be observed that the smaller the lamination thickness, the higher the system power density; there is an optimal value for the magnetic column diameter that maximizes the system power density. When a = 1 mm, the system power density can reach 4.9 mW / cm². 3 Compared to the power density of 0.3 mW / cm² corresponding to a = 9 mm, 3 The improvement effect can reach 16 times; when d=6mm, the system power density can reach 4.9mW / cm². 3 Compared to the power density of 3.2 mW / cm² corresponding to d = 10 mm. 3 The improvement can reach 1.5 times. Therefore, optimizing the lamination thickness and the magnetic column diameter can effectively improve the system power density. Under the limited total core size, the lamination thickness should be designed to be the minimum value of 1mm and the magnetic column diameter should be designed to be the optimal value of 6mm.

[0115] When the coil is fully wound around the magnetic core, the lamination thickness 'a' is designed to be at its minimum, and the magnetic column diameter 'd' is designed to be at its optimal value, the power density D is obtained. P Regarding the coil wire diameter d w The fourth power density function, the function curve is shown in the attached figure. Figure 8 As shown, there exists an optimal value for the coil wire diameter that maximizes the system power density. When d w When the thickness is 0.2 mm, the system power density can reach 4.9 mW / cm². 3 Compared to d w =0.4mm corresponds to a power density of 0.8mW / cm³3 The improvement effect can be up to 6 times. Therefore, designing the coil wire diameter can effectively improve the system power density. Under the limited total core size, the coil wire diameter should be designed to the optimal value of 0.2mm.

[0116] After the above steps, d should be set. c =30mm, a=1mm, d=6mm, d w =0.2mm.

[0117] This power density enhancement method is based on the power density expression of a non-intrusive magnetic field energy harvesting system. It comprehensively considers the influence of the parameters of the H-type magnetic core and the energy harvesting coil on the system power density, and proposes a power density enhancement method that designs the number of coil turns, optimizes the lamination thickness and magnetic column length, and designs the coil wire diameter. This method enables the system to achieve a high power density and avoids the need for simulation-guided system optimization.

[0118] In summary, the power density calculation and improvement methods for the non-invasive magnetic field energy harvesting system proposed in this invention provide a theoretical system design and optimization method that can effectively improve the power density of the non-invasive magnetic field energy harvesting system.

[0119] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the power density of a non-invasive magnetic field energy harvesting system, characterized in that: The non-intrusive magnetic field energy harvesting system includes a primary side, a secondary side, an electric energy conversion module and a resistor R S The load on the primary side includes a current of I B , self-sensitivity is L B The secondary side includes a self-inductance of L S , internal resistance is R S , the current is I S The energy taking coil and the energy taking coil wound by the energy taking coil, with an equivalent resistance of R core H-type magnetic core, the power conversion module includes an input voltage V O The load voltage of the full-bridge rectifier is V D , the mutual inductance between the energy extraction coil and the busbar is M; the H-type magnetic core includes a magnetic column with a side length of d and a length of l, and two laminates with a side length of b and a thickness of a respectively arranged at the center positions of both ends of the magnetic column, d<b, and the height of the energy extraction coil wound on the magnetic column is d c , the corresponding number of coil turns is N, the wire diameter and insulation layer thickness of the energy extraction coil are d w , σ; the power density calculation method comprises the steps of: S1. The power conversion module and the load are equivalent to a resistance of R O The equivalent load of the H-type magnetic core is equivalent to a side length of d and a length of l eq =2a+b-d+l equivalent strip core; S2. Calculate the induced voltage U at both ends of the energy taking coil S :U S =ωMI B , ω is the busbar current I B Angular frequency; S3. Calculate the power P on the equivalent load O : in A=d 2 is the effective cross-sectional area of ​​the energy extraction coil, is the magnetic induction intensity at the location of the energy extraction coil, μ0 is the vacuum magnetic permeability, λ is the vertical distance from the center of the H-type magnetic core to the busbar, μ eff is the effective magnetic permeability of the H-type magnetic core, μ eff The relative magnetic permeability μ of the magnetic core r and l eq , d jointly determine, N is determined by l, d c d w , d, and σ jointly determine R S The coil material resistivity ρ and l, d c d w , d, and σ are jointly determined; S4. Calculate the power density D of the non-invasive magnetic field energy harvesting system P :D P =P O / V,V=2ab 2 +d 2 l represents the volume of the H-type magnetic core.

2. The power density calculation method of the non-invasive magnetic field energy harvesting system according to claim 1, characterized in that: In step S3, μ eff Specifically expressed as: D M is the demagnetization coefficient used to measure the strength of the demagnetization field, and D M By l eq , d jointly decide.

3. The power density calculation method of the non-invasive magnetic field energy harvesting system according to claim 2, characterized in that: In step S3, D M Specifically expressed as: Intermediate variable K eq =2l eq / d, intermediate variable r eq =[1-(2 / K eq ) 2 ] 0.5 ; Then μ eff Specifically expressed as:

4. The power density calculation method of the non-invasive magnetic field energy harvesting system according to claim 2, characterized in that: In step S3, N is specifically expressed as:

5. The power density calculation method of the non-intrusive magnetic field energy harvesting system according to claim 2, characterized in that: In step S3, R S Specifically expressed as:

6. The power density calculation method of the non-invasive magnetic field energy harvesting system according to any one of claims 2 to 5, characterized in that: In step S4, D P Specifically expressed as: The intermediate variables α, β, ε, δ, γ, and κ are expressed as follows:

7. A method for improving the power density of a non-invasive magnetic field energy harvesting system, characterized in that: By jointly optimizing the height d of the energy extraction coil c , the thickness a of the lamination, the diameter d of the magnetic column and the coil wire diameter d w To improve the power density D calculated in claim 6 P .

8. The method for improving the power density of the non-invasive magnetic field energy harvesting system according to claim 7, characterized in that: Joint optimization of coil height d c , the thickness of the lamination a, the diameter of the magnetic column d and the wire diameter d of the energy taking coil w To improve the power density D calculated in claim 6 P The specific steps include: X1. Determine the power density D according to actual needs P In the expression of c , a, d, d w Other parameters except d c , a, d, d w The first power density function of X2, set a, d, d w are all constant values, and the first power density function is obtained with respect to d c The second power density function, at d c Within the value range of the second power density function, the d c As d c The optimal value of c '; X3. Set c =d c ' and d w is a constant, a third power density function of the first power density function with respect to a and d is obtained, and within the respective value ranges of a and d, a and d when the third power density function obtains the maximum value are taken as the optimal values ​​of a and d, which are recorded as a' and d' respectively; X4. Set c =d c ', a=a', d=d', and the first power density function is obtained with respect to d w The fourth power density function, at d w Within the value range of d w As d w The optimal value of w '; X5. Set c =d c ', a=a', d=d', d w =d w '.

9. The method for improving the power density of the non-invasive magnetic field energy harvesting system according to claim 8, characterized in that: In step X2, d c The optimal value of d c '=b.

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