An optimization method for the toroidal magnetic core of an invasive current transformer

Abstract

The present invention belongs to the technical field of mutual inductors and relates to a method for optimizing a toroidal core of an intrusive mutual inductor. The method establishes a mutual inductor equivalent model based on a mutual inductor circuit model, designs a vector diagram of the relationship between the induced electromotive force and the current on the secondary side, and provides the primary side current in combination with relevant principles to derive the secondary side output voltage. The secondary coil output voltage is derived by setting parameters, and the secondary side output power is further derived. By analyzing the influencing factors of the secondary coil output voltage and the secondary side output power, the conditions for maximizing the secondary side coil output voltage and output power are provided. Through analysis, it is concluded that while keeping the core cross-sectional circumference, the secondary coil resistance, and the primary coil current unchanged, the core cross-sectional area can be increased by changing the size of the core cross-sectional area, so as to improve the parameter values of the secondary side coil output voltage and output power, thereby optimizing the structure of the toroidal core.

Description

Technical Field

[0001] The invention belongs to the technical field of mutual inductors, and in particular relates to an optimization method for a toroidal magnetic core of an intrusive mutual inductor. Background Art

[0002] High-voltage overhead transmission lines are crucial in my country's power system, transporting electricity over long distances from power stations to various power-consuming areas. However, due to their exposure to the outdoors, these transmission lines often face a variety of potential threats and challenges, such as extreme weather, damage from external forces, and aging equipment. Therefore, real-time monitoring of these lines is crucial for preventing accidents and ensuring the stability and security of power supply. Currently, power supply methods used for online monitoring of high-voltage transmission lines include batteries, solar energy, vibration energy, and laser technologies. While these methods each have their advantages, in-depth analysis and comparison have revealed that they have limitations in meeting the needs for long-term, stable power supply and may not fully meet the development needs of online monitoring systems.

[0003] The presence of alternating electric and magnetic fields around high-voltage transmission lines offers the potential for developing new energy harvesting methods. Using current transformers (CTs) to inductively extract power from transmission lines has become a widely adopted and increasingly popular power supply technology due to its low cost, strong environmental adaptability, ease of operation, long power supply cycles, and stable power output. The core of this method lies in the current transformer, which senses and extracts electrical energy from high-voltage transmission lines to power monitoring equipment. By directly utilizing the electromagnetic field of the transmission lines, this method is independent of external energy sources, resulting in greater sustainability and reliability. Furthermore, this method offers low maintenance costs and a long service life, helping to reduce overall operating expenses. Using current transformers to inductively extract power not only provides stable and continuous power support for online monitoring systems for high-voltage overhead transmission lines, but also, due to its high efficiency and cost-effectiveness, is expected to become a key direction for future developments in power system monitoring technology.

[0004] High-voltage transmission lines generate alternating magnetic fields, and energy can be extracted using the principle of electromagnetic induction. A typical solution is a current transformer (CT). Specifically, a CT energy harvesting device is installed near the transmission line. When AC current flows through the transmission line, the CT's secondary coil induces a voltage. This voltage is then processed through modules such as rectification, filtering, surge protection, and voltage stabilization to power the equipment.

[0005] Current transformers (CTs) are primarily categorized into two types: measuring CTs and supply CTs. Measuring CTs use multi-turn windings to measure larger currents and are suitable for low- and medium-voltage applications, such as power monitoring in residential and commercial buildings. Supply CTs, which attach directly to high-voltage conductors, are used in high-voltage systems, such as substations and transmission lines, to monitor current flow and provide protection and control. Both types are used in power systems to accurately measure current, provide overcurrent protection, and facilitate power grid analysis and management.

[0006] CT energy harvesters can be categorized as non-invasive or invasive, depending on their structure and installation location. These devices are designed to efficiently harvest energy from power system busbars or transmission lines, with the specific implementation depending on the technical requirements and application environment.

[0007] Non-invasive devices are characterized by the non-closed structure of their magnetic core, which allows the device to be placed directly on the surface of the high-voltage transmission line busbar without physically intruding the circuit system. The advantages of this design lie in the device's simple deployment and high versatility, making it particularly suitable for applications where installation space is limited or there are strict requirements on the invasiveness of the equipment, such as switch cabinets, substation busbars, and transmission cables. In addition, non-invasive devices have a wide range of adaptability and can be applied to busbars of various sizes and current specifications. However, due to the non-closed nature of the magnetic core structure, its coupling efficiency is lower, resulting in lower output power and power density than invasive devices under the same busbar current conditions.

[0008] Invasive devices achieve higher coupling coefficients and input power by embedding the magnetic field source within the energy harvesting module. This structural design offers significant advantages in energy conversion efficiency and is particularly suitable for applications requiring higher power output, such as large industrial facilities or high-load equipment. Despite this, the installation process of invasive devices is relatively complex and typically requires precise installation in specific locations. This not only increases the difficulty and cost of installation, but can also cause additional mechanical stress on busbars or transmission lines due to the large size and weight of the device, thereby accelerating the aging process of the equipment and structure and affecting the overall stability and safety of the system.

[0009] In summary, when selecting an appropriate CT energy harvesting device, it is important to consider its ease of installation, energy efficiency, cost, and potential long-term impact on the power system. Proper design and installation strategies can effectively leverage the advantages of these devices while mitigating their potential risks and adverse effects. Summary of the Invention

[0010] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for optimizing the annular core of an intrusive mutual inductor.

[0011] In order to achieve the purpose of the present invention, we will adopt the following technical solutions to implement it:

[0012] A method for optimizing a ring core of an intrusive mutual inductor comprises the following steps:

[0013] S1. Equivalently convert the rectifier circuit and its subsequent circuits into resistive impedances, and establish an equivalent model of the transformer energy source based on the equivalent power supply topology.

[0014] S2. Based on the transformer energy source equivalent model established in step S1, while ignoring the secondary coil leakage inductance and the subsequent circuit line loss, the expression of the transformer energy source equivalent model is established based on the electromagnetic induction law and the full current law:

[0015]

[0016] Where H m is the magnetic field strength inside the coil; l is the average magnetic circuit strength; I m is the excitation current; E2 is the secondary voltage of the coil; f is the frequency of the AC current, which is 50Hz; Φ m is the magnetic flux; S is the cross-sectional area of the core; B m is the magnetic induction intensity inside the coil; μ0 is the vacuum magnetic permeability, which is 4π×10-7H / m; μ r is the relative magnetic permeability of the core material; H m is the magnetic field strength of the primary coil; N1 and N2 are the turns of the primary and secondary coils respectively; I1 and I2 are the primary and secondary currents respectively;

[0017] S3. Based on the expression in step S2, a vector diagram of the relationship between the secondary-side induced electromotive force and the current is established. Combining the principles of electromechanics and the vector relationship between the secondary-side induced electromotive force and the current in the ring core structure of the intrusive transformer, the solution is:

[0018]

[0019] S4. Based on the expression established in step S2 and the solution of step S3, derive the secondary side output voltage E2. Based on the secondary side output voltage E2, derive the secondary coil output voltage U2 by setting the parameter ɑ. Then, derive the secondary side output power P based on the secondary coil output voltage U2. Wherein:

[0020] The expression of the parameter ɑ is:

[0021]

[0022] The expression of the secondary side output voltage E2 is:

[0023]

[0024] The expression of the secondary side coil output voltage U2 is:

[0025]

[0026] The expression of the secondary side output power P is:

[0027]

[0028] S5. When the intrusive transformer is powered by power supply and the magnetic core is not saturated, by analyzing the factors affecting the secondary coil output voltage U2 and the secondary side output power P, it is concluded that if and only if R=αN2 2 When , the secondary coil output voltage U2 and output power P take the maximum value;

[0029] S6. Based on the analysis results of step S5 and the relationship between the various parameters of the ring core structure of the intrusive transformer, it is found through analysis that: while keeping the core cross-sectional perimeter L, the secondary coil resistance, and the primary coil current unchanged, the core cross-sectional area can be increased by changing the size of the core cross-sectional area to increase the value of the parameter ɑ of the secondary coil output voltage U2 and the output power P, thereby optimizing the structure of the ring core; wherein:

[0030] The dimension is the radial length a of the core cross section;

[0031] The relationship between the parameters is as follows:

[0032] a=(Do-Di) / 2

[0033] L=(a+W)×2

[0034] Where L is the circumference of the core cross section; a is the radial length of the core cross section; W is the width of the core cross section; Do is the outer diameter of the annular core; and Di is the aperture of the annular core.

[0035] As a preferred solution of the present invention, when there is no current fluctuation, reducing the magnetic path length l and increasing the core cross-sectional area S can increase the secondary side output voltage and secondary side output power.

[0036] As a preferred solution of the present invention, the derivation process of the secondary coil output voltage U2 is as follows:

[0037]

[0038] According to the expression of secondary side output voltage E2:

[0039] set up Then the secondary coil output voltage U2 is:

[0040]

[0041] Arranging formula (4) yields:

[0042]

[0043] As a preferred solution of the present invention, when the intrusive transformer is powered by an energy source, the secondary side output voltage is related to the primary side current of the coil, the number of turns of the secondary side coil, the magnetic permeability, size and load of the magnetic core.

[0044] As a preferred solution of the present invention, when the magnetic core is not saturated, the secondary side output power reaches a maximum value.

[0045] As a preferred solution of the present invention, the outer diameter Do and width W of the annular magnetic core can vary with the change of the radial length a.

[0046] As a preferred solution of the present invention, the output voltage U2 and the output power P of the secondary coil can vary with the change of the radial length a.

[0047] Beneficial effects

[0048] The present invention verifies through simulation experiments that, when the core cross-section perimeter L is equal and the secondary coil resistance is equal, the power-taking capacity of the mutual inductor with an elliptical cross-section core is better than that of a rectangular cross-section core;

[0049] When the primary coil input current is small, the magnetic core does not experience magnetic saturation, and the maximum output power of the transformer with an elliptical cross-section core is about 34% higher than that of the transformer with a rectangular cross-section core. However, the maximum output power density of the transformer with an elliptical cross-section core is only about 1.3% lower than that of the transformer with a rectangular cross-section core. Only a small increase in the core volume is needed to improve the transformer's power supply capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is the equivalent model of the mutual inductor energy extraction circuit;

[0051] Figure 2 The vector diagram of the relationship between the induced electromotive force and the current on the secondary side;

[0052] Figure 3 Schematic diagram of the structure of the transformer core;

[0053] Figure 4 is the graph of the induced voltage of the secondary coil changing with the radial length;

[0054] Figure 5 The graph of the secondary coil output power changing with radial length;

[0055] Figure 6The figure shows the variation of the induced voltage of the secondary coil of the rectangular core mutual inductor with the number of turns of the secondary coil and the equivalent load of the secondary coil;

[0056] Figure 7 The figure shows the variation of the induced voltage of the secondary coil of the elliptical core mutual inductor with the number of turns of the secondary coil and the equivalent load of the secondary coil;

[0057] Figure 8 The output power of the secondary coil of the rectangular core mutual inductor changes with the number of turns of the secondary coil and the equivalent load of the secondary coil;

[0058] Figure 9 The output power of the secondary coil of the elliptical core mutual inductor changes with the number of turns of the secondary coil and the equivalent load of the secondary coil;

[0059] Figure 10 The figure shows the variation of the output power density of the rectangular core mutual inductor with the number of turns of the secondary coil and the equivalent load of the secondary coil;

[0060] Figure 11 This is a graph showing the variation of the output power density of the elliptical core mutual inductor with the number of secondary coil turns and the secondary coil equivalent load. DETAILED DESCRIPTION

[0061] The present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0062] As an embodiment of the present invention, Figures 1 to 5 As shown, a method for optimizing the ring core of an intrusive mutual inductor includes the following steps:

[0063] In order to analyze the factors affecting the output voltage and output power of the energy-taking coil, the rectifier circuit and its subsequent circuit are equivalent to resistive reactance. Based on the equivalent power supply topology, an equivalent model of the transformer energy-taking power supply is established, as shown in the following example: Figure 1 shown.

[0064] Ignoring the secondary coil leakage inductance and the subsequent circuit line loss, based on the law of electromagnetic induction and the full current law, we can obtain:

[0065]

[0066] Where H m is the magnetic field strength inside the coil; l is the average magnetic circuit strength; I m is the excitation current; E2 is the secondary voltage of the coil; Φ m is the magnetic flux; S is the cross-sectional area of the core; B m is the magnetic induction intensity inside the coil; N1, N2 are the turns of the primary and secondary coils; I1, I2 are the primary and secondary currents.

[0067] Since the parameters such as coil line loss, core hysteresis loss, eddy current loss and leakage inductance voltage drop loss are small, they can be ignored when analyzing the inductive energy of the transformer power supply. Therefore, this paper uses the simplified relationship vector diagram of the secondary side induced electromotive force and current for analysis and calculation, as shown in the following example: Figure 2 shown.

[0068] Combining the relevant principles of electrical engineering with Figure 3 The relationship between the induced electromotive force and the current vector on the secondary side can be solved as follows:

[0069]

[0070] According to equations (1) and (2), the secondary side output voltage is:

[0071]

[0072] set up Then the secondary coil output voltage U2 is:

[0073]

[0074] Arranging formula (4) yields:

[0075]

[0076] From the secondary side output voltage, the secondary side output power P is:

[0077]

[0078] If and only if R = αN2 2 When , the secondary side output voltage U2 and output power P reach their maximum values. Equations (5) and (6) show that when the transformer is powered, the secondary side output voltage is related to the primary side current of the coil, the number of turns of the secondary side coil, the magnetic permeability and size of the core, and the load. When the core is not saturated, the output power reaches its maximum value. In addition, when the current is stable, reducing the magnetic path length l and increasing the core cross-sectional area S can increase the secondary side output voltage and output power.

[0079] When the cross-sectional perimeter L of the core is constant and the number of turns Ns of the secondary coil is also constant, the coil resistance of the secondary coil is constant. By ensuring a constant cross-sectional perimeter L and continuously changing the cross-sectional dimensions of the rectangular and elliptical cores, the core area and area distribution can be optimized, thereby improving the parameter α in equations (5) and (6).

[0080] The dimensions of the transformer are: aperture Di = 65mm, core cross-section circumference L = 218mm. The outer diameter Do and width W of the optimized transformer will vary with the radial length a of the core cross-section. The relationship between the dimensions is as follows: Figure 3 As shown;

[0081] The relationship between the parameters is as follows:

[0082] a=(Do-Di) / 2

[0083] L=(a+W)×2

[0084] The number of turns Ns of the secondary coil is set to 250 turns, the secondary coil load RL is 250 ohms, and a is the radial length of the rectangle, which is also the radial length of the elliptical cross section. Keeping the circumference of the core cross section unchanged, when the primary coil current I = 20A, the induced voltage of the secondary coil changes with the radial length as shown below Figure 4 As shown, the output power of the secondary coil varies with the radial length as Figure 5 shown.

[0085] When the transformer core aperture D i = 65 mm, the core cross-section circumference L = 218 mm, the secondary coil turns Ns = 250, and the secondary coil load RL = 250 Ω, the transformer's power supply performance is optimal when the radial length of the core cross-section is 43 ± 2 mm. Cores with elliptical cross-sections perform better than those with rectangular cross-sections.

[0086] As an embodiment of the present invention, Figure 6 and Figure 7 As shown in the figure, the radial length a of the rectangular cross-section core and the elliptical cross-section core is determined to be 43mm. When the primary coil input current Ip = 20A, the power-taking capacity comparison of the mutual inductor of the two cores is obtained as follows:

[0087] 1. When the number of turns of the secondary coil is constant, the induced voltage of the secondary coil increases with the increase of the load of the secondary coil, and finally the induced voltage tends to saturation (the corresponding voltage is called saturation voltage);

[0088] 2. The larger the number of turns of the secondary coil, the greater the saturation voltage of the secondary coil, and the greater the minimum load corresponding to the saturation voltage;

[0089] 3. Comparing the elliptical and rectangular cores, it is found that the saturation voltage of the elliptical core is about 30% higher than that of the rectangular core under the same number of coil turns.

[0090] As an embodiment of the present invention, Figure 8 and Figure 9 As shown in the figure, when the core is not saturated, the maximum output power of the transformer with an elliptical core is about 34% higher than that of the transformer with a rectangular core.

[0091] As an embodiment of the present invention, Figure 10 and Figure 11 As shown in the figure, when the core is not saturated, the maximum output power density of the transformer with an elliptical core is only about 10W / m lower than that of the transformer with a rectangular core. 3 , only about 1.3% lower.

[0092] The technical solution of the present invention is described in detail above in conjunction with the embodiments / drawings, but the present invention is not limited to the above technical solution. For ordinary technicians in this technical field, after knowing the contents recorded in the present invention, they can make several equivalent transformations and substitutions without departing from the principles of the present invention. These equivalent transformations and substitutions should also be regarded as falling within the scope of protection of the present invention.

Claims

1. A method for optimizing an annular core of an intrusive mutual inductor, characterized in that: The steps include: S1. Equivalent the rectifier circuit and its subsequent circuit to resistive reactance, and establish a transformer energy-taking power supply circuit model based on the power supply equivalent topology. S2. Based on the transformer energy source circuit model established in step S1, while ignoring the secondary coil leakage inductance and the subsequent circuit line loss, an equivalent model of the transformer energy source is established based on the electromagnetic induction law and the full current law: Where H m is the magnetic field strength inside the coil; l is the average magnetic circuit strength; I m is the excitation current; E2 is the secondary voltage of the coil; f is the frequency of the AC current, which is 50Hz; Φ m is the magnetic flux; S is the cross-sectional area of the core; B m is the magnetic induction intensity inside the coil; μ0 is the vacuum magnetic permeability, which is 4π×10-7H / m; μ r is the relative magnetic permeability of the core material; H m is the magnetic field strength of the primary coil; N1 and N2 are the turns of the primary and secondary coils respectively; I1 and I2 are the primary and secondary currents respectively; S3. Based on the equivalent model of the transformer energy source, a vector diagram of the relationship between the secondary-side induced electromotive force and current is established. Combining the principles of electrical machinery with the vector relationship between the secondary-side induced electromotive force and current in the ring-shaped magnetic core structure of the intrusive transformer, the following solution is obtained: S4. Based on the equivalent model of the transformer energy source and the solution of step S3, derive the secondary side output voltage E2. Based on the secondary side output voltage E2, derive the secondary coil output voltage U2 by setting the parameter ɑ. Then, derive the secondary side output power P based on the secondary coil output voltage U2. Where: The expression of the parameter ɑ is: The expression of the secondary side output voltage E2 is: The expression of the secondary side coil output voltage U2 is: The expression of the secondary side output power P is: S5. When the intrusive transformer is powered by power supply and the magnetic core is not saturated, by analyzing the factors affecting the secondary coil output voltage U2 and the secondary side output power P, it is concluded that if and only if R=αN2 2 When , the secondary coil output voltage U2 and output power P take the maximum value; S6. By analyzing the relationship between the analysis results of step S5 and the parameters of the ring core structure of the intrusive transformer, it is found that: while keeping the core cross-sectional perimeter L, the secondary coil resistance, and the primary coil current unchanged, the core cross-sectional area can be increased by changing the size of the core cross-sectional area to increase the value of the parameter ɑ of the secondary coil output voltage U2 and the output power P, thereby optimizing the structure of the ring core; wherein: The dimension is the radial length a of the core cross section; The relationship between the parameters is as follows: a=(Do-Di) / 2; L = (a + W) × 2; Where L is the circumference of the core cross section; a is the radial length of the core cross section; W is the width of the core cross section; Do is the outer diameter of the annular core; and Di is the aperture of the annular core.

2. The optimization method of an intrusive mutual inductor ring core according to claim 1, characterized in that: When there is no current fluctuation, reducing the magnetic circuit length l and increasing the core cross-sectional area S can increase the secondary side output voltage and secondary side output power.

3. The optimization method of an intrusive mutual inductor ring core according to claim 1, characterized in that: The derivation process of the secondary coil output voltage U2 is as follows: According to the expression of secondary side output voltage E2: set up Then the secondary coil output voltage U2 is: Arranging formula (4) yields:

4. The method for optimizing an annular core of an intrusive mutual inductor according to claim 1, characterized in that: When the intrusive transformer is powered by an energy source, the secondary side output voltage is related to the primary side current of the coil, the number of turns of the secondary side coil, the magnetic permeability and size of the magnetic core and the load.

5. The method for optimizing an annular core of an intrusive mutual inductor according to claim 1, characterized in that: When the core is not saturated, the secondary side output power reaches its maximum value.

6. The method for optimizing an annular core of an intrusive mutual inductor according to claim 1, characterized in that: The outer diameter Do and width W of the annular magnetic core can vary with the radial length a.

7. The method for optimizing an annular core of an intrusive mutual inductor according to claim 1, characterized in that: The secondary coil output voltage U2 and output power P can vary with the change of radial length a.

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