Design and optimization for current transformer core based on magnetic field analysis

Abstract

In order to ensure the safety and reliability of power system, more and more monitoring and maintenance equipment on transmission lines are being used. However, these equipment would not work without the supply of power. At present, the current transformer has been widely used in the on line power acquisition device. As an important part of the current transformer, the performance magnetic core has great influence on the power acquisition. In this paper, the core parameters of the current transformer in the on-line power acquisition device are designed, and the parameters such as core material and air gap length are optimized and verified by simulation as well.

Keywords

Current transformer magnetic core ferrimagnetic materials air gap length simulation

1. Introduction

With the continuous expansion of the power grid, transmission line condition monitoring and maintenance equipment have been installed more and more, to ensure the stability of these equipment power supply is the first problem to be solved. At present, in all kinds of power supply, the current transformer is widely used in power acquisition methods for its good reliability and little influence by environmental factors [1, 2]. But in this method, when the current in the transmission wire is low, the power collection device has less power, which there is a dead zone of power acquisition supply [3, 4].

In view of the above problems, the method of current transformer taking energy is analyzed in this paper. In order to take the higher power from the line to meet the power demand of the on-line monitoring equipment, based on the conventional TA method, in this method, according to the analysis of the equivalent circuit, magnetic circuit and maximum power, the core material, air gap, secondary side winding and cross-sectional area of the magnetic core are designed. The optimum matching parameters of the electromagnetic core are optimized so that the device can work normally while maintaining high power. Through modeling and simulation, the results show the optimized magnetic core parameters make the magnetic core have better performance.

2. Structure of electrical device based on current transformer

Based on the current transformer induction power acquisition device structure is shown in Fig. 1. Different from the current transformer, the secondary winding is not a direct short circuit, but is connected with on-line monitoring, maintenance or other electrical equipment [5, 6], generally, the operating power of these devices is about 50 W or so.

Figure 1.

Structure of induction charging device.

Its principles are: When the transmission line passes through the alternating current, it produces an alternating magnetic field around it and an inductive electromotive force is produced in the secondary side coil. Therefore, the inductive ac current is obtained on the secondary side, through the rectifier bridge, the ac current is converted to dc current, then by reducing voltage and stabilizing voltage, the dc current is supplied to the on-line monitoring and maintenance equipment, the energy storage power such as battery can also be charged [7, 8].

The circuit model of the electrical device in Fig. 1 is shown in Fig. 2. In Fig. 2, $N_{1}$ , $N_{2}$ are the number of turns of the primary winding and the secondary wingding, respectively. $\Phi$ is the main magnetic flux, while $i_{1}$ , $i_{2}$ are primary and secondary side current [9, 10].

Figure 2.

Circuit model of induction charging device.

3. Analysis of the acquisition energy principle for TA

The induction circuit model of Fig. 2 is analyzed by circuit and magnetic circuit, and the principle of acquisition energy is shown in Fig. 3.

Figure 3.

Schematic diagram of TA induction charging.

When the sinusoidal AC current is input on the primary side, according to the law of electromagnetic induction, the following equations are obtained:

$\displaystyle U_{2}\approx E_{2}=4.44fN_{2}\phi_{m}$ (1) $\displaystyle\phi_{m}=B_{m}S$ (2) $\displaystyle B_{m}=\mu H_{m}=\mu_{0}\mu_{r}H_{m}$ (3) $\displaystyle H_{m}\cdot l=N_{1}i_{0}$ (4)

In Fig. 3 and Eqs (1)–(4):

$E_{2}$ – the effective value of secondary side-inducible EMF $f$ – power frequency, 50 Hz $N_{2}$ – the number of turns of the secondary wingding $\Phi_{m}$ – magnetic flux amplitude $B_{m}$ – magnetic induction amplitude $S$ – magnetic core cross section $\mu$ – magnetic permeability $\mu_{0}$ – vacuum magnetic permeability, $\mu_{0}=4\pi\times 10^{-7}$ H/m $\mu_{r}$ – relative magnetic permeability $H_{m}$ – Magnetic field intensity amplitude $l$ – Average length of magnetic circuits $i_{0}$ – exciting current, in the case of no load, it is equal to the primary side wire current $i_{1}$ $N_{1}$ – the number of turns of the primary wingding, for the transmission line is one thick wire, so $N_{1}=$ 1

Calculated by Eqs (1)-(4), inductive voltage validity on secondary side of TA is shown in Eq. (5):

$\displaystyle U_{2}=4.44fN_{2}i_{0}\mu S/l$ (5)

From Eq. (5), the inductive voltage on secondary side $U_{2}$ is in proportion to $N_{2}$ , $i_{0}$ , $\mu$ and $S$ . While $U_{2}$ is inversely proportional to $l$ .

This paper focuses on designing the parameters of magnetic core in small current condition, such as magnetic permeability $\mu$ , cross-sectional area $S$ and magnetic circuit length $l$ .

4. Electromagnetic analysis of the TA acquisition energy device

Because the transmission line serves as a primary side winding through the magnetic core, only the open air gap core can be installed outside the line. Set the TA open core outside the transmission line, the secondary winding coil is directly and uniformly wound on the core, which is connected with the secondary side loads to constitute the loop, as shown in Fig. 4. Figure 5 is the circuit topology of Fig. 4.

Figure 4.

Model diagram of conventional TA power supply device.

Figure 5.

Circuit topology.

In Fig. 5, suppose the current of the transmission line is $i_{1}$ and the exciting current is $i_{0}$ . When the secondary side is no-load, the current flowing through the TA is $i_{1}$ which is all used to establish excitation magnetic field. However, when the load is connected on the secondary side, part of the $i_{1}$ establishes a magnetic field and the other part of the current shunts to the load. This TA method is simple in structure and convenient to get energy, but when the transmission line current is small, the secondary load branch current is also small, so it is difficult to meet the power demand.

Suppose that the air gap length between the two parts of the magnetic core with open air gap in Fig. 4 is $\delta$ , and the inner and outer diameter of the magnetic core is respectively $a$ and $b$ , the thickness of the magnetic core is $h$ . The profile of the magnetic core model is shown in Fig. 6.

Figure 6.

Profile of magnetic core model.

Equation (6) can be known from the magnetic potential balance:

$\displaystyle N_{1}I_{1}=Hl+H_{\delta}\cdot 2\delta$ (6)

In Eq. (6), $N_{1}$ is the number of turns of the primary wingding, $H$ is the magnetic strength of magnetic core, $l$ is the length of the magnetic circuit, $H_{\delta}$ is the air gap magnetic field strength. To facilitate the calculation, equivalent the magnetic strength of the whole TA to $H_{1}$ and the length of the magnetic circuit to $l_{1}$ , then Eq. (6) can be simplified as Eq. (7):

$\displaystyle N_{1}I_{1}=H_{1}l_{1}$ (7)

By Eq. (3), Eq. (8) could be derived:

$\displaystyle B_{1}=\mu_{1}H_{1}=\mu_{0}\mu_{r}H_{1}$ (8)

According to Eqs (7) and (8), the equivalent permeability of the TA core is Eq. (9):

$\displaystyle\mu_{1}=\frac{\mu_{0}\mu_{r}l_{1}}{\varepsilon l+\mu_{r}\cdot 2\delta}$ (9)

In Eq. (9), $\varepsilon$ is the edge effect coefficient of the air gap magnetic field; for it is approximated as no edge effect, $\varepsilon$ is taken as 1.

According to the amperometric loop theorem, the magnetic flux density at any radius of the conductor in the core is Eq. (10):

$\displaystyle B_{m}=\frac{\sqrt{2}\mu_{1}i_{m}}{2\pi\cdot r}$ (10)

Then the magnetic flux of the core can be obtained as Eq. (11):

$\displaystyle\phi_{m}=\int_{s}B_{m}\cdot ds=\frac{\sqrt{2}\mu_{1}i_{m}(t)}{2% \pi\cdot r}\int_{a}^{b}{\frac{1}{r}}dr=\frac{\sqrt{2}\mu_{1}i_{1}\cos(\omega% \cdot t)}{2\pi\cdot r}\ln\frac{b}{a}h$ (11)

The output voltage $U_{2}$ of TA secondary side can be obtained by substituting Eq. (11) into Eq. (1):

$\displaystyle U_{2}\approx E_{2}=-N_{2}\frac{\text{d}\phi(t)}{dt}=\sqrt{2}N_{2% }\mu_{1}fi_{m}\sin(\omega t)\ln\frac{b}{a}h$ (12)

According to Eq. (12), the secondary side output voltage is proportional to the number of secondary side turns $N_{2}$ , core equivalent permeability $\mu_{1}$ , transmission line current $i_{1}$ , core internal and external diameter ratio $\frac{b}{a}$ , and the thickness $h$ . Keep the inner diameter $a$ to be constant, the output voltage of the secondary side is proportional to cross-sectional area $S$ of magnetic core. For the permeability $\mu$ is determined by the core material and shape,the cross-sectional area $S$ is determined by the volume weight of the core,therefore, the influence factors of TA secondary side induction voltage $U_{2}$ are mainly determined by the core material and core volume.

According to Eq. (8), when the core opens an air gap of $\delta$ , the reluctance of the magnetic circuit is increased, so the magnetic core equivalent permeability $\mu$ drops sharply, then the TA secondary side induction EMF $E_{2}$ decreases, that is, the secondary side voltage $U_{2}$ decreases, which result in the conventional TA to take power is too small to meet the line monitoring, maintenance equipment and other load power requirements.

In addition to permeability $\mu$ , core air gap $\delta$ , cross-sectional area $S$ and the number of secondary side turns $N_{2}$ are all related to the size of the charging power. Therefore, in order to improve the output power of online charging power supply, it is necessary to optimize the magnetic core design and determine the optimal matching parameters of TA magnetic core.

From the above analysis, it can been seen that:in order to avoid the magnetic core permeability decline,the air gap length $\delta$ cannot be designed too large. Considering the core volume and weight, the selected cross-sectional area S should also be reduced appropriately. This paper focuses on the design of these two parameters of the TA, the FEM is used to analyze the magnetic field and by comparing with the conventional TA parameters the optimal matching parameters are selected.

5. Select and optimize the parameters of electromagnetic core

5.1 Magnetic core material selection

The choice of magnetic core material is related to the permeability of the magnetic core, and the permeability of the magnetic core affects the load voltage and the power of the secondary side. Therefore, the choice of magnetic core material needs to be considered in a comprehensive way, so that the magnetic core can not only meet the small current to get enough power but also can not easily saturated in the large current. In this paper, three materials are selected for comparative analysis, two of which are the most widely used silicon steel sheet and permalloy alloy, and the other one is the latest nanocrystalline material [11, 12, 13]. The basic magnetic parameters of the three materials are shown in Table 1.

Table 1
Basic magnetic parameters of three materials

Basic magnetic parameter	Silicon steel sheet	Permalloy	Nanocrystalline
Saturation magnetic induction intensity (B/T)	2.1	0.7	1.2
Initial permeability (H/m)	1500	100000	100000
Maximum permeability (H/m)	40000	$>$ 450000	$>$ 400000
Coefficient of laminated	0.97	0.7	0.7
Iron loss 50 HZ (W/kg)	1.2	0.5	0.18

It can be seen from Table 1 that the saturation magnetic induction intensity B of silicon steel sheet is the largest, which is not very easy to saturate. However, its initial permeability (1500) and maximum permeability (40,000) are relatively small, and the iron consumption (1.2) value is also relatively large. The magnetic saturation induction strength (0.7) of permalopoly alloy is the smallest. At the same time, this material is more easily saturated, but its initial permeability ( $>$ 450000) and the maximum permeability are both several tens of times larger than silicon steel sheet, and the iron consumption (0.5) is two to three times lower than that of silicon steel sheet. Iron based nanocrystals, on the other hand, have the advantages of the above two materials, such as high magnetic saturation induction intensity (1.2t), high initial permeability (100000) and maximum permeability ( $>$ 400000), which are similar to those of permor alloy, small initial starting current and good electromagnetic performance. At the same time, the thickness of the nanocrystal strip core is very small, and the insulation between each layer of strip leads to a very small cross section area of eddy current generation, which effectively inhibits the eddy current loss, so its iron loss (0.18) is very low, only 1/6-1/3 of that of silicon steel sheet [14].

From the above analysis, it can be seen that when the line current of nanocrystal magnetic core is small, that is, when the magnetic field strength is weak, its high initial permeability can make the secondary side get more voltage and larger power. Moreover, this material has a relatively large magnetic saturation induction intensity, which can cooperate with the magnetic core air gap when the magnetic field strength is strong. Even if the current of the transmission line is large, that is, hundreds of amperes, it will not be saturated, which is quite suitable for the TA power supply of the transmission line. Therefore, nanocrystals with relative permeability of about 300000 H/m are selected as magnetic core materials.

5.2 Selection of air gap length

After determining the core material, the core air gap length $\delta$ should also be determined. If the magnetic core is opened with an air gap of length $\delta$ , its equivalent permeability will drop sharply, which will reduce the obtaining voltage on the secondary side and lead to insufficient charging power. In order to make the TA get more power when the line current is small, the gap length $\delta$ of the magnetic core should be shortened as far as possible. Under the current nanocrystalline cutting process, the minimum length $\delta$ of magnetic core air gap can be controlled at about 0.1 mm. In this paper, the box mounting method is adopted, so the air gap length $\delta$ of the magnetic core can only be limited to about 0.2 mm.

5.3 Second turn number selection

When the volume and weight of the magnetic core are determined, it is most feasible to optimize the core by changing the core material and gap length. However, the influences of the number of turns of the secondary winding $N_{2}$ and the cross-sectional area of the magnetic core $S$ on the charging power cannot be ignored. Therefore, the number of secondary turns and the cross-sectional area of the magnetic core should also be selected.

In order to get more shunt current, the impedance of secondary winding of magnetic core should be reduced. The secondary impedance mainly comes from line impedance, 0.6 mm copper wire is used to make the secondary winding to reduce the line impedance. Known from the analysis of Section 3, to reduce the resistance $R^{\prime}_{2}$ and the leakage inductance $L^{\prime}_{lk2}$ of the secondary side, the secondary winding circle number $N_{2}$ should be the bigger the better, but considering the withstand voltage value of the matching capacitance in secondary side and the full use of the area of the magnetic core, finally the number of the secondary winding turns is selected as $N_{2}=18$ .

5.4 The choice of magnetic core area

From the analysis in Section 3, it can be seen that the magnetic circuit length $l$ , outer diameter $b$ of the magnetic core and thickness $h$ that affect the taking power are all reflected by the cross-sectional area $S$ of the magnetic core. The cross section of the magnetic core is designed with the volume and weight of the magnetic core as small as possible. Equation (13) can be obtained from Eq. (12), the voltage of secondary side is proportional to the thickness $h$ and the ratio of the inner and outer diameter $b/a.$

$\displaystyle U_{2}=\sqrt{2}N_{2}\mu_{1}fi_{m}\sin({\omega t})\ln\frac{b}{a}h$ (13)

Equation (13) shows that, if the internal diameter $a$ is kept unchanged, the secondary magnetomotive force is also proportional to the cross-sectional area $S$ of the magnetic core. When the core material is determined as nanocrystals, the core’s equivalent permeability $\mu_{1}$ remains unchanged. The number of turns on the secondary side $N_{2}$ is determined to be 18. Assuming that the transmission line current $i_{1}$ is ac 50 A, the secondary side voltage is only related to the ratio of external and internal diameter $b/a$ and the thickness $h$ , which is proportional. However, this paper focuses on the design to obtain enough power in the case of small current, so it is necessary to consider reducing the weight and volume of the magnetic core as far as possible, so that the secondary side can also obtain a large voltage and power. Based on the weight and volume limitations of the magnetic core, the outer diameter $b$ is 120 mm, the inner diameter $a$ is 60 mm, the thickness $h$ is 60 mm, and the sectional area $S$ is the core parameters of 1800 mm ${}^{2}$ .

6. Modeling and simulation of TA core

6.1 The establishment of magnetic core model

In order to analyze the magnetic field in the magnetic core above, drawing the 3D solid model of magnetic core in the maxwell area for simulation, the parameter of the magnetic core are: outer radius of the magnetic core $b=$ 120 mm, inner radius of the magnetic core $a=$ 40 mm, thickness $h=$ 60 mm, sectional area $S=$ 1800 mm ${}^{2}$ , and air gap length $\delta=$ 0.2 mm. The electromagnetic core model is taken as shown in Fig. 7.

The drawing order of entity model is as follows:

(1)
cylinder with outer diameter of 60 mm;
(2)
after dividing the YZ plane as the symmetric plane, the remaining half of cylinder A is left;
(3)
copying the mirror image of semi-cylinder A to the other side is semi-cylinder B;
(4)
the semi-cylinders A and B were shifted along the positive and negative X axes, respectively, and the translation distance was the length of the air gap;
(5)
cylinder C with inner diameter of 20 mm;
(6)
select semi-cylinder A, B and C to perform Boolean operation to obtain hollow cylinder, that is, two magnetic core semi-cylinders;
(7)
the wire with an inner diameter of 2 mm, which is the primary winding.

Then the whole solid model is completed.

Figure 7.
Model diagram of TA core

Figure 8.
B-H curve of nanometer crystal.

6.2 Simulation of magnetic core material

In Fig. 7, the cross section of the primary winding of the magnetic core is set as the input and output sections of the external excitation source. The input is 50 A and 50 Hz sinusoidal ac, the air gap length is set as 0.2 mm, and the range of magnetic induction intensity B is set as 0.05 T–0.8 T. Simulation results will be generated when the core model, material properties, excitation conditions, establishment solver and mesh differentiation parameters are all set. The magnetic field distribution of nanocrystalline, permalloy and silicon steel sheet are compared.

(1) According to Section 4.1, nanocrystals of model 1K107 are selected as TA core materials in this paper, and their B-H curves are shown in Fig. 8.

The simulation results of magnetic core density B of nanocrystalline 1K107 are shown in Fig. 9.

Figure 9.

Magnetic core model simulation of nanocrystalline 1K107.

It can be seen from Fig. 9, the color of the magnetic core from the edge to the center from light blue to red is deepening, and the magnetic induction intensity is increasing. The magnetic induction intensity B of the nanocrystal core is at least 0.15 T and at most 0.8 T, and the average magnetic induction intensity is 0.31 T. Even in the case of a small 50 A current, a stronger magnetic field can be obtained through a higher initial permeability, so that higher voltage and power can be obtained on the secondary side.

(2) The model 1J79 of permalloy is selected as the core material of the TA. The simulation results of the magnetic density B of the core of permalloy 1J79 are shown in Fig. 10.

Figure 10.

Model simulation of permalloy 1J79

In Fig. 10, the color of the magnetic core from the edge to the center from light blue to yellow green is deepening, and the magnetic induction intensity is increasing. The minimum magnetic induction intensity B of the permalloy core is 0.15 T, the maximum is 0.58 T, and the average magnetic induction intensity is 0.26 T. In the case of the 50 A small current, like nanocrystal materials, permalopoly can obtain stronger magnetic field through high initial permeability, thus get higher voltage and take power on the secondary side.

(3) The silicon steel sheet of model dr510-50 is selected as the TA core material. The simulation results of magnetic core density B of silicon steel sheet dr510-50 are shown in Fig. 11.

From Fig. 11, it can be seen that the color of the magnetic core from the edge to the center is continuously deepened from dark blue to green, and the magnetic induction intensity keeps increasing. The magnetic induction intensity B of the core of silicon steel sheet is at least 0.1 T and at most 0.8 T, and the average magnetic induction intensity is 0.15 T. At the same low current of 50 A, the magnetic conductivity of silicon steel sheet is not as strong as that of nanocrystalline and permalloy materials. The voltage needed to induce the secondary side of a strong enough magnetic field cannot be obtained.

Based on the above simulation results, in Table 2, the simulation data of magnetic induction intensity B of three core materials, nanocrystal 1K107, permaloy 1J79 and silicon steel sheet dr510-50 are compared. It can also be seen from the color of the simulation Figure that the nanocrystal has better performance. The values of specific parameters are shown in Table 2.

Table 2

Experimental data of on-line energy acquisition method for transmission lines based on impedance matching

Magnetic core material	Minimum magnetic density (T)	Maximum magnetic density (T)	Mean magnetic density (T)
1k107 nanocrystals	0.15	0.8	0.31
Permalloy 1J79	0.15	0.58	0.26
Silicon steel sheet DR510 50	0.1	0.8	0.15

Figure 11.

Model simulation of silicon steel sheet dr510-50.

According to the data in Table 2, by simulating the magnetic density B distribution of nanocrystals 1K107, 1J79 and silicon steel sheet dr510-50 at 20 time points within 0.2 s, the comparative analysis shows that the average magnetic induction intensity of silicon steel sheet is small under the condition of low ac current of 50 A. The average magnetic induction intensity of both permalloy alloy and nanocrystals is relatively large. The average magnetic density of nanocrystals (0.31 T) is the highest, which is twice the average magnetic density of silicon steel sheet (0.15 T) and much larger than that of silicon steel sheet. Therefore, nanocrystals with high initial permeability are the best materials for magnetic core.

6.3 Simulation of core air gap length

According to Section 4.2, the core air gap length $\delta$ is limited to 0.2 mm. In order to more intuitively analyze the influence of air-gap length on magnetic density $B$ distribution in the magnetic core, the air-gap length of nanocrystal 1K107 magnetic core is simulated as 0.1 mm, 0.15 mm, 0.2 mm, 0.25 mm and 0.3 mm, respectively.

Input 50 A and 50 Hz sinusoidal current, and the range of magnetic induction intensity $B$ is set as 0.05 T–0.8 T. The difference is to change the length of the air gap. When the length of the air gap changes from 0.1 mm to 0.3 mm, the simulation results are as follows:

(1)
When the air gap length is 0.1 mm, the simulation results of magnetic density $B$ of nanocrystal 1K107 are shown in Fig. 12.

Figure 12.
Nanocrystalline 1K107 magnetic core model simulation with an air gap of 0.1 mm.

Figure 13.
Simulation of nanocrystal 1K107 magnetic core with an air gap of 0.15 mm.

From Fig. 12, when the air gap length is 0.1 mm, for the nanocrystal 1K107 magnetic core,the minimum of the magnetic density B is 0.26 T, the maximum value is 0.8 T, and the average magnetic induction intensity is 0.58 T.
(2)
When the air gap length is 0.15 mm, the simulation results of magnetic density B of nanocrystal 1K107 are shown in Fig. 13. At this time, the minimum of the magnetic density B is 0.21 T, the maximum value is 0.8 T, and the average magnetic induction intensity is 0.42 T.
(3)
While the air gap length is 0.2 mm, the simulation results of magnetic density B of nanocrystal 1K107 are shown in Fig. 14. It is shown that the minimum of the magnetic density B is 0.15 T, the maximum value is 0.8 T, and the average magnetic induction intensity is 0.31 T.

Figure 14.
Simulation of nanocrystal 1K107 magnetic core with an air gap of 0.2 mm.

(4)
When the air gap length is 0.25 mm, the simulation results of magnetic density B of nanocrystal 1K107 are shown in Fig. 15. The magnetic density B is 0.10 T at the minimum and 0.53 T at the maximum, and the average magnetic induction intensity is 0.21 T.

Figure 15.
Simulation of nanocrystalline 1K107 magnetic core with an air gap of 0.25 mm.

(5)
When the air gap length is 0.3 mm, the simulation results of magnetic density B of nanocrystal 1K107 are shown in Fig. 16. The magnetic density B is 0.05 T at the minimum and 0.31 T at the maximum, and the average magnetic induction intensity is 0.15 T.

Comparing the different air gap lengths in (1)–(5), it can be known that: in the case of low ac 50 A current, if the range of magnetic induction intensity $B$ is set to 0.05 T–0.8 T, when the air gap length $\delta$ changes, the color of the magnetic core from the edge to the center deepens continuously from dark blue to red, and the magnetic induction intensity $B$ increases continuously.

According to the simulation results in Figs 12–16, in Table 3,the simulation data of magnetic induction intensity B with the length of magnetic core air gap of nanocrystal 1K107 being 0.1 mm, 0.15 mm, 0.2 mm, 0.25 mm and 0.3 mm, respectively, are compared.

Table 3
Magnetic density when air gap length changes

Air gap length (mm) Minimum magnetic density (T) Maximum magnetic density (T) Mean magnetic density (T)

0.1 0.26 0.8 0.58

0.15 0.21 0.8 0.42

0.2 0.15 0.8 0.31

0.25 0.10 0.53 0.21

0.3 0.05 0.31 0.15

Figure 16.
Nanocrystalline 1K107 magnetic core model simulation with an air gap of 0.3 mm.

Analysis the data in Table 3 which the magnetic density distribution of nanocrystalline 1K107 at 20 points in 0.2 s with different core air gap length are simulated, when the primary winding current is 50 A, as the air gap of nanocrystalline core changes around 0.2 mm, the average magnetic induction intensity decreases with the increase of air gap length $\delta$ . The reason is the smaller is the air gap of the core, the greater is the permeability.

Under the current nanocrystalline cutting process, the minimum length of magnetic core air gap can be controlled at about 0.1 mm. Since the box mounting method is adopted in the project, the length $\delta$ of the magnetic core air gap can only be limited to about 0.2 mm, and a smaller air gap does not accord with the installation requirements, while equivalent permeability is not the best choice if the air gap is larger than 0.2 mm. Moreover, it can be seen from Fig. 18 that the magnetic density of nanocrystalline 1K107 magnetic core of 0.2 mm air gap is already very large, the distribution of the magnetic density is uniform and concentrated, so the best the air gap length is 0.2 mm.
7. Conclusion

In this paper, the magnetic circuit of the current transformer of the online power acquisition device is studied. The magnetic core parameters of the current transformer with a bus current of 50 A are analyzed and the optimization design is adopted. The magnetic field of optimized magnetic core parameters is analyzed. Through the establishment of 3D models in the Maxwell software, the transient magnetic field is solved, and the modeling and simulation of the electric TA core are completed. On the basis of theoretical analysis, the excellent properties of nanocrystalline cores are confirmed by simulation results, and the magnetic density B distribution of 0.1 mm–0.3 mm length around 0.2 mm is simulated. It is also proved that the change of air gap length about 0.2 mm has best effect on the magnetic density. The results of simulation proved that the optimized scheme can meet the demand of power taking under low current.

Because the relative permeability of the core is not a constant, but a function of the current, the relative permeability itself will change in the process of changing the bus current. Especially after approaching the saturation region, the degree of its decline is also increasing. Therefore, in the case of different bus currents, TA how to obtain the required power is a problem to be solved later.

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Air gap length (mm)	Minimum magnetic density (T)	Maximum magnetic density (T)	Mean magnetic density (T)
0.1	0.26	0.8	0.58
0.15	0.21	0.8	0.42
0.2	0.15	0.8	0.31
0.25	0.10	0.53	0.21
0.3	0.05	0.31	0.15