Simulation of Axial Magnetic Field in Vacuum Arc Interrupters at Intermediate Frequency

Jiang Yuan Li Qing Xia Lina Wu Jianwen Jia Bowen Xia Shangwen

Simulation of Axial Magnetic Field in Vacuum Arc Interrupters at Intermediate Frequency

Jiang Yuan1Li Qing1Xia Lina1Wu Jianwen2Jia Bowen2Xia Shangwen2

（1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China 2. School of Automation Science and Electrical Engineering Beihang University Beijing 100083 China）

Characteristics of axial magnetic field (AMF) vacuum interrupters in intermediate-frequency (IF, 400-800Hz) power system of more electric aircraft is researched in this paper. The AMF distribution is solved by Maxwell. It can be concluded by the calculation as follows: In the process of current change, the axial magnetic field changes slower in the central region than in other regions. The peak area of the magnetic field is located between the interlaced slots, and there is a significant residual magnetic field in the center area at current zero. When the frequency increases, the eddy effect is so serious that the magnetic flux density of the AMF decreases. For the center point, the residual magnetic field is stronger and the lag phase is bigger on account of the frequency increase, which will prevent the arc plasmas from diffusing. The eddy effect can be reduced by adding the number of slot in the contact blade. The maximum of the magnetic flux density is increased approximately linearly by adding the rotation angle of contact. The influence of magnetic field hysteresis on the breaking capacity of the vacuum interrupter is verified by experiments including arc appearance and arc voltage.

More electric aircraft, axial magnetic field, vacuum interrupters, intermediate frequency, eddy current effect

0 Introduction

In recent years, more-electric/all-electric aircraft has become the focus of research around world. Compared to a constant frequency power supply system in traditional aircraft, electricity is generated by a frequency-varying generator and the current frequency is in the range of 360-800Hz in the intermediate frequency (IF) power supply system, such as in A380, B787 and C919[1-2]. As the frequency and current increase, the interruption process becomes difficult, then a new type circuit breaker is required to ensure the electrical safety of the aircraft[3-4]. Vacuum circuit breakers have been widely used in medium/low voltage power systems, and are potentially suitable for use in the IF power supply system[5-9].

For the axial magnetic field (AMF) type vacuum interrupter, an axial magnetic field will be generated when current is through the contact coil, which can improve the interruption ability of the vacuum interrupter[10]. The research shows that an appropriate AMF can make the arc diffuse in the high current mode. As a result, the arc energy and the degree of ablation on the contact surface are reduced[11-13].

At present, numerical method is usually used to study the magnetic field distribution in electrical equipment. 3D finite element method has been used to analyze the magnetic field characteristics of the AMF interrupter and the calculated results were very close to the measured results[14-15]. Liu Zhiyuan analyzed AMF distribution in slot-type axial magnetic field contacts with and without iron plates, using commercial 3D FEM electromagnetic field simulation software Maxwell 3D[16]. Shi Zongqian investigated the influence of the distribution of AMF on high current vacuum arc with three pairs of specially designed testing electrodes generating a conventional bell-shaped AMF profile and different saddle-shaped AMF distributions. The transient AMF distribution was computed by a commercial software Ansys[17]. A. Henon studied the interruption ability of vacuum circuit breakers with AMF. The numerical model involves three-dimensional AMF simulations and the experimental study evaluates their performance in short-circuit interruption tests. The calculations are analyzed for AMF distribution[18].

The above research results mainly focus on the power frequency, and do not involve the situation when the frequency is increased to 360-800Hz. The AMF distribution in vacuum interrupter in IF is studied in this paper, and magnetic flux density at current peak (CP) and current zero (CZ) moment are paid attention. Considering the simulation and experimental results, eddy current effect and current interruption ability influenced by frequency is analysed. The effect on magnetic field hysteresis and maximum value of magnetic induction intensity by contact structure, such as the number of contact blade slots and the angle of cup coil, is also analyzed.

1 AMF Interrupters Model

The structure of cup-type AMF vacuum contact is shown in Fig.1. The AMF contact consists of conductive rod, coil, contact blade and stainless steel support. The arc area is between the two contacts.

Fig.1 The structure of cup-type AMF vacuum interrupter

The main structural parameters of the cup-type AMF contact are shown in Tab. 1, and= π/3 and= 6 is chosen as a basic contact.

Tab.1 Parameters for AMF Interrupters

In this paper, Maxwell 3D electromagnetic field finite element module in ANSYS is used to analyze the magnetic field characteristics in the AMF contact[19]. The current frequency is 400-800Hz, and the effective value is 1kA. The contact blade material is CuCr50 and the electrical conductivity is 1.044×107S/m[16]. It is supposed that the arc is a cylinder with the same diameter to contact diameter and the same height to separation distance, and the arc conductivity is 400S/m. The selection is based on the experimental results of IF vacuum arc: as the contact diameter is 41mm and the separation is 3mm, the maximum arc voltage is about 60V when current is 10kA[5]. The calculation field is 10 times the size of the model, and the simulation is terminated when the error criterion of calculation matrix is set to less than 1% in the software.

2 Simulation Results

2.1 AMF Distribution at CP Moment

When the current frequency is 400Hz, the AMF distribution at CP moment is shown in Fig.2, in which point Q refers to the center of the magnetic field, and point P refers to the maximum magnetic flux density. The line between P and Q is a specified observation diameter.

Fig.2 AMF distribution at CP moment (f=400Hz)

It can be seen from the simulation results that the magnetic flux density in the contact center is significantly lower than that in the surrounding area at CP moment. There are six peak areas, which must be related to the form of slots on the surface of contact blade and the staggered placement of contacts (see Fig. 1). As the current flows along the shortest path, the slot shortens the conduction path of the eddy current and the eddy current decreases. Therefore, the magnetic flux intensity of the AMF between the two slots is higher and the delay phase is less. However, in the middle of the contact blade, the eddy current has a large closed conduction path, and the AMF at this area is greatly affected by the eddy current, with low magnetic flux density and large delay phase. The distribution of this multi-peak region may be the reason that makes the cathode spots and arc columns appear multi-distribution[5-6].

2.2 AMF Distribution at CZ Moment

Fig.3 shows the AMF distribution at the CZ moment with current frequency of 400Hz.

Fig.3 AMF distribution in middle plane at CZ moment (f = 400Hz)

As at CZ moment, there are 13 peak areas of magnetic flux density in the middle plane, among which 12 are in two adjacent slots where the contact is staggered, and 1 is in the center.is higher in the central peak area. Fig.4 shows the magnetic flux density in the middle plane of P-Q diameter at different current phases.

It can be seen that, before the current peak, the AMF of each point in P-Q diameter increases with the increase of current. However the increase rate of the center is slow and theis lower than that of other regions. At CP moment, the maximumat point P reaches 15.94mT, and at this time,of point Q is only 10.53mT. After CP, the further away from the center, the faster the AMF decreases, whereis almost zero. In the center, the AMF decrease slowly and there is residual magnetic field, which is consistent with Fig.3. The residualat point Q is about 3.67mT. The change process also indicates that the magnetic field of the contact center is the most affected by the eddy current, and the hysteresis of AMF is the most obvious. In the interruption process, residual plasmas in arc gap will be under the control of residual magnetic field over a long phase and are difficult to spread quickly at IF. Moreover, if the residual magnetic field is strong, the interruption may be failed under the transient recovery voltage (TRV) after CZ[20-21].

Fig.4 Magnetic flux density of P-Q diameter at different current phases

2.3 AMF Hysteresis

When the current frequency increases from 400Hz to 800Hz, the distribution of AMF is similar to that at 400Hz. The effect of frequency on the center point Q is shown in Fig.5.

With the frequency increases, the hysteresis of AMF is much more obvious. When the frequency is 400Hz, the residual magnetic flux density of Q is 2.80mT at CZ, and the hysteresis phase is about 20°. When the frequency is 800Hz, the residual magnetic flux density of Q is 3.65mT, and the hysteresis phase is much higher than 30°. And the effect of frequency on point P is shown in Fig.6.

Fig.6 Magnetic flux density of P

With the frequency increases, the maximum value of P reduces. When the frequency is 400Hz, the maximum magnetic flux density of P is 15.94mT, and when the frequency is 800Hz, the maximum value of P is 15.72mT.

It can be seen that as the current frequency increases, the eddy current effect of the AMF will be stronger, causing the magnetic flux density of the eddy current magnetic field much stronger. In order to maintain a vector synthesis relationship, the amplitude ofdecrease, and the hysteresis increases. Therefore, the eddy current effect and the hysteresis phenomenon will be strengthened by the increase of frequency.

Interruption ability experiment is carried out in AMF type vacuum interrupter. Vacuum circuit breaker of AMF type with contact materials of CuCr50 and a diameter of 41mm is selected for experiment in this section, with an open distance of 3mm. During the experiment, the current frequency is changed, and the current peak values of successful and failed breaking at different frequencies are obtained, as shown in Tab.2. Thesuccesscolumn in Tab.2 indicates the maximum first-half current peak value of the successful breaking whereas thefailedcolumn represents the current peak value when the breaking fails. For each frequency, the limit breaking test is carried out for more than 10 times. It should be noted that when the current frequency is 500Hz and current peak is 16.5kA. Sometimes the breaking is successful and sometimes it isn’t. The current value 16.5kA is considered to be the critical value of breaking. There is a similar situation for 15.5kA at 600Hz.

Tab.2 Results of interruption experiment at different frequency

Fig.7b shows the current and arc image of the vacuum arc at a frequency of360Hz.Don the time axis represents the current zero-crossing moment. When the current crosses zero, the post-arc discharge channel can be observed from the arc image, and the post-arc current can be clearly observed in the current curve. This is because the magnetic field hysteresis caused by the eddy current effect hinders the diffusion of the remaining plasma. A similar phenomenon can also be found in the current and arc image of the 500Hz vacuum arc as shown in Fig.7c.

Fig.7 Interruption experiment at different frequency (AMF, CuCr50, 41mm)

3 Discussion

3.1 Eddy Current Effect

The eddy effect will cause a magnetic field hysteresis. As the cycle time is changed with variation in frequency, the delay time is not sufficient to explain the hysteresis. Thus, in this paper, current phase, is introduced to analyze the AMF distribution with the same instantaneous current value but with different frequency. For example, current phase is π/2 (90°) at CP time. The current is given by

wherepeakis the current peak,is the frequency andis the current phase. The AMF,, in the contact gap is related to the current magnetic fieldi, generated by the current, and eddy current magnetic fielde, generated by the eddy currente.

According to Maxwell's equations, if displacement current is not taken into account, then there will be

As known from Equ.(2), the current, which flows through the contacts, is in the same phase as the current magnetic fieldi. The eddy currente, is inducted by AMF and the eddy current magnetic field,e, lags behindby π/2. The composition of the AMF is shown in Fig. 8, in which the angle,, indicates the phase by which the current magnetic fieldi, lags behind the AMF.

Fig.8 The AMF generated by the contacts

While the current frequency is constant and the amplitude increases,iandewill increase in proportion; thus the hysteresis phase,, is constant. However, if the current amplitude is constant and the frequency increases, the amplitude ofiis constant and the amplitude ofeincreases. To maintain a vector synthesis relationship, the amplitude ofmust decrease, as well as the hysteresis phase α must increase, as displayed in Fig.8b. Therefore, the eddy current effect and the hysteresis phenomenon will be strengthened by the increase of frequency.

3.2 Slot Number of Blade

The AMF type vacuum interrupters with 6 and 4 slots are displayed in Fig.9.

Fig.9 AMF type vacuum interrupters with 6 and 4 slots

As the current flows along the shortest path, the slot will shorten the conduction path of the eddy current. The slot number of contact blade will affect the distribution of AMF. When the current frequency is 400 Hz and the slot number 4, the AMF distribution is shown in Fig.10.

Compared with the vacuum interrupter with 6 slots, the peak area of magnetic flux density reduces from 6 to 4 at CP moment. While at CZ, it decreases from 13 to 9. It indicates that the number of peak areas of AMF is related to the slot number and staggered placement of contacts. And in Fig.11, the effect of frequency change on theat the center point Q and P is shown.

Fig.10 AMF in the middle plane (f = 400Hz, n = 4)

Fig.11 Magnetic flux density ofQ and P at different frequencies

As the frequency increases, the hysteresis of AMF is much more obvious. When the frequency is 400Hz, the residual magnetic flux densityQrofQis 3.88mT at CZ, and the hysteresis phase is about 20°. When the frequency is 800Hz, the residual magnetic flux densityQrofQ is 5.00mT, and the hysteresis phase is much higher than 35°. As the frequency is 400Hz, the maximum magnetic flux density of P is 14.85mT, and when the frequency is 800Hz, the maximum value of P is 15.53mT. Compared with the data in 2.3, when the slot number of blade is reduced from 6 to 4, as shown in Tab. 3, for the center point Q, the hysteresis is much more obvious at CZ. For the point P, the maximum value of magnetic flux density decreases. It can be seen that the decrease of the slot number makes the eddy effect more obvious.

Tab.3 Magnetic flux density for Q and P

3.3 Angle of Coil

The AMF type vacuum interrupters with= π/2, π/3, π are displayed respectively in Fig.12.

Fig.12 AMF type vacuum interrupters with γ = π/2, π/3, π

When the current frequency is 400Hz and= π/2 and π, the AMF distribution at CP are shown in Fig.13.

As can be seen from Fig.13, the rotation angle of the coil affects the maximum value of the AMF. Then the relation between the maximum value of magnetic flux density and rotation angle at CP moment can beobtained, as shown in Fig.14. Withincreases, the maximum value of the magnetic induction intensity increases approximately linearly, and the change trend is independent of frequency. For example at 400Hz, the maximum magnetic flux density is 13.42mT for= π/2, and the maximum magnetic flux density is 21.38mT for= π.

Fig.14 Relation between the maximum value of magnetic flux density and rotation angle of coil

4 Conclusion

The AMF distribution in vacuum interrupter in IF (400-800Hz) system of more electric aircraft is studied in this paper.

1) In the process of current variation, the change of magnetic field in the central region lags behind that in other regions. At CP moment, there are peak areas of magnetic flux density where the contact slot is staggered. And there is obvious residual magnetic field in the central area at CZ.

2) As the frequency increases, the eddy effect becomes more obvious, weakening the magnetic induction intensity of the AMF. For the center point, the frequency increase leads to the increase of residual magnetic field at CZ, and the hysteresis phase of magnetic field is much bigger. The effect of magnetic field hysteresis on breaking ability is verified by experiments.

3) The eddy effect can be reduced by increasing the slot number of blade. When the rotation angle of the coil is increased, the maximum magnetic flux density in the middle plane increases approximately linearly.

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中頻條件下真空滅弧室的縱向磁場仿真

蔣 原1李 擎1夏麗娜1武建文2賈博文2夏尚文2

（1. 工業(yè)過程知識自動化教育部重點實驗室（北京科技大學(xué)自動化學(xué)院） 北京 100083 2. 北京航空航天大學(xué)自動化科學(xué)與電氣工程學(xué)院 北京 100083）

該文研究了中頻400～800Hz條件下縱磁真空滅弧室內(nèi)的磁場特性，利用Ansys Maxwell求解了三維瞬態(tài)縱向磁場分布。由計算結(jié)果可知：在電流變化的過程中，中心區(qū)域縱向磁場的變化明顯滯后于其他區(qū)域。電流峰值時在觸頭片開槽交錯放置的位置有磁場峰值區(qū)域，電流過零時中心區(qū)域有明顯剩磁。當頻率增加時，渦流效應(yīng)更明顯，使縱向磁場的磁感應(yīng)強度值減弱。對中心點，頻率提高導(dǎo)致過零時剩磁增加，磁場滯后相位更明顯，影響電弧擴散。增加觸頭片開槽數(shù)可以減弱渦流效應(yīng)，而增加觸頭杯座槽旋轉(zhuǎn)角，觸頭中間平面磁感應(yīng)強度的最大值近似線性增加。文中通過分析電弧形態(tài)和電壓等實驗結(jié)果驗證了磁場滯后對真空滅弧室的開斷能力的影響。

多電飛機 縱向磁場 真空滅弧室 中頻 渦流效應(yīng)

TM561

10.19595/j.cnki.1000-6753.tces.L90123

This work is supported by National Natural Science Foundation of China (51977002), and Guangdong Basic and Applied Basic Research Foundation (No.2020A1515110725), Aviation Science Fund (2020Z025074001), and Fundamental Research Funds for the Central Universities (FRT-TP-19-035A1).

June 25, 2020;

January 4, 2021.

male, Member IEEE, PhD, Major research interests include the theory and application of avia-vacuum arcs, electrical appliances detection and fault diagnosis, intelligent micro-grid and new energy technology.E-mail: jiangy_luckystar@163.com

, male, Professor, PhD, Major research interests include intelligent control and intelligent optimization.E-mail: liqing@ies.ustb.edu.cn (Corresponding author)

（編輯 郭麗軍）