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# Conceptual design of a high-speed electromagnetic switch for a modified flux-coupling-type SFCL and its application in renewable energy system

- Lei Chen
^{1}Email author, - Hongkun Chen
^{1}, - Jun Yang
^{1}, - Zhengyu Shu
^{2}, - Huiwen He
^{3}and - Xin Shu
^{4}

**Received:**9 March 2016**Accepted:**13 May 2016**Published:**17 June 2016

## Abstract

The modified flux-coupling-type superconducting fault current (SFCL) is a high-efficient electrical auxiliary device, whose basic function is to suppress the short-circuit current by controlling the magnetic path through a high-speed switch. In this paper, the high-speed switch is based on electromagnetic repulsion mechanism, and its conceptual design is carried out to promote the application of the modified SFCL. Regarding that the switch which is consisting of a mobile copper disc, two fixed opening and closing coils, the computational method for the electromagnetic force is discussed, and also the dynamic mathematical model including circuit equation, magnetic field equation as well as mechanical motion equation is theoretically deduced. According to the mathematical modeling and calculation of characteristic parameters, a feasible design scheme is presented, and the high-speed switch’s response time can be less than 0.5 ms. For that the modified SFCL is equipped with this high-speed switch, the SFCL’s application in a 10 kV micro-grid system with multiple renewable energy sources are assessed in the MATLAB software. The simulations are well able to affirm the SFCL’s performance behaviors.

## Keywords

- Conceptual design
- Electromagnetic repulsion mechanism (ERM)
- Flux-coupling-type SFCL
- High-speed switch
- Micro-grid system

## Background

For the modern electric power systems, one of the major challenges and demands is how to solve the continually increasing fault currents (Shuai et al. 2015; Li et al. 2015). In the case of that the fault currents cannot be timely limited and interrupted, a number of problems will be caused, such as the failure of electric device and the expansion of power supply interrupted region (Lapthorn et al. 2011; Im et al. 2014). At present, owing to the unique technical advantages of superconducting materials (Malginov et al. 2013a, b; Guan et al. 2015), superconducting fault current limiters (SFCLs) can be thought of as the highly competitive auxiliary devices to assist the electric power systems against short-circuit faults. On this background, lots of research works have been carried out, and different kinds of SFCLs have been proposed (Didier and Lévêque 2014; Firouzi et al. 2015; Chen et al. 2015a, b; Martini et al. 2015; Reiss 2015).

In terms of the proposed SFCLs, they can be approximately classified as resistive and inductive SFCLs. Our research group has suggested a modified flux-coupling-type SFCL, which is a resistive-inductive type (hybrid type) SFCL, and is able to theoretically enhance the transient performance of an electrical system more efficiently (Chen et al. 2015c, d; Deng et al. 2015). This flux-coupling-type SFCL is to suppress the short-circuit current by controlling the magnetic path through a high-speed switch. In other words, the high-speed switch’s operating characteristics will directly affect the SFCL’s performance behaviors and engineering application. From this perspective, the study of a feasible design scheme for the switch is necessary and meaningful.

In this paper, the conceptual design of the high-speed switch with electromagnetic repulsion mechanism (ERM) used in a 10 kV class SFCL is done, and also the application of the SFCL in a micro-grid system with multiple renewable energy sources is assessed. The article is organized in the following manner. “Theoretical analysis” section presents the SFCL’s structural principle, discusses the computational method for the high-speed switch’s electromagnetic force, and builds the dynamic mathematical model. In “Numerical calculation and simulation study” section, calculation analyses and transient simulations are performed to verify the electromagnetic switch’s design scheme and the SFCL’s performance. In “Conclusions” section, conclusions are summarized and next steps are prospected.

## Theoretical analysis

### Theoretical presentation of the flux-coupling-type SFCL

_{cs}and a superconducting coil (SC). The switch S

_{cs}and the SC are respectively connected in series with the CT’s primary and secondary windings, which are wound in reverse directions. The metal oxide arrester (MOA), whose expected function is to suppress switching overvoltage, is connected in parallel with the CT.

*L*

_{1},

*L*

_{2}are recorded as the winding self-inductances, respectively, and

*M*is the mutual inductance. In addition,

*Z*

_{s}is the circuit impedance and

*S*

_{load}is the circuit load.

*R*

_{SC}/

*R*

_{moa}is recorded as the SC/MOA’s normal-state resistance.

Since it is convenient to investigate the CT’s characteristics by using the equivalent circuit whose parameters are expressed in terms of mutual-inductance and self-inductances, the SFCL’s impedance characteristic can be studied more clearly. According to the CT’s equivalent circuit, the SFCL’s electrical equivalent structure is shown in Fig. 1b.

_{cs}is under the closed state and the SC is maintained in the zero-resistance state. Herein, the CT’s operating impedance

*Z*

_{ct}will play a decisive role on the SFCL’s performance characteristic. The analysis of the impedance

*Z*

_{CT}is conducted. Actually,

*Z*

_{CT}is the ratio of the transformer voltage

*U*

_{CT}and the transformer current

*I*

_{CT}. The voltage

*U*

_{CT}denotes the voltage over the two terminals of the CT’s primary or secondary inductance, and it can be shown in Fig. 1. In regard to the current

*I*

_{CT}, it denotes the total currents which respectively flow through the CT’s primary inductance

*L*

_{1}and secondary inductance

*L*

_{2}. And namely if the CT can be regarded as a black box with an input current and a same output current,

*I*

_{CT}is the sum of

*I*

_{1}and

*I*

_{2}. From the electric relationship demonstrated in Fig. 1,

*Z*

_{CT}can be expressed as:

When the coupling coefficient *k* and the transformation ratio *n* can be respectively expressed as \(k = M/\sqrt {L_{1} L_{2} }\) and \(n = \sqrt {L_{1} /L_{2} }\), \(Z_{CT} = \varvec{j}{{\upomega }}L_{2} (1 - k^{2} )n^{2} /(n^{2} + 2kn + 1)\) is obtained. In the case of that an iron core is used to maximize the coupling, *k* will be approximate to 1 and *Z*
_{CT} ≈ 0. The non-inductive coupling is achieved, and the MOA is “short-circuited”. Consequently, the SFCL will not affect the main circuit.

_{cs}will be opened rapidly, and meanwhile the MOA may suppress the overvoltage caused by the switching operation. Since the electromagnetic relationship is changed by the controlled switch, the non-inductive coupling will pass away, and also the fault current in the SC will make the superconductor be quenching. The modified SFCL’s current-limiting impedance can be calculated as:

_{cs}has been opened, the physical-circuit electrical connection between the CT’s primary and secondary inductances will be replaced by the magnetic-circuit coupling connection. According to the inductive coupling characteristic (Chen et al. 2010, 2014), the relationship between the two currents can be derived by:

According to Eqs. (2) and (3), the impedance *Z*
_{SFCL} can be rewritten as: \(Z_{SFCL} = [R_{\text{SC}} + {\text{j}}\omega L_{ 2} + \left( {kn\omega L_{ 2} } \right)^{ 2} /\left( {R_{moa} + n^{ 2} \omega L_{ 2} } \right)\). In view of \(R_{moa} \gg n^{ 2} \omega L_{ 2} ,Z_{SFCL} \approx R_{\text{SC}} + {\text{j}}\omega L_{ 2}\) can be obtained. Compared to the original flux-coupling-type SFCL which is purely inductive (Ren et al. 2010; Chen et al. 2015e), the suggested SFCL is a resistive-inductive type (hybrid type) SFCL, which can potentially bring more contributions, such as inhibiting the fluctuations of active power and reactive power, restraining electromagnetic oscillations as well as providing critical protection to relevant power equipment (Chen et al. 2009).

In light of the SFCL’s structure and principle, the following requirements related to the high-speed switch can be obtained: (1) the switch may accurately interrupt the coil current to ensure the SFCL’s reliable action; (2) the switch may carry out the interrupting operation within milliseconds to ensure the SFCL’s rapid response. Considering the practical application of switch technology in the field of SFCL, a high-speed switch based on electromagnetic repulsion mechanism (ERM) has received lots of attention from research scholars (Lim et al. 2010, 2014; He and Wang 2014). Herein this kind of switch is adopted for the modified flux-coupling-type SFCL, and the switch’s operating principle and mathematical modeling will be stated in the next section.

### Principle and modeling of the switch with ERM

*r*and

*R*are respectively the two single-turn coils’ radiuses, and

*x*is the spatial distance between them. According to electromagnetic theory, the mutual inductance

*M*

_{st}between the two coils can be expressed as:

*k*

_{ st }, B(

*k*

_{ st }), and

*E*(

*k*

_{ st }) are respectively expressed as \(k_{st} = 2\sqrt {\frac{Rr}{{x^{2} + (R + r)^{2} }}}\), \(B(k_{st} ) = \int_{0}^{\pi /2} {\frac{d\alpha }{{\sqrt {1 - k_{st}^{2} \sin^{2} \alpha } }}}\), \(E(k_{st} ) = \int_{0}^{\pi /2} {\sqrt {1 - k_{st}^{2} \sin^{2} \alpha } d\alpha }\).

*i*

_{0}and

*i*

_{1}, the electromagnetic force

*F*

_{st}between them can be shown in:

*F*

_{total}between the electrified coil and the copper disc is computed in:

*N*

_{0}is the number of turns of the electrified coil;

*i.*e. is the current flowing through the electrified coil; the copper disc is equivalent to

*N*

_{1}turns of wire-loops in which different eddy currents

*i*

_{p}are induced;

*M*

_{jp}is the mutual inductance between any two coaxial single-turn coils;

*m*expresses the mass of the copper disc and its link system;

*f*(

*x*) denotes the movement resistance including gravity as well as friction, and the mechanical motion equation related to the spatial distance

*x*is also given. For the calculation of different eddy currents (

*i*

_{1},

*i*

_{2},

*i*

_{3}…

*i*

_{ N1 }), Eq. (7) can be obtained.

*C*

_{ e }is the charging capacitance;

*E*

_{ e }is the capacitor voltage’s initial value;

*R*

_{j}indicates a single-turn coil’s electrical resistance;

**A**is the inductance coefficient matix with

*N*

_{1}+ 1 dimension (Li et al. 2004).

*t*is the calculation step;

*j*is the discretization time.

On the basis of the aforementioned equations, theoretical analysis and mathematical calculation of the electromagnetic repulsion force can be performed, and further it can lay a foundation for the subsequent conceptual design of the switch.

## Numerical calculation and simulation study

### Design of the switch and its performance calculation

As the switch’s operating characteristic is determined by its electromagnetic force in principle, a few key factors related to the electromagnetic force are assessed during the numerical calculations. The initial conditions are set as *N*
_{0} = 15, *N*
_{1} = 20, *x* = 10 mm (maximum stroke), *r* = 15 mm, *R* = 12 mm, *E*
_{e} = 200 V, Δ*t* = 1 μs, and *C*
_{e} = 53,000 μF.

*N*

_{1}to

*N*

_{0}is fixed to 1.3, and the copper disc’s thickness is set as 5.4 mm. It is observed that, the peak value of the current across the electrified coil will decrease with the increase of

*N*

_{0}, and meanwhile the current’s rate of rise will be limited. Considering that the electromagnetic force has a close relation to the coil current, which is affected by the number of turns of the coil, Fig. 5 shows the impacts of adjusting the number of turns of the electrified coil on the switch’s electromagnetic force. The ratio of

*N*

_{1}to

*N*

_{0}is still fixed to 1.3, and the copper disc’s thickness is 5.4 mm. With the augment of

*N*

_{0}, the electromagnetic force’s peak value will increase firstly and then decrease. For that

*N*

_{0}is respectively set as 5, 15, 30 and 45, the electromagnetic force’s peak value will reach to its maximum 458930N (

*N*

_{0}= 15) and minimum 91540N (

*N*

_{0}= 45), and the switch’s least and longest response time is respectively 0.8 and 2.56 ms.

*N*

_{0}= 15,

*N*

_{1}= 60,

*x*= 10 mm,

*r*= 15 mm, and

*R*= 5 mm). Obviously, the eddy current appeared in the spatial overlap between the copper disc and the electrified coil is relatively large, and it will reach to the maximum in the copper disc’s 18th wire-loop. It may be inferred that, if the copper disc has the similar or comparable size as the electrified coil, the switch’s operating efficiency can be greatly improved. In view of it, this philosophy should be seriously carried out in the next design scheme.

*N*

_{0}= 15,

*N*

_{1}= 25,

*x*= 10 mm (contact maximum stroke),

*r*= 30 mm,

*R*= 20 mm,

*E*

_{e}= 220 V,

*C*

_{e}= 53000 μF, and the copper disc’s thickness is set as 5.4 mm. In accordance with this scheme, the electromagnetic force’s peak value can reach to 957640N, and the switch’s response time can be reduced to 0.45 ms. Figures 7 and 8 show the switch’s performance behaviors under the design scheme. Note that, during the following transient simulations, the SFCL will configure this high-speed electromagnetic switch, and the SFCL’s application in a micro-grid system with multiple renewable energy sources will be assessed in the MATLAB software.

### Application of the SFCL in a renewable energy system

Main simulation parameters of the system model

| |

DG1/DG2/DG3 | 180 kW/100 kW/150 kW |

Transmission line | 0.27+j0.347 Ω/km, 2 km |

Load 1/load 2 | 350 kW/250 kW |

PCC voltage/frequency | 10 kV/50 Hz |

| |

Primary inductance | 50 mH/70 mH |

Coupling coefficient/coil ratio | 0.99/0.5 |

Superconducting coil | 10 Ω/30 Ω |

Concerning the dynamic simulation model of the DG1, its main circuit is described as follows. The PV array is connected to the input side of a boost converter and its output side is connected to the DC link capacitor. Further, a three-phase voltage source (VSI) is adopted to maintain constant DC voltage and supply sinusoidal current to the micro-grid. For the boost converter, the maximum power point tracking (MPPT) control is used to ensure the PV generation system’s operating efficiency. Details can be achieved in (Nanou and Papathanassiou 2014; Mohanty et al. 2014).

In regard to the modeling of the DG2, it is based on fixed-speed wind turbine (FSWT). FSWT technically adopts the induction generator (IG) and is connected to the micro-grid through a transformer. The MATLAB software library provides a standard model for the induction generator, and for the models of the wind turbine and the drivetrain system, details can be obtained in (Firouzi and Gharehpetian 2013; Ouchbel et al. 2014).

*R*

_{n}denotes the SFCL’s normal-state resistance;

*τ*is the time constant. The SFCL’s time-domain characteristic is stated as that,

*t*

_{0},

*t*

_{1}, and

*t*

_{2}indicate the quench-starting time, the first recovery-starting time, and the secondary recovery-starting time, respectively.

*a*

_{1},

*b*

_{1},

*a*

_{2}, and

*b*

_{2}are respectively the function coefficients. During the simulation, it is designed that the SC will enter the normal state within 4 ms, and after the fault is removed, the SC’s recovery time is set as 0.5 s, so as to match up the auto-reclosing operation.

In view of the modeling of the DG3, it includes the controller, LCL filter, three-phase half-bridge voltage converter, chopper and superconducting magnet, and its main structure can be according to (Zhu et al. 2012). It should be noted that, the DG3 will be served as a master-control DG, which is potentially used to stabilize the micro-grid system’s voltage and frequency under the islanded condition.

When the micro-grid is under normal state, the DGs’ overall active power will be controlled as 300 kW (*P*
_{DG1} + *P*
_{DG2} + *P*
_{DG3} = 300 kW). That is to say, the micro-grid’s power shortage with the capacity value of 300 kW will be supported by the main network. Furthermore, the simulation conditions of the external fault are set as that, a three-phase ground fault happens at *t* = 1 s; the fault resistance is 1 Ω; duration of the fault is 0.2 s.

*t*= 1.14 s, the voltage drop in the PCC may deeply affect the power exchange between the main network and the micro-grid. Under this fault, the exchange power’s direction is reverse, and the micro-grid will provide energy to the main network. Owing to the use of the SFCL, the fluctuating margin of the exchange power can be reduced to a certain extent. Moreover, the micro-grid frequency’s fluctuating amplitude can reach to 0.18 Hz in the case of without SFCL, and it may be suppressed within the level of 0.1 Hz when the SFCL is employed.

Note that, different current-limiting parameters of the SFCL are adopted here, and the main reason is to assess how the change of the current-limiting parameters can affect the SFCL’s performance. For the optimization of those parameters, detailed works will be done in the next articles.

## Conclusions

In this paper, the conceptual design of a high-speed switch with electromagnetic repulsion mechanism is performed for a modified flux-coupling-type SFCL, and also the application of the SFCL in a micro-grid with multiple renewable energy sources are assessed. According to theory analysis and parameter design, the electromagnetic switch’s response time can be less than 0.5 ms, and it can meet the requirements of the SFCL for high-speed control. Furthermore, based on the performance simulations of the SFCL equipped with this high-speed switch, the SFCL is able to quickly and availably suppress the fault current contributed by the DG units in the micro-grid system, and meanwhile improve the voltage sag and reduce the frequency fluctuations. As a result, the suggested SFCL’s service practicability can be well confirmed.

In the near future, a small-scale lab prototype of the SFCL will be made, and the current-limiting experiment will be done. Related experiment results will be reported in later articles.

## Declarations

### Authors’ contributions

Author LC helped design the study, analyze the data, and write the manuscript. Author HC helped conduct the study. Author JY helped analyze the data. Author ZS helped conduct the literature survey. Author HH helped draft the manuscript. Author XS helped edit the manuscript. All authors read and approved the final manuscript.

### Acknowledgements

This work was in part supported by the National Natural Science Foundation of China (51507117), Wuhan Planning Project of Science and Technology (2013072304010827), and Natural Science Foundation of Hubei Province of China (2014CFB706).

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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