Analysis and Performance of the Self Excited Eddy Current...

J Electr Eng Technol.2017; 12(1): 459-465 http://dx.doi.org/10.5370/JEET.2017.12.1.459

459Copyright The Korean Institute of Electrical Engineers

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Analysis and Performance of the Self Excited Eddy Current Brake

Sooyoung Cho*, Teachul Jeong*, Jaenam Bae**, Changhee Yoo*** and Ju Lee†

Abstract – This paper describes a performance analysis of self-excited eddy current brake(SECB). Stator winding of SECB is connected by capacitor instead of voltage source, and SECB’s braking force is generated by L-C resonance. SECB has wide range of driving and nonlinear inductance as well. Therefore, it is important to select capacitance based on the value of inductance. This paper discusses about the process of deciding capacitance and the change of resonance frequency based on the inductance change in each speed. Also the braking force was confirmed by the experimental model of SECB.

Keywords: Self-excited Eddy Current Brake(SECB), Self-excited Induction Generator(SEIG), Resonance, Electric retarder, Braking force

1. Introduction Brake for vehicles and railroad cars is a very important

system for stopping on precise location and with safety. However, mechanical brake has problems such as heat, noise, and dust generation because of mechanical friction. In order to overcome such weaknesses, a research on electric eddy current brake is currently being done. Since an eddy current brake is a non-contacting system, it is not only free from the friction problem, but can also solve the problem of heat, noise and dust generation caused by friction. Furthermore, the responding speed is outstanding because the system runs by an electrical input.

There are three kinds of eddy current brakes. For making excitation, one is composed of winding at the stator and it is applying a current to the coil. [1] Another is making excitation using permanent magnet. [2, 3] The other is the method of excitation blending winding and permanent magnet. [4-6] The system for applying dc current at the winding, however, has demerits which it needs to control electrical input. The system using permanent magnet also has weakness such as difficulty in controlling flux, requirement of high cost and the possibility causing demagnetization in high temperature environment. Therefore, in order to solve the problems started above, an eddy current brake which this paper suggests is made to work self-excited system by connecting capacitor in series at winding. Since this kind of SECB can generate braking force by LC resonance, it does not need further electric control and can solve demagnetizing problems of permanent magnet.

This paper analyzes nonlinear characteristic of inductance of SECB, and dealt with capacitance estimation procedure for LC resonance. Also, it analyzed variation of resonance frequency within the field of SECB’s driving speed. And it compared finite-element analysis of SECB model and experimental results of production model.

2. Principle of Self-excited Eddy Current Brake

2.1 Series LC resonance Series LC resonance occurs when the size of the

impedance of inductance and capacitance is the same while inductance and capacitance are connected in series. If the size of the two impedance is the same, the size of current and voltage becomes the same; however, the phase angle will be different at 180. Therefore, reactive power becomes 0, and the generated electric power at circuit becomes maximum.

Series LC resonance frequency is

1 [Hz]

2sf LCπ= (1)

where L is inductance and C is capacitance.

Also, quality factor is reactive power of inductance or capacitance to the average electric power at resonance point. This is for showing the area of resonance point. Quality factor of series LC resonance is

2 sLs

f LXQ

R Rπ

= = (2)

where XL is reactance and R is resistance.

That is, if the loss level by resistance against the reactive power of inductance or capacitance is low, quality factor

† Corresponding Author: Dept. of Electrical Engineering, Hanyang University, Korea. ([email protected])

* Dept. of Electrical Engineering, Hanyang University, Korea. ([email protected], [email protected])

** Dept. of Electrical Engineering, Dongyang Mirae University, Korea. ([email protected])

*** Designed Team, Sangsin Brake, Korea. ([email protected]) Received: June 30, 2016; Accepted: September 1, 2016

ISSN(Print) 1975-0102ISSN(Online) 2093-7423


460 J Electr Eng Technol.2017; 12(1): 459-465

becomes bigger, and the area of resonance becomes narrower and stronger.

2.2 Principle of Self-excited eddy current brake

In order to explain the principle of SEIG, d-q trans-

formation circuit of SEIG is shown in Fig. 1. Through the circuit, the inductance of a stator and a rotor is

s ls mL L L= + (3) r lr mL L L= + (4)

If droλ , qroλ is remnant magnetic flux of initial rotor,

flux linkage of d, q axis is

( )dr m ds dr lr dr dro m ds r dr droL i i L i L i L iλ λ λ= + + + = + + (5)

( )qr m qs qr lr qr qro m qs r qr qroL i i L i L i L iλ λ λ= + + + = + + (6) The d, q axis voltage of rotor having electrical angular

velocity of rotor rω is

( ) ( )r qr r m qs r qr r qro r m qs r qr drL i L i L i L i Kω λ ω ω λ ω= + + = + + (7)

( ) ( )r dr r m ds r dr r dro r m ds r dr qrL i L i L i L i Kω λ ω ω λ ω= + + = + + (8)

where drK and qrK are constants created by remnant magnetic flux of core.

Through the process, d-q axis voltage equation of SEIG is shown in below.

In order to judge whether the eddy current brake comes to the condition of self-excitation, it needs to solve the equation, in which the denominator of the stator current becomes zero. This equation is called characteristic equation. If the characteristic equation has a root of real positive number, the current and voltage of eddy current brake of LC series circuit will increase during transient state, and it will be driven by self-exited method. On the other hand, if the characteristic equation does not have root making real part of positive, the current and voltage of eddy current brake are decreased during transient, and it will not be driven. Therefore, SECB has to have denominator, in which the characteristic equation’s root of stator current makes the real part of positive. Through the Eq. (9), d-axis current of the stator is shown as the Eq. (10). [7,8]

3. Self-excited Eddy Current Brake Model

SECB model presented in this paper is shown in Fig. 2

and specification of SECB is shown as Table 1. In order to obtain SECB’s braking force using LC resonance, capacitor should be connected to the stator winding in series. Also as mentioned in the previous chapter 2, characteristic equation’s root of denominator of stator current equation should have real part of positive in order to make SECB. Therefore, SECB firstly composed stator winding which has great affection on magneto-motive force(MMF) and then selected capacitance for setting self-excited up considering driving area.

Fig. 1. d-q model of SEIG: (a) d-axis circuit; (b) q-axis

circuit

1 0 000 1 00

00

qs cqos s m

s s m ds cdo

m r m r r r r qr qr

r m m r r r r dr dr

i VR pL pC pLR pL pC pL i V

pL L R pL L i KL pL L R pL i K

ω ωω ω

⎡ ⎤ ⎡ ⎤+ +⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ + +

= +⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ − + − −⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥+ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(9)

( )( ) ( )( )

( ) ( )( )

2 22 2 2 2 2

2 2 2

2 2 2 2 4 2 2 3 2 2 2

3 2 2 2 3 2 3 2

1

,

ds

s s m r r m r r m r r

r r r r

s s m r r m r r r cdo

m r r cqo m r r qr m s s d

UiR pL pC p L R pL pL L pL R

where R pL Lp C R pL pC p C L R pL p C L R L V

p C L R V p C L L K p C L R pL KU

ω ω

ωω

ω ω

=⎡ ⎤+ + − + + Δ + Δ⎣ ⎦Δ = + +

⎡ ⎤− Δ + + Δ − Δ + − Δ⎣ ⎦− Δ − Δ + Δ +

=( )2

r

pCΔ

(10)

Sooyoung Cho, Teachul Jeong, Jaenam Bae, Changhee Yoo and Ju Lee

http://www.jeet.or.kr 461

3.1 Inductance variation by the current change Since the current of SECB increases by LC resonance,

flux linkage and inductance are changed through resonance process. Magnetic flux ( )phaseψ and inductance ( )phaseL created at one phase according to increase of current is shown in Fig. 3 and Fig. 4. That is, magnetic flux of SECB increases according to increase of the phase current. However, the increasing rate of magnetic flux has been decreased after the areas of around 11[Arms] because of the effect of magnetic flux saturation. Also, the value of inductance increases during initial start-up, however it has been decreased after the areas of around 11[Arms] because of decline in increasing magnetic flux rate compared to

generated current. The distribution of magnetic flux density when LC

resonance converges is shown in Fig. 5. Through the figure, we can notice that magnetic flux saturation partially occurs at Drum and Braket.

3.2 Inductance change in operation speed

Braking force of SECB is generated by the LC resonance

and the current and flux linkage is changed along with the driving speed. Fig. 6 shows the inductance of SECB according to the generated current in each speed. That is,

Fig. 4. Inductance of one phase according to the increase

of current (at 800[rpm])

Fig. 5. Distribution of magnetic flux density at steady state

(at 800[rpm])

Fig. 6. Inductance change in operation speed

Table 1. Specification of self-excited eddy current brake

Contents Required power Unit Outer Diameter 460 mm Stack Length 81.5 mm

Number of phases 3 Number of poles 6

Resistance per phase (50) 0.81 Ω Capacitance per phase 1680 uF

Speed range 600 ~ 1100 rpm

Fig. 2. Self-excited eddy current brake model

Fig. 3. Generated magnetic flux at one phase according to

the increase of current (at 800[rpm])



this model increases current and decreases inductance according to increasing speed.

3.3 Self-excited map

Due to the change of current value along with the

driving speed, the parameter of SECB is changed, and the self-excited map of SECB is changed as well. Also, Fig. 6 shows that the phase current is 35[Arms], 50[Arms] and 59[Arms]. Based on the results of Fig. 6, driving available area when the phase current of 35[Arms], 50[Arms], 59[Arms] flow is shown in Figs. 7-9. Also, since the stator resistance value of SECB on this paper is 0.81[Ω](※50[] standard), the capacitance value which is being satisfied by all areas is 1,700[uF] maximum.

3.4 Characteristic of torque according to capacitance

Capacitance is a storage device, and the larger amount

of energy can be stored as the capacitance becomes bigger. However, there is limit on the capacitance value for self-

excited characteristic. At chapter 3.3, the limitation value of capacitance is 1,700[uF] for satisfying all operating speed. Based on this, Fig. 10 shows torque graph according to the change of capacitance value. Through the graph, the bigger capacitance is, the greater torque can be generated. Therefore, the value of capacitance is determined as 1,680 [uF](=120[uF]×14) considering cost and capacitance combination of one phase.

3.5 Change of resonance frequency in each speed

Considering capacitance of one phase, resonance

frequency can be obtained through formula (1). That is, because of the reason that inductance decreases along with the increase of speed, resonance frequency increases

Fig. 7. Self-excited Map (at I_phase=35[Arms])



Fig. 10. Torque according to capacitance (at 800[rpm])

Fig. 11. Change of resonance frequency according to the

speed

Fig. 12. Slip-torque curve of SECB



inversely and it is shown in Fig. 11. Also, along with the relationship with slip formula (11), slip-torque curve of SECB is shown in Fig. 12. That is, SECB is driven by regenerative braking area (s<0).

s

s

n ns

n−

= (11)

where s is slip, ns is synchronous speed and n is rotor speed.

4. Verification through Finite-element Analysis Based on the capacitance which is selected at chapter 3,

the result of finite-element analysis(FEA) is shown in

Figs. 13-15. These figure show that braking torque, current and voltage converge at steady state, because proper capacitance is selected for LC resonance.

5. Experimental Result Prototype of SECB is made by considering size

limitation and operation speed, and then it verified torque characteristics. Fig. 16(a) shows the part of Braket and Pole, and Fig. 16(b) shows Drum. Also, a system combining Braket, Pole and Drum and connecting capacitor at winding is shown in Fig. 17.

The experiment of SECB is conducted considering 10 seconds driving condition. Through an experiment, torque, phase current and phase voltage wave are obtained at 800[rpm] and these are shown in Figs. 18-20. So, it can be seen that the braking force exerted well because of proper capacitance. Also, experimental braking torque decreased with the time because temperature increased along with the braking time.

(a) (b)

Fig. 16. (a) Braket and pole; (b) Drum

Fig. 17. SECB system

Fig. 13. Torque through FEA (at 800[rpm])

Fig. 14. Phase current of through FEA (at 800[rpm])

Fig. 15. Phase voltage of through FEA (at 800[rpm])



Fig. 18. Torque through the experiment (at 800[rpm])

Fig. 19. Phase current through the experiment (at 800[rpm])

Fig. 20. Phase voltage through the experiment (at 800[rpm])

Fig. 21. Generated start-up torque of SECB according to

operation speed

The experimental result of SECB according to operation speed is shown in Fig. 21. Based on the results, it was designed to have bigger braking force at high speed than at low speed in order to get a fast braking force.

6. Conclusion This paper suggested SECB in order to substitute

mechanical brake being used at vehicles and railroad cars, and analyzed the performance. SECB needs to be self-excited using the principle of LC resonance in order to generate current and voltage at winding. Since inductance of SECB is changed based on the size of current and the resistance is already set, the capacitance should be estimated considering these parameters. Also, it was found that resonance frequency varies by the change of inductance due to the current change generated at different driving speeds. In addition, it was confirmed that SECB is driven through regenerative braking.

Acknowledgements This work was supported in part by the Energy

Efficiency and Resources, Korea Institute of Energy Technology Evaluation and Planning, and in part by the Ministry of Trade, Industry, and Energy, Korea. (No. 2013T100200023)

This work was supported by the Human Resources Program in Energy Technology of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 2015 4030200900)

References

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[7] D. Seyoum, C. Grantham, and F. Rahaman, “The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine,” IEEE Trans. Ind. Appl., vol. 39, no. 4, pp. 936-944, Jul./ Aug. 2003.

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Sooyoung Cho She received the B.S. degree in electrical engineering from Myongji University, Yongin, Korea in 2013 and the M.S. degrees in electrical engineering from Hanyang University, Seoul, Korea in 2015. Since 2015, she has been pursuing the Ph.D. degree at the Department of Electrical Engineer-

ing, Hanyang University. Her research interests include design, analysis, testing and control of motor/generator; power conversion systems; and applications of motor drive.

Taechul Jeong He received the B.S. degree in electrical engineering from Hanbat University, Daejeon, Korea in 2010, and the M.S. and Ph.D. degree in electrical engineering from Hanyang University, Seoul, Korea in 2012 and 2016, respectively. Currently, he is postdoctoral student in Hanyang

University. His main research interests include electric machinery and numerical analysis of electromagnetic field.

Jaenam Bae He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Hanyang University, Seoul, Korea in 2004, 2006, and 2010, respectively. He is currently an Assistant Professor with the Department of Elec-trical Engineering, Dongyang Mirae University, Seoul, Korea. His main

research interests include electric machinery and its drives, numerical analysis of electromagnetic field, and applications of motor drives such as electric vehicles.

Changhee Yoo He received the B.S., M.S. degrees in Mechanical engineering from Yeungnam University, Daegu, Korea in 1995, 2013, respectively. Currently, he is a Chief Researcher with the Design Team, Sangsin Brake, Daegu, Korea. His main research interests include brake system, auto-

motive applications of electro-magnetic retarder system, such as commercial vehicle.

Ju Lee He received his M.S. degree from Hanyang University, Seoul, South Korea, in 1988, and his Ph.D. from Kyusyu University, Japan in 1997, in Electrical Engineering. He joined Hanyang University in September 1997, and is currently a Professor of the Division of Electrical and Biomedical

Engineering. His main research interests include electric machinery and its drives, electro-magnetic field analysis, new trans-formation systems such as hybrid electric vehicles (HEV), and high-speed electric trains and standardization. He is a member of the IEEE Industry Applications Society, Magnetics Society, and Power Electronics Society.

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