Surge Characteristics of a Twisted Pair

SHOHEI KATO and MD. SOLAIMANToyo University, Japan

SUMMARY

We used the method of moments (MoM), which is anumerical electromagnetic field computation method, tostudy the surge characteristics of twisted pair single-phaseelectric power lines. The results show that wires strandedwith less than several turns per meter have almost the samesurge characteristics as parallel lines, but the surge imped-ance decreases in tens of % when the number of strandsincreases. To verify the simulation results, we measured thesurge characteristics of a model line of twisted pair experi-mentally, and there is good accordance between them. It ispossible to simulate the surge in twisted pair covered withpolymer dielectric insulators by MoM.

Moreover, we studied the surge characteristics oftwisted pair which is inserted into a metal tube. Accordingto the results, the effect of the strand is smaller than that infree space without the metal pipe. There are two propaga-tion modes in common mode: fast surge and slow surge.Few influences of the number of strands on the surgevelocity occur in the fast propagation surge, but the increaseof the surge impedance and the slowdown of the propaga-tion speed are caused by twining in the slow propagationmode. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn,167(3): 1–9, 2009; Published online in Wiley InterScience(www.interscience.wiley.com). DOI 10.1002/eej.20737

Key words: method of moments; twisted pair;surge analysis; surge impedance.

1. Introduction

Twisted wires are widely used for both signal linesand power cables because they offer lower impedance andlower noise in differential mode. However, the surge char-acteristics of twisted pairs remain largely unknown. Fur-thermore, when twisted pairs are employed for networkcables, their transmission characteristics may be a problem

when implementing high-speed communications. In suchcases, numerical electromagnetic field analysis is applied[1]. The transmission characteristics of power cables arealso involved in the latest technologies of high-speed powerline communications (PLC). In addition, in the overvoltageanalysis of power distribution lines, elucidation of surgepropagation characteristics is necessary for precise analy-sis.

Multiple twisted strands are used for power cables indistribution lines in order to reduce loss, and much researchon their surge characteristics has been performed. Theequivalent circuit constants are incorporated into EMTPand other circuit simulators. The present study considerstwisted wires made of a small number of insulated conduc-tors. The surge characteristics of twisted pairs are importantnot only for power lines but also for the insulation ofinverter-fed motors [2].

It has been a common opinion that in case of a lowtwist rate, twisted pairs can be approximated by straightwires. In addition, experimental results obtained with reallines suggest that, except for certain cable lines, twistingcan be ignored in the surge analysis of transmission anddistribution lines. However, the range in which the straight-wire approximation applies has not been defined, and mosttwisted pairs employed in control circuits have a high twistrate. Hence, the approximation may not be appropriate.

Among numerical methods of electromagnetic fieldanalysis, the method of moments (MoM) has been used forsurge analysis in transmission lines because it allows easymodeling of three-dimensional conductor configurations[3, 4]. With twisted pairs, it is difficult to obtain analyticsolutions in terms of a two-dimensional problem, eventhough we may consider two-dimensional spatial peri-odicity of the electromagnetic field. In addition, twistedpairs are often laid along broken or curved lines rather thanstraight lines. Thus, we employed the method of momentsto investigate the surge characteristics of single-phasetwisted-pair lines [5, 6]. In particular, we examined how thesurge impedance (characteristic impedance) and propaga-tion speed depend on the twist rate.

© 2009 Wiley Periodicals, Inc.

Electrical Engineering in Japan, Vol. 167, No. 3, 2009Translated from Denki Gakkai Ronbunshi, Vol. 127-A, No. 6, June 2007, pp. 321–327

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2. Analytic Model and Method

2.1 Analytic model

The conductor’s radius is 1 mm, the insulation thick-ness is 1 mm, and the axial length of the twisted pair is 4m. The relative dielectric permittivity of the insulation is 4.The insulated wires are twisted in a tight spiral. Bare wiresare also analyzed in order to examine the influence of theinsulation on surge characteristics. The bare wires are as-sumed to have the same spatial configuration as the insu-lated wires, and no spacers between wires are assumed.

2.2 Analytic method

The method of moments is used for numerical elec-tromagnetic field analysis. This method is basically linearin the frequency domain, and therefore the nonlinear char-acteristics of the insulator cannot be processed, and theinverse Fourier transform is required in order to obtain thetemporal characteristics in surge analysis. In this study,frequency step is set to 4 MHz, and the calculation isperformed at 128 sample points. However, only half thedata are used for the inverse Fourier transform. Therefore,the time resolution is 1.4 ns.

When dealing with metal conductors, the metal sur-face can be represented by two approximation methods,based on triangular elements or thin wires, respectively.Here we use the thin-wire approximation of a perfect con-ductor because the conductor’s diameter is small comparedto its length, and the frequency dependence of the conduc-tor’s impedance (skin effect and frequency dependence ofresistance) is ignored. When dealing with the insulationcoating, too, the use of triangular elements would be diffi-cult because of limitations of computer memory and com-puting time, and hence we apply a method used previouslyfor the lightning channel model [7]. This approximationtechnique [8] is widely used for numerical electromagneticfield analysis based on the MoM. In particular, thin wiresare coated with a dielectric, and the phase variation ofconductor’s current is taken into account. To validate thismethod, we analyzed models of metal conductors and in-sulators in a twin-lead line (which corresponds to a zerotwist rate in twisted pair analysis), based on triangularelements and thin wires, and examined the magnitude andtime variation of the voltage and current. Good agreementwas confirmed. In the thin-wire approximation, the conduc-tor is represented by 1-cm segments. We use about 2000segments, though the number varies with twist rate.

A power source is connected to one end of a line, andthe other end is open. The surge impedance of the line canbe found from the voltage and current at the input terminal,and the propagation speed can be found from the time

variation of the waveform. This is an imitation of thereflection method used in the measurement of surge char-acteristics. The line current is found from the wire-segmentcurrents, and the variation of the current along the line canbe obtained as well. However, only the voltage and currentat the input and output terminals are required in order toobtain the propagation speed and surge impedance.

3. Surge Analysis of Twisted Pair in Free Space

We found the surge characteristics of a twisted pairin free space, with no ground and no other conductorsconnected directly or coupled via a potential difference.Since there are no other conductors, surge phenomenabetween the two wires are limited to differential mode. Weuse the MoM to analyze the relations between the twist rateand surge characteristics such as the surge impedance orpropagation speed.

3.1 Analysis based on method of moments

Figure 2 shows the source current found assuming aunit step voltage. With internal resistance of the powersource being Rs = 50 Ω, a negative current flows after thearrival of a wave reflected from the open end. On the otherhand, the current is nearly zero after the arrival of thereflected wave at 85 Ω. Due to the variation of the powersource resistance, the wave reflected from the open end isabsorbed on the power source side, and then remains nearlyzero, which corresponds to the surge impedance shown inFig. 3. When the twist rate is low, the surge characteristicis very similar to that of parallel wires, and the effect of thetwisted pair appears above 10 turns per meter.

The propagation speed is found from the time takenby the wave reflected from the open end to arrive at the inputend (when the current begins to decrease), and the linelength (4 m). The relationship between the propagationspeed and the twist rate is illustrated in Fig. 4. Here thepropagation speed is normalized to the speed of light c. Aswith the surge impedance, a decrease in speed appears whenthe twist rate exceeds 10 turns per meter. Twisting resultsin longer conductors, and hence there is an apparent de-crease in the propagation speed. However, the decrease in

Fig. 1. Twisted pair model in free space.

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speed caused by longer conductors should be about 85% at50 turns per meter, but Fig. 4 shows a much greater decline.

As suggested by Figs. 3 and 4, twisting decreasesboth the surge impedance and the propagation speed. Thisis because the inductance decreases due to the strong effectof magnetic flux cancellation caused by the current flowingin the opposite direction. In addition, the conductor be-comes longer, and the electrostatic capacitance between thewires per unit axial length increases apparently.

According to transmission line theory, the surge im-pedance and propagation speed are expressed as follows:

If only the inductance L decreased, then the propagationspeed would increase; however, due to the increase in the

electrostatic capacitance C, both the impedance and speeddecrease.

Insulation contributes to the electrostatic capacitancebetween the wires, which results in a decrease of the surgeimpedance and propagation speed. To evaluate this de-crease, we analyzed the surge characteristics by the thin-wire approximation, while ignoring the insulation in theanalytic model, as shown by the dotted lines in Figs. 3 and4. In the case of bare wires with a twist rate of 0 (that is,parallel conductors), the surge impedance of wires spaced4 mm apart is given by

where d is the distance between the two wires and a is thewire radius.

The value thus calculated is 166 Ω, which agrees wellwith the results of analysis.

As shown in Fig. 3, the surge impedance is about 145Ω for parallel insulated wires. The surge impedance ofinsulated conductors is given by

Here εe is the effective relative permittivity. The resultsobtained by the MoM indicate that the effective relativepermittivity is 1.3, which is smaller than the relative dielec-tric permittivity of the insulation (that is, 4). This is becausethe insulation occupies only part of the space between thetwo wires.

3.2 Comparison with experimental results

We performed experiments to validate the analyticalresults. Measurements were performed on a 4.5-m line ofVCTF vinyl cab-tire round cord (with the sheath removed)with a cross section of 2 mm2 and insulation thickness of

Fig. 2. Current response of twisted pair (50 turns/m). Fig. 4. Propagation speed versus twist rate.

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Fig. 3. Surge impedance versus twist rate.

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0.6 mm, used for distribution lines in accordance with JISC3306 specifications. This cord is close to the analyticmodel in terms of size, but is multi-wire rather than single-wire.

(1) Insulated parallel wires Figure 5 shows the volt-age and current at the input end in the case of a step voltagesource with an internal resistance of 25 Ω. The current wasmeasured by a current probe (Tektronix CT-2) and anoscilloscope (Tektronix TDS430A) using a Rogowski coilwith a coefficient of 1 V/A. The diagram shows a dampedoscillation that can be attributed to the measuring system,but the average voltage and current values of 12 V and 80mA, respectively, observed before the arrival of the re-flected wave from the open end suggest that the surgeimpedance of the line is 150 Ω. In addition, the propagationspeed is about 0.70c.

(2) Insulated twisted wires A twisted pair with alength of 4.5 m at a twist rate of 50 turns per meter wasfabricated using the same wires. The experimental resultsobtained with a step generator are shown in Fig. 6. Thevoltage and current values of 11 V and 120 mA, respec-tively, observed before the arrival of the reflected wave fromthe open end suggest that the surge impedance is 92 Ω.Propagation speed is about 0.53c.

We obtained the step wave response by applying theMoM to the experimental line, while assuming that theVVF cord had a relative dielectric permittivity of 3. Thewaveforms thus obtained are shown in Figs. 7 and 8, whichcorrespond to Figs. 5 and 6, respectively.

In the case of parallel wires, the surge impedance isabout 139 Ω, and the propagation speed is 0.79c. In case ofa twisted pair, the respective values are 92 Ω and 0.59c.Thus, the experiments and simulations give a difference ofabout 10%; better agreement might be achieved by using a

Fig. 6. Input voltage and current of insulated twistedpair (experimental results at 50 turns/m).

Fig. 5. Input voltage and current of insulated untwistedpair (experimental results).

Fig. 7. Voltage and current of insulated parallelconductors.

Fig. 8. Voltage and current of insulated twisted pair(simulation results at 50 turns/m).

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more accurate model (finer wire segments, patch approxi-mation of insulator, etc.). However, in this study, the MoMoffered rather good accuracy with a simple insulationmodel. This seems quite sufficient for the purpose of surgeanalysis.

4. Surge Characteristics of Twisted Pair in a MetalTube

It was shown above that surge analysis of a twistedpower can be performed by the MoM. However, we con-sidered only a single-phase line placed in free space. Inaddition, only differential mode was analyzed. These con-ditions seem appropriate for power distribution lines placedhigh above the ground, but twisted pairs used in low-voltagecontrol circuits or communications lines are often locatednear the ground level. Thus, we use the MoM to analyze thesurge characteristics of a single-phase twisted pair placedinside a metal tube.

The greatest advantage of numerical analysis is thatresults can be obtained under conditions that are difficult toset in experiments. Inside a metallic tube, complicatedoscillations occur due to multiple propagation modes, aswill be explained below. In experiments, voltage and cur-rent waveforms are likely to have induced noise superim-posed on them, and it is difficult to measure the voltage andcurrent accurately. On the other hand, by using the MoM,the surge characteristics can be analyzed under variousconditions, although due attention must be paid to the meshsize.

4.1 Analytic model

Considering that some distribution lines inside build-ings and equipment are run inside metal tubes, we analyzethe aforementioned twisted pair line in a metal tube. Weassume a power cable composed of a metal sheath with aradius of 4 mm and two phase conductors.

The conductors are modeled by wires with a radiusof 1 mm, coated with a 1-mm-thick insulator. The totallength of the twisted pair line is 4 m. The metal tube has aradius of 4 mm and an arbitrary thickness. In addition, theconductors have infinite conductivity, and the relative di-electric permittivity of the insulation is 4. The insulatedwires are twisted in a tight spiral.

The analytical model is shown in Fig. 9. The MoMmodel of two insulated wires is the same as that consideredabove for free space, and the surface of the metal tube isrepresented by triangular elements of arbitrary thickness.The cross section of the metal tube is approximated by anonagon, and a total of 2907 triangular elements are em-ployed.

In this case, we may assume differential mode withpropagation between two conductors, common mode with

propagation between the metal tube and the conductors, andTEM mode along the axis of the metal tube.

4.2 Analytic results for twisted pair in metaltube

(1) Differential mode Figure 10 shows the current ofa unit-step voltage source when a power source with aninternal resistance of 85 Ω is applied between the twoconductors. This voltage waveform is very similar to thatin free space (Fig. 2).

The current drops sharply due to the wave that arrivesat the power source after reflection from the open end. Thepropagation speed found from this drop in timing anddistance (line length) is shown in Fig. 11 (normalized to thespeed of light c). Because of the variation of the powersource resistance, the wave reflected from the open end isabsorbed on the power source side and then remains nearlyzero, which corresponds to the surge impedance shown inFig. 12. As is evident from the diagram, the surge imped-ance and propagation speed drop due to the effect of thetwisted pair when the twist rate exceeds 20 turns per meter.Compared to free space (without the metal tube), this effectappears at a higher twist rate. This can be explained by thefact that the electrostatic capacitance between the twisted

Fig. 9. Simulation model of twisted pair in metal tube.

Fig. 10. Current response of twisted pair in metal tubeunder differential mode (50 turns/m).

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wires and the metal tube is large, and is parallel to thecapacitance between the conductors. As a result, variationof the induction has a relatively weak influence. The effectof the metal tube is also observed in the surge impedanceas shown in Fig. 12. Namely, the surge impedance is onlyabout 60% as great as in Fig. 3. In addition, comparisonbetween Figs. 11 and 4 shows that the propagation speedalso decreases.

(2) Common mode Here the power source is con-nected between one of the wires and the metal tube, and aresistance of 10 kΩ is connected to the other end of the wirein order to obtain the voltage. The other wire is open at thepower source side, and a resistance of 10 kΩ is connectedto the other end in order to obtain the induced voltage

Figure 13 shows the terminal voltage of both conduc-tors when the internal resistance of the power source is 74Ω and the twist rate is 50 turns per meter. For both conduc-tors, the voltage surge arrives at about 18 ns. The propaga-

tion speed obtained from this timing and distance, andnormalized to the speed of light c, is shown in Fig. 14 as v1.In addition, the voltage rises to that of the power source atabout 28 ns. The propagation speed obtained from thistiming is shown in Fig. 14 as v2. The fast surge propagationspeed v1 remains nearly constant regardless of the twist rate,and the slow surge propagation speed v1 decreases withincreasing twist rate. This decrease occurs because theinductance of the twisted wire increases with the twist rate,that is, with the number of turns.

We assume that the initial surge in Fig. 13 is closelyrelated to the TEM wave propagating along the axis of themetal tube. This surge is not a current flowing in theconductor, but instead represents a mode of electromag-netic wave propagation. The surge propagation speed andimpedance of a coaxial cable with the diameters of the outerand inner conductor being D and d, respectively, are ex-pressed as follows:

Fig. 11. Propagation speed versus twist rate for twistedpair in metal tube under differential mode.

Fig. 12. Surge impedance versus twist rate for twistedpair in metal tube under differential mode.

Fig. 13. Voltage at energized conductor and inducedconductor in metallic tube (50 turns/m).

Fig. 14. Propagation speed versus twist rate in commonmode.

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As indicated by Fig. 14, the propagation speed v1 ofthe initial surge is about 0.74c at any twist rate. This isequivalent to a coaxial cable whose insulation has a relativedielectric permittivity of 1.82. However, a relative permit-tivity of 4 was assumed in the analysis. The reason for thedifference is that only part of the metal tube is filled withinsulation. The initial-step peak value in Fig. 13 is 0.68.Using a power source voltage of 1 V and an internalresistance of 74 Ω, calculation of the line’s surge impedancefor a fast surge gives about 39 Ω. This value corresponds tothe surge impedance of a coaxial cable with an inner con-ductor of 3.4 mm and an outer conductor 8 mm in diameter.Considering the two wires in terms of a coaxial cable, thewires should be equipotential, and no surge should occur.The terminal voltage between the two wires obtained by theMoM is shown in Fig. 15. Except for a small fluctuationthat can be attributed to numerical calculation errors, a fastsurge does not appear before 27 ns, and while only a slowsurge propagates. Electromagnetic surge analysis of barecoils in free space [9] too indicates electric field compo-nents propagating near the conductors.

Regarding the slow surge in Fig. 13, we found thesurge impedance as the internal resistance of the powersource at which the source voltage was reached. The rela-tionship between this surge resistance and twist rate isillustrated in Fig. 16. In addition, the impedance withrespect to the fast surge is also shown in the diagram. Theslow surge impedance increases with the twist rate due tothe effect of the coil inductance.

On the other hand, for the fast surge, the differencefrom the slow surge in propagation speed is small at twistrates below 40 turns per meter, as is evident from Fig. 14,

and the surge impedance becomes smaller, which may bedue to an inaccurate peak value in the buildup portion ofFig. 13. As the twist rate is increased, the fast surge imped-ance tends to increase similarly to the slow one, and remainsas small as the slow one at a twist rate of 0 (untwisted wires).

In Fig. 13, the voltage of the induced phase reachesabout 70% of the applied voltage for the fast surge, andabout 35% for the slow surge. In the former case, the voltagechanges little with the twist rate, but it increases with thetwist rate in the latter case.

4.3 Comparison between experiments andanalysis

In our analysis, the fast and slow surge componentsappear in twisted wires in a metal tube. We performedexperiments to confirm the existence of these components.A twisted pair model with a twist rate of 50 turns per meterwas fabricated using the same insulated wires as describedin Figs. 5 and 6. The wires were placed inside a copper tubewith an inner diameter of 6 mm, an outer diameter of 8 mm,and a length of 4 m. The vinyl insulation was flattened inorder to stuff the wires into the tube.

The terminal voltage waveforms corresponding toFig. 13 are shown in Fig. 17. In this case, however, both theinput and output ends of the twisted pair were terminatedby a matching resistance of 50 Ω. In addition, unlikeanalysis, we used not an ideal step voltage but one with a3-ns rise time, as shown in Fig. 5. The voltage rises in asimilar pattern for both conductors, and a damped oscilla-tion appears above 4 ns. After that, however, the voltage inthe energized conductor remains at a constant level, but itdrops to zero in the other conductor. A steplike variationdue to fast and slow components, as in Fig. 13, is observednear 4 ns, but is very small.

Fig. 16. Surge impedance versus twist rate in commonmode.

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Fig. 15. Voltage between two conductors in metal tube.

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Figure 18 presents simulation results obtained for thesame conditions as in the experiments. Here the voltagesource produced a double exponential waveform with awavefront of 3 ns and a wavetail of 100 µs. The propagationspeed of the slow surge in Fig. 18 is about 10% lower thanthat in Fig. 17. As regards the surge impedance, its valuefound from the voltage at the input end was 93 Ω (meas-ured) and 95 Ω (calculated) for the slow surge, and 50 Ω(measured) and 37 Ω (calculated) for the fast surge. Quitegood agreement was obtained for the slow surge, but thedifference was substantial for the fast surge. To explain thedifference, we may consider nonuniform twisting (due tomanual fabrication), excessively slow build-up of the inputpulses, disregard of line loss, and so on.

The appearance of the fast and slow surges validatesthe analytic method and the simulation model. However,

further investigation with an improved measuring systemand the MoM model is required.

5. Conclusions

We performed an electromagnetic field analysis of asingle-phase twisted pair by the method of moments. Wefound that the surge characteristics of the twisted pair arehardly different from those of parallel conductors so longas the twist rate is several turns per meter. However, as thetwist rate increases, the surge impedance decreases to sev-eral tenths. Measurement of the surge characteristics of atest line produced good agreement with the results obtainedby the method of moments. Thus, we confirmed that nu-merical electromagnetic field analysis based on the methodof moments is appropriate for surge analysis of a twistedpair.

In addition, we performed a surge analysis of atwisted pair placed in a metal tube. We found that the effectof twisting on the surge characteristics in differential modeshows up as a decrease in the surge impedance and propa-gation speed. On the other hand, in common mode, twopropagation modes exist. The influence of twist rate is weakfor the fast surge; in the slow surge, however, the surgeimpedance increases and the propagation speed decreaseswith increasing twist rate.

REFERENCES

1. Chamberlin K, Komisarek K, Sivaprasad K. Amethod of moments solution to the twisted-pair trans-mission line. IEEE Trans Electromagnetic Compati-bility 1995;37:121–126.

2. Hayakawa N, Okubo H. Partial discharge charac-teristics of inverter-fed motor coil samples under ACand surge voltage conditions. IEEE Electrical Insula-tion Magazine 2005;21:5–10.

3. Kato S, Elarbi R, Mochizuki A, Zaima E. Surgeresponse analysis of tower grounding by numericalelectromagnetic field analysis. Trans IEE Japan1995;115-B:970–977. (in Japanese)

4. Hasegawa I, Kato S, Hirai T, Takinami T, Okabe S.Analysis of electromagnetic field transient on branchfeeders by numerical electromagnetic field computa-tion. Trans IEE Japan 2002;122-A:664–669. (inJapanese)

5. Kato S. Surge analysis of single phase twisted pairline. 2005 National Convention Record IEE Japan,No. 7-102. (in Japanese)

6. Kato S. Common mode surge analysis of single phasetwisted pair line. Proc 2005 Annual Conference ofPower & Energy Society IEE Japan, No. 291. (inJapanese)

Fig. 17. Terminal voltage of twisted conductors inmetal tube (experimental results, 40 turns/m).

Fig. 18. Terminal voltage of twisted conductors inmetal tube (simulation results, 40 turns/m).

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7. Kato S, Takinami T, Hirai T, Narita T, Okabe S.Lightning channel model in numerical electromag-netic field simulation by numerical electromagneticfield analysis. Proc 2001 Annual Conference onPower & Energy Society IEE Japan, No. 374, p 273.(in Japanese)

8. Popovic BD. Analysis and synthesis of wire anten-nas. Wiley; 1991.

9. Elarbi R, Kato S, Mochizuki A, Zaima E. Transientelectric field in winding. 9th International High Volt-age Symposium, 83591-83594, 1995.

AUTHORS (from left to right)

Shohei Kato (member) graduated from Yokohama National University in 1971, completed the doctoral program at theUniversity of Tokyo in 1976, and joined the faculty of Toyo University as a lecturer. He was appointed a professor in 1993. Hisresearch interests are high-voltage measurement, numerical electromagnetic field analysis, electric discharge phenomena, andsurge analysis. He holds a D.Eng. degree.

MD. Solaiman (student member) received his B.Sc. degree in electrical and electronic engineering from BangladeshInstitute of Technology in 1996 and M.Sc. degree from Toyo University in 2006. Presently he is working toward his Ph.D.degree at Toyo University. He is a student member of IEE and the IEE Power Engineering Society of Japan.

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