research article theoretical modeling and implementation

Research ArticleTheoretical Modeling and Implementation of Traveling WaveSensor Based on PCB Coils

Zewen Li Tuofu Deng Xiangjun Zeng Feng Deng and Lei Shu

Hunan Province Key Laboratory of Smart Grids Operation and Control School of Electrical and Information EngineeringChangsha University of Science and Technology Hunan 410076 China

Correspondence should be addressed to Zewen Li lzw0917163com

Received 10 October 2014 Accepted 24 April 2015

Academic Editor Aldo Minardo

Copyright copy 2015 Zewen Li et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Based on analyzing characteristics of Rogowski coil a new type of PCB traveling wave sensor with simple structure highlinearity and anti-interference ability is proposed The sensor has fine physical structure which can effectively resist externalelectromagnetic interference by anti-interference measurement In addition it can greatly improve mutual inductance based onsimple combinations Simulations show that the new PCB traveling wave sensor can validly extract and deliver traveling wavesignal and therefore realize fault location and protection accurately

1 Introduction

With the power system expanding the voltage class pro-moting and higher network security requirements accuratefault location becomes an important safeguard for fast fault-clearing and improving of the power system [1ndash5]The actiontime of travelling wave protection is much less than the lowerfrequency protection [6 7] The accuracy of travelling wavesignal detection directly influences the accuracy of travellingwave fault location and the reliability of travelling waveprotection So accurate detection of travelling wave signal hasbecome the direction of travelling wave technology [8ndash11]

Current transformer and inductive voltage transformerscan transfer the highest band signal and polarity of wave headwithout delaying [12 13] It can be used for fault travellingwave protection and positioning analysis based on travellingwave head But complicated software methods are necessaryto identify and extract the wave head effectively In CanadaBC Hydrorsquos 500KV transmission grid fault travelling wavepositioning system was installed The sensor of travellingwave is a small electric reactor in series with CVTrsquos groundelectrode to extract the voltage travelling wave signal [14 15]The system can detect all kinds of travelling wave signalseffectively But because the primary system wiring need bechanged when electric reactor is installed this does not meet

Chinarsquos power system operation standard so it is hard tobe applied and spread In [16 17] a dedicated travellingwave sensor based on Rogowski coil theory was studiedmuff-coupling on CVTrsquos ground wire Measure the currenttravelling wave at which ground through CVT can reflectthe line voltage travelling wave It has no direct electricconnectionwith primary equipment and has advantages suchas small delay errors good frequency response and highsensitivity But the induction coil of travelling wave sensorneed bewoundmanually or windingmachine It is not sowelldistributed on the secondary side winding The coefficientsof mutual induction and anti-interference are of big errorseven producing the same time Coilrsquos transient response ishard to remain the same and with low stability It is hard tomeet the demand of nanosecond synchronization accuracy intraveling-wave detection

In order to ensure the consistency for different coefficientof mutual inductance of traveling wave sensor to boost anti-interference of coil the primary conductor and secondarycoil are both printed on the PCB board Their locations wererelatively stable and coiled uniformly The consistency fordifferent coefficient of mutual inductance of traveling wavesensor and the magnetic coupling are enhanced A uniquespiral winding method is adopted to wind the secondary coilto resist outside magnetic interference

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 598194 7 pageshttpdxdoiorg1011552015598194

2 Journal of Sensors

2 Operating Characteristics of Rogowski Coil

Rogowski coil is a fairly mature current measuring deviceconsisting of a bandpass filter with ideal amplitude-fre-quency phase-frequency and transient characteristics whichhas been widely used to measure large current surge TakingRogowski coil tomeasure pulsed current themeasured signalis almost unrestricted Rogowski coils are nonsaturated underany circumstances thus being able to measure nanosecondrise time of current It also has nondirect electrical contactwith the primary side of the circuit Clearly the simpleimplementation of the first two requirements of the sensorand the detection delay is very short

Rogowski coil has two kinds of working status the statusof self-integration and differentiation [18] Rogowski coil ana-lyzed in this paper is under the status of self-integration Inequivalent circuit 1 there are equations as follows accordingto Kirchhoff rsquos current law

minus119872

1198891198941119889119905

= 119871

1198891198942119889119905

+ 1199031198942 + 119894119877119877119871 (1)

1198942 = 1198620119889119906

119888

119889119905

+

119906

119888

119877

119871

(2)

Assuming 11205961198620 ≫ 119877

119871 then 119894

119888asymp 0 at this time it can be

seen that 1198942 = 119894

119877 thus (1) could be shown as

minus119872

1198891198941119889119905

= 119871

1198891198942119889119905

+ (119903 +119877

119871) 1198942 (3)

When electric resistance 119903 + 119877

119871is small enough or the

change rate of current is large enough there is 120596119871 ≫ 119903 + 119877

119871

(3) can be changed into

minus119872

1198891198941119889119905

= 119871

1198891198942119889119905

(4)

Based on (4) it can be obtained that

1198942 =119872

119871

1198941 (5)

Substituting 119871 with 119873 sdot 119872 in (5) the following equationcan be obtained

1198942 =1119873

1198941 (6)

Therefore the output voltage is

119906

119871= 1198942 sdot 119877119871 =

119877

119871

119873

1198941 (7)

According to the above analysis only when the sampleresistance is small (typically a few ohms or less) or a largechange rate of current could formula (7) be set upThereforeRogowski coil operating under the status of self-integration issuitable for measuring rapid changes in short time travelingwave pulses

i2

L

r

ic

c0

iR

RL uL

e(t) = minusMdi1

dt

Figure 1 Equivalent circuit of magnetic level gauge measurementcircuit

In Figure 1 it could be known that the transfer function ofRogowski coil under the status of self-integration is as follows[19]

119867(119904) =

119880

119871 (119904)

1198682 (119878)

=

119872119904

11987111986201199042+ (119871119877

119871+ 1199031198620) sdot 119904 + (119903119877

119871+ 1)

(8)

The amplitude-frequency characteristic is1003816

1003816

1003816

1003816

119867 (119895120596)

1003816

1003816

1003816

1003816

=

119877

119871

119873 sdot

radic

(1 + 119903119877

1198711198620119871)

2+ (1198620119877119871120596 minus (119877

119871+ 119903) 119871120596)

2

(9)

The phase-frequency characteristic is

120593 (119895120596) = minus arctan1198620119877119871120596 minus 119877

119871+ 119903120596119871

1 + 119877

1198711198620119871

(10)

Using high-frequency small-signal analysis of parallelresonant circuit theory you can get the upper frequency andthe lower frequency

Upper frequency 119891119867=

121205871198771198711198620

Lower frequency 119891119871=

119877

119871+ 119903

2120587119871

(11)

According to the above analysis of upper frequency lowerfrequency and amplitude-frequency characteristic formulasthe device based on Rogowski coil can be designed to extractfault traveling wave

3 PCB Traveling Wave Sensor

31 Design Principle Based on the Rogowski coil principlePCB traveling wave sensor with simple structure high linear-ity and anti-interference ability is designed with the responsefrequency range of 10 kHzsim100MHz Its lower frequency is10 kHz and the power system frequency signals and 200 timesless harmonic signal can be filtered out So PCB travelingwave sensor also has a high-pass filter function which canbe directly used in extracting high-frequency traveling wavesignal in fault location and protection

Journal of Sensors 3

12

InputOutput

Figure 2 PCB traveling wave sensors schematic

Calculation principle of PCB traveling wave sensors isderived from the law of electromagnetic induction andAmperersquos law just as traditional Rogowski coil 119890(119905) =

minus119872(119889119868119889119905) 119872 = (1198731205830ℎ2120587)ln(119877119886119877119887) (119877119886 is coil diameter119877

119887is coil diameter and ℎ is coil height)PCB traveling wave sensor is designed by computer-

aided software and distributed evenly printed conductors onthe printed circuit board Printed wire replaces conventionalRogowski coil winding and the thickness of PCB Rogowskicoil replaces the traditional frame As shown in Figure 2 1stands for the primary coil of the sensor and 2 stands for thesecondary one Using digital processing technology in PCBtraveling wave sensor can ensure the coil equal area from thecraft winding evenly spread and accuracy in the productionIts production can be done automatically by simply inputtingthe data into computer numerical control machine tools withhigh production efficiency and coil parameters consistency

32 Design Scheme PCB traveling wave sensor has one layeror several layers Each layer has four subcoils or even alarger number of subcoils in the same plane (the size of eachrectangular subcoil is gradually and uniformly increased andsubcoils are distributed symmetrically and sequentially con-nected in series) Subcoils on different layers are connectedby vias Signal output from the first and last end-socketsconstitutes the secondary coil A traveling wave sensor PCBcoil tightly wound adjacent to each other on each half of thesubcoils constituting one turn or loop

The secondary coil gets a maximum induced current andthe winding directions of the primary coil and the secondarycoil of the subcoils are closely linked By theoretical analysisand experimental tests the wiring rules of primary and thesecondary coils are as follows

(1) The number of the secondary coils should be even

(2) The adjacent secondary coils on each layer should bestaggered in clockwise and counterclockwise turn

(3) To eliminate the interference subcoils of the sec-ondary coils are designed to be equilateral polygon

Clockwise Anticlockwise

Anticlockwise Clockwise

Figure 3 Trend of the secondary coil



Figure 4 Optimal path of the primary coil

(4) The secondary coil may be designed on one or morelayers and connected in series to increase the inducedcurrent

(5) The primary coil and the secondary coil should bematched along the optimal routing path

As shown in Figure 3 ldquoclockwiserdquo and ldquoanticlockwiserdquoshow the trendof the secondary coils Current direction in theprimary coil to make max induced current in the secondarycoil is shown by the ldquoarrowrdquo Obviously the optimal path ofthe primary coil winding is shown in Figure 4

Following the rules above we designed a PCB travelingwave sensor with the winding direction shown in Figure 5 Ithas the following characteristics

(1) The secondary coils were distributed on two layers ofthe PCB

(2) The subcoils of the secondary coils were formedhexagonal in order to reduce the reverse current inthe secondary coil around the corner

(3) The utilization rate of primary coil edges is 1622which can induce larger current in the secondary coil


Clockwise Anticlockwise Clockwise Anticlockwise

Anticlockwise Clockwise Anticlockwise Clockwise

Figure 5 PCB traveling wave sensors winding

Anticlockwise

1 2 3 4

5678

Interference 3

Clockwise Clockwise Anticlockwise

Anticlockwise AnticlockwiseClockwise Clockwise

Interference 2 Interference 1

Figure 6 Interference analysis

33 Interference Analysis Taking the sensor winding as anexample the anti-interference analysis is shown as follows

(1) When interference 1 is applied in a direction which isshown in Figure 6 induction coils 1 and 2 3 and 4 5and 6 and 7 and 8 generate electromotive force withequal amplitude but opposite direction The pairs offorces canceled each other out in series so that theinterference cannot affect the PCB production linewave sensor

(2) When interference 2 is applied in the direction shownin Figure 6 induction electromotive force coils 1 and8 2 and 7 3 and 6 and 4 and 5 produce equal andopposite direction thus they cancel each other out inseries which does not interfere with PCB travelingwave impact sensor

(3) When interference 3 is applied in any direction it canbe decomposed into interference 1 and interference 2in this condition there is no impact on PCB travelingwave sensor Perpendicular to the PCB interferencebecause of no hinge and with the secondary coil thesecondary coils will not be interfered with

The principle of proposed PCB production line wavesensor is of the same principle with conventional Rogowskicoil which are both winding uniformly on skeleton Thedifference of them is that the traditional type of wire usesenameled wire but the planar coil based on PCB uses holesto pass through the top and bottom surface of the printedcircuit board PCB boards are all multipanel The structure

1

2

3

d a

ci(t) e(t)

Figure 7 Equivalent figure of large current PCB air-core coil

can be manufactured easily with the current designing andmanufacturing process and the winding density is symmet-rical The estimate method of self-inductance coefficient andmutual inductance coefficient is the same as the traditionalRogowski coil but it is more with higher anti-interferenceability

4 Mutual Inductance Calculation

For example in Figure 2 a width of a conductor is 119863 andhas a certain thickness of the line and secondary spiralcoil centerline overlap therefore the flux linkage effect isequivalent to the design in Figure 7

As current 119894(119905) is flowing in the centerline of the spiral coilat position 1 current 119894(119905) in the electromotive force induced incoil 1 is 0 From literature [20] the current 119894(119905) on a conductorwith mutual inductance coefficient of spiral coil 2 can beexpressed as follows

119872 = int

119889+119886

119889

12058302120587119909

times 119886119889119909+int

119889+119886minus119888

119889+119888

12058302120587119909

times (119886 minus 2119888) 119889119909

+ sdot sdot sdot + int

119889+119886minus(119899minus1)119888

119889+(119899minus1)119888

12058302120587119909

times [119886 minus 2 (119899 minus 1) 119888] 119889119909

=

12058302120587119909

119899

sum

119896=1[119886 minus 2 (119896 minus 1) 119888] 119889 + 119886 minus (119896 minus 1) 119888

119889 + (119896 minus 1) 119888

(12)

In (12) the physical significance of 119886 119887 and 119888 is shownin Figure 7 119899 is the single spiral coil number and 1205830 is thepermeability of vacuum

So 119878(119889) and119872(119889) can be obtained

119878 (119889) = [119886 minus 2 (119896 minus 1) 119888] ln 119889 + 119886 minus (119896 minus 1) 119888119889 + (119896 minus 1) 119888

119872 (119889) =

12058302120587

119899

sum

119896=1119878 (119889)

(13)

Figure 7 double panel (positive and negative of all fourhelical coils) total mutual inductance is

1198721 = 2times [2119872(119889) minus119872 (119889+ 119886+ 119888)] (14)


Grounding capacitance Coupling capacitance Grounding capacitance

Primary side Secondary side

Coilinductance

C1

C1

C1

C1

C1

C3

C3

C3

C3

C3

C2

C2

C2

C2

C2

K

K

K

L

R

L

R

L

R

L2

R2

L2

R2

L2

R2

K2

K2

K2

Figure 8 PCB traveling wave sensor simulation model

RLC RLC RLC RLC RLC RLC RLC RLC RLC RLC

RLCRLCRLCRLCRLCRLCRLCRLCRLCRLC

Lr1

c1 K1

L1R1

C12

L2R2

K2c2

Lr2

Figure 9 ATP simulation model of PCB traveling wave sensors

In order to increase the coefficient of mutual inductancethe multiple double layers panel is connected in series andthe induction electromotive force at the end of the combinedcoil is equal to each panel output accumulation of inductionelectromotive force

119872 = 1198991198721 (15)

Assuming the geometries of coils of each layer are thesame their self-inductance 119871 and stray capacitance 119862 shouldmeet the following equation

119871 = 1198711 +1198712 + sdot sdot sdot 119871119899 = 119899119871

119899

1119862

=

11198621

+

11198622

+ sdot sdot sdot +

1119862

119899

=

119862

119899

1198621

(16)

The combined natural frequency of the coil can beobtained by (16) expression

119891 =

12120587radic119871119862

=

1

2120587radic1198991198711 (1198621119862119899)=

12120587radic11987111198621

(17)

It can be seen from expression (17) that although 119899 layerPCB panel after the combination of equivalent mutual induc-tance coefficient increases for 119899 times inherent frequency isconstant

5 Simulation Analysis

A PCB traveling wave sensor simulation model is shownin Figure 8 and the actual circuit simulation is shown inFigure 91198771 11987111198772 and 1198712 are resistor and inductor per unitfor high and low voltagewindings (including interturn induc-tance and mutual inductance) respectively Specific values ofthe parameters are chosen as follows 1198771 = 1198772 = 1Ω 1198711 =

29mH and 1198712 = 18mH 1198621 1198622 are grounding capacitance1198621 = 700 pF 1198622 = 300 pF 1198701 1198702 are vertical (interturn)equivalent capacitance for high and low voltage windingrespectively1198701 = 300 pF1198702 = 100 pF 1198711199031 1198711199032 are parasiticinductance ground for high and low voltage winding 1198711199031 =

50 pF 1198711199032 = 10 pF 11986212 are capacitance between windings11986212 = 22 pF Lumped parameter 119873 is the number of unitsconnected in cascade and the general value of119873 is between10 and 20 After repeat comparison 119873 is set to be 10 in themodel


6

4

2

0

minus2

00

10

02 04 06 08 10

(ms)

(kV

)

8

(file tr3pl4 x-var t) v XX0164-XX0012 v XX0004-XX0158 v XX0004

Step wave

Waveform of primary side

Waveform of secondary side

(a) When step wave simulation waveforms

Lightning wave

Waveform of primary sideWaveform of secondary side

1000

800

600

400

200

(V)

0

00

minus200

02 04 06 08 10

(ms)(file tranformer3pl4 x-var t) v XX0164-XX0012 v XX0004-XX0158 v XX0004

(b) When lightning wave simulation waveforms



2500

(V)

1600

700

minus200

minus1100

minus2000

00 05 10 15 20 25 30

(ms)(file tranformer3pl4 x-var t) v XX0164-XX0012 v XX0004-XX0158

(c) When sine wave (0∘) simulation waveforms



4

1

minus2

minus5

minus8

minus11

00 05 10 15 20 25 30

(ms)

(V)

minus14

(file tranformer3pl4 x-var t) v XX0164-XX0012 v XX0004-XX0158

(d) When sine wave (90∘) simulation waveforms

Figure 10 PCB traveling wave traveling wave propagation simulation waveform sensor

Figure 9 is the EMTP simulation model Figure 10 showsthe secondary waveforms of PCB traveling wave sensor whenthe primary inputs are respectively step wave lightningwave and sine wave with initial phase angle are 0∘ and 90∘

It could be seen from Figure 10 that the input signal andthe output signal occur almost simultaneously in the incep-tion of electrostatic induction The electrostatic inductionvoltage is related to the secondary load of voltage transformerImpact generates an oscillation signal in the second signaloutput circuit When the primary coil input wave is atright angles there is a larger secondary coil electrostaticinduction voltage and a smaller electric current throughthe electromagnetic induction voltage The free oscillationvoltage does not exist Secondary circuit is simulated underthe right angle wave signals the oscillation signal can begenerated and the main frequency of the oscillation is theinherent frequency of the secondary system

6 Conclusion

(1) A new type of PCB traveling wave sensor has beenproposed which has large mutual inductance stronganti-interference ability and highmeasurement accu-racy

(2) Based on calculations it has been proved that witha simple combination PCB traveling wave sensor isable to improve its mutual inductance effectively

(3) Simulation results have shown that the new PCB trav-eling wave sensor can effectively extract and delivertraveling wave signals thus realizing fault locationand protection accurately

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The paper was supported by the National Natural ScienceFund Project (51207013 51377012) Hunan Province Scienceand TechnologyMajor Project (2012FJ1003) Hunan ProvinceScience Fund for Distinguished Young Scholars (2015JJ1001)Hunan Province Department of Education Key Projects(14A002) and Hunan Province Universities IndustrializationCultivation Project of Scientific and Technological Achieve-ments (13CY008)

References

[1] S Nourizadeh M J Karimi A M Ranjbar and A ShiranildquoPower system stability assessment during restoration based onawide areameasurement systemrdquo IETGeneration Transmissionand Distribution vol 6 no 11 pp 1171ndash1179 2012


[2] D R Costianu N Arghira I Fagarasan and S St IliesculdquoA survey on power system protection in smart gridsrdquo UPBScientific Bulletin Series C Electrical Engineering vol 74 no 1pp 139ndash146 2012

[3] R Mardiana H Al Motairy and C Q Su ldquoGround fault loca-tion on a transmission line using high-frequency transient volt-agesrdquo IEEE Transactions on Power Delivery vol 26 no 2 pp1298ndash1299 2011

[4] M S Choi S J Lee D S Lim et al ldquoA new fault location algo-rithm using direct circuit analysis for distribution systemsrdquoIEEE Transactions on Power Delivery vol 19 no 1 pp 35ndash412004

[5] H Livani and C Y Evrenosoglu ldquoA fault classification andlocalization method for three-terminal circuits using machinelearningrdquo IEEE Transactions on Power Delivery vol 28 no 4pp 2282ndash2290 2013

[6] WWu Y Lv and B Zhang ldquoOn-line operating risk assessmentof hidden failures in protection systemrdquo Zhongguo DianjiGongcheng Xuebao vol 29 no 7 pp 78ndash83 2009

[7] H-B Jia H-B Qian and Y-L Qi ldquoTraveling-wave location forthe single phase grounding fault of distribution networkrdquoPowerSystem Protection and Control vol 40 no 23 pp 93ndash97 2012

[8] J Qin X Chen and J Zheng ldquoStudy on dispersion of travellingwave in transmission linerdquo Proceedings of the CSEE vol 19 no9 pp 27ndash35 1999

[9] M Gilany D K Ibrahim and E S Tag-Eldin ldquoTraveling-wave-based fault-location scheme for multiend-aged undergroundcable systemrdquo IEEE Transactions on Power Delivery vol 22 no1 pp 82ndash89 2007

[10] X Zeng Y Zhou Z Liu and G Lin ldquoThe sensor of traveling-wave for fault location in power systemsrdquo in Proceedingsof the International Conference on Power System Technology(POWERCON rsquo04) vol 2 pp 1518ndash1521 November 2004

[11] F Zhang Z-C Pan H-F Zhang W Cong and L-L Ma ldquoNewalgorithm based on traveling wave for location of single phaseto ground fault in tree type distribution networkrdquo Proceedingsof the CSEE vol 27 no 28 pp 46ndash52 2007

[12] X Liu K Guo and G Ye ldquoExperimental study on the impulse-voltage transmission characteristics of inductive voltage trans-formersrdquo Gaodianya Jishu vol 37 no 10 pp 2385ndash2390 2011

[13] S-N Luo Z-B Tian and X-C Zhao ldquoPerformance analysis ofair-core current transformerrdquo Proceedings of the Chinese Societyof Electrical Engineering vol 24 no 3 pp 108ndash113 2004

[14] L Wang and B Fang ldquoSimulations on transient characteristicsof 500 kV capacitor voltage transformerrdquo Gaodianya Jishu vol38 no 9 pp 2389ndash2396 2012

[15] T Yamada E Kurosaki N Yamamoto and M MatsumotoldquoDevelopment of simple coupling-capacitor voltage trans-former for GISrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting pp 269ndash274 February 2001

[16] C Xianghui Z Xiangjun M Hongjiang L Zewen and DFeng ldquoRogowski sensor for power grid traveling wave basedfault locationrdquo in Proceedings of the 9th International Conferenceon Developments in Power Systems Protection (DPSP rsquo08) pp438ndash443 Glasgow UK March 2008

[17] Q Chen H-B Li M-M Zhang and Y-B Liu ldquoDesign andcharacteristics of two Rogowski coils based on printed circuitboardrdquo IEEE Transactions on Instrumentation and Measure-ment vol 55 no 3 pp 939ndash943 2006

[18] E Abdi-Jalebi and R McMahon ldquoHigh-performance low-cost Rogowski transducers and accompanying circuitryrdquo IEEETransactions on Instrumentation and Measurement vol 56 no3 pp 753ndash759 2007

[19] X Chu X Zeng F Deng and L Li ldquoNovel PCB sensor basedon rogowski coil for transmission lines fault detectionrdquo in Pro-ceedings of the IEEE Power and Energy Society General Meeting(PES rsquo09) pp 1ndash4 IEEE Calgary Canada July 2009

[20] K-W Lee J-N Park S-H Yang et al ldquoGeometrical effects inthe current measurement by Rogowski sensorrdquo in Proceedingsof the International Symposium on Electrical InsulatingMaterials(ISEIM rsquo01) pp 419ndash422 2001

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Submit your manuscripts athttpwwwhindawicom

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DistributedSensor Networks



2 Operating Characteristics of Rogowski Coil

Rogowski coil is a fairly mature current measuring deviceconsisting of a bandpass filter with ideal amplitude-fre-quency phase-frequency and transient characteristics whichhas been widely used to measure large current surge TakingRogowski coil tomeasure pulsed current themeasured signalis almost unrestricted Rogowski coils are nonsaturated underany circumstances thus being able to measure nanosecondrise time of current It also has nondirect electrical contactwith the primary side of the circuit Clearly the simpleimplementation of the first two requirements of the sensorand the detection delay is very short

Rogowski coil has two kinds of working status the statusof self-integration and differentiation [18] Rogowski coil ana-lyzed in this paper is under the status of self-integration Inequivalent circuit 1 there are equations as follows accordingto Kirchhoff rsquos current law

minus119872

1198891198941119889119905

= 119871

1198891198942119889119905

+ 1199031198942 + 119894119877119877119871 (1)

1198942 = 1198620119889119906

119888

119889119905

+

119906

119888

119877

119871

(2)

Assuming 11205961198620 ≫ 119877

119871 then 119894

119888asymp 0 at this time it can be

seen that 1198942 = 119894

119877 thus (1) could be shown as

minus119872

1198891198941119889119905

= 119871

1198891198942119889119905

+ (119903 +119877

119871) 1198942 (3)

When electric resistance 119903 + 119877

119871is small enough or the

change rate of current is large enough there is 120596119871 ≫ 119903 + 119877

119871

(3) can be changed into

minus119872

1198891198941119889119905

= 119871

1198891198942119889119905

(4)

Based on (4) it can be obtained that

1198942 =119872

119871

1198941 (5)

Substituting 119871 with 119873 sdot 119872 in (5) the following equationcan be obtained

1198942 =1119873

1198941 (6)

Therefore the output voltage is

119906

119871= 1198942 sdot 119877119871 =

119877

119871

119873

1198941 (7)

According to the above analysis only when the sampleresistance is small (typically a few ohms or less) or a largechange rate of current could formula (7) be set upThereforeRogowski coil operating under the status of self-integration issuitable for measuring rapid changes in short time travelingwave pulses

i2

L

r

ic

c0

iR

RL uL

e(t) = minusMdi1

dt

Figure 1 Equivalent circuit of magnetic level gauge measurementcircuit

In Figure 1 it could be known that the transfer function ofRogowski coil under the status of self-integration is as follows[19]

119867(119904) =

119880

119871 (119904)

1198682 (119878)

=

119872119904

11987111986201199042+ (119871119877

119871+ 1199031198620) sdot 119904 + (119903119877

119871+ 1)

(8)

The amplitude-frequency characteristic is1003816

1003816

1003816

1003816

119867 (119895120596)

1003816

1003816

1003816

1003816

=

119877

119871

119873 sdot

radic

(1 + 119903119877

1198711198620119871)

2+ (1198620119877119871120596 minus (119877

119871+ 119903) 119871120596)

2

(9)

The phase-frequency characteristic is

120593 (119895120596) = minus arctan1198620119877119871120596 minus 119877

119871+ 119903120596119871

1 + 119877

1198711198620119871

(10)

Using high-frequency small-signal analysis of parallelresonant circuit theory you can get the upper frequency andthe lower frequency

Upper frequency 119891119867=

121205871198771198711198620

Lower frequency 119891119871=

119877

119871+ 119903

2120587119871

(11)

According to the above analysis of upper frequency lowerfrequency and amplitude-frequency characteristic formulasthe device based on Rogowski coil can be designed to extractfault traveling wave

3 PCB Traveling Wave Sensor

31 Design Principle Based on the Rogowski coil principlePCB traveling wave sensor with simple structure high linear-ity and anti-interference ability is designed with the responsefrequency range of 10 kHzsim100MHz Its lower frequency is10 kHz and the power system frequency signals and 200 timesless harmonic signal can be filtered out So PCB travelingwave sensor also has a high-pass filter function which canbe directly used in extracting high-frequency traveling wavesignal in fault location and protection


12

InputOutput




























Anticlockwise

1 2 3 4

5678

Interference 3










1

2

3

d a

ci(t) e(t)






119872 = int

119889+119886

119889

12058302120587119909

times 119886119889119909+int

119889+119886minus119888

119889+119888

12058302120587119909

times (119886 minus 2119888) 119889119909


119889+119886minus(119899minus1)119888

119889+(119899minus1)119888

12058302120587119909


=

12058302120587119909

119899

sum


119889 + (119896 minus 1) 119888

(12)




119872 (119889) =

12058302120587

119899

sum

119896=1119878 (119889)

(13)


1198721 = 2times [2119872(119889) minus119872 (119889+ 119886+ 119888)] (14)




Coilinductance

C1

C1

C1

C1

C1

C3

C3

C3

C3

C3

C2

C2

C2

C2

C2

K

K

K

L

R

L

R

L

R

L2

R2

L2

R2

L2

R2

K2

K2

K2




Lr1

c1 K1

L1R1

C12

L2R2

K2c2

Lr2



119872 = 1198991198721 (15)


119871 = 1198711 +1198712 + sdot sdot sdot 119871119899 = 119899119871

119899

1119862

=

11198621

+

11198622

+ sdot sdot sdot +

1119862

119899

=

119862

119899

1198621

(16)


119891 =

12120587radic119871119862

=

1

2120587radic1198991198711 (1198621119862119899)=

12120587radic11987111198621

(17)







6

4

2

0

minus2

00

10

02 04 06 08 10

(ms)

(kV

)

8


Step wave




Lightning wave


1000

800

600

400

200

(V)

0

00

minus200

02 04 06 08 10





2500

(V)

1600

700

minus200

minus1100

minus2000

00 05 10 15 20 25 30





4

1

minus2

minus5

minus8

minus11

00 05 10 15 20 25 30

(ms)

(V)

minus14






6 Conclusion






Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










12

InputOutput




























Anticlockwise

1 2 3 4

5678

Interference 3










1

2

3

d a

ci(t) e(t)






119872 = int

119889+119886

119889

12058302120587119909

times 119886119889119909+int

119889+119886minus119888

119889+119888

12058302120587119909

times (119886 minus 2119888) 119889119909


119889+119886minus(119899minus1)119888

119889+(119899minus1)119888

12058302120587119909


=

12058302120587119909

119899

sum


119889 + (119896 minus 1) 119888

(12)




119872 (119889) =

12058302120587

119899

sum

119896=1119878 (119889)

(13)


1198721 = 2times [2119872(119889) minus119872 (119889+ 119886+ 119888)] (14)




Coilinductance

C1

C1

C1

C1

C1

C3

C3

C3

C3

C3

C2

C2

C2

C2

C2

K

K

K

L

R

L

R

L

R

L2

R2

L2

R2

L2

R2

K2

K2

K2




Lr1

c1 K1

L1R1

C12

L2R2

K2c2

Lr2



119872 = 1198991198721 (15)


119871 = 1198711 +1198712 + sdot sdot sdot 119871119899 = 119899119871

119899

1119862

=

11198621

+

11198622

+ sdot sdot sdot +

1119862

119899

=

119862

119899

1198621

(16)


119891 =

12120587radic119871119862

=

1

2120587radic1198991198711 (1198621119862119899)=

12120587radic11987111198621

(17)







6

4

2

0

minus2

00

10

02 04 06 08 10

(ms)

(kV

)

8


Step wave




Lightning wave


1000

800

600

400

200

(V)

0

00

minus200

02 04 06 08 10





2500

(V)

1600

700

minus200

minus1100

minus2000

00 05 10 15 20 25 30





4

1

minus2

minus5

minus8

minus11

00 05 10 15 20 25 30

(ms)

(V)

minus14






6 Conclusion






Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Anticlockwise

1 2 3 4

5678

Interference 3










1

2

3

d a

ci(t) e(t)






119872 = int

119889+119886

119889

12058302120587119909

times 119886119889119909+int

119889+119886minus119888

119889+119888

12058302120587119909

times (119886 minus 2119888) 119889119909


119889+119886minus(119899minus1)119888

119889+(119899minus1)119888

12058302120587119909


=

12058302120587119909

119899

sum


119889 + (119896 minus 1) 119888

(12)




119872 (119889) =

12058302120587

119899

sum

119896=1119878 (119889)

(13)


1198721 = 2times [2119872(119889) minus119872 (119889+ 119886+ 119888)] (14)




Coilinductance

C1

C1

C1

C1

C1

C3

C3

C3

C3

C3

C2

C2

C2

C2

C2

K

K

K

L

R

L

R

L

R

L2

R2

L2

R2

L2

R2

K2

K2

K2




Lr1

c1 K1

L1R1

C12

L2R2

K2c2

Lr2



119872 = 1198991198721 (15)


119871 = 1198711 +1198712 + sdot sdot sdot 119871119899 = 119899119871

119899

1119862

=

11198621

+

11198622

+ sdot sdot sdot +

1119862

119899

=

119862

119899

1198621

(16)


119891 =

12120587radic119871119862

=

1

2120587radic1198991198711 (1198621119862119899)=

12120587radic11987111198621

(17)







6

4

2

0

minus2

00

10

02 04 06 08 10

(ms)

(kV

)

8


Step wave




Lightning wave


1000

800

600

400

200

(V)

0

00

minus200

02 04 06 08 10





2500

(V)

1600

700

minus200

minus1100

minus2000

00 05 10 15 20 25 30





4

1

minus2

minus5

minus8

minus11

00 05 10 15 20 25 30

(ms)

(V)

minus14






6 Conclusion






Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Coilinductance

C1

C1

C1

C1

C1

C3

C3

C3

C3

C3

C2

C2

C2

C2

C2

K

K

K

L

R

L

R

L

R

L2

R2

L2

R2

L2

R2

K2

K2

K2




Lr1

c1 K1

L1R1

C12

L2R2

K2c2

Lr2



119872 = 1198991198721 (15)


119871 = 1198711 +1198712 + sdot sdot sdot 119871119899 = 119899119871

119899

1119862

=

11198621

+

11198622

+ sdot sdot sdot +

1119862

119899

=

119862

119899

1198621

(16)


119891 =

12120587radic119871119862

=

1

2120587radic1198991198711 (1198621119862119899)=

12120587radic11987111198621

(17)







6

4

2

0

minus2

00

10

02 04 06 08 10

(ms)

(kV

)

8


Step wave




Lightning wave


1000

800

600

400

200

(V)

0

00

minus200

02 04 06 08 10





2500

(V)

1600

700

minus200

minus1100

minus2000

00 05 10 15 20 25 30





4

1

minus2

minus5

minus8

minus11

00 05 10 15 20 25 30

(ms)

(V)

minus14






6 Conclusion






Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










6

4

2

0

minus2

00

10

02 04 06 08 10

(ms)

(kV

)

8


Step wave




Lightning wave


1000

800

600

400

200

(V)

0

00

minus200

02 04 06 08 10





2500

(V)

1600

700

minus200

minus1100

minus2000

00 05 10 15 20 25 30





4

1

minus2

minus5

minus8

minus11

00 05 10 15 20 25 30

(ms)

(V)

minus14






6 Conclusion






Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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