Design and Experimental Study of a Current Transformer with a Stacked PCB Based on B-Dot

sensors

Article Design and Experimental Study of a Current Transformer with a Stacked PCB Based on B-Dot

Jingang Wang 1, Diancheng Si 1,*, Tian Tian 2 and Ran Ren 2 1 State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing 400044, China; [email protected] 2 Chongying Electric Power Design Institute, Chongying 401121, China; [email protected] (T.T.); [email protected] (R.R.) * Correspondence: [email protected] or [email protected]; Tel.: +86-155-2004-1152

Academic Editor: Vittorio M. N. Passaro Received: 15 January 2017; Accepted: 29 March 2017; Published: 10 April 2017

Abstract: An electronic current transformer with a B-dot sensor is proposed in this study. The B-dot sensor can realize the current measurement of the transmission line in a non-contact way in accordance with the principle of magnetic ﬁeld coupling. The multiple electrodes series-opposing structure is applied together with differential input structures and active integrating circuits, which can allow the sensor to operate in differential mode. Maxwell software is adopted to model and simulate the sensor. Optimization of the sensor structural parameters is conducted through ﬁnite-element simulation. A test platform is built to conduct the steady-state characteristic, on-off operation, and linearity tests for the designed current transformer under the power-frequency current. As shown by the test results, in contrast with traditional electromagnetic CT, the designed current transformer can achieve high accuracy and good phase-frequency; its linearity is also very good at different distances from the wire. The proposed current transformer provides a new method for electricity larceny prevention and on-line monitoring of the power grid in an electric system, thereby satisfying the development demands of the smart power grid.

Keywords: non-contact; magnetic ﬁeld coupling; current transformer; current monitoring

1. Introduction In a power system, the accurate measurement of power-frequency current is an important approach in ensuring the reliable operation of a power distribution network. The accuracy, convenience, and speed of current transformers play a signiﬁcant role in electric energy measurement, system monitoring and diagnosis, and power system fault analysis in smart power grids. Given that traditional electromagnetic current transformers (CTs) contain an iron core, their ferromagnetic effect tends to produce linear saturation and ferromagnetic resonance problems as well as insulation and volume and bandwidth response problems [1]. The method of current measurement by using Rogowski coil has been proposed [2,3], resulting in high measurement accuracy and good transient response. However, this kind of method based on the Rogowski coil targets high-frequency lightning current measurements, pulse current measurements, and partial discharge measurements on power cables, and the current loop to be measured must pass through the coil [4–13]. Current measurement methods based on the B-dot principle have been studied [14–16], resulting in high measurement accuracy and bandwidths reaching MHz. A B-dot coil is actually a special type of Rogowski coil that calculates the wire current via retroduction by sensing the change of magnetic ﬁeld generated by the current-carrying wire. Compared with a normal Rogowski coil, a B-dot coil does not need to pass through the coil [17]. Most studies based on the B-dot principle focus on high-frequency current measurement (MHz, kA level) by a sensor under the self-integral state, such as in a lightening

Sensors 2017, 17, 820; doi:10.3390/s17040820 www.mdpi.com/journal/sensors Sensors 2017, 17, 820 2 of 17

Sensorsfocus 2017on ,high-frequency17, 820 current measurement (MHz, kA level) by a sensor under the self-integral2 of 17 state, such as in a lightening current and plasma discharge pulse current [18–21]. In comparison, currentonly a andfew plasmastudies discharge have examined pulse current the performance [18–21]. In comparison, of B-dot sensors only a fewin measuring studies have currents examined in thedifferential performance mode. of B-dot sensors in measuring currents in differential mode. InIn thethe paper,paper, aa B-dotB-dot sensorsensor isis proposedproposed basedbased onon magneticmagnetic fieldfield coupling,coupling, andand aa non-contactnon-contact electronicelectronic currentcurrent transformer transformer with with stacked stacked printed printe circuitd circuit board board (PCB) (PCB) is proposed. is proposed. By analyzingBy analyzing the workingthe working principle principle and theand working the working mode mode of the B-dotof the sensorB-dot andsensor its influencingand its influencing factors, afactors, method a formethod differential for differential input and input multiple and electrodemultiple series-opposingelectrode series-opposing is introduced, is introduced, with the aim with of designingthe aim of adesigning transformer a transformer that can be operatedthat can inbe differential operated modein differential for measuring mode the for power measuring frequency the currentpower offrequency power system. current Theof power proposed system transformer. The proposed has the transformer following has advantages: the following good advantages: phase-frequency good characteristic,phase-frequency good characteristic, linearity, simple good structure, linearity, and simple easy installation. structure, Itand offers easy an installation. alternative for It electricityoffers an larcenyalternative prevention for electricity and on-line larceny monitoring prevention ofand a poweron-line gridmonitoring in an electric of a power system grid and in meetsan electric the developmentsystem and meets requirements the development of smart powerrequirements grids. of smart power grids.

2.2. PrinciplePrinciple ofof CurrentCurrent MeasurementMeasurement

2.1.2.1. PrincipalPrincipal forfor B-DotB-Dot TheThe B-dotB-dot probeprobe isis aa RogowskiRogowski coilcoil withwith aa specialspecial structure,structure, andand measuresmeasures thethe currentcurrent indirectlyindirectly byby measuringmeasuring thethe changingchanging magneticmagnetic ﬁeldfield builtbuilt byby thethe changingchanging currentcurrent [[17].17]. TheThe principleprinciple forfor thethe B-dotB-dot currentcurrent measurementmeasurement isis shownshown inin FigureFigure1 .1.

Figure 1. B-dot coil magnetic field induction. Figure 1. B-dot coil magnetic ﬁeld induction.

Here, r is the distance from the plane of the probe to the conductor, r0 is the radius of the probe coil, Here,S is ther is area the enclosed distance fromby the the probe plane coil, ofthe B is probe the magnetic to the conductor, inductionr 0intensityis the radius generated of the by probe the coil,currentS is at the a given area enclosed moment, by and the R probeis a pure coil, resistance.B is the magnetic induction intensity generated by the currentAccording at a given to moment, the law of and elecR tromagneticis a pure resistance. induction, when r0 << r, the induced probe voltage in the magneticAccording field to the is given law of by electromagnetic induction, when r0 << r, the induced probe voltage in the magnetic ﬁeld is given by dt () dit () et() dψ(t) 0µ0 dS di(t ) e(t) = −= − dS (1)(1) dtdtx22 rπr dtdt µ0 To make M = 0 dS, then M s 2πr dS To make 2r , then di(t) e(t) = −M (2) dt di() t et() M (2) In Equation (1), coil magnetic flux is ψ, S is the activedt area of the probe coil, and r is the distance from probe center to the electrified wire. From Equation (2), the output voltage of the probe is proportional to theIn differential Equation wire(1), coil current. magnetic Thus, flux by calculating is ψ, S is thethe integral active ofarea the of induced the probe electromotive coil, and forcer is the of thedistance probe, from the wire probe current center can to be the calculated. electrified wire. From Equation (2), the output voltage of the probe is proportional to the differential wire current. Thus, by calculating the integral of the 2.2.induced Sensor electromotive Design force of the probe, the wire current can be calculated. Based on the principle of B-dot coil current measurement, the PCB air-core coil sensor is designed. Its structure is shown in Figure2. The top layer coil is reversely connected in series with the corresponding bottom coil through vias, and a total of eight air-core coils are placed successively in a series to form a loop. Obviously, the electromotive force of the coils is superimposed in sequence.

SensorsSensors 2017 2017, 17, 17, 820, 820 3 of3 of17 17

2.2.2.2. Sensor Sensor Design Design BasedBased on on the the principle principle of of B-dot B-dot coil coil current current me measurement,asurement, the the PCB PCB air-core air-core coil coil sensor sensor is is designed.designed. Its Its structure structure is isshown shown in in Figure Figure 2. 2. The The top top layer layer coil coil is isreversely reversely connected connected in in series series with with thethe corresponding corresponding bottom bottom coil coil through through vias, vias, and and a atotal total of of eight eight air-core air-core coils coils are are placed placed Sensors 2017, 17, 820 3 of 17 successivelysuccessively in in a aseries series to to form form a aloop. loop. Obviou Obviously,sly, the the electromotive electromotive force force of of the the coils coils is is superimposedsuperimposed in in sequence. sequence. By By a pplyingapplying the the Rogowski Rogowski coil coil principl principle, e,the the returning returning turn turn coils coils can can eliminateByeliminate applying the the interference theinterference Rogowski magnetic magnetic coil principle, field field from from the the the returning external external turnenvironment environment coils can [22]. eliminate[22]. In In the the present the present interference paper, paper, themagneticthe idea idea of of fieldthe the returning fromreturning the externalturn turn design design environment is isadopted. adopted. [22 Hence,]. Hence, In the the presentthe d ,d d, ’d coils’ paper, coils are are the adopted adopted idea of as the as compensating returningcompensating turn coils.designcoils. When When is adopted. the the sensor sensor Hence, is is thesubject subjectd, d’ coilsto to extern areextern adoptedalal disturbance disturbance as compensating in in the the magnetic coils.magnetic When field, field, the the sensorthe d dcoil iscoil subject can can counteracttocounteract external the disturbancethe interference interference in theflux flux magnetic in in the the a, ab field,,, bc, coilsc coils the tod to coila acertain certain can counteract extent. extent. the interference flux in the a, b, c coils to a certain extent.

i(t) i(t) ′ b b′ b b

d? d ′ d? a a d a a′

c ′ c c c′

顶层顶层底层底层

Figure 2. Series-opposing structure of the printed circuit board (PCB) air-core coil. FigureFigure 2. 2.Series-opposing Series-opposing structure structure of of the the prin printedted circuit circuit board board (P (PCB)CB) air-core air-core coil. coil.

AsAs shown shown in in Figure Figure 3a,3 3a,a, an anan air-core air-coreair-core coil coilcoil is is isequivalent equivalent equivalent to toto N N N square square square coils. coils. coils. Here, Here,Here, r ris is isthe thethe distance distancedistance fromfrom the the point point on on the the coil coil to to the the wire, wire, a ais is the the width width of of the the outermos outermostoutermost layert layer of of the the air-core air-core coil, coil, c isc isthe the distancedistance between betweenbetween the thethe turns turns turns of of of the the coil, coil, dd isdis theisthe the distance distance distance from from from the the the outermost outermost outermost coil coil coil to theto to the center the center center of the of of the wire, the wire,andwire, andN andis N the N is isnumberthe the number number of turns of of turns ofturns a singleof of a asingle single air-core air-core air-core coil. co In coil. Figureil. In In Figure Figure2, the 2, distances 2, the the distances distances of each of of air-coreeach each air-core air-core coil to the wire are given by da, d , da c, bd respectively,c d where d is equalb to dc. c coilcoil to to the the wire wire are are given given by byb d d, ad, d, dbd, d, cd, d respectively,d respectively, where whereb d d isb isequal equal to to d d. c.

d d d+kcd+kc a a b-2kcb-2kc I I I c c I drdr r r c c i(ti)(t) i(it)(t) a a a-2kc a-2kc

(a()a a) asingle-core single-core coil coil (b()b calculation) calculation of of rectangular rectangular coil coil flux flux Figure 3. Principle of magnetic induction in a single-core coil. Figure 3. Principle of magnetic induction in a single-core coil.

AccordingAccording to to the the law law of of electromagnetic electromagnetic induction, induction, the the flux flux of of a asingle single turn turn coil coil in in Figure Figure 3b 3b is is According to the law of electromagnetic induction, the ﬂux of a single turn coil in Figure3b is givengiven by by given by ψ(t) = R B(t)dS S (3) R d+b−kc µ0i(t) = d+kc 2πr a − 2kc dr The total ﬂux of a single air-core coil is expressed as

n−1 n−1 µ0i(t) d+b−kc Φ(t) = ∑ ψ = ∑ 2π (a − 2kc) ln d+kc k=0 k=0 (4) dΦ(t) e(t) = − dt Sensors 2017, 17, 820 4 of 17

 ()tBtdS  () S (3) dbkc 0it() (2)akcdr dkc 2r The total flux of a single air-core coil is expressed as nn11 it() dbkc ()takc 0 (  2 )ln( ) kk002 dkc (4) dt() Sensors 2017, 17, 820 et() 4 of 17 dt

FromFrom thethe mathematical mathematical relationship, relationship, we knowwe know that whenthat whend = 0, thed = ﬂux 0, theΦ will flux reach Φ will the maximumreach the value,maximum so the value, induced so the voltage induced is the voltage maximum is the value.maximum value. InducedInduced electromotiveelectromotive forceforce ofof PCBPCB air-coreair-core coilcoil isis givengiven byby

et() eabcd () t e () t e () t e () t (5) e(t) = ea(t) + eb(t) + ec(t) − ed(t) (5)

n1 n−1 0it()  dabd kc a d kc a d kc et( )µ0i(t) ( a  2 kc ) ln(da − kc )  2ln( a + db − kc )  ln( a + dd − ) kc (6) e(t) = −  (a − 2kc) ln d a kc+ 2 ln d kc− ln d kc (6) ∑ k 0  −abd− +  + k=0 π da a kc db kc dd kc

2.3.2.3. Sensor under Self-IntegratingSelf-Integrating ModeMode

AsAs shown in Figure 44,, whenwhen thethe valuevalue of sample resistance RRa aisis small small and and 1/ 1/ωCω0C >>0 >> Ra, Rthena, then ic ≈ ≈ ≈ i0,c and0, i andR ≈ i2i,R andi 2when, and the when current thecurrent change changerate is larger, rate is namely, larger, namely,when di2 when/dt is quitedi2/dt large,is quite we have large, we have didi12 di MML1 ≈ L 2 (7)(7) dtdt dt ThenThen thethe samplesample resistanceresistance voltagevoltage isis expressedexpressed asas

MM u uiR≈02i R aa= iRi 1R (8)(8) 0 2 a LL 1 a Now,Now, thethe output output voltage voltage of theof the sample sample resistance resistan isce in directis in direct proportion proportion to the measuredto the measured current; here,current; coil here, self-inductance coil self-inductance L serves as L an serves integral. as an Hence, integral. the externalHence, the integrating external circuit integrating is not required,circuit is becausenot required, the circuit because itself achieves the circuit integral itself function. achieves Such aintegral status is calledfunction. self-integrating Such a status status [is11 ,13called,14]. Underself-integrating this status, status the sensor[11,13,14]. is suitable Under for this the stat measurementus, the sensor of high-frequencyis suitable for the current measurement rather than of ahigh-frequency low-frequency current current. rather than a low-frequency current.

i2 M i1 L r ic iR

e C0 Ra u0

Figure 4.4. Equivalent circuit ofof thethe sensorsensor underunder self-integratingself-integrating mode.mode.

2.4.2.4. Sensor under Differential ModeMode

a a 2 WhenWhen RRa isis largelarge ((RRa >> rr)) and and the variation ofof didi2/dtdt isis small small (relatively (relatively low-frequency), low-frequency), thethe PCBPCB air-coreair-core coilcoil equivalentequivalent circuitcircuit isis similarsimilar toto aa purepure resistanceresistance circuit.circuit. AtAt thisthis time,time, thethe sensorsensor outputoutput voltagevoltage isis givengiven byby di (t) u (t) ≈ −M 1 (9) 1 dt

At this moment, an integrating circuit must be connected to the sensor so that the output voltage and measured current can have a direct ratio with each other. This kind of working condition is called differential status or external integral status. In Figure5, the transfer function in the measurement link is expressed as

U1(s) Ms G1(s) = = (10) I1(s) LC s2 + L + rC s + r + 1 0 Ra 0 Ra Sensors 2017, 17, 820 5 of 17 Sensors 2017, 17, 820 5 of 17 di() t ut() M 1 1 di() t (9) dt1 ut1() M (9) dt At this moment, an integrating circuit must be connected to the sensor so that the output voltageAt thisand moment,measured an current integrating can havecircuit a directmust beratio connected with each to theother. sensor This so kind that ofthe working output conditionvoltage and is called measured differential current status can orhave external a direct integral ratio status. with each other. This kind of working conditionIn Figure is called 5, the differential transfer function status or in externalthe measurement integral status. link is expressed as In Figure 5, the transfer function in the measurement link is expressed as Us1  Ms Gs1  Us1  Ms Gs Is1  2 Lr (10) 1 LC00 s rC s 1 Is Lr 1  2 RRaa (10) LC00 s rC s 1 Sensors 2017, 17, 820  5 of 17 RRaa The active integral link is given by The active integral link is given by The active integral link is given by us0  R2 1 Gs2  (11) us0  R2 1 Gs us112 RRCs1 2 ( ) (11) u0us112s R RRCs2 11 G2(s) = = − (11) The transfer function of the whole systemu1(s is) givenR 1byR 2Cs + 1 The transfer function of the whole system is given by MR The transfer function of the whole system is given by 2 s MRR1 2 Gs G12  s G  s s MRR 2 (12) Gs G s G s  2 Lr1 s  12   RCs2011 LCsR1 rC 0 s (12) G(s) = G1(s)·G2(s) = −  Lr (12) 2 RRaa RCs2011  LCs rC 0 s  RCs + 1 LC s2 +L + rC s + r +1 2  0 RRRaaa 0 Ra  The transfer function is required to draw a Bode figure, as shown in Figure 6. The transfer function is required to draw a Bode figure, as shown in Figure 6. The transfer function is required to draw a Bode ﬁgure, as shown in Figure6.

R2 CR2 i 2 C u M i  0 i 2 L r i i R OPA u 1 M c R 1  0 i L r i R OPA 1 e ic R u1 1  C0 Ra e u1 C0 Ra

Figure 5. Equivalent circuit of the sensor with active integral. Figure 5. Equivalent circuit of the sensor withwith activeactive integral.integral.

LG dB 1 LG dB c 1 21  de 2 B / 21 d ec 1 2 20 / d 4  B 20lg 0/ d 1  d 20 RC2 M MR 4 B  20lg a 0/ MR 20lg d d RC2 a M MR B e 20lg RC2  Ra a r c MR 20lg  d Rra a e 20lg RC2  Ra  r c O 1 Rra  1  l    O RC1 h 1    2 LC0 l h  RC2 LC 0 Figure 6. Amplitude-frequency characteristic of a sensor with an active integrator (lg is a base— Figure 6. Amplitude-frequency characteristic of a sensor with an active integrator (lg is a base—10 10 logarithm). logarithm).Figure 6. Amplitude-frequency characteristic of a sensor with an active integrator (lg is a base—10 logarithm). Based on Ra >> rr, ,the the system’s system’s upper upper and and lower lower cut-off cut-off frequency frequency are are simplified simpliﬁed respectively respectively as as Based on Ra >> r, the system’s upper and lower cut-off frequency are simplified respectively as ( f ≈ 1 l 2πR2C √1 (13) fh ≈ 2π LC0

The frequency band is given by

1 1 ∆ f = fh − fl = √ − (14) 2π LC0 2πR2C

In Equation (13), the lower cut-off frequency of the system is determined by the feedback resistance R2 and the integral capacitance C, whereas the upper cut-off frequency is determined by the coil parameters. The system sensitivity is given by

MR 1 M S = |G(jω)| = 2 = (15) R1 R2C R1C Sensors 2017, 17, 820 6 of 17

 1  fl   2 RC2

 1 (13)  fh   2 LC0

The frequency band is given by 11 fffhl    (14) 2 LC0 2 RC2

MR2 1 M Sensors 2017, 17, 820 SGj  6(15) of 17 RRCRC12 1

In Equation (14), the sensitivity of the system can be improved by reducing R1, and the lower In Equation (14), the sensitivity of the system can be improved by reducing R1, and the lower cut-off frequency can be reduced by increasing the R2. Therefore, the integral link can be utilized to cut-off frequency can be reduced by increasing the R2. Therefore, the integral link can be utilized to properly adjust the cut-off frequency. Using the Bo Bodede function of MATLAB software to analyze the transfer functionfunction ofof thethe system, system, we we ﬁnd find that that the th uppere upper cut-off cut-off frequency frequency of the of sensorthe sensor can reach can reach MHz, MHz,and the and lower the cut-offlower frequencycut-off frequency is close tois 0close Hz. Therefore,to 0 Hz. Therefore, when the when sensor the is operating sensor is inoperating differential in differentialmode, it can mode, meet it the can requirements meet the requirements of low frequency of low current frequency measurement, current measurement, which is suitable which for is suitablemeasuring for andmeasuring monitoring and monitoring power frequency power current. frequency current.

2.5. Anti-Interference Anti-Interference Sensor Analysis Interference magnetic field ﬁeld can be decomposed into two components: parallel parallel to to the the PCB PCB board board and perpendicular to the PCB board.

2.5.1. Magnetic Magnetic Field Component Parallel to the PCB Board When the magneticmagnetic fieldfield isis parallelparallel to to the the PCB PCB board, board, as as shown shown in in Figure Figure7a, the7a, the direction direction of the of themagnetic magnetic field field is parallel is parallel to the to air-core the air-core coils, coils, and the and magnetic the magnetic flux passing flux pa throughssing through these coils these is coils zero; ishence, zero; nohence, induced no induced electromotive electromotive force is generated.force is generated.

b´ b´ d´ a ´ d´ a´ c´ c´

Interference magnetic field component vertical to PCB board

(a) Interference magnetic field component (b) Interference magnetic field component parallel to PCB board vertical to PCB board

FigureFigure 7. InfluenceInﬂuence of of the the external external interference interference magnetic field. ﬁeld.

2.5.2. Magnetic Field Component Vertical to the PCB Board

When the external magnetic field is a uniform magnetic field, the magnetic fluxes through the four air-core coils have the same size, and the induced electromotive forces are equal in size and opposite in direction. Due to the reverse series of the coils, the induced electromotive forces cancel each other out, as shown in Figure7b. Therefore, the air-core coils can resist the interference of the uniform magnetic field. The external interference current is taken as an example for this analysis. When the external magnetic field is not uniform, the current in the plane of the PCB board can produce a magnetic field perpendicular to the air-core coils. As shown in Figure8, the interference current i(t) is located on the side of the PCB board. The distances of interference currents to each air-core coil are da, db, dc and dd. The length of the outer coil is a, the width is b, the turn pitch is c. Sensors 2017, 17, 820 7 of 17

2.5.2. Magnetic Field Component Vertical to the PCB Board When the external magnetic field is a uniform magnetic field, the magnetic fluxes through the four air-core coils have the same size, and the induced electromotive forces are equal in size and opposite in direction. Due to the reverse series of the coils, the induced electromotive forces cancel each other out, as shown in Figure 7b. Therefore, the air-core coils can resist the interference of the uniform magnetic field. The external interference current is taken as an example for this analysis. When the external magnetic field is not uniform, the current in the plane of the PCB board can produce a magnetic field perpendicular to the air-core coils. As shown in Figure 8, the interference current i(t) is located on the side of the PCB board. The distances of interference currents to each air-core coil are da, db, dc andSensors dd2017. The, 17 length, 820 of the outer coil is a, the width is b, the turn pitch is c. 7 of 17

Figure 8. TheThe calculations calculations of interference magnetic.

According to Equation (3),

n−n11  it() d a kc ()takcµ0i0(t) ( 2 )ln( da a + a − kc ) Φa(t)a =  a − 2kc ln (16)(16) ∑k 0 2 rdkc+ k=0 2πr ada kc

n−1n1 µ0i0(itt()) dbdb+ aa kc− kc Φ (t)b =()takc (a − 2 2kc )ln(ln ) (17)(17) b ∑ + k=0k02π2r rdkcbdb kc

n−1 n1µ0i(t) dc + a − kc Φ (t) = 0it()a − 2kc ln dc  a kc (18) c()takc∑ (  2 )ln(+ ) c k=0 2πr dc kc (18) k 0 2 rdkcc  n−1 µ0i(t) dd + a − kc Φd(t) = n1 a − 2kc ln (19) ∑ 0it() dd  a+ kc k=0 2πr dd kc d ()takc (  2 )ln( ) (19) k 0 2rdkc The total flux generated by the interference current in thed air-core coil is The total flux generated by the interference current in the air-core coil is Φ(t) =()ttttt2 Φ 2[a t ()− Φb ()t − Φ ()c t + ()]Φd t (20) abcd (20) In Figure 99,, thethe magneticmagnetic fieldfield intensityintensity decaysdecays rapidlyrapidly alongalong thethe radialradial directiondirection ofof thethe wire,wire, and at a distance of 0.5 m from the wire, it decays to about 3%. The influence influence of the magnetic field field generated byby otherother wires wires can can be ignoredbe ignored when when the otherthe other wires wires are away are fromaway the from wire the to be wire measured to be measuredby more than by more 0.5 m. than The 0.5 transmission m. The transmission lines are usually lines are overhead usually linesoverhead in the lines operation in the ofoperation the power of thesystem, power and system, the wire and spacing the wire is much spacing larger is thanmuch 0.5 larger m. Therefore, than 0.5 them. measurementTherefore, the accuracy measurement can be accuracyachieved can as long be achieved as the distance as long is as maintained. the distance Once is maintained. the PCB air-core Once the coil PCB sensor air-core is applied coil sensor in more is appliedcomplexSensors 2017 in scenes,, more17, 820 complex the adjacent scenes, phase the interference adjacent phase must interference be considered. must be considered. 8 of 17

Figure 9. Magnetic ﬁeldfield curve aroundaround the wire inin 100100 A.A.

3. Design of the Current Transformer

3.1. Sensor Optimization Based on Finite Element Simulation The Ansoft Maxwell software is used to build the model of the conducting wire. The wire radius is set to 2.5 mm, and the current is set to 100 A. The variation curve of the magnetic field intensity around the wire is shown in Figure 9. As can be seen, the magnetic field intensity decays rapidly along the radial direction of the wire. At the distance of 0.5 m from the wire, it decays to about 3% of the maximum value. Therefore, when the current is measured by the sensor, the measuring points should be in the vicinity of the conductor region. According to Equation (7), major factors influencing the sensor mutual induction coefficient are coil length, distance between turns, and the number of turns. Coil length and number of turns can influence the PCB size, whereas the distance between turns can affect the frequency response of the sensor. Finite element in Ansoft Maxwell software is applied to optimize the above parameters and guarantee proper mutual induction coefficient. The simulation settings are as follows: connecting transmission wire of 5 m with current of 50 Hz and 100 A, wire radius of 2.5 mm, region size that is 300% of the calculation model, and border region calculation of 0 to simulate the situation wherein the magnetic field at the infinite point is 0, as shown in Figure 10. Based on the simulation, the model is further optimized and improved to obtain higher voltage output. The distribution of the magnetic field is shown in Figure 11. The calculation of the magnetic flux density of the sensor coil is performed by using the Maxwell software. Then, the output voltage of the sensor is calculated based on the flux data obtained. After considering all the parameters and the output voltage, a set of suitable parameters is selected to determine the structure of PCB air-core coil. The coil parameters are shown in Table 1.

Figure 10. Finite element calculation model.

Sensors 2017, 17, 820 8 of 17

Figure 9. Magnetic field curve around the wire in 100 A.

3. Design of the Current Transformer

3.1.Sensors Sensor2017, 17Optimization, 820 Based on Finite Element Simulation 8 of 17 The Ansoft Maxwell software is used to build the model of the conducting wire. The wire radius3. Design is set of theto 2.5 Current mm, and Transformer the current is set to 100 A. The variation curve of the magnetic field intensity around the wire is shown in Figure 9. As can be seen, the magnetic field intensity decays rapidly3.1. Sensor along Optimization the radial Based direction on Finite of the Element wire. Simulation At the distance of 0.5 m from the wire, it decays to aboutThe 3% Ansoft of the Maxwell maximum software value. is Therefore, used to build when the modelthe current of the conductingis measured wire. by Thethe wiresensor, radius the measuringis set to 2.5 points mm, and should the be current in the is vicinity set to 100 of the A. Theconductor variation region. curve of the magnetic field intensity aroundAccording the wire to is shownEquation in Figure(7), major9. As factors can be seen,influencing the magnetic the sensor field intensitymutual decaysinduction rapidly coefficient along arethe coil radial length, direction distance of the between wire. At turns, the distance and the ofnu 0.5mber m fromof turns. the wire,Coil length it decays and to number about 3% of ofturns the canmaximum influence value. the Therefore,PCB size, whereas when the the current distance is measured between byturns the can sensor, affect the the measuring frequency points response should of thebein sensor. the vicinity Finite ofelement the conductor in Ansoft region. Maxwell software is applied to optimize the above parameters and Accordingguarantee toproper Equation mutual (7), major induction factors coefficien influencingt. The the sensorsimulation mutual settings induction are coefficient as follows: are connectingcoil length, transmission distance between wire of turns, 5 m andwith the current number of 50 of Hz turns. and Coil100 A, length wire andradius number of 2.5 ofmm, turns region can sizeinfluence that theis 300% PCB size,of the whereas calculation the distance model, betweenand border turns region can affect calculation the frequency of 0 to response simulate of the situationsensor. Finite wherein element the magnetic in Ansoft field Maxwell at the software infinite ispoint applied is 0, to as optimize shown in the Figure above 10. parameters Based on andthe simulation,guarantee proper the model mutual is further induction optimized coefficient. and The improved simulation to obtain settings higher are as voltage follows: output. connecting The distributiontransmission of wire the magnetic of 5 m with field current is shown of 50 in Hz Figure and 10011. A, wire radius of 2.5 mm, region size that is 300%The of the calculation calculation of model, the magnetic and border flux region density calculation of the sensor of 0 to simulatecoil is performed the situation by wherein using the Maxwellmagnetic software. field at the Then, infinite the point output is 0, voltage as shown of inthe Figure sensor 10 .is Based calculated on the simulation,based on the the flux model data is obtained.further optimized After considering and improved all the to parameters obtain higher and voltage the output output. voltage, The distributiona set of suitable of the parameters magnetic isfield selected is shown to determine in Figure the11. structure of PCB air-core coil. The coil parameters are shown in Table 1.

Sensors 2017, 17, 820 Figure 10. Finite element calculation model. 9 of 17

d a

Figure 11. PCBPCB air-core air-core coil magnetic simulation calculation.

Table 1. Design parameters for single-layer PCB air-core coil structure. The calculation of the magnetic ﬂux density of the sensor coil is performed by using the Maxwell Number of Turns (n) Length (cm) Electrode Width (mil) Distance Between Electrodes (mil) software.Coil Then, the output voltage of the sensor is calculated based on the ﬂux data obtained. 4 × 25 38 8 8

Based on the parameters, the total magnetic flux of the coil in a, b, c, d, which are obtained from the simulation are −2.28 × 10−6, −2.32 × 10−6, −2.31 × 10−6 and −5.04 × 10−7 Wb, respectively. Thus, the total magnetic influx of the CT based on PCB planar-type air-core coil is given by

66 2 abcd     2  6.41  10  12.82  10 Wb

The mutual induction efficient is expressed as  M  . (21) I The output voltage of the whole transformer is given by di( t ) d 100sin(100 t ) et() M  M Amplitude: E  4.03 mV dt dt Finally, the PCB air-core coil sensor is fabricated by calculating the coil parameters [23]. The impedance of the sensor coil itself is measured by using Agilent 4294A (Agilent Technologies Inc., Santa Clara, CA, USA), as shown in Figure 12. Measurement is done within the scope of 40 Hz to 4 MHz. The induction and capacitance parameters have certain fluctuations. The result is shown in Table 2.

Figure 12. Parameter measurement of the PCB air-core coil sensor.

Sensors 2017, 17, 820 9 of 17

d Sensors 2017, 17, 820 a 9 of 17

c After considering all the parameters and the output voltage, a set of suitable parameters is selected to determine the structure of PCB air-core coil. The coil parameters are shown in Table1.

Table 1. Design parameters for single-layer PCB air-core coil structure. Figure 11. PCB air-core coil magnetic simulation calculation.

Number of Turns (n) Length (cm) Electrode Width (mil) Distance Between Electrodes (mil) Coil Table 1. Design parameters for single-layer PCB air-core coil structure. 4 × 25 38 8 8 Number of Turns (n) Length (cm) Electrode Width (mil) Distance Between Electrodes (mil) Coil 4 × 25 38 8 8 Based on the parameters, the total magnetic flux of the coil in a, b, c, d, which are obtained from −6 −6 −6 −7 the simulationBased on the are parameters,−2.28 × 10 the, −total2.32 magnetic× 10 , flux−2.31 of ×the10 coil andin a, −b,5.04 c, d, ×which10 areWb, obtained respectively. from Thus,the simulation the total magneticare −2.28 influx× 10−6, of −2.32 the CT× 10 based−6, −2.31 on PCB× 10− planar-type6 and −5.04 × air-core 10−7 Wb, coil respectively. is given by Thus, the total magnetic influx of the CT based on PCB planar-type air-core coil is given by −6 −6 Φ = 2 × ψa + ψ + ψc − ψ = 2 × 6.41 × 10 = 12.82 × 10 Wb b d 66 2 abcd     2  6.41  10  12.82  10 Wb The mutual induction efficient is expressed as The mutual induction efficient is expressed as  Φ M M= −. . (21) I I The output voltage of the whole transformertransformer isis givengiven byby

didi((t ) d 100sin(100d100 sin(100 tπ ) t) e(ett)() =−M · = − MM· AmplitudeAmplitude: : E = 4.03E mV 4.03 mV dt dtdt Finally, the PCB PCB air-core air-core coil coil sensor sensor is isfabricated fabricated by bycalculating calculating the thecoil coilparameters parameters [23]. [The23]. Theimpedance impedance of the of thesensor sensor coil coil itself itself is ismeasured measured by by using using Agilent Agilent 4294A 4294A ( (AgilentAgilent Technologies Technologies Inc., Inc., Santa Clara, CA, CA, USA), USA), as as shown shown in in Figure Figure 12. 12 .Meas Measurementurement is is done done within within the the scope scope of of 40 40 Hz Hz to to 4 4MHz. MHz. The The induction induction and and capacitance capacitance parameters parameters have have certain certain fluctuations. ﬂuctuations. The The result result is shown in Table2 2..

Figure 12. Parameter measurement of th thee PCB air-core coil sensor.

Table 2. Inner impedance parameter of PCB air-core coil.

Resistance Induction Fluctuating Deviation Capacitance Fluctuating Deviation PCB Air-core coil 25.75 Ω 149.36 µH 5 µH 37.2 pF 8 pF SensorsSensors 2017 2017, ,17 17, ,820 820 1010 of of 17 17

TableTable 2. 2. Inner Inner impedance impedance parameter parameter of of PCB PCB air-core air-core coil. coil.

ResistanceResistance InductionInduction Fluctuating Fluctuating Deviation Deviation Capacitance Capacitance Fluctuating Fluctuating Deviation Deviation PCBPCB Air-core Air-core coil coil 25.7525.75 Ω Ω 149.36149.36 μ μHH 55 μ μHH 37.2 37.2 pF pF 8 8pF pF Sensors 2017, 17, 820 10 of 17 3.2.3.2. Device Device Design Design for for the the Electronic Electronic Transformer Transformer 3.2. DeviceInIn considerationconsideration Design for the ofof Electronic thethe lowlow Transformeroutputoutput voltagevoltage ofof thethe single-blocksingle-block PCBPCB sensor,sensor, multi-blockmulti-block PCBsPCBs areare connectedInconnected consideration inin aa seriesseries of the toto low improveimprove output outputoutput voltage voltagvoltag of theee single-block[24].[24]. TheThe transformertransformer PCB sensor, structurestructure multi-block isis designeddesigned PCBs are asas connectedshownshown in in Figure inFigure a series 13, 13, and toand improve consists consists output of of the the sensor, voltagesensor, signal [signal24]. The acquisition acquisition transformer unit, unit, structure and and signal signal is designedprocessing processing as unit. shownunit. in FigureTheThe 13output output, and signal consistssignal of of ofthe the the sensor sensor sensor, is is signalcollected collected acquisition by by a a circuit circuit unit, with with and a a signal differential differential processing amplifying amplifying unit. structure structure [25,26].[25,26].The TheThe output differentialdifferential signal ofamplifieramplifier the sensor circuitcircuit is is collectedis mainlymainly bycomposedcomposed a circuit ofof with aa differentialdifferential a differential amplifieramplifier amplifying AD620AD620 structure(Analog(Analog [Devices25Devices,26]. The Inc.,Inc., differential Norwood,Norwood, amplifier MA,MA, USA)USA) circuit andand is mainlygaingain resistor.resistor. composed TheThe of AD620AD620 a differential performsperforms amplifier aa differentialdifferential AD620 (Analogoperationoperation Devices onon thethe Inc., outputoutput Norwood, signalsignal toto MA, removeremove USA) thethe and cocommon-mode gainmmon-mode resistor. signalsignal The AD620 withwith thethe performs samesame polaritypolarity a differential inin thethe operationinterferinginterfering on signal.signal. the output Simultaneously,Simultaneously, signal to remove ththee differentialdifferential the common-mode modemode signalsignal signal withwith oppositewithopposite the polaritysamepolarity polarity isis amplified,amplified, in the interferingandand thisthis differentialdifferential signal. Simultaneously, modemode signalsignal the isis a differentiala usefuluseful signalsignal mode wewe signal wantwant with toto obtain.obtain. opposite ThisThis polarity notnot onlyonly is amplified, increasesincreases and thethe thisoutputoutput differential of of the the transformer, transformer, mode signal but but is aalso also useful restrains restrains signal the wethe common wantcommon to obtain. mode mode Thisinterference,interference, not only such increasessuch as as high-frequency high-frequency the output of thenoisenoise transformer, signal. signal. but also restrains the common mode interference, such as high-frequency noise signal.

FigureFigureFigure 13.13. 13. AA A modelmodel model ofof of thethe the currentcurrent current transformertransformer transformer structure.structure. structure.

ForForFor thethe the integralintegral integral link, link, link, an an an active active active integrator integrator integrator with with with an an an inertial inertial inertial element element element acts acts acts as aas as circuit a a circuit circuit for restoringfor for restoring restoring the originalthethe originaloriginal signal. signal.signal. When WhenWhen measuring measuringmeasuring the current thethe currentcurrent of the high-voltage ofof thethe high-voltagehigh-voltage transmission transmissiontransmission line, as an line,line, electronic asas anan transformer,electronicelectronic transformer, transformer, introducing introducing introducing the AD module the the AD AD and module module WIFI technology and and WIFI WIFI technology istechnology convenient, is is convenient, convenient, after which after theafter datawhich which is sentthethe data todata the is is remotesent sent to to terminalthe the remote remote using terminal terminal WIFI using technology.using WIFI WIFI technology. technology.

4.4.4. TestTest Test ResultResult Result AnalysisAnalysis Analysis

4.1.4.1.4.1. TestTest Test PlatformPlatform Platform AAA currentcurrent current testtest test platformplatform platform isis is builtbuilt built toto to simulatesimulate simulate thethe the currentcurrent current measurementmeasurement measurement environmentenvironment environment ofof of thethe the powerpower power distributiondistributiondistribution network.network.network. TheTheThe structurestructurestructure ofofof thethethe platformplatfoplatformrm isisis shownshownshown ininin FigureFigureFigure 14 14.14.. BothBothBoth the thethe traditional traditionaltraditional electromagneticelectromagneticelectromagnetic currentcurrentcurrent transformertransformertransformer (CT,(CT,(CT, HL-3,HL-3,HL-3, 0.20.0.22 level)level)level) [[27],27[27],], andandand the thethe designed designeddesigned transformer transformertransformer areareare usedusedused at atat the thethe same samesame time timetime to toto conduct conductconduct current currentcurrent measurement measurmeasurementement for forfor the thethe power powerpower wire wirewire in the inin platform.thethe platform.platform. Here, Here,Here, the WIFIthethe WIFI WIFI technology technology technology is no is is longer no no longer longer needed needed needed because because because of the of oflow the the powerlow low power power output. output. output.

FrequencyFrequency PowerPower line line CT CT PowerPower Load Load PowerPower PCBPCB currentcurrent transformertransformer

SignalSignal acquisitionacquisition OscilloscopeOscilloscope circuitcircuit

Figure 14. Test platform structure. FigureFigure 14. 14. Test Test platform platform structure. structure.

The test platform is shown as Figures 15 and 16; it uses the program-controlled convertor (type: JJ98DD53D, Shandong Jingjiu Science and Technology Co., Ltd., Jinan, China) as the power supply and the high-power resistance is considered the load. The oscilloscope (Tektronix, DPO2014B, Sensors 2017, 17, 820 11 of 17 Sensors 2017, 17, 820 11 of 17 The test platform is shown as Figures 15 and 16; it uses the program-controlled convertor (type: The test platform is shown as Figures 15 and 16; it uses the program-controlled convertor (type: JJ98DD53D, Shandong Jingjiu Science and Technology Co., Ltd., Jinan, China) as the power supply JJ98DD53D,Sensors 2017, 17 Shandong, 820 Jingjiu Science and Technology Co., Ltd., Jinan, China) as the power 11supply of 17 and the high-power resistance is considered the load. The oscilloscope (Tektronix, DPO2014B, and the high-power resistance is considered the load. The oscilloscope (Tektronix, DPO2014B, Beaverton, OR, USA) is applied as a waveform display and measuring equipment. The CT is used Beaverton,Beaverton, OR, OR, USA) USA) is is applied applied as as a waveform displaydisplay andand measuringmeasuring equipment.equipment. The The CT CT is is used used as the measurement standard to realize the calibration of the designed transformer. The amplitude, asas the the measurement measurement standard standard to to realize realize the calibr calibrationation of thethe designeddesigned transformer.transformer. The The amplitude, amplitude, phase position, and waveform are compared to verify the performance of the designed transformer. phasephase position, position, and and waveform waveform are are compared toto verifyverify thethe performanceperformance of of the the designed designed transformer. transformer.

Variable frequency power supply Variable frequency power supply Oscilloscope Oscilloscope

HighHigh power power loadload

CT DCDC powerpower supply supply Sensor

FigureFigure 15. Test platform.

FigureFigureFigure 16. 16. SensorSensorSensor test physical picture. picture.picture.

4.2.4.2.4.2. Steady-State Steady-State Steady-State Performance Performance Performance TestTest Test OnOnOn the the the above above above test test test platform,platform, platform, thethe the sensorsensor sensor is is fixed ﬁxed aboveabove thethe wire,wire,wire, and andand the thethe vertical verticalvertical relative relative relative distance distance distance DD Dis is kept iskept kept invariant, invariant, invariant, as as as shownshown shown inin inFigureFigure Figure 14. 14 The. The current current output output isis adjustedadjusted is adjusted gradually.gradually. gradually. In In Inaddition, addition, addition, the the the secondary CT is connected to a resistive load for I-V conversion. The output waveform of the secondarysecondary CTCT isis connectedconnected toto aa resistiveresistive load for I-V conversion. TheThe outputoutput waveformwaveform ofof thethe designed transformer and the CT is displayed via oscilloscope, as shown in Figure 17. The oscilloscope designeddesigned transformertransformer andand thethe CTCT isis displayed via oscilloscope, asas shownshown inin FigureFigure 17.17. TheThe channel 1 shows the output waveform of the designed transformer, whereas channel 2 shows the CT oscilloscopeoscilloscope channel channel 11 showsshows thethe outputoutput waveform of the designeddesigned transformer,transformer, whereaswhereas channel channel 2 2 output waveform. showsshows the the CT CT output output waveform.waveform. In Figure 17, the output waveform of the transformer is basically the same as that of the CT, which indicates that the transformer has good steady-state response characteristics. If φ < 0, the phase of the designed transformer’s output voltage is delayed. As stipulated in IEC60044-8-2002 Standard [28], ratio error ε% and phase position difference φ are respectively deﬁned as KnUs − Ip ε% = × 100%, (22) Ip

φ = φs − φp (23)

Here, Us is the output voltage of the designed transformer, Kn is the rated transformation ratio, Ip is the current in the wire, φp is the phase position(a) of the designed transformer, and φs is the phase position of the standard CT. (a)

Sensors 2017, 17, 820 11 of 17

Variable frequency power supply Oscilloscope

High power load

CT DC power supply Sensor

Figure 15. Test platform.

Figure 16. Sensor test physical picture.

4.2. Steady-State Performance Test On the above test platform, the sensor is fixed above the wire, and the vertical relative distance D is kept invariant, as shown in Figure 14. The current output is adjusted gradually. In addition, the secondary CT is connected to a resistive load for I-V conversion. The output waveform of the designed transformer and the CT is displayed via oscilloscope, as shown in Figure 17. The Sensorsoscilloscope2017, 17 ,channel 820 1 shows the output waveform of the designed transformer, whereas channel12 of17 2 shows the CT output waveform.

Sensors 2017, 17, 820 (a) 12 of 17

(b)

(c)

Figure 17. The steady state waveform of the designed transformer and the current transformer (CT). (CT). (a) f = 50 50 Hz, Hz, II == 10 10 A, A, DD == 5 5 mm; mm; (b (b) )f f= =50 50 Hz, Hz, I =I =23 23 A, A, DD = =5 mm; 5 mm; (c) ( cf) =f 1=501 50Hz, Hz, I =I 9= A, 9 A,D =D 5= mm. 5 mm.

In Figure 17, the output waveform of the transformer is basically the same as that of the CT, First, we adjust the power to current changes between 0 A and 40 A; then, when the output current which indicates that the transformer has good steady-state response characteristics. If φ < 0, the changes, the amplitude and frequency of both the CT and the transformer output voltage are recorded, phase of the designed transformer’s output voltage is delayed. and the waveform is saved. Finally, the experimental data are collated, and the ratio difference and As stipulated in IEC60044-8-2002 Standard [28], ratio error ε% and phase position difference φ phase difference of the transformer are calculated. The results are shown in Table3. In this Table, I is are respectively defined as n the rated current, Im is the wire current, and Up is the output voltage of the transformer.

KUns I p  % 100% , (22) Table 3. Accuracy measurementI p for the current transformer (D = 1 mm).

◦ Measuring Point Im/A Up/mv ε%(±) φ/( )  s p . (23) 2% In 0.602 60.62 0.70 2.0 I Here, Us is the output5% voltagen of the 1.511designed transformer, 151.87 0.51 Kn is the rated 1.9 transformation ratio, 10% In 3.024 303.62 0.40 1.6 Ip is the current in the wire, φp is the phase position of the designed transformer, and φs is the phase 20% In 6.013 599.42 0.31 1.5 position of the standard CT.40% In 12.161 1208.29 0.64 1.5 First, we adjust the power60% In to current18.06 changes 1818.36between 0 0.68A and 40 A; 1.4 then, when the output current changes, the amplitude80% In and frequency24.120 of both 2419.32 the CT 0.30and the transformer 1.3 output voltage are recorded, and the waveform100% In is saved.30.060 Finally, the 3016.12 experimental 0.34 data are 1.3 collated, and the ratio 120% In 36.042 3625.12 0.58 1.2 difference and phase difference of the transformer are calculated. The results are shown in Table 3. In this Table, In is the rated current, Im is the wire current, and Up is the output voltage of the transformer.

Table 3. Accuracy measurement for the current transformer (D = 1 mm).

Measuring Point Im/A Up/mv ε %(±) φ/(°) 2% In 0.602 60.62 0.70 2.0 5% In 1.511 151.87 0.51 1.9 10% In 3.024 303.62 0.40 1.6 20% In 6.013 599.42 0.31 1.5 40% In 12.161 1208.29 0.64 1.5 60% In 18.06 1818.36 0.68 1.4 80% In 24.120 2419.32 0.30 1.3 100% In 30.060 3016.12 0.34 1.3 120% In 36.042 3625.12 0.58 1.2

Sensors 2017, 17, 820 13 of 17 Sensors 2017, 17, 820 13 of 17 The results above show the following: 1) InThe Table results 3, within above showthe rated the following:current range from 2% to 120%, the transformer ratio error ε% < (1) 0.9%,In Table and3 ,the within phase the difference rated current φ < range 3°. Thus, from the 2% todesigned 120%, the transformer transformer has ratio high error measurementε% < 0.9%, accuracy.and the phase difference φ < 3◦. Thus, the designed transformer has high measurement accuracy. 2)(2) InIn Figure Figure 17 17 and and Table Table 3,3, a a small error cancan bebe foundfound inin the the phase phase position, position, which which may may be be due due to to thethe parasitic parasitic capacitance capacitance between between the the coils coils and and the the resulting coilcoil inductance.inductance.

4.3.4.3. Linearity Linearity Test Test OnOn the the test test platform,platform, thethe linearity linearity performance performance is tested. is tested. The testThe is test done is viadone three via steps: three (1) steps: adjust 1) adjustthe distance the distance from thefrom sensor the sensor (PCB board) (PCB toboard) the wire, to the taking wire, 5 mmtaking as a5 unitmm (changeas a unit the (change height ofthe heightlifting of column lifting incolumn Figure in 16 Figure); (2) gradually 16); 2) gradually adjust the adjust output the current output from current 0 A to from 40 A; 0 andA to (3) 40 record A; and 3)the record data. the The data. experimental The experimental data when data the when distance the D distance is 5 mm D are is shown5 mm are in Tableshown4. in Table 4.

TableTable 4. 4. OutputOutput voltage voltage of of the transf transformerormer underunder differentdifferent currents currents ( D(D= = 5 5 mm, mm,f f= = 50 50 Hz). Hz).

Uc/mV Up/mV I/A Uc/mV Up/mV I/A Uc/mV Up/mV I/A Uc/mV Up/mV I/A 60 264 1.99 632 2880 22.01 121 56860 264 4.01 1.99 632 680 2880 312022.01 23.97 180 121860 568 6.02 4.01 680 744 3120 336023.97 26.01 226 1120180 860 7.98 6.02 744 808 3360 360026.01 27.99 292 1380226 1120 10.03 7.98 808 848 3600 384027.99 30.02 352 1600292 1380 12.01 10.03 848 920 3840 416030.02 32.02 396 1880352 1600 13.99 12.01 920 968 4160 432032.02 34.02 464 2160396 1880 16.03 13.99 968 1020 4320 456034.02 36.01 516 2360464 2160 17.97 16.03 1020 1080 4560 472036.01 37.99 580 2640516 2360 20.01 17.97 1080 1140 4720 504037.99 40.02 580 2640 20.01 1140 5040 40.02 In fitting the experimental data of transformer and CT, the horizontal axis represents the outputIn voltage fitting theof the experimental transformer, data whereas of transformer the vert andical CT, axis the represents horizontal the axis CT. represents The fitting the outputcurve is shownvoltage in of Figure the transformer, 18. The ratio whereas of the the linear vertical fitting axis curve represents is the thecorrection CT. The fittingfactor curveof the istransformer shown in error.Figure 18. The ratio of the linear fitting curve is the correction factor of the transformer error.

4.0 D=5mm D=10mm

4.0 3.0 /V p /V p U U 2.0 2.0

1.0

0.0 0.0 0.0 0.4U /V 0.8 1.2 0.00.40.81.2U /V c c (a) 5 mm (b) 10 mm 3.0 2.0 D=15mm D=20mm

1.5 2.0 /V /V p p U U 1.0

1.0 0.5

0.0 0.0 0.0 0.3 0.6U /V 0.9 1.2 0.0 0.4U /V 0.8 1.2 c c (c) 15 mm (d) 20 mm

Figure 18. Cont.

Sensors 2017, 17, 820 14 of 17 Sensors 2017, 17, 820 14 of 17

1.5 D=25mm D=30mm 1.0 /V 1.0 p U /V p

U 0.5 0.5

0.0 0.0 0.0 0.3 0.6U /V 0.9 1.2 0.00.40.81.2 c Uc/V (e) 25 mm (f) 30 mm

Figure 18. Curve fitting of current at different distances Figure 18. Curve fitting of current at different distances Moreover, linearity is tested when D has the values of 10, 15, 20, 25, and 30 mm. The data are shownMoreover, in Table 5. linearity is tested when D has the values of 10, 15, 20, 25, and 30 mm. The data are shown in Table5. Table 5. Transformer fitting data under various distances. Table 5. Transformer fitting data under various distances. Dstance/D Fitting Correction Coefficient Congruence Mean Error Maximum Phase Difference φ (°) Dstance/5 mmD Fitting Correction 4.39 Coefficient Congruence 0.0041 Mean Error Maximum Phase 1.5 Difference φ (◦) 10 mm 3.49 0.0027 2.0 5 mm15 mm 4.39 2.29 0.0041 0.0017 2.1 1.5 10 mm20 mm 3.49 1.59 0.0027 0.0026 2.5 2.0 15 mm25 mm 2.29 1.17 0.0017 0.0032 2.8 2.1 20 mm 1.59 0.0026 2.5 30 mm 0.86 0.0018 3.2 25 mm 1.17 0.0032 2.8 30 mm 0.86 0.0018 3.2 The test results show the following:

(1) AsThe shown test results in Figure show 18, the each following: point is extremely close to the fitting line, which indicates good linearity of the designed transformer. (2)(1) InAs Table shown 5, inthe Figure designed 18, each transformer point is extremelymaintains close a small to the phase fitting error line, whichat different indicates distances. good However,linearity ofas thecan designed be seen transformer. in Table 5, the first-order fitting correction factor with the CT is (2) graduallyIn Table 5reduced., the designed This finding transformer means maintainsthat when athe small distance phase from error the at designed different transformer distances. toHowever, the wire asbecomes can be seencloser, in Tablethe transformer5, the first-order linea fittingrity also correction improves. factor However, with the CT as isthe gradually distance increases,reduced. the This phase finding error means tends that to when enlarge. the distanceChances from are that the designedwhen the transformer distance is to closer, the wire the magneticbecomes induction closer, the line transformer through linearitythe sensor also is improves. denser, and However, then the as theimpact distance of interference increases, the on thephase environment error tends surrounding to enlarge. Chances the sensor are becomes that when re thelatively distance weak. is closer, When the the magnetic distance induction is far, the sensorline throughbecomes the more sensor susceptible. is denser, and then the impact of interference on the environment surrounding the sensor becomes relatively weak. When the distance is far, the sensor becomes 4.4. On-offmore Operation susceptible. Test 4.4.On On-Off the test Operation platform, Test the transient performance of the designed transformer is tested under the on-off state. The sensor is fixed above the wire, and the relative position remains constant. Under On the test platform, the transient performance of the designed transformer is tested under differentthe on-off current state. levels, The sensor the power is fixed is switched above the of wire,f suddenly and the so relative as to cut position off the remains current, constant. then the oscilloscopeUnder different is used current to record levels, the the waveform power is switchedresponse offof suddenlyvoltage attenuation so as to cut for off both the current, the designed then transformerthe oscilloscope and the is used CT. to record the waveform response of voltage attenuation for both the designed transformer and the CT. In Figure 19, the results show that the output waveform of the transformer closely follows the change of current, and its output voltage is reduced within a certain period to 10% of the peak before the fault in a very short period of time. Furthermore, the waveform no longer fluctuates. Therefore, the designed transformer can effectively reflect and track the changes in the current in the wire.

Sensors 2017, 17, 820 15 of 17

Sensors 2017, 17, 820 15 of 17 Sensors 2017, 17, 820 15 of 17

Figure 19. Switching transient waveform (I = 30 A, D = 5 mm, f = 50 Hz).

In Figure 19, the results show that the output waveform of the transformer closely follows the change of current, and its output voltage is reduced within a certain period to 10% of the peak before the fault in a very short period of time. Furthermore, the waveform no longer fluctuates. Therefore, the designedFigure 19.transformer Switching transientcan effectivel waveformy reflect (I = 30 and A, Dtrack = 5 mm, the fchanges = 50 Hz). in the current in the wire. Figure 19. Switching transient waveform (I = 30 A, D = 5 mm, f = 50 Hz). In Figure 19, the results show that the output waveform of the transformer closely follows the 4.5. Frequency Test 4.5.change Frequency of current, Test and its output voltage is reduced within a certain period to 10% of the peak beforeThisThis the experimentexperiment fault in a isveryis done done short to verify toperiod verify the of performance thetime. pe Furthermore,rformance of the transformerof the the waveform transformer under no different longerunder frequencies. fluctuates.different frequencies.AccordingTherefore, tothe According the designed analysis to transformer ofthe the analysis test data canof ofthe effectivel the test linearity dayta reflectofof the the linearityand transformer, track of the the thechanges transformer, smaller in distancethe the current smallerD has in distanceathe smaller wire. D phase has a error, smaller so thephase selected error, distance so the selected for testing distance is set tofor is 5testing mm. Theis set corresponding to is 5 mm. dataThe correspondinglinear ﬁtting is data shown linear in Figure fitting 20 is. shown in Figure 20. 4.5. Frequency Test 20 This experiment is done to verify the performance of the transformer45Hz under different 50Hz frequencies. According to the analysis of the test data of the linearity of the55Hz transformer, the smaller 60Hz distance D has a smaller15 phase error, so the selected distance for testing65Hz is set to is 5 mm. The corresponding data linear fitting is shown in Figure 20. 70Hz

/V 100Hz p U 20 10 45Hz 50Hz 55Hz 60Hz 15 65Hz 5 70Hz

/V 100Hz p U 10 0 0.2 0.4 0.6 0.8 1.0 1.2 U /V c 5 FigureFigure 20. 20. VoltageVoltage fitted ﬁtted curve curve under under different different frequencies frequencies

InIn Figure Figure 20,20, the the output output0 voltage voltage of of the the designed designed transformer transformer has has good good linearity linearity under under different different 0.2 0.4 0.6 0.8 1.0 1.2 frequencies.frequencies. ThisThis findingfinding means means that that the the transformer tranUsformer/V has good has frequencygood frequency response response under low under frequency. low c frequency.Limited by Limited the output by powerthe output and frequencypower and of frequency the power of supply, the power there issupply, no longer there a need is no to longer conduct a needmore to performance conduct more tests performanceFigure of the designed20. Voltage tests transformer fittedof the curve designed under at higher differenttransformer current frequencies andat higher higher current frequency. and higher frequency. 5. ConclusionsIn Figure 20, and the Future output Prospects voltage of the designed transformer has good linearity under different 5. Conclusion and Future Prospects frequencies.In this paper, This byfinding studying means the that relationship the tran betweensformer thehas currentgood frequency in the wire response and its surrounding under low magneticfrequency.In this field, paper,Limited a non-contactby by studying the output electronicthe relationshippower current and frequencybetween transformer the of currentthe based power in on the supply, the wire magnetic andthere its fieldis surrounding no couplinglonger a magneticprincipleneed to conduct isfield, proposed. a morenon-contact According performance electronic to the tests experimental current of the detransformersigned results, transformer comparedbased on withatthe higher magnetic the traditional current field and coupling CT, higher when principlethefrequency. designed is proposed. transformer According is used to to measure the experimental the power frequency results, compared current, the with results the demonstratetraditional CT, that whenit has verythe designed good steady-state transformer and transientis used characteristicsto measure the as power well as highfrequency accuracy. current, At the the same results time, 5. Conclusion and Future Prospects the results show that it has excellent linearity when the measuring distance is changing. In addition, the currentIn this transformerpaper, by studying has good the accuracy relationship and smallbetween phase the error. current in the wire and its surrounding magnetic field, a non-contact electronic current transformer based on the magnetic field coupling principle is proposed. According to the experimental results, compared with the traditional CT, when the designed transformer is used to measure the power frequency current, the results

Sensors 2017, 17, 820 16 of 17

In further studies, more performance tests of the designed transformer shall be carried out at higher currents and higher frequencies. To improve the anti-interference capacity of the sensor, research on phase compensation to the sensor will also be done, along with an investigation into the structural optimization of the sensor.

Acknowledgments: This work was supported by and the National Natural Science Foundations of China (Grant No. 51677009). Author Contributions: Jingang Wang is the head of the research group that conducted this study, and he proposed the improved structure of the sensor. Ran Ren and Tian Tian conducted experimental data collection. Diancheng Si mainly carried on the simulation of sensors, data analysis, the design of the hardware circuit, and the main writing of the manuscript. And all authors contributed to the writing and revision of the manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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