th Internationa Symposium Topica Probems in the Fied of Eectrica and Power Engineering Pärnu, Estonia, January -5, Magnetic fied sensor coi in fast transient measurement appication Lauri Kütt, Jaan Järvik Tainn University of Technoogy auri.kutt@ttu.ee, jaanvik@cc.ttu.ee Abstract Induction coi sensor is basicay the simpest magnetic fied senor. Some researchers have estabished that it woud be one of the most perfect sensors avaiabe [], as it provides exceent sensitivity, bandwih, owest noise etc. characteristics. Furthermore, it provides the possibiity to measure high-frequency currents from a stance, in a non-intrusive way. This said, it is reasonabe to assume its characteristics are prefect for measurements of current traveing waves on the power ines, for the appication of faut ocating. However, it turns out that in this case one woud need to take into use a much more compicated mode of the current sensor coi. Keywords Magnetic fied sensor, fast transients, partia scharge measurement. Introduction Due to its simpest construction and trivia operating principes magnetic fied sensor coi has been known and used for over a hundred years. To make a magnetic coi sensor, one woud need to make a coi consisting of N turns of wire. Operating principe is based on the Faraday s aw dψ e= where e eectromotive force; Ψ fux inkage; t time. This means that the eectromotive force depends on the rate of change of the fux inkage acquired by the coi oop area. Fux inkage is determined the coi fux and number of turns in the coi ψ = w Φ where w number of turns in sensor coi; Φ magnetic fux. Magnetic fux is determined by magnetic fux density and the coi area Φ = B A where B magnetic fux density; A magnetic sensor coi area. Magnetic fux density is reated to magnetic fied strength B=µ H where µ reative magnetic permeabiity; H magnetic fied strength. Obviousy, strength of magnetic fied is reative to actua current vaue H I where I current. As the mechanism of the magnetic fied source is not determined, the more precise magnetic fied strength formua wi not be estabished. Taking into account the above, magnetic sensor coi output can be written as di e Awµ This formua in essence hods a the factors that make up the magnetic sensor coi sensitivity. First of a, the arger the area of the coi, the arger the output. More turns in coi means more output. Higher reative magnetic permeabiity eads to greater output. Most important in our appication woud be the rate of current change of the observed appication. Appication of current measurement Every wire, which has some current passing through it, has aso a magnetic fied around it. As The magnetic fied ines are ocated perpencuar to the wire, the maximum fux inkage (i.e coi coud hod maximum numbers of magnetic fied ines) can be achieved when sensing coi is aso perpencuar to the wire. This is foowed by a sma step, in order to measure current in a wire the magnetic sensor shoud be paced in the vicinity of the wire to be measured (see fig. ). In case of DC, magnetic fied density near the wire can be cacuated as I B= µ a π where stance from wire; a frame ength; µ magnetic constant 4*-7 H/m. 7
Figure. Appication of magnetic oop for measurement of current aong a wire. B is magnetic fux density created by the current passing through the wire. In order to assess the magnetic fux acquired by the coi, the magnetic fux shoud be integrated to make up the area of the Frame µ Φ= π I µ ai ad = n π This presents the reation between current, coi area and its stance from wire the current is observed on. Taking into account that the geometrica mensions shoud be constant in time, votage output of the magnetic coi can be expressed by dψ wdφ wµ a e= = = n π From the fundamentas there is a we-known reation between eectromotive force, inductance and current e= L In this way, one coud aso use mutua inductance to express the reation between coi output EMF and current in a wire [] e= M wµ a M = n π where M mutua inductance between wire and magnetic oop. This kind of current measurement system has many benefits, aowing non-intrusive measurement with exceent and gavanic separation from the measured circuit. Latter woud make it perfect for the measurement of high-votage circuits. On the downside it coud be stated that it measures rather we the high frequency eectric currents ony, as its sensitivity is rather ow on ower frequencies. For measuring the traveing waves from short-circuits and partia scharges, this type of sensor seems rather perfect. Sensor characteristics For testing the performance of the sensor, a specia coi was buit. Criteria for buing the coi were foowing: ) Coi system had to have wide bandwih to detect the signas with smaest durations and highest frequencies. ) Coi had to provide as high output as possibe for the high-frequency signas. For the first criterion, one shoud estabish a reation between the bandwih of the coi and its physica buid. As it turns out from the eectric fied theory appications, there is a quite good reation between coi eectrica characteristics and its mensions. A magnetic coi equivaent circuit can be described in the simpest way with a capacitor, inductor and a resistor [3] (see fig. ). Figure. Equivaent circuit of a coi sensor Inductance is the coi inductance L, one of the most natura properties of a coi. Cacuation on exact inductance vaue is very compex, thus many work on the approximate formuas has been done. One of the most we-known and proven is work by Wheeer [4] and Wheeers formua for a short coi woud be = r r L µ w r,48 n + π +, 5arcsh π b b where r coi raus; b coi ength. Second component is the resistance R that represents wire resistance and skin effect due to the high frequency currents. Skin effect can be taken into account when cacuating the wire resistance at a particuar frequency: ρ L R δ π ( D δ ) where ρ characteristic resistance of materia; δ skin depth at particuar frequency; L conductor ength; D conductor ameter. Third component in the circuit is the capacitor, which is made up from stray capacitance of the coi. Stray capacitance is a natura phenomenon in every eectric device that has associations with eectric fieds. Stray capacitance of a coi was intensey stued by Medhurst [5], who aso estabished an empirica reation for finng out the stray capacitance based on the coi geometrica data. Medhurst formua for a cyindrica coi is b C = r,6 +,8+ r,7 b / r 8
Bandwih of the sensor is determined mainy by the first resonant frequency. In case of coi without any adtiona circuitry, the resonant frequency can be cacuated as f = π LC For testing a sensor was created with coi ength 35 mm and ameter of mm (see fig. 3). Its cacuated parameters woud be: capacitance C = 5.76 pf inductance L =.97 µh resistance is very sma and wi be negected resonant frequency f = 47. MHz. Coi was prepared as a centre-tapped coi, to ensure better separation of the capacitive infuences, when grounng with the centre tap. It wi be shown beow in this paper, why the centre tap is especiay usefu in such appication. Distance of the coi centre was set to 3 cm from the wire measured. Figure 4. Current sensing coi testing set-up. Test generator used was a partia scharge caibrator, which output represented a puse typica to PD with sma magnitude. During testing, puses with magnitude of µc were used. Waveform of such a puse on the wire at the ocation of the sensor coi is presented in Figure 5. The puse was in duration short enough to fit fuy in the power ine wire. This means that it was is a form of a eectromagnetic wave on the power ine wire. 8 6 Line votage Signa (V) 4 Figure 3. Sensor coi used for testing. High frequency current measurements A target appication for this magnetic oop measurement system was set up using simiar components as in rea meum-votage stribution network (fig. 4). Power ine wire was a meters ong A-overhead ine wire with cm in ameter. The wire was set at. meters above ground pain. The characteristic impedance of the ine was around 33 Ω. Line was terminated in the end so that the refections woud be at minimum eve. Aso, the input to the wire from generator was matched with the impedance to the ine. Schematic overview of the testing set-up is presented in figure. Measurements were done in the ocation where the sensor coi was instaed, this was at haf the wire ength. Votage between ground and the ine was measured, to observe the ine votage waveform. It was presumed that current on the ine had the same magnitude as determined by reation between impedance and votage on the transmission ine. This is because there was no sensor avaiabe that coud have captured actua current waveform at high enough frequency (over MHz). - -4-4 6 Time (ns) Figure 5. Partia scharge signa used for testing Response of the Rogowski coi was captured using LeCroy Wavesurfer 4Xs type oscioscope. It was determined by testing that the oscioscope probes had the equivaent capacitance of.6 pf. Testing resuts Waveforms obtained during testing have been presented in Figure 6. To observe the resuts, there has to be one further consideration of coi common mode and fferentia mode output. Common mode here is the signa measured between each coi termina and ground. Differentia mode is the signa measured between coi terminas themseves. Magnetic signa, induced by current passing through the wire, provides a fferentia output. Basicay this output is a fference between the two common mode measurements. When common mode signa from each end of the coi is simiar at the same timeframe, it incates capacitive couping. 8 9
In order to fit a responses to the graph, there has been some scaing of the resuts. This is because the common mode signas are very strong compared to the fferentia signas. This incates a reay strong effect of capacitive couping on this kind of magnetic sensor set-up. As the observed current in the power ine has very high frequency characteristics, it has effects to the,,5 sensor response. Namey, the sensor resonance frequency is very cose to the actua current signa frequency components. This makes response of the sensor to osciate. Due to this, one woud need a good mode of the sensor coi to interpret the sensor output for restoring the origina signa. CoiG CoiG Line votage, Coi x5 Signa (V),5 -,5 -, - 4 6 8 Time (ns) Figure 6. Coi output to the partia scharge puse on the ine. Coi G votage between coi termina and ground (centre tap); CoiG votage between coi termina and ground (centre tap); Line votage votage between power ine wire and ground; Coi - votage between coi terminas and. Some votage vaues have been ampified or weakened ( x -mark with ratio vaue). Mode of the sensor In the first approach, the sensor mode woud be simpe and consist of ony inductor, mutua inductance and coi capacitance. However, based on the measurement system and coi set-up we can concude that some adtiona improvements woud be necessary. First of a, the power ine and coi have capacitive couping. This is the factor that brings strong capacitive couping effects and is represented by capacitor C LINE. Second, measurement system circuits need to be added. In present case, this woud be formed by oscioscope probe capacitance, C OSC. Third, there are some adtiona capacitances between ground and sensor coi. Though very sma, they might present an important part in the coi operation, C G. There is aso capacitance between the two ends of the coi, C TT. Figure 7. Circuit mode of a centre tap current sensing coi sensor Mode with such components is presented in figure 7. As it can be seen, this mode is quite compex. Furthermore, it presents some further fferences between the osciation modes of common mode and fferentia mode, which shoud be taken into account.
Discussion and concusions The response of the sensor coi presents two fferent resonant characteristic frequencies. First one is observed with common mode signas. It can be observed to have a 39 MHz frequency, which is quite cose to the initia cacuated theoretica resonant frequency (47. MHz). However, the oscioscope probes present itsef roughy times higher capacitance than the coi itsef. How woud this be possibe? Reason for this seems to be the centre tap. Namey, the centre tap vides the coi into coi system, each having turns instead of 4 turns. Such smaer coi has much greater resonant frequency. In adtion, capacitance changes aso. This presents quite a good virtue of the centretapping, as without the centre-tap the resonant frequency woud have been ower. The fferentia signa response from the sensor however shows another resonant frequency, being even at 45 MHz. The reason for this can be traced to mutua inductance between the invidua - turn cois. Namey, fferentia mode and common mode signas magnetic fieds act in fferent rections in this kind on -coi system. In common mode case, the magnetic fied in one coi weakens the fied of another coi, fferentia mode magnetic fieds reinforce each other. Direct mathematica soution for this is under work and authors intend to present this in future papers. This type of sensor is in essence simiar to a Rogowski coi device, which has been stued more intensey in the appications for highvotage power ines [6]. Rogowski coi has a very nice benefit of proving arger output response than the singe coi sensor. However, if the number of turns woud be reduced for Rogowski coi, its sensitivity woud not be as good any more. Unfortunatey rarey observed, the Rogowski coi aso suffers from capacitive couping in simiar manner to the sensor coi described above. In concusion it can be said that the magnetic fied sensor coi has a quite good and definitey westinguishabe response to the high-frequency currents passing through the power ine wires. However work on this wi have to continue, to investigate the shieng effects and other possibiities to decrease the capacitive infuences. It woud be rather simpe to shied the sensor coi eectricay, however in this case there woud be a set-back in operating bandwih. Acknowedgements Authors thank Estonian Archimedes Foundation (Interscipinary project Optima energy conversion and contro in Smart and Microgrids within the framework of Doctora Schoo of Energy and Geotechnoogy-II; DoRa8) for financia support of this study. Aso many thanks to prof. Matti Lehtonen and Tatu Nieminen from Aato University for proving support and hep in aboratory testing. References. Tumanski, S., Induction Coi Sensors a Review, Meas. Sci. Techno. 7 8 R3.. Ida, N., Engineering Eectromagnetics (Second Etion), Springer New York, 4. 3. Gran, G., Kazimierczuk M. K., Massarini, A., Reggiani U., Stray Capacitances of Singe- Layer Soenoid Air-Core Inductors, IEEE Transactions on Industry Appications, Vo. 35, No. 5, September/October 999. 4. Wheeer, H.A., Inductance Formuas for Circuar and Square Cois, Proceengs of the IEEE, Vo. 7, No., December 98. 5. Medhurst, R. G., H.F. Resistance and Sefcapacitance of singe-ayer soenoids, Wireess Engineer, February 947. 6. G. M. Hashmi, M. Lehtonen, and A. Ehaffar, Modeing of Rogowski Coi for On-ine PD Monitoring in Covered-Conductor Overhead Distribution Networks, 9th Internationa Conference on Eectricity Distribution (CIRED7), Vienna, Austria, Paper No. 7, 7.