Smart Characterization of Rogowski Coils by Using a Synthetized Signal

sensors

Article Smart Characterization of Rogowski Coils by Using a Synthetized Signal

Alessandro Mingotti * , Lorenzo Peretto and Roberto Tinarelli Department of Electrical, Electronic and Information Engineering, Guglielmo Marconi Alma Mater Studiorum, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy; [email protected] (L.P.); [email protected] (R.T.) * Correspondence: [email protected]

Received: 8 May 2020; Accepted: 11 June 2020; Published: 13 June 2020

Abstract: With the spread of new Low-Power Instrument Transformers (LPITs), it is fundamental to provide models and characterization procedures to estimate and even predict the LPITs’ behavior. In fact, distribution system operators and designers of network models are looking for all forms of information which may help the management and the control of power networks. For this purpose, the paper wants to contribute to the scientific community presenting a smart characterization procedure which easily provides sufficient information to predict the output signal of a Low-Power Current Transformer (LPCT), the Rogowski coil. The presented procedure is based on a synthetized signal applied to the Rogowski coil. Afterwards, the validity of the procedure is assessed within the Matlab environment and then by applying it on three off-the-shelf Rogowski coils. Simulations and experimental tests and results involving a variety of distorted signals in the power quality frequency range and by adopting a quite simple measurement setup demonstrated the effectiveness and the capability of the procedure to correctly estimate the output of the tested device.

Keywords: rogowski coil; characterization; power quality; low-power current transformer; distorted signal; modeling

1. Introduction The Instrument Transformers (ITs) scenario has been radically changed after the introduction of so called Low-Power Instrument Transformers (LPITs) or sensors [1]. This new generation of transformers will facilitate the management and control of the modern power networks, which are now populated by several new actors such as Renewable Energy Sources (RES), electric vehicles, storage systems, and intelligent electronic devices. In terms of standards, ITs are well documented by the IEC 61869 series, in which two general documents describing the inductive ITs and the LPITs are the IEC 61869-1 [2] and -6 [3], respectively. All other documents of the series, instead, address every detail related to the operation of the transformers, from the accuracy performance to the normal and special tests that have to be performed on the ITs. Of course, the standards do not contain all possible solutions to issues that may arise when dealing with the ITs (e.g., speciﬁc accuracy tests vs. one or more inﬂuence quantities); however, the standard is evolving and changing day-by-day, including in each new version aspects that were not stressed in the previous one. Even if ITs are not the most critical asset of the grid, such as cable joints [4–6] and insulators may be [7–9], studies on them are always clear and current. As a matter of fact, the IT is a key element that provides information on what is happening to the power network in every single instant. Furthermore, ITs are the source of information for those algorithms [10–14] that manage and control the power network. Hence, the quantities provided by the transformers have to be as accurate as possible in every

Sensors 2020, 20, 3359; doi:10.3390/s20123359 www.mdpi.com/journal/sensors Sensors 2020, 20, 3359 2 of 16 operating condition of the network. To that end, the literature provides several works in which the accuracy of both ITs and LPITs is assessed in a variety of situations that may affect the network normal operation. For example, studies on current transformers (CTs) can be found in [15,16]. Electronic voltage transformers accuracy has been studied in [17,18], while sources of error for inductive voltage transformers (VTs) have been analyzed in [19,20]. Finally, the impact of VTs on the normal operation of the grid has been evaluated in [21–23]. In light of all above, this paper focuses on a particular type of Low-Power Current Transformer (LPCT), the Rogowski coil [24–27]. Thanks to its versatility, working principle, reduced dimensions, and ease of installation, in the last decade the Rogowski coil has been implemented in many applications [28] and has been subject to a variety of different studies to improve its knowledge and operation. For example, it is commonly adopted for the detection of partial discharges (PD) [29,30]. Furthermore, its large bandwidth makes it suitable for different high frequency applications [31–33]. Instead, in [34–38] the authors present several applications where the Rogowski coil is implemented to perform diagnostic and predictive maintenance measurements (for cable joints, motors, feeders, onsite calibration, etc.). In terms of accuracy, the standard IEC 61869-10 [39] provides some guidelines to assess LPCTs, while in [40–43] their performance is evaluated for different operating conditions. The aim of this paper is to provide a characterization procedure capable of collecting sufficient information from the Rogowski coil to estimate its output voltage when a variety of distorted test signals are injected. This is somehow related to the modeling of the Rogowski, of which the literature provides a range of works [44–48], but also includes omitting the information of the model and simply relying on a simplified impulse response of the device (as detailed in the next section). The developed procedure presented, which is based on a synthetized signal, can help the work of (i) network model designers, who have to include in their models all the electric assets spread among the grid; (ii) distribution system operators (DSOs) who have to deeply know how their networks operate to fully control and manage them. Therefore, the frequency range adopted in the manuscript is 50–2500 Hz, which is the power quality frequency range, in order to prove the effectiveness of the presented calibration procedure. However, a variety of new synthetized signals might be developed for whatever desired frequency range. Afterwards, the procedure is tested within the Matlab environment to assess is applicability. Finally, three off-the-shelf Rogowski coils have been characterized with the proposed procedure to validate their effectiveness in an actual scenario. The experimental validation procedure involves a variety of distorted testing signals with a harmonic content that varies within the power frequency limits. The remainder of the work is structured as follows. Section2 describes the mathematic approach that supports the overall work and the smart characterization procedure. The assessment of the procedure performed by using the Matlab environment has been tackled in Section3. The measurement setup used to perform the experimental validity tests is explained in Section4. As for the tests and results, they are detailed in Sections5 and6, respectively. Finally, the conclusion of the work and some final comments are contained in Section7.

2. Mathematical Approach The mathematical backbone of this section is divided into two diﬀerent parts. One is dedicated to the understanding of the Rogowski coil working principle and to what could be an ideal way to obtain its transfer function. A second part is then focused on using the gathered information to detail the solution for a smart characterization, namely, the aim of this work. Sensors 2020, 20, x FOR PEER REVIEW 3 of 16

2.1. Theoretical Background

2.1.1. Rogowski Coil The paper addresses the characterization of Rogowski coils. They can be easily recognized (see its simplified schematic in Figure 1) as a conductor wound over an insulating material (the return SensorsconductorSensors2020 2020, 20, is20, 3359,omitted x FOR PEER for REVIEWthe sake of clarity). This aspect is what differentiate them from the inductive33 of of 16 16 current transformers, wound over iron materials, and it is what guarantees their linear behavior. From2.1. Theoretical Figure 1 Backgroundthe working principle of a Rogowski coil can be described. The primary conductor, 2.1. Theoretical Background which has current () has to be measured, goes inside the coil and gives an output voltage () , described2.1.1. Rogowski by: Coil 2.1.1. Rogowski Coil The paper addresses the characterization of Rogowski() coils. They can be easily recognized (see The paper addresses the characterization ( of) =− Rogowski coils. They can be easily recognized (see(1) its its simplified schematic in Figure 1) as a conductor wound over an insulating material (the return simplified schematic in Figure1) as a conductor wound over an insulating material (the return conductor conductor is omitted for the sake of clarity). This aspect is what differentiate them from the inductive is omittedFrom for(1) theit is sake easy of to clarity). conclude This that aspect the output is what voltage diﬀerentiate is proportional them from to the the inductive derivative current of the current transformers, wound over iron materials, and it is what guarantees their linear behavior. transformers,primary current wound and over to ironthe materials,mutual inductance and it is what between guarantees conductors their linear . behavior. Furthermore, From Figure() 1is From Figure 1 the working principle of a Rogowski coil can be described. The primary conductor, theideally working 90° shifted principle compared of a Rogowski to () coil. can be described. The primary conductor, which has current which has current () has to be measured, goes inside the coil and gives an output voltage () , ip(t) hasAs tofor be the measured, equivalent goes circuit inside of thethe coilRogowski, and gives it is an typically output voltagedescribed,us( tas), describedin Figure by:2, with two described by: impedances, and . The former impedance consists of the series between a resistor and an inductor, whereas the latter impedance includes thdie pparallel(t)() between a capacitor and the burden us(t())==−M (1) (defined in [39]). No further details on the impedances − aredt detailed here because they are not involved in whatFrom follows (1) it andis easy hence to outconclude of scope. that the output voltage is proportional to the derivative of the

primary current and to the mutual inductance between conductors . Furthermore, () is ideally 90° shifted compared to (). As for the equivalent circuit of the Rogowski, it is typically described, as in Figure 2, with two

impedances, and . The former impedance consists of the series between a resistor and an inductor, whereas the latter impedance includes the parallel between a capacitor and the burden (defined in [39]). No further details on the impedances are detailed here because they are not involved in what follows and hence out of scope.

FigureFigure 1. 1. SimpleSimple Rogowski coil coil schematic. schematic.

From (1) it is easy to conclude that the output voltage is proportional to the derivative of the primary current and to the mutual inductance between conductors M. Furthermore, us(t) is ideally 90◦ shifted compared to ip(t). As for the equivalent circuit of the Rogowski, it is typically described, as in Figure2, with two impedances, ZS and ZP. The former impedance consists of the series between a resistor and an inductor, whereas the latter impedance includes the parallel between a capacitor and the burden (deﬁned in [39]). No further details on the impedancesFigure 1. are Simple detailed Rogowski here because coil schematic. they are not involved in what follows and hence out of scope.

Figure 2. Rogowski coil equivalent circuit.

FigureFigure 2. 2. RogowskiRogowski coil coil equivalent equivalent circuit. circuit.

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2.1.2. Transfer Function To deal with Rogowski coils, exploiting their linear behavior, the impulse response (IR), that is the output of a linear device when the input is an impulse, might be the easiest solution. In fact, ideally, the IR provides the transfer function of a Rogowski coil, hence, modeling it becomes straightforward. Unfortunately, the practical application of an impulse, hence obtaining the IR, is not that simple. The reason is due to the technical limitation of the typical instrumentation—in terms of resolution and capability of reproducing a real impulse—and the resulting actual IR which clearly differs from the ideal one (constant value in the frequency domain). To better clarify this aspect, note Figure 3 where the comparison between the frequency spectra of the ideal and the real IR is provided (the picture does not refer to any test, it is only a theoretical example). As a matter of fact, the spectrum of an ideal IR is a constant line which describes the same amplitude for all frequency components Sensors 2020, 20, 3359 4 of 16 from minus to plus infinite (in the graph only a portion of the frequency axes is presented for obvious reasons). Turning to the actual one, it decreases after being flat for a defined range of frequencies, 2.1.2.which Transfer depends Function on the instrumentation adopted to generate the impulse signal. The consequential conclusion is that, when a real impulse is applied to any device, its response should be carefully To deal with Rogowski coils, exploiting their linear behavior, the impulse response (IR), that is the analyzed and it will differ from one frequency to another. output of a linear device when the input is an impulse, might be the easiest solution. In fact, ideally, the IR provides the transfer function of a Rogowski coil, hence, modeling it becomes straightforward. 2.2. Synthetized Signal Unfortunately, the practical application of an impulse, hence obtaining the IR, is not that simple. The reasonConsidering is due tothe the peculiarities technical limitation of the device of the to typical be tested instrumentation—in and the limitations terms of of the resolution IR test, andit is capabilitypossible to of design reproducing and synthetize a real impulse—and a particular sign theal resulting to be used actual for testing IR which the clearlyRogowski diff erscoils. from the idealFirst one (constantof all, the valuefrequency in the range frequency that has domain). to be tackled To better by clarify the characterization this aspect, note process, Figure3 and where the thefrequency comparison resolution between has the to frequency be defined spectra (dependi of theng ideal on and the the application real IR is providedwhere the (the procedure picture does is notapplied). refer toIn any our test,case, it the is only power a theoretical quality frequency example). range, As a 50 matter Hz–2500 of fact, Hz, the is spectrumconsidered of together an ideal with IR is a constant50 Hz resolution line which (i.e., describes 50 harmonic the same components). amplitude for The all choice frequency is due components to the typical from application minus to plus of infiniteRogowski (in thecoils graph to onlymeasure a portion the ofcurrent the frequency in the axesmedium is presented voltage for distribution obvious reasons). networks, Turning and to theconsequently actual one, the it decreasesneed for measurements after being flat that for ainclude defined up range to the of 50th frequencies, harmonic which [2]. depends on the instrumentationThe second adoptedstep is to to generate generate a thefrequency impulse domain signal. Thesignal, consequential such as the conclusionone depicted is that, in Figure when 4, a realwhich impulse reflects is the applied previous to any choice. device, In its the response picture, should is the be number carefully of analyzed non-zero and components it will differ and from onethe total frequency number to another.of bins (or samples) of the signal (odd in the case considered in Figure 4).

Figure 3. 3.Comparison Comparison between between the real the (dash-dotted real (dash-dotted line) and line) ideal and (solid ideal line) impulse(solid line) response impulse (IR). response (IR). 2.2. Synthetized Signal Considering the peculiarities of the device to be tested and the limitations of the IR test, it is possible to design and synthetize a particular signal to be used for testing the Rogowski coils. First of all, the frequency range that has to be tackled by the characterization process, and the frequency resolution has to be deﬁned (depending on the application where the procedure is applied). In our case, the power quality frequency range, 50 Hz–2500 Hz, is considered together with a 50 Hz resolution (i.e., 50 harmonic components). The choice is due to the typical application of Rogowski coils to measure the current in the medium voltage distribution networks, and consequently the need for measurements that include up to the 50th harmonic [2].

The second step is to generate a frequency domain signal, such as the one depicted in Figure4, which reﬂects the previous choice. In the picture, K is the number of non-zero components and N the total number of bins (or samples) of the signal (odd in the case considered in Figure4). To determine K, it should be considered as the result of the application of a Fourier Transform, which has a mean value plus one set of the desired number of harmonic components, H for example (and of course a set of mirrored, i.e., complex conjugate, negative components). Overall, K = 1 + H + H, and for the considered case, H = 50 and hence K = 101. However, the frequency domain signal can be designed for whatever range of frequency and frequency step. Sensors 2020, 20, x FOR PEER REVIEW 5 of 16

SensorsSensors 20202020,,20 20,, 3359x FOR PEER REVIEW 55 ofof 1616

Figure 4. Bins in the frequency domain, representing the final test signal.

To determine , it should be considered as the result of the application of a Fourier Transform, which has a mean value plus one set of the desired number of harmonic components, for example (and of course a set of mirrored, i.e., complex conjugate, negative components). Overall, =1 , and for the considered case, =50 and hence = 101. However, the frequency domain signal can be designed for whatever range of frequency and frequency step. It is well-known that the signal in Figure 4 results in a sinc-shaped signal () in the time domain; of course,FigureFigure it 4. is Bins 4. a Binsportion in inthe the frequencyof frequency a sinc, which domain, domain, is an representingrepresenting infinite time the the ﬁnaldomain final test test signal. function. signal. Such a signal, shown in Figure 5, it is described by: It is well-known that the signal in Figure4 results in a sinc-shaped signal s(t) in the time domain; To determine , it should be considered as thesin (/) result of the application of a Fourier Transform, of course, it is a portion of a sinc, which is an() inﬁnite= time domain function. Such a signal, shown(2) in which has a mean value plus one set of the desiredsin (/) number of harmonic components, for example Figure(and of5 ,course it is described a set of mirrored, by: i.e., complex conjugate, negative components). Overall, =1 where is the variable used for the samples andsin( introducedπnK/N) in Figure 4. , and for the considered case, =50 sand(t) =hence = 101. However, the frequency domain signal(2) can beConsequently, designed for whatever the final rangesignal of to frequency be usedsin forand(π nthe frequency/N smart) characterization step. test is () and the whereRogowskiIt nisis well-known the coil variable response usedthat to itthe for may thesignal be samples referred in Figure and to, introduced 4just results for simplicity, in in a Figure sinc-shaped as4. Sinc Response signal () (SR). in the time domain; of course, it is a portion of a sinc, which is an infinite time domain function. Such a signal, shown in Figure 5, it is described by: sin (/) () = (2) sin (/) where is the variable used for the samples and introduced in Figure 4. Consequently, the final signal to be used for the smart characterization test is () and the Rogowski coil response to it may be referred to, just for simplicity, as Sinc Response (SR).

FigureFigure 5. Time 5. Time domain domain waveform, waveform, obtained from from the the frequency frequency domain domain signal signal in Figure in Figure4. 4.

Consequently,Another significant the ﬁnal factor signal that to becan used be used for the before smart performing characterization the tests test isis sgathered(t) and the from Rogowski Section coil2.1.1 response and, in to particular, it may be referredfrom (1). to, In just fact, for with simplicity, (1) being as Sinc one Responseway of expressing (SR). the input–output relationAnother of the signiﬁcant Rogowski factor coil, that it is can possible be used to before predict performing what the SR the could tests is be. gathered In detail, from in Sectiona qualitative 2.1.1 and,way in for particular, the moment, from it (1). is possible In fact, with to note (1) beingin Figure one 6 way the ofexpected expressing time the and input–output frequency domain relation (left of theand Rogowski right) signal coil, resulting it is possible from to SR predict test. Figure what 6, the which SR could is just be. a way In detail, to understand in a qualitative what would way for be thethe moment, Rogowski it iscoil possible SR, has to been note obtained in Figure deriving6 the expected (). time and frequency domain (left and right) signalFigure resulting 5. Time from domain SR test. waveform, Figure6, which obtained is just from a way the to frequency understand domain what would signal be in theFigure Rogowski 4. coilSensors SR, has2020, been 20, x FOR obtained PEER REVIEW deriving s(t). 6 of 16 Another significant factor that can be used before performing the tests is gathered from Section 2.1.1 and, in particular, from (1). In fact, with (1) being one way of expressing the input–output relation of the Rogowski coil, it is possible to predict what the SR could be. In detail, in a qualitative way for the moment, it is possible to note in Figure 6 the expected time and frequency domain (left and right) signal resulting from SR test. Figure 6, which is just a way to understand what would be the Rogowski coil SR, has been obtained deriving ().

FigureFigure 6. Expected6. Expected time domaintime domain and frequency and frequency domain (left doma andin right) (left signals and right) obtained signals from theobtained Sinc Responsefrom the (SR) Sinc test Response applied to (SR) the Rogowski test applied coil. to the Rogowski coil.

Concluding, the synthetized () is going to be assessed in Section 3, by performing simulations in the Matlab environment, to understand if its application within the procedure produce satisfying results; then is used in Section 4 to perform the tests on three off-the-shelf Rogowski coils. Afterwards, the resulting SR is adopted as a simplified but more efficient IR to predict the Rogowski coils’ output voltage.

2.3. Smart Characterization Tests The smart characterization introduced in this work is based on two simple tests. The first one consists of acquiring the SR of the Rogowski coil under test (RUT) (ℎ()) when it is measuring the () signal defined in the previous section.

The second test consists of measuring, with the RUT, a 50 Hz primary current () and the RUT voltage response () (same notation of Figure 2). The measured primary current is then convoluted with ℎ() to obtain the estimated RUT’s response ():

() = (),ℎ()= () ℎ(−) (3) These two tests allow the user to completely know the behavior of his Rogowski coil. In fact,

from the ratio of the rms values of () and () it is possible to find the scaling coefficient introduced by the convolution application. In other words, to avoid the user needing to find the mathematic relation between the amplitudes of the convoluted signal and the input signals, a simple and practical test is included in the characterization procedure. Hence:

() =() ∗ (4)

Once and ℎ() are found, it is possible to apply the convolution operation to whatever () current, to be injected into the Rogowski coil, and estimate its voltage response. At a glance, it is possible to note how this two-measurements calibration procedure is shorter and faster than the common characterization techniques adopted to characterize the Rogowski coils.

3. Simulation in Matlab Environment In this section the SR procedure and its validation is addressed by simulations in the Matlab environment. In particular, it is described how the Rogowski coil input–output relation, required for the simulations, has been implemented, which tests have been performed, and the related results.

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Concluding, the synthetized s(t) is going to be assessed in Section3, by performing simulations in the Matlab environment, to understand if its application within the procedure produce satisfying results; then is used in Section4 to perform the tests on three o ff-the-shelf Rogowski coils. Afterwards, the resulting SR is adopted as a simplified but more efficient IR to predict the Rogowski coils’ output voltage.

2.3. Smart Characterization Tests The smart characterization introduced in this work is based on two simple tests. The ﬁrst one consists of acquiring the SR of the Rogowski coil under test (RUT) (h(t)) when it is measuring the s(t) signal deﬁned in the previous section. The second test consists of measuring, with the RUT, a 50 Hz primary current iP(t) and the RUT voltage response us(t) (same notation of Figure2). The measured primary current is then convoluted with h(t) to obtain the estimated RUT’s response use(t):

+ Zin f use(t) = conv(iP(t), h(t)) = iP(τ)h(t τ)dτ (3) − in f − These two tests allow the user to completely know the behavior of his Rogowski coil. In fact, from the ratio of the rms values of use(t) and us(t) it is possible to find the scaling coefficient r introduced by the convolution application. In other words, to avoid the user needing to find the mathematic relation between the amplitudes of the convoluted signal and the input signals, a simple and practical test is included in the characterization procedure. Hence:

use(t) = us(t) r (4) ∗

Once r and h(t) are found, it is possible to apply the convolution operation to whatever iP(t) current, to be injected into the Rogowski coil, and estimate its voltage response. At a glance, it is possible to note how this two-measurements calibration procedure is shorter and faster than the common characterization techniques adopted to characterize the Rogowski coils.

3.1. Rogowski Coil Model Implementation In accordance with what is presented in Section 2.1.1, the Rogowski coil behavior has been simulated implementing (1). Therefore, all test signals selected in the following are going to be computed through (1). In other words, the derivative of the test signals is going to be multiplied by a generic factor M to simulated the Rogowski coil response (the choice of M does not aﬀect the procedure validation). The choice of adopting such a simple, but meaningful, input–output relation of the Rogowski has been taken to test the eﬀectiveness of the proposed characterization procedure.

3.2. Test Descritpion To assess the proposed procedure a list of distorted signals has been selected and generated. In Table1 such signals and their harmonic content are listed. As can be seen, test #a1 is a simple 50 Hz signal for a preliminary evaluation. Afterwards, tests #b1 to #g2 include the 50 Hz component In plus a variety of harmonic content from the 2nd to the 25th harmonic. Such a choice has been made to be Sensors 2020, 20, 3359 7 of 16 aligned with the Standards IEC 519 [49] and 50160 [50]. However, the aim of these tests is to prove the validity of the characterization procedure in a variety of harmonic content of the signals.

Table 1. List of tests including the 50 Hz component plus harmonic content.

Test Harmonic Content Test Harmonic Content

#a1 50 Hz #d3 12th, 3% of In #b1 3rd, 10% of In #e1 25th, 10% of In #b2 3rd, 6% of In #e2 25th, 6% of In #b3 3rd, 3% of In #e3 25th, 3% of In #c1 7th, 10% of In #f1 3rd, 5th,7th, all 6% of In #c2 7th, 6% of In #f2 3rd, 5th,7th, all 3% of In #c3 7th, 3% of In #g1 2nd, 4th,6th, all 6% of In #d1 12th, 10% of In #g2 2nd, 4th,6th, all 3% of In #d2 12th, 6% of In

All waveforms #a1–#g2 simulates the primary currents to be measured by the Rogowski. Therefore, they have been (i) convoluted with the signal h(t) to obtain the estimated Rogowski coil output voltage and (ii) they have derived according to (1), to obtain the “real” response of the Rogowski coil. It is then from the comparison of these two results that is possible to appreciate the applicability of the smart characterization.

3.3. Results and Comments To assess at a glance the applicability of the procedure, we have chosen to evaluate the results with the composite error, a well-known time domain based index which allows for appreciating the differences between two signals. It is defined, in the discrete domain and implementing the above defined variables, as: q 1 PN 2 (rus(n) use(n)) N 1 − εD = 100 (5) Us ∗ where Us is the rms value of us(n), and N is the number of considered samples. Note that the composite error is a severe index because it reflects the amplitude and phase variation between two signals. Therefore, for each of the tests in Table1 εD has been calculated and listed in Table2.

Table 2. Composite error value for each test of Table1.

Test εD [%] Test εD [%] #a1 0.00632796 #d3 0.02680057 #b1 0.00813769 #e1 0.15427063 #b2 0.00707059 #e2 0.13827713 #b3 0.00652614 #e3 0.09980934 #c1 0.02587633 #f1 0.01933962 #c2 0.01808575 #f2 0.01187221 #c3 0.01099543 #g1 0.0150594 #d1 0.05940332 #g2 0.00966692 #d2 0.04536823

As can be seen in the table, all εD values remain within 0.1% with the exception of tests #e1 and #e2 that are below 0.16%. Even in those two cases, it is not possible to distinguish the time domain waveform of the estimated and “real” signals. This is conﬁrmed looking at Figure7 where use(t) and us(t) are plotted for test #d1 (Figure7a). However, the slight di ﬀerence between the two signals is only appreciable in the zoomed portion of graph in Figure7b. The reason why those two tests present higher values of εD may be attributed to the presence of high harmonic components compared to the others signals. In fact, it emerges from Table2 that (i) εD slightly increases for signals with high Sensors 2020, 20, x FOR PEER REVIEW 8 of 16 Sensors 2020, 20, x FOR PEER REVIEW 8 of 16 #d1 0.05940332 #g2 0.00966692 #d1 0.05940332 #g2 0.00966692 #d2 0.04536823 #d2 0.04536823

As can be seen in the table, all values remain within 0.1% with the exception of tests #e1 and As can be seen in the table, all values remain within 0.1% with the exception of tests #e1 and #e2 that are below 0.16%. Even in those two cases, it is not possible to distinguish the time domain #e2 that are below 0.16%. Even in those two cases, it is not possible to distinguish the time domain waveform of the estimated and “real” signals. This is confirmed looking at Figure 7 where () waveform of the estimated and “real” signals. This is confirmed looking at Figure 7 where () and () are plotted for test #d1 (Figure 7a). However, the slight difference between the two signals and () are plotted for test #d1 (Figure 7a). However, the slight difference between the two signals is only appreciable in the zoomed portion of graph in Figure 7b. The reason why those two tests is only appreciable in the zoomed portion of graph in Figure 7b. The reason why those two tests present higher values of may be attributed to the presence of high harmonic components Sensorspresent2020 higher, 20, 3359 values of may be attributed to the presence of high harmonic components8 of 16 compared to the others signals. In fact, it emerges from Table 2 that (i) slightly increases for compared to the others signals. In fact, it emerges from Table 2 that (i) slightly increases for signals with high order harmonics; (ii) and increases when the harmonic percentage with respect signals with high order harmonics; (ii) and increases when the harmonic percentage with respect orderto the harmonics;50 Hz signal (ii) increases and εD increases (comparison when between the harmonic tests 1 percentageand 3 for each with letter, respect e.g., to #b1 the and 50 Hz #b3 signal). increasesto the 50 (comparisonHz signal increases between (comparison tests 1 and 3between for each tests letter, 1 and e.g., 3#b1 forand each#b3 letter,). e.g., #b1 and #b3).

(a) (b) (a) (b) Figure 7. Time domain graph of test #d1 (a) and a zoomed portion of it (b). FigureFigure 7. 7.TimeTime domain domain graph graph of testtest#d1 #d1( a()a and) and a zoomeda zoomed portion portion of it of (b ).it (b). From Table 2 and Figure 7 it is possible to conclude that the smart characterization presented in FromFrom Table Table2 2and and Figure Figure7 it7 isit is possible possible to to conclude conclude that that the the smart smart characterization characterization presented presented in in Section 2 is fully applicable and effective, in a simulating environment, to estimate and hence predict SectionSection2 2is is fully fully applicable applicable and and e effective,ffective, in in a a simulatingsimulating environment,environment, to to estimate estimate and and hencehence predictpredict the Rogowski coil behavior with all distorted signals tested. thethe Rogowski Rogowski coil coil behavior behavior with with all all distorted distorted signals signals tested. tested. In light of the results, the purpose of the next section is to assess the effectiveness of the smart InIn light light of of the the results, results, the the purpose purpose ofof the the next next section section isis toto assess assess thethe eeffectivenessffectiveness ofof the the smart smart characterization with experimental tests and by using off-the-shelf Rogowski coils. characterizationcharacterization with with experimental experimental tests tests and and by by using using o off-the-shelfff-the-shelf Rogowski Rogowski coils. coils. 4. Measurement Setup 4.4. MeasurementMeasurement SetupSetup Two measurement setups have been adopted to perform the tests. Both are depicted in Figure 8, TwoTwo measurement measurement setups setups have have been been adopted adopted to to perform perform the the tests. tests. BothBoth areare depicteddepicted inin FigureFigure8 8,, wherein configurations (a) and (b) can be distinguished. whereinwherein configurations configurations (a) (a) and and (b) (b) can can be be distinguished. distinguished.

Figure 8. Measurement setup adopted for the two different tests, SR test using configuration (a), mainFigure tests 8. Measurement performed with setup configuration adopted (b for). the two different tests, SR test using configuration Figure 8. Measurement setup adopted for the two different tests, SR test using configuration (a), main tests performed with configuration (b). 4.1. Sinc(a), Responsemain tests Measurement performed Setupwith configuration (b).

4.1. SincConﬁguration Response Measurement (a) in Figure Setup8 has been used to apply the developed signal s(t) to obtain the SR of 4.1. Sinc Response Measurement Setup the RUT. The measurement setup consists of:

Function Generator (FG) Keysight 33220A. It allows for generating arbitrary waveforms and • it features a sampling frequency of 50 MSa/s, frequency resolution of 1 µHz, and a frequency accuracy of (20 ppm + 3 pHz). ± Transconductance Fluke 52120A. Used to transduce the voltage of the FG into a current. Its main • accuracy features are listed in Table3. A primary shunt, 1 mΩ resistor, to measure the current generated by the transconductance and • injected into the RUT. The uncertainty associated with the shunt is 0.01%. Before all tests, the shunt Sensors 2020, 20, 3359 9 of 16

has been characterized in the power quality frequency range selected in this work. The results conﬁrm the stability of the shunt in all ranges of frequency, with measured variations in the order of 2 10 6 Ω. × − The RUTs. Three off-the-shelf Rogowski coils have been selected to be tested. They are distinguished • as A, B, and C for the sake of privacy and because the calibration procedure is independent of the Rogowski type. Their features are collected in Table4. Note that the three RUTs are slightly diﬀerent one from another, hence the testing sample for the procedure is not limited to only one type of device. Finally, the number of turns of A, B, and C, is not provided because (i) the manufacturers do not give such a characteristic; (ii) it is information that is not required to perform the presented tests. 16-bit PicoScope 5442D. Used to collect both outputs from the RUTs and from the shunt via BNC • cables. The oscilloscope features 4 channels, 200 MHz bandwidth, sample rate up to 62.5 MSa/s at 16-bit resolution, input ranges 10 mV to 20 V, and gain accuracy of 0.5% of the signal. ± ± ±

Table 3. Accuracy characteristics of the Fluke 52120.

Current Range % of Output % of Range 2 0.015 0.070 20 0.015 0.060 120 0.015 0.020

Table 4. Rogowski coil under test (RUT) main features.

Feature A B C Type Split-core Split-core Split-core Inner Diameter 150 mm 115 mm 75 mm Accuracy 1% 1% 1% ± ± ± Ratio 1000 A/333 mV 1000 A/100 mV 1000 A/100 mV

In brief, the synthetized signal s(t) that has been reproduced has a current signal with the system FG plus transconductance to be measured by the primary shunt and the RUT. Afterwards the voltage signals of these two devices have been collected by the PicoScope for further analysis.

4.2. Main Measurement Setup Configuration (b) of Figure8 has been used for the experimental validation tests. What di ffers from configuration (a) is the use of the Fluke Calibrator 6105A instead of the FG. The choice easily set the harmonic content of the list of test signals #b1 to #g2. Some of the relevant Fluke characteristics are listed in Table5; as for the accuracy, the limits specified in Table3 apply.

Table 5. Main characteristics of the Fluke 6105A.

Frequency Accuracy 50 ppm ± Amplitude Resolution 6 digits Full Range Alone 20 A

Overall, the described measurement setup can be considered a quite simple and typically adopted one. In fact, when the need is to inject distorted currents, the choice is mainly focused on transconductance ampliﬁers or high-power function generators depending on the desired current amplitudes. Sensors 2020, 20, 3359 10 of 16

5. Experimental Tests

5.1. Characterization Tests The smart characterization introduced in Section 2.3 has been performed with the measurement setup described in the previous section. The first test, the SR with configuration (a), has been performed fixing a sampling frequency of 1 MSa/s and an acquiring window of 20 ms. The 20 ms window has been extracted from an acquisition of 1 s to ensure the stability of the acquired signal. As for the amplitude, the peak of s(t) has been fixed, for all RUTs, at 100 A. The second test, which is the 50 Hz current acquisition, has been performed with a sampling frequency of 1 MSa/s, using the configuration (b) of the measurement setup, acquiring 10 periods of the signal extracted from a 1 s window. Afterwards, the r coefficients (see Equation (4)) have been computed for the three RUTs (rA, rB, and rC, respectively). For all tests (above mentioned and in what follows), the Picoscope bandwidth has been limited at its allowed minimum, 20 MHz; moreover, a 20 kHz digital filter has been set to further reduce the noise affecting the measurements.

5.2. Validation Tests To experimentally validate the authors’ hypothesis that the presented characterization procedure can be used to estimate the output voltage of a Rogowski coil, a set of 17 tests has been performed (distinguished from #a1 to #g2). Such tests are the same used to assess the procedure in the Matlab environment in order to have a direct comparison. Among the tests, each letter corresponds to a different harmonic content, while the number indicates a different amplitude of the harmonic compared to the 50 Hz component In. All tests from #a1 to #g2 have been performed with In = 75 A, a sampling frequency of 1 MSa/s and acquiring 10 periods of the signals from a 1 s window. Summarizing, all signals from #a1 to #g2 have been reproduced with the configuration b) of the measurement setup in Figure8. Then, both primary and secondary signals of the RUTs have been collected; the primary has been used for the secondary estimate, the secondary, for the final comparison. The estimate of the RUTs’ responses to signals from #a1 to #g2 has been performed by applying (3) as detailed above.

6. Experimental Results and Discussion

6.1. Characterization Results The SR results, after the injection of s(t) to the three RUTs, are depicted in Figure9. As can be seen, the three graphs confirm that (i) the three generic RUTs have very similar responses to s(t), (ii) the hypothesis made in Section2 regarding the Rogowski coil behavior is correct. However, even if not visible from the picture, according to each RUT manufacture, the SR could be more or less affected by the presence of noise. This effect is very slightly evident in RUT B. Once the SR has been obtained, the results of the 50 Hz current injection into the RUTs can be used to determine r for each RUT. In accordance with (4), the values for rA, rB, and rC are 15.7595, 15.8091, and 13.1676, respectively. The coefficients can then be used to scale the convolution results of each test defined in Section 5.2. Sensors 2020, 20, 3359 11 of 16 Sensors 2020, 20, x FOR PEER REVIEW 11 of 16

Figure 9. 9.SR SR of of RUTs RUTs A, A, B, andB, and C. C.

6.2. ResultsOnce of the the SR Validation has been Tests obtained, the results of the 50 Hz current injection into the RUTs can be usedAs to described determine in Section for each 3.3 RUT., all In results accordance are presented with (4), the by values using for the composite, , and error are 15.7595, index (see15.8091, (Equation and 13.1676, (5))). Therefore, respectively. in Table The6 coefficients, for each test can signal then be#a1 usedto #g2to scaleand the for eachconvolution RUT, the resultsεD valuesof each are test listed. defined It is thein Section result of 5.2. the comparison between the estimated signal, by implementing the characterization procedure, and the RUTs voltage response measured during the experimental tests. In6.2. the Results table, three of the signiﬁcantValidation Tests digits have been used to represent the results considering their absolute value andAs described that they arein expressedSection 3.3, as all a percentage.results are presented by using the composite error index (see

(Equation (5))). Therefore, in Table 6, for each test signal #a1 to #g2 and for each RUT, the values are listed. It is the result of the comparison between the estimated signal, by implementing the characterization procedure, and the RUTs voltage response measured during the experimental tests. In the table, three significant digits have been used to represent the results considering their absolute value and that they are expressed as a percentage.

SensorsSensors2020 2020, 20, 20, 3359, x FOR PEER REVIEW 1212 of of 16 16

Table 6. values for each test of Table 1 and for each RUT. Table 6. εD values for each test of Table1 and for each RUT. [%] [%] Test Test RUT A ε RUTD [%] B RUT C RUT A RUTεD [%] B RUT C Test Test #a1 RUT0.752 A RUT2.57 B RUT1.89 C #d3 RUT1.64 A RUT2.76 B RUT1.82 C #a1#b1 0.7521.024 2.573.01 1.892.49 #e1 #d3 4.58 1.64 3.27 2.76 2.36 1.82 #b1#b2 1.0240.814 3.012.79 2.492.12 #e2 #e1 3.76 4.58 3.18 3.27 2.17 2.36 #b2#b3 0.8140.782 2.792.73 2.121.95 #e3 #e2 2.46 3.76 2.74 3.18 2.15 2.17 #b3#c1 0.7822.77 2.733.03 1.952.20 #f1 #e3 2.17 2.46 3.13 2.74 2.06 2.15 #c1 2.77 3.03 2.20 #f1 2.17 3.13 2.06 #c2#c2 1.951.95 3.173.17 1.911.91 #f2 #f2 1.26 1.26 2.71 2.71 2.37 2.37 #c3#c3 1.201.20 2.932.93 1.761.76 #g1 2.01 2.01 2.75 2.75 1.95 #d1#d1 3.473.47 2.652.65 2.212.21 #g2 1.25 1.25 2.79 2.79 2.32 #d2#d2 2.712.71 2.73 2.73 1.89 1.89

SeveralSeveral comments comments can can be be formulated formulated from from the the table tabl consideringe considering that that (i) (i) each each RUT RUT has has a a di differentfferent responseresponse vs. vs. noise, noise, vs. vs. harmonics;harmonics; (ii)(ii) eacheach RUTRUT comescomes from from a a di differentfferent manufacturer, manufacturer, hence hence the the technologytechnology implemented implemented varies varies from from one one to theto the other; other; (iii) (iii) the the distortion distortion included included in the in the test test signals signals is quiteis quite vary, vary, hence hence it properly it properly stresses stresses theRUT. the RUT. AA general general comment comment is is that, that, looking looking at at all all RUTs, RUTs, the the results results are are quite quite promising promising considering considering that that nonenone of of the the results results exceed exceed 4.5%. 4.5%. This This means means that that neither neither in in amplitude amplitude nor nor in in phase phase the the estimate estimate of of the the signalssignals is is never never higher higher than than that that percentage. percentage. A A second second general general comment comment is is that, that, on on average, average, the theε D valuesvalues for for RUT RUT B areB are higher higher than than the otherthe other two. two. However, However, this is this perfectly is perfectly in line in with line the with higher the noisehigher dependencenoise dependence of RUT of B, RUT as detailed B, as detailed above. above. AA third third and and last last general general comment comment is is aimed aimed at at confirming confirming what what obtained obtained during during the the simulation simulation tests:tests: the the higher higher the the distortion distortion of theof the primary primary signal, signal, the higherthe higher is the isε Dthevalue. value. As an As example, an example, for tests for #c1tests to #c3#c1 ofto RUT#c3 of A, RUT which A, involvewhich involve a 7th harmonic a 7th harmonic of percentages of percentages 10, 6, and 10, 3% 6, and compared 3% compared to the 50 to Hz the component,50 Hz component, the εD values the are values 2.77, are 1.95, 2.77, and 1.95, 1.20%, and respectively. 1.20%, respectively. This example This example can be extendedcan be extended to all RUTsto all and RUTs to alland test to signals.all test signals. ForFor the the sake sake of of completeness, completeness, in in Figure Figure 10 10 for for time time domain, domain, graphs graphs of of the the results results have have been been presented.presented. In In particular, particular, theythey referrefer toto (a)(a) test #f1, (b) (b) test test #g1#g1 (for(for RUT RUT A), A), and and (c) (c) test test #c1#c1, (d), (d) test test #d1 #d1(for(for RUT RUT B). B). As As appears appears clear clear from from the the picture, picture, th thee estimateestimate ofof thethe secondarysecondary signalsignal is is almost almost undistinguishableundistinguishable from from the the reference reference measured measured signal. signal. MovingMoving to to the the frequency frequency domain,domain, thethe percentage variation variation between between the the 50 50 Hz Hz component component of ofthe themeasured measured and and estimated estimated signals signals are are0.08%, 0.08%, 0.01%, 0.01%, 0.98%, 0.98%, and 0.02%, and 0.02%, for the for cases the cases(a), (b), (a), (c), (b), and (c), (d) andof Figure (d) of Figure 10, respectively. 10, respectively. As for Asthe for harmonic the harmonic components, components, the cases the (c) cases and (c) d) and in Figure (d) in Figure10 involve 10 involveonly one only harmonic one harmonic component, component, hence hence their their computed computed percentage percentage variation variation compared toto the the measuredmeasured one one are are 3.07% 3.07% and 2.55%,and 2.55%, respectively. respectively. Such values Such confirmvalues theconfirm effectiveness the effectiveness of the proposed of the characterizationproposed characterization procedure. procedure.

(a) (b)

Figure 10. Cont.

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(c) (d) (c) (d) Figure 10. Comparison graph of the test #a1 results for RUT A. FigureFigure 10. 10. ComparisonComparison graph graph of of the the test test#a1 #a1results results for RUT for RUT A. A. Finally, it is interesting to compare, in the frequency domain, the estimate of a harmonic Finally,Finally, it isit interesting is interesting to compare, to compare, in the frequencyin the frequency domain, thedomain, estimate the of estimate a harmonic of componenta harmonic component among the three RUTs. Such a comparison is shown in the graph of Figure 11 where the amongcomponent the three among RUTs. the Such three a comparisonRUTs. Such is a showncomparison in the is graph shown of Figurein the graph11 where of Figure the 12th 11 harmonic where the 12th harmonic of case #d3 is compared among the RUTs. From the graph the goodness of the of12 caseth harmonic #d3 is compared of case among#d3 is thecompared RUTs. Fromamong the th graphe RUTs. the goodnessFrom the ofgraph the estimationthe goodness obtained of the estimation obtained applying the characterization procedure is clear. applyingestimation the obtained characterization applying procedure the characterization is clear. procedure is clear.

. . Figure 11. Graph with the comparison between the estimated and the actual magnitude of the 12th harmonicFigure included11. Graph in with case #d3,the forcomparison the three RUTs. between the estimated and the actual magnitude of Figure 11. Graph with the comparison between the estimated and the actual magnitude of the 12th harmonic included in case #d3, for the three RUTs. Inthe light 12th of theharmonic presented included results in it iscase possible #d3, for to concludethe three thatRUTs. the experimental results confirm what was obtained in the simulation tests. It is worth highlighting the benefits introduced by synthetized sin In light of the presented results it is possible to conclude that the experimental results confirm signal;In in fact,light it of acts the as presented a filter outside results the it selected is possible bandwidth to conclude allowing that thethe consequential experimental reconstructionresults confirm what was obtained in the simulation tests. It is worth highlighting the benefits introduced by ofwhat the signal was fromobtained the convolutionin the simulation operation. tests. It is worth highlighting the benefits introduced by synthetized sin signal; in fact, it acts as a filter outside the selected bandwidth allowing the synthetizedOn the other sin hand, signal; the in real fact, conditions it acts introduceas a filter variables outside that the are selected not considered bandwidth in the allowing simulating the consequential reconstruction of the signal from the convolution operation. environment.consequential For reconstruction example, (i) theof the noise sign introducedal from the from convolution the RUTs operation. and/or by the acquisition system; On the other hand, the real conditions introduce variables that are not considered in the (ii) theOn uncertainties the other introduced hand, the byreal the conditions measurement introd chain.uce However,variables fromthat theare presented not considered results itin has the simulating environment. For example, (i) the noise introduced from the RUTs and/or by the beensimulating confirmed environment. that, even including For example, the real (i) aspects the no ofise an introduced in-laboratory from measurement, the RUTs theand/or proposed by the acquisition system; (ii) the uncertainties introduced by the measurement chain. However, from the characterizationacquisition system; procedure (ii) the is euncertaintiesffective and fully introduc applicable.ed by Itthe is worthmeasurement commenting chain. on However, the measurement from the presented results it has been confirmed that, even including the real aspects of an in-laboratory setuppresented adopted. results In fact,it has to been implement confirmed the proposedthat, even characterizationincluding the real a veryaspects simple of an and in-laboratory common measurement, the proposed characterization procedure is effective and fully applicable. It is worth equipmentmeasurement, has beenthe proposed deployed. characterization Furthermore, procedure it is fully consistentis effective (andand fully even applicable. simpler, due It is to worth the commenting on the measurement setup adopted. In fact, to implement the proposed characterization consideredcommenting range on ofthe frequencies) measurement with setup the oneadopted. used In to fact, perform to implement the sweep the frequency proposed test. characterization a very simple and common equipment has been deployed. Furthermore, it is fully consistent (and a veryOverall, simple results and arecommon comforting equipment from dihasfferent been points deploye of view.d. Furthermore, First of all, it the is simulationfully consistent tests are(and even simpler, due to the considered range of frequencies) with the one used to perform the sweep validatedeven simpler, from the due experimental to the considered results. range In other of words,frequencies) the smart with characterization the one used to procedure perform hasthe beensweep frequency test. provenfrequency to be test. effective. Hence, with a faster characterization procedure than the well-known sweep Overall, results are comforting from different points of view. First of all, the simulation tests are frequencyOverall, test it results is possible are comforting to obtain the from transfer different function points of of the view. RUT. First Second, of all, in the light simulation of the previous tests are validated from the experimental results. In other words, the smart characterization procedure has conclusionvalidated andfrom of the the experimental simplicity of theresults. characterization In other words, developed, the smart it is worthcharacterization furthering procedure study in this has been proven to be effective. Hence, with a faster characterization procedure than the well-known been proven to be effective. Hence, with a faster characterization procedure than the well-known sweep frequency test it is possible to obtain the transfer function of the RUT. Second, in light of the sweep frequency test it is possible to obtain the transfer function of the RUT. Second, in light of the

Sensors 2020, 20, 3359 14 of 16 direction. In fact, the aim of the following studies, now that it has been proved the characterization validity, will be to understand its capabilities and limits extending the range of experimental/simulating studies and the number of Rogowski coils tested.

7. Conclusions The paper introduces a new smart characterization procedure for Rogowski coils. The process consists of injecting a synthetized signal in the primary windings of the Rogowski and of measuring the secondary voltage. With such a response, it is possible to estimate the secondary response of a variety of primary distorted currents. The application of this characterization aims at helping in-field and laboratory operators, to simplify and accelerate their tests by using a typical and very simple measurement setup. In the paper, the smart characterization has been firstly described from a mathematical perspective; afterwards, it has been tested with the Matlab environment. Finally, the characterization has been applied on three off-the-shelf Rogowski coils, testing its applicability using a variety of distorted primary signals. Both simulative and experimental results confirm the validity of the presented characterization and stimulate further research on the topic. In fact, the possibility of estimating the behavior of low-power current transformers is a task highly required by the power network model designers and distributed system operators.

Author Contributions: Conceptualization, A.M. and R.T.; methodology, R.T.; validation, L.P.; formal analysis, R.T.; investigation, A.M.; resources, L.P.; data curation, A.M.; writing—original draft preparation, A.M.; writing—review and editing, R.T. All authors have read and agreed to the published version of the manuscript. Funding: This research has been partially funded by the European project EURAMET 17IND06 “Future Grid II: Metrology for the next-generation digital substation instrumentation”. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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