External Magnetic Fields Effect on Harmonics Measurements with Rogowski coils

—The power quality (PQ) problem is spreading among the distribution network (DN) since intelligent electronic devices (IED) are being installed. Their presence is crucial because they introduce several benefits for the network observability and management. However, the consequent power quality degradation has to be seriously tackled. To this purpose, measurement instruments should be capable of measuring the electrical quantities even in presence of distortion. Furthermore, the new added distortion has to be summed to the typical influence factors affecting the measurement instruments (like temperature, electromagnetic fields, humidity, etc.). Therefore, this paper presents a study on a specific low-power current transformer (LPCT), the Rogowski coil. In detail, the influence of external magnetic fields, on the Rogowski accuracy performance, is evaluated when the device is measuring distorted signals (with an increasing level of distortion). The aim is to study the combined effect of the magnetic fields and of the distorted currents on the measurement performance of a Rogowski coil. Therefore, an ad-hoc measurement setup and tests are developed in this work to assess 3 off-the-shelf Rogowski coils. From the results it can be concluded that the presence of external magnetic fields does not influence the harmonics evaluation, but it does influence the evaluation of the 50 Hz component.


I. INTRODUCTION
The spread of Intelligent Electronic Devices (IEDs) is increasing every day. This results into two main consequences: (i) the increased complexity of the network and of its equipment; (ii) the effect on the power quality level due to the IED presence. The former consequence is mainly solved by System Operators (SOs) who have to manage and control the network. However, their work is typically facilitated by control algorithms and new techniques developed by researchers [1][2][3].
The SO aim is to maintain the voltage quality within the limits defined in the IEC 50160 [4]. Therefore, the second consequence becomes highly important and has to be properly addressed. To this purpose, the new generation of Low-Power Instrument Transformers (LPITs) [5], which is replacing the legacy inductive one, has the characteristic for facing the power quality problems. In fact, they typically feature reduced dimensions, wider bandwidth, higher immunity to external influence quantities, compared to the inductive instrument transformers (ITs).
Therefore, this paper studies a particular kind of LPIT, the Rogowski coil. Its high rate of adoption in the distribution network (DN) is clearly justified by its flexibility, ease of installation, wide bandwidth, etc.
Aim of this work is to assess the Rogowski performance, in presence of external magnetic fields, when it is measuring distorted currents. Of course, both influence quantities and distorted currents are topics well stressed in literature as far as the Rogowski is involved. In particular, [6][7][8] treat the harmonic analysis and measurement issues related to Rogowski coils, suggesting countermeasures. In [9][10][11][12], instead, the effect of influence quantities like temperature, geometry, magnetic fields, etc., is studied.
The added value of this work is to assess the change in the Rogowski accuracy performance when the external magnetic field is affecting a Rogowski coil measuring a distorted current.
What follows is structured as: Section II briefly describes the working principle of a Rogowski coil. The measurement setup and the experimental tests developed within this work are presented in Section III and IV, respectively. Finally, Section V and VI provides the results and the conclusion of the work, respectively.

A. Rogowski coils operating principle
Rogowski coils are low-power current transformers (LPCTs) which are based on the same working principle as conventional iron-core current transformers (CTs).
What makes a difference between these two is that Rogowski coils are wound over a non-magnetic core, typically an air-core. Its peculiarity is that such core cannot saturate, resulting in a linear behavior devoid of saturation issues.
Rogowski coils are placed around a conductor in which the unknown current (i) has to be measured.
The schematic of an LPCT is depicted in Fig. 1. In it, the cross-section S and the radius R of the device can be distinguished. The output voltage us is proportional to the rate of change of the measured current i: The 19NRM05 project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme". , (1) where M is the mutual inductance between the considered conductors.
As clearly indicated in (1), the phase angle between the Rogowski coil primary current and the secondary voltage is ideally π/2. Nevertheless, this value differs from the ideal one by an angle introduced by the coil parasitic parameters.
As the objective of this work involves the study of the performances of Rogowski coils under the influence of external magnetic fields, it is worth marking some further remarks about the structure of the considered LPCTs.
In fact, owing to the weak coupling between primary and secondary windings, Rogowski coils are designed in such a way that the undesirable influence of external conductors is minimized. For this reason, two wire loops are typically connected in electrically opposite directions which helps in cancelling the electromagnetic fields coming from the outside of the coil loop.
External magnetic fields as an influence quantity have already been considered in the relevant Standards, where a specific test has been designated to verify the influence of other phases on the accuracy of LPCTs [13].
The difference of both ratio and phase errors between measurements at the rated conditions and in presence of external fields shall be within 1/3 of the error limits of the relevant accuracy class [13].
In the next section, the measurement setup adopted for performing tests is described. • Calibrator. Fluke 6105A controlling the transconductance Fluke 52120A is used to produce a reference primary current (Iref), either sinusoidal or distorted. The calibrator accuracy characteristics are listed in Table I. The values in the table refers to the performance of the transconductance when controlled with the calibrator.

IV. EXPERIMENTAL TESTS
In this Section, the experimental tests performed on the measurement setup illustrated in Fig. 2 and detailed in Section III are presented. This Section intends to present the measurement conditions and the evaluated parameters obtained from the preliminary assessments.

A. Testing conditions and configurations
According to the setup shown in Fig. 2, the combination of Fluke Calibrator and Transconductance is used to generate a reference current (Iref) which is set equal to 100 A for all tests.
The three commercial Rogowski coils (R1, R2, R3) are wrapped around the conductor in which Iref is flowing. Their output voltages, Vr1, Vr2, Vr3, are acquired using the NI 9238 DAQ board.
It is also worth noting that a reference voltage (Vref) generated in the calibrator and equal to 500 mV is also acquired on one of the 4 channels of the DAQ. This signal aims at providing the phase reference needed to assess the phases of the Rogowski coils under test.
All the acquired signals are post-process in a PC using LabVIEW and MATLAB environments. A Fourier analysis is performed over 10000 Samples acquired at a sampling rate of 50000 (Samples/s)/ch, corresponding to an observation window of 200 ms. For each test 100 measurements are performed.
The tests described in Sections IV-B and -C are performed for all three Rogowski coils loaded with their rated burden (2 MΩ, see [5]). Furthermore, two positioning configurations are implemented. The first testing condition consists in placing the primary conductor perfectly centered with respect to the Rogowski coils' symmetry axes. This configuration, from here on after, is referred to as T1, for the sake of brevity. Results obtained from T1 configuration will be considered as a reference for the other configuration.
The second testing arrangement, instead, intends to study the effects of external magnetic fields due to proximity effects on the sensors when an external conductor is adjacent to it. The current value in the external conductor is the same as that in the main conductor. It is worth underlying that, even in this second configuration, the conductor is still centered with respect to the sensors' axes. This configuration, from here on after, is referred to as T2.
The two different configurations, resulting into two variations of the measurement setup, are illustrated respectively in Fig. 3 (a, b). For both figures, the Rogowski coil is represented in green, the solid black line represents the primary conductor in which a current Iref is flowing, and the two dotted red lines represent the symmetry axes of the sensor. In what follows the characteristics of the current injected through the primary conductor are detailed and distinguished between sinusoidal (Section B) and distorted signals (Section C).

B. Sinusoidal Tests
In these tests a pure sinusoidal current of 100 A RMS at 50 Hz (Iref) is applied. The specifications illustrated in Section IV A hold for these tests. To evaluate the performances of the three sensors, the following errors are used: a) Ratio error : it is calculated according to [5] as: where is the rated transformation ratio, ! is the RMS value of the primary current and " is the RMS value of the secondary voltage (both extracted as the 50 Hz component of the signal).
This error is computed for all 3 Rogowski coils and for both configurations T1 and T2 to evaluate the difference in the two cases. b) Phase error # : in order to compute this error the reference voltage (Vref) described in the previous Section III is used as a phase reference. This signal is used to compute the phase displacement introduced by the sensors which is theoretically equal to $/2, as shown in (1).
The phase error # is computed according to [5] as: where is the secondary phase and ! is the primary one. Analogously to , # is calculated for both T1 and T2 configurations.

C. Harmonic Tests
For these set of tests, using configurations T1 and T2, a rated current of 100 A RMS is injected via the calibrator and the transconductance. Superimposed to the 50 Hz component there are several combinations of harmonics (according to [14]).
Four different tests, referred to as A to D, are performed with an increasing harmonic content as specified in Table  III. In particular, from left to right, there is: the name of the test, the order h of the considered harmonic, the percentage of the amplitude of the h-th harmonic with respect to the 50 Hz component (h%), the corresponding amplitude of the harmonic (Ih), the reference THD set by the calibrator (THDcal) and regarded as a reference, and the actual RMS of the reference current Iref, provided by the calibrator when setting 100 A. These tests aim at assessing the performances of the Rogowski coils when it is simultaneously affected by a distorted current and by external magnetic fields. The attained results are used to calculate the following parameters:

a) Harmonic currents in [A]
: performing the Fourier analysis on the output signal, the measured harmonic currents are evaluated and compared with respect to their reference values (Ih) set in the calibrator to assess the distortion introduced by the sensors.
which is then compared to its reference value measured by the calibrator (THDcal). In (4), 3,456 is the 50 Hz component of the current Iref, 7,456 is the h-harmonic current, and N is the number of harmonic components. All these parameters are computed for both T1 and T2 configurations and presented in the next section. Note, ratio and phase error have been calculated, even in distorted conditions, only for the 50 Hz component.

V. TEST RESULTS
In this Section the most significant results obtained from the tests illustrated in the previous Section IV are presented in the same order as they were introduced. Fig. 4 presents the results obtained from Test D. This test, according to Table III, comprises the highest number of harmonics. The figure presents the measured harmonic currents Ih in [A] as a function of the harmonic order h. The data represented with red color refer to the harmonic current set in the calibrator (see Table III) and have to be regarded as a reference.
In the same figure, darker colors represent tests performed in configuration T1. Respectively dark yellow, blue and green illustrate the results of Rogowski coils R1, R2 and R3. Following the same rationale, lighter colors present the results of Rogowski coils R1, R2 and R3 (yellow, blue and green, respectively) in configuration T2.
As depicted in Fig. 4, it is evident that the measured harmonic currents Ih by the three Rogowski coils under test are not strongly affected neither by the sensors themselves nor by the presence of external magnetic fields. Indeed, comparable results are obtained for all sensors and in both T1 and T2 configurations. A worsening in the estimation of harmonic content is present for low-order harmonics up to the 9 th . Results for the harmonic configurations A to C are not presented, for the sake of brevity, because fully aligned with what above described.
The second parameter which has been evaluated is the THD. Fig. 5 shows the THD obtained applying Eq. (4) using the current components extracted with the FFT.
The graph presents the results obtained in all tests, namely A, B, C and D, for the three Rogowski coils and in both configurations T1 and T2. Red, blue, green and yellow color bars respectively refer to Test A, B, C and D whose reference THD value is presented in Fig. 5 with the darkest shade, and it corresponds to the value shown in Table III, Section IV (THDcal).
In Fig. 5, the two lighter colors, presented in all four test cases, respectively refer to the THD obtained using configurations T1 and T2.
The results shown in the graph of Fig. 5 confirm what has been previously observed in Fig. 4, meaning that the estimation of harmonic current components is not strongly affected by the intensity of the harmonic content (Tests A to D do not play any major role in this evaluation) nor by the presence of an external magnetic field affecting the primary conductor. Therefore, considering the negligible variation of the measured parameters, no zoomed pictures of the results has been reported for the sake of brevity.  The results shown in Fig. 6 depict both the ratio errors measured in pure sinusoidal conditions (darkest color) and the ones obtained in presence of high harmonic content (lighter colors), namely in Tests A to D, for all three Rogowski coils. The orange shades present the outcomes obtained from configuration T1, whereas the blue ones the results from configuration T2.
No reference color bar has been shown as, clearly, an ideal Rogowski coil should have an ε approaching zero.
The graph illustrated in Fig. 6 provides some interesting results regarding the behavior of the three devices under test in presence of external magnetic fields.
Precisely, it could be noticed that the presence of an external field in the nearby of the primary conductor not always implies a worsening in the performance of the sensor. Indeed, R2 ε reduces more than 50 % in configuration T2 with respect to its reference case T1 (note that all ε values presented refer to the 50 Hz component).
On the other hand, R1 results show that T2 configuration played a major role in the deterioration of the performances, as the ε has more than doubled with respect to T1.
Finally, R3 presents another different behavior compared to the other two devices under test. In this case, not only did the ε worse its performance in T2, but it also changed sign.
A final remark concerns the harmonic content present in the four tests A to D which have been carried out. It is worth noting that the number of harmonics does not strongly influence the ε for all three Rogowski coils R1, R2 and R3. Indeed, what has been measured for the pure sinusoidal case is comparable with all four harmonic tests.
Lastly, Fig. 7 shows φ ; in [rad] obtained applying both a pure sinusoidal waveform and in the four distorted Tests A to D. The color code used in Fig. 6 is replicated in Fig. 7 as well, for the sake of clarity. In addition, in Fig. 7 a redcolored indicator has been added to represent the ideal π/2 phase displacement introduced by the coil.
Some of the considerations previously done for Fig. 6 hold true also in this case, namely the configuration T2 tends to strongly affect φ ; with respect to T1 case.
Lastly, φ ; does not significantly vary depending on the intensity of the harmonic content, albeit higher fluctuations are visible in case of R3.
Having analyzed all the achieved results, it can be concluded that the amount of the harmonic content does not significantly impact the evaluation of harmonic currents, the THD, ε, and φ ; . However, it has been highlighted that on the one hand the harmonic evaluation is not affected by the presence of magnetic fields. On the contrary, the evaluation of the 50 Hz components is strongly affected by it, leading to a worsening of the Rogowski performances.

VI. CONCLUSIONS
This work presents a study involving the evaluation of the harmonic content by Rogowski coils both in rated conditions and in presence of external magnetic fields.
The latter type of tests is taken into account as the Standards do not provide specific information concerning the evaluation of the harmonic content in presence of nearby magnetic fields.
The results have shown that the intensity of harmonic content does not play any major role in the estimation of ratio and phase errors, instead the presence of magnetic fields strongly influence these two quantities.
The outcomes have shown that this influence quantity does not necessarily imply a worsening in the performances of the LPCTs, but rather an inconstant behavior which is not influenced by the intensity of the harmonic distortion.