High-Frequency Current Transformer With Variable Air Gap for Power Cable Monitoring

This article deals with partial discharge (PD) measurement on power cables, while they are in operation (online monitoring). In terms of sensitivity, high-frequency current transformers (HFCTs) are the most suitable sensors for this task, but they are prone to magnetic saturation when monitoring power cables online. To counteract saturation, the magnetic ring core of the HFCT is usually split into two halves to create air gaps. We show that a variable air-gap length is required to maximize the HFCT sensitivity, and that the optimal air-gap length depends on the actual operating point of the power cable. Accordingly, we present a concept for the construction of an HFCT capable of self-adjusting its air-gap length during operation. The air-gap control strategy is explained in detail and tested with a prototype. In addition, we propose a method for PD detection based on a combination of an analog peak detector circuit followed by a software algorithm. The developed PD sensor is immune to magnetic saturation, always operates at its optimum operating point, and can, therefore, detect PD pulses with much higher sensitivity than comparable sensors with a fixed air-gap length. Our tests prove that the sensor system works as intended and will be further improved in the future.


I. INTRODUCTION
D ISTRIBUTION system operators (DSOs) distribute elec- trical energy at the medium-voltage level (6-30 kV) mainly via power cables.Many of those power cables are decades old, and the condition of their insulation system deteriorates over time, potentially leading to insulation failure, cable breakdown, and outages.As of today, DSOs cannot assess the insulation quality of their power cables, because they lack the appropriate sensors.Therefore, there is a need for effective methods to monitor the insulation condition of power cables and detect any signs of degradation or failure before they cause significant problems.
Partial discharge (PD) measurements are an effective tool for this task.PDs can be defined as localized electrical discharges that occur at defects within the insulation layer of the cable system.They are, thus, an indicator of poor insulation quality.PDs are weak current pulses with amplitudes in the mA range and pulse duration of only a few nanoseconds.By measuring PD pulses, insulation defects can be identified early, so that the DSO can take corrective action before a cable failure occurs, i.e., act proactive instead of reactive.Such a condition-based maintenance strategy helps to determine the risk of insulation failure, prevent power outages, reduce maintenance costs, and improve the overall reliability of the power system.
Successful condition-based maintenance requires continuous PD measurement on all power cables operated by a DSO and, thus, a large number of PD sensors.Such continuous online monitoring with real-time data is always superior to periodic offline measurements.
To measure PD pulses on power cables, inductive sensors, so-called high-frequency current transformers (HFCT), are widely used.HFCT sensors are built on a ferromagnetic toroidal core and have a high sensitivity to measure PD pulses, provided their core material is not magnetically saturated.However, when monitoring a power cable online with an HFCT, the cable's operating current often causes magnetic saturation [1], [2].This operating current has a frequency of 50 or 60 Hz, and its amplitude varies between 0 and the rated current of the power cable, which can be up to several hundred amperes.Accordingly, during online monitoring, the HFCT sensors are exposed to high magnetic fields that will saturate their core no matter what ferrite material is used.Saturation lowers the sensitivity of the HFCT, leads to inaccurate measurements, and thus difficulty in detecting the weak PD signals [3].
Using a split-core HFCT is a common solution to address the issue of magnetic saturation during PD measurements on power cables, but split-core HFCTs have lower sensitivity compared with solid-core sensors due to the air gaps.Therefore, to maximize the accuracy and sensitivity of a split-core HFCT, the length of its air gaps should be as short as possible, but also as long as necessary to avoid magnetic saturation.This optimal air-gap length depends on the amplitude of the 50 Hz operating current of the power cable, which changes over time, so there is no one-length-fits-all answer.
In a previous article [3], we analyzed the optimal air-gap length of split-core HFCTs in online power cable monitoring.We concluded that the air-gap length has to change over time to always achieve maximum sensitivity in PD measurement.Our optimized HFCT design for a measurement bandwidth of 0-10 MHz.The core is split and the length of each air gap d air can be adjusted (both air gaps are always of equal length).The core has the shape of a toroid to maximize its magnetic efficiency [5].
Based on this result, we developed the idea of an HFCT sensor with active air-gap control.The concept of this new PD sensor has already been presented in a conference paper [4], and this article is an extension of it.Compared with the previously published work, this article offers the following new contributions: 1) improved air-gap control circuit and proof of concept based on experiments (servomotor control); 2) method for reducing the sampling frequency of the HF measurement without loss of information (analog preprocessing); 3) method for detecting PD pulses in the HFCT measurement and proof of concept based on simulations.This article is structured as follows.Section II briefly reviews the state of the art in HFCT sensors and summarizes our previous research.In Section III, we then present the concept and operation of our improved HFCT sensor with air-gap control in detail.Finally, a conclusion is drawn in Section IV.

II. OVERVIEW OF OUR PREVIOUS RESEARCH
HFCTs are often used to measure PD currents flowing in a power cable.The sensors mainly consist of a ferromagnetic toroidal core and a secondary winding with n 2 turns wound around it (see Fig. 1).For measurement, the toroid is attached to the end termination of the power cable, either around its inner or outer conductor (shielding) [1].
Once installed, the sensor's magnetic core couples the magnetic field of the power cable current i 1 .The magnetic flux in the core then, in turn, induces a measurable voltage u L in the secondary winding.The power cable current i 1 consists of the 50 Hz operating current with amplitudes of several tens to hundreds of amperes plus any superimposed PD signals with pulse amplitudes of a few milliamperes.
PD pulses are nanosecond pulses and, thus, characterized by a high-frequency (HF) spectrum up into the MHz range.The input current, therefore, has measurable components in two different frequency ranges (50 Hz and HF).HFCTs are designed to be sensitive to the HF signals.Ceramic ferrite cores made of nickel-zinc (NiZn) mixtures are mainly used for this purpose.These cores are well suited for sensitive measurements in the HF range, but, on the other hand, are Fig. 2. Optimal air-gap length function of our split-core HFCT.The optimal air-gap length d air,opt increases with the operating current of the power cable I 1,50 Hz .Further information on the measurement procedure and data verification can be found in [3].
prone to saturation caused by the magnetic field of strong currents.For NiZn materials, saturation already starts at current strengths of a few amperes.Thus, when performing online PD measurements, the 50 Hz operating current of the power cable becomes a problem and saturates the HFCT core.With saturation, sensitive PD measurements are no longer possible [4].
In [6], we have shown that successful online monitoring of power cables requires a PD sensor with a measurement bandwidth of 10 MHz to detect the majority of all PD pulses.Subsequently, in another previous publication [7], we optimized an HFCT sensor design for this measuring bandwidth of 0-10 MHz.The resulting sensor can be seen in Fig. 1.Our HFCT is built on a toroidal ferrite core with n 2 = 3.The core is made of a NiZn ferrite from the manufacturer Fair-Rite (material No. 43) with a size of 63.5 × 102.6 × 15.9 mm.The core is split into two halves, creating two air gaps of length d air .Both air gaps are always of equal length.
In [3], we then investigated the optimal air-gap length d air,opt for our split-core HFCT.With optimal air-gap length, magnetic saturation is avoided during online monitoring of power cables while ensuring maximum sensitivity of the HFCT.The results show that the optimal air-gap length is not constant, but varies with the amplitude of the 50 Hz operating current of the power cable I 1,50 Hz (rms value); see Fig. 2. As the operating current increases, the optimal air-gap length also increases.The relationship is not linear, but corresponds approximately to the following function: If the HFCT sensor is not operated with optimal air-gap length, there will be a loss of sensitivity.If the air gap is shorter than the optimum, the sensitivity decreases sharply due to core saturation.If the air gap is longer than necessary to avoid the saturation, the sensitivity also decreases due to worse coupling (for a more detailed discussion, see the PD measurements in [3] and [4]).Since PD signals are difficult to detect anyway, a loss of sensitivity cannot be accepted.The HFCT should, therefore, always be operated close to its optimum to measure PDs with maximum sensitivity.Hence, to always achieve maximum sensitivity during online PD monitoring, the HFCT should be able to automatically self-adjust the length of its air gaps to the amplitude of the 50 Hz operating current.As far as the authors are aware, no such HFCT system exists to date.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

III. CONCEPT OF A SPLIT-CORE HFCT WITH AIR-GAP CONTROL
To change the air-gap length of the HFCT during operation, a sensor design is required that allows both halves of the split core to move relative to each other.To widen the air gaps, the core halves must move apart; to shorten them, they must move back toward each other.Fig. 3 shows our solution how to construct such a device.In our design, the left half of the core is movably mounted on a base plate, so that its position can be changed relative to the right half.This motion is driven by an electric servomotor.The position of the right half of the core is fixed.Fig. 3 shows the CAD design with the air gap fully closed, while Fig. 4 shows a photograph of the manufactured prototype with the air gap open by a few mm.
A good overview of the entire sensor system is given in Fig. 5.It can be seen that the output of the HFCT winding is terminated with a load resistor R L = 50 .The output voltage of the HFCT u L (t) is then further processed for both air-gap control and PD detection.Both tasks are handled by separate microcontrollers.An Arduino measures the 50 Hz Fig. 5. Overview of the complete PD sensor system based on a split-core HFCT with air-gap control.The air-gap length of the HFCT is controlled by the Arduino, while the LPC4370 microcontroller monitors the power cable for PDs.component of u L (t) and takes over control of the servomotor for optimal adjustment of the air-gap length of the split-core HFCT.The Arduino's analog-to-digital converter (ADC) has a default sampling frequency of f s,Ard = 9600 Hz, which is sufficient for accurate 50 Hz measurements.The second microcontroller is an LPC4370 from the manufacturer NXP, which is much faster and, thus, continuously monitors the HF component of u L (t) for PD pulses.The LPC4370 is equipped with a high-speed ADC with a maximum sampling frequency of f s,LPC = 80 MHz and a sampling resolution of 12 bit [8].The microcontroller is available as a development board called LPC-Link 2.
In the following, all blocks mentioned in Fig. 5 are explained in detail.For this purpose, the CAD design of the new prototype is first described in more detail in Section III-A.Section III-B then explains how to control the servomotor to avoid magnetic saturation.Subsequently, all blocks related to the PD measurement are discussed in Section III-C.

A. Design of the Prototype
All parts of the prototype, except for the ferrite core and winding, are designed using CAD software and then printed using a 3-D printer (fused deposition modeling).The construction consists mainly of three printed elements, which can be better seen in Fig. 6.There are two brackets printed from black filament, on which the two halves of the core are mounted.The third element is a base plate printed from gray filament to which one of the brackets, and thus one half of the core, is attached via a sliding rail system.The rails have the shape of a trapezoid (dovetail).The servomotor is equipped with a printed gear wheel and is also mounted on the base plate with a strong superglue.The gear wheel drives a gear rack that moves the bracket along the sliding rails, which can be better seen in Fig. 4. The two halves of the construction are connected by snap locks, so that they can be easily separated at any time for installation; compare Figs. 4 and 6.The snap locks are also glued to the printed parts with superglue.During manufacture, all printed parts are assembled first, and the core and copper winding are attached last.The winding is fed through holes in the printed parts at various points to guide it and hold it in position.Both ends of the winding are connected to a Fig. 6.Manufactured prototype in open state for installation.The two halves of the sensor are connected by snap locks and can be easily separated.In the photograph, the BNC connector is soldered to the winding-a pluggable BNC connector would be better to further facilitate the installation of the sensor around a power cable.
BNC connector where the HFCT output voltage u L (t) can be measured.
The servomotor used is an MG90S type motor.This type of servo is inexpensive and lightweight and has a torque of about 1.8 (kg/cm) at an operating voltage of 5 V, which is sufficient to move one half of the ferrite core (weight of about 175 g).The rotation angle of the servomotor ϕ can be adjusted between 0 • and 180 • with a resolution of 1 • .An integrated position control loop guarantees high precision.The angle set point is specified by the Arduino microcontroller, which controls the air-gap length in this way.Fig. 4 shows how a rotation of the servomotor is converted into a translational movement of the left half of the core.The position of the right half of the core does not change.With this design, it is possible to vary the air-gap length between 0 and approximately 12.4 mm, which corresponds to changing the rotor angle from 180 • to 0 • .The relationship between the air-gap length d air of the HFCT and the rotation angle ϕ of the servomotor is a linear function Thus, the smallest possible step width of ±1 • corresponds to a minimum length change of ±0.0687 mm.

B. Servomotor Control
The servomotor is controlled by an Arduino Nano microcontroller.In this section, our method for automatic air-gap control of the HFCT sensor is explained in detail.
The optimal air-gap length of our split-core HFCT d air,opt depends on the 50 Hz operating current of the monitored power cable I 1,50 Hz .If the amplitude of this operating current was known, the optimal air-gap length could be simply set according to (1).Unfortunately, it is not possible to measure I 1,50 Hz directly or to calculate it indirectly from the amplitude of the HFCT output voltage ûL , because the transfer function Output voltage of the HFCT prototype measured at increasing 50 Hz operating currents and, thus, at increasing levels of core saturation (while d air = 0 mm).At I 1,50 Hz = 2 A, the HFCT is not saturated, and u L is sinusoidal with f = 50 Hz (linear measurement).The other two measurements are not sinusoidal, indicating magnetic core saturation (nonlinear measurement).
of an HFCT with air-gap control is nonlinear.Any change in air-gap length results in a change of the HFCT transfer function, so there is no simple relationship between u L (t) and I 1,50 Hz .Thus, (1) cannot be used for the air-gap control.Instead, the saturation level of the HFCT core is determined from the u L (t) measurement.
1) Determination of the Level of Core Saturation: Fig. 7 shows how an HFCT measures the 50 Hz operating current of a power cable and how core saturation affects this measurement.For this figure, our HFCT is installed around an electrical conductor carrying a 50 Hz current with rms values I 1,50 Hz of 2, 10, and 50 A. The air-gap length is kept constant at d air = 0 mm.At I 1,50 Hz = 2 A, the measured output voltage is sinusoidal, which means there is no core saturation, and the input current is measured correctly (linear operation).As the amplitude of the 50 Hz current increases, the measured output voltage becomes more and more nonsinusoidal due to increasing core saturation, i.e., its harmonic distortion increases (nonlinear operation).Calculating the total harmonic distortion (THD) of the 50 Hz component of the measured HFCT output voltage u L (t), therefore, provides a good measure for determining the saturation level of the core [9].If the output voltage is sinusoidal, the THD approaches 0, which means that the HFCT core is free of magnetic saturation [3].
To calculate the THD, the Fourier transform of the measured voltage must first be calculated, i.e., u L (t) Then, the THD value can be calculated as follows [10]: where U L,i is the ith harmonic (150, 250 Hz, . ..) and U L,1 is the fundamental component of the HFCT output voltage spectrum (50 Hz).Therefore, for servomotor control, the Arduino first digitizes the 50 Hz component of the HFCT output voltage u L (t), then performs a Fourier transform of the measurement, and then calculates its THD content.THD values above 0 indicate nonlinear HFCT operation and, thus, saturation.Then, the air-gap length needs to be extended.
2) Inverting Amplifier: So, it is necessary to measure the 50 Hz component of u L (t) continuously, although the HFCT Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. is optimized for measuring signals in the HF range up to 10 MHz and its sensitivity at 50 Hz is very low.Accordingly, measurements of the 50 Hz component of u L (t) have low amplitudes in the mV range, as shown in Fig. 8 (top).For this figure, the 50 Hz operating current of the power cable I 1,50 Hz is increased from 20 to 300 A, while the air-gap length of the HFCT is set to its optimum according to (1).With optimal air-gap length and, thus, unsaturated HFCT core, the measured HFCT output voltage is sinusoidal for all 50 Hz currents.Although I 1,50 Hz is varied over a wide range, the measured voltages look quite similar.Their amplitudes ûL range from about 35 to 60 mV.Thus, at optimal air-gap length, the amplitude of the 50 Hz component of the HFCT output voltage is always ûL < 60 mV (tested for all operating currents up to I 1,50 Hz < 350 A).Amplitudes larger than ûL > 60 mV only occur when the air gap is too short and core saturation occurs.
So, the 50 Hz component of the HFCT output voltage is a sine of about ±60 mV, while the input range of the Arduino's ADC allows for 0-5 V.Because of the different voltage levels, the HFCT output voltage u L (t) is not directly connected to the Arduino, but amplified before.For this task, a low-cost and widely used operational amplifier of type LM324N is used.The amplifier circuit is shown in Fig. 9.The circuit works as an inverting amplifier and adds an offset voltage of 2 V to the input signal.The amplified voltage at the output of the operational amplifier circuit can be calculated as follows [11]: The gain is set to G ≈ 25, so that the amplified voltage u L,amp (t) gives a sine wave oscillating in the range of about 2±1.5 V (at optimal air-gap length).A higher gain factor is not possible, because the operational amplifier is operated from a single supply voltage of 5 V, which is provided by the Arduino.With this supply voltage, the output voltage of the LM324N operational amplifier is limited to about 0.3-3.8V (it is not a rail-to-rail amplifier).The input signal u L (t) is connected to the operational amplifier via a coupling capacitor C 1 .
After amplification, the voltage u L,amp (t) is connected to an analog input pin of the Arduino Nano and, thus, to a channel of its ADC.The signal measured by the Arduino is shown in Fig. 8 (bottom).The amplified signal levels now fit well with the input specifications of the Arduino's ADC of 0-5 V.The figure also shows that the Arduino measurement is almost free of HF noise due to the low sampling frequency (only the 50 Hz component is measured).
3) Additional Settings: After digitizing and measuring the amplified signal, the Arduino performs a fast Fourier transform (FFT) with the measured data.The spacing between two frequencies of the Fourier transform f step,FFT (frequency resolution) depends on the sampling frequency f s of the ADC and the number of samples N measured (block length) Due to the limited memory of the Arduino, the number of samples of one measurement is limited to N = 128 when using FFT commands.So, with the Arduino's default sampling frequency of f s,Ard = 9600 Hz, the resolution in the frequency domain would be f step,FFT = (9600 Hz/128) = 75 Hz.These frequency steps are inadequate, because the harmonics of the Fourier transform of a 50 Hz sinusoidal signal are 150, 250 Hz, and so on.For better resolution in the frequency domain, the sampling frequency is lowered to f s,Ard = 1600 Hz.The frequency resolution of the Fourier transform is then f step,FFT = (1600 Hz/128) = 12.5 Hz.This is a good trade-off to avoid information loss during digitization: 1600 Hz is a sufficient resolution in the time domain, and 12.5 Hz is, at the same time, a suitable step size in the frequency domain.
After the Fourier transform of u L,amp (t), the THD value of the measurement is calculated according to (3).The THD calculation is performed based on the first seven harmonics (150, 250, . . ., 750 Hz).The Fourier transform now contains a dc component, which is due to the dc offset of the operational amplifier.This dc component is simply ignored in all calculations.A pure sine signal would result in a THD factor of 0. In reality, however, the THD value never drops to 0 due Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.to possible harmonics in the 50 Hz current of the power cable and the omnipresent measurement noise.Thus, the calculated THD value is always somewhat higher than in theory.
For further clarification, Fig. 10 shows THD measurements recorded with our HFCT prototype and the Arduino at different operating points.For this figure, the 50 Hz operating current of the power cable is increased from 20 to 300 A, while the air-gap length of the HFCT is varied between 0 and 3 mm.The optimal air-gap length function from ( 1) is plotted along with the THD measurements (blue line).
It can be seen, that the area without core saturation, below the blue line, is characterized by THD values less than 1%.Therefore, in our laboratory environment, the THD threshold for distinguishing between saturated and unsaturated HFCT core is 1%, which is a good compromise for clearly detecting saturation while ensuring sufficient robustness against noise.As soon as a THD value greater than 1% is calculated, the HFCT's air-gap length must be increased.
4) Air-Gap Control Algorithm: To better understand the sequence of the Arduino program, see the flowchart in Fig. 11.After starting, the ADC of the Arduino is initialized first, and its sampling frequency is set to f s,Ard = 1600 Hz.Then, a measurement of the initial angle ϕ 0 of the servomotor is performed.The servo has a built-in potentiometer that provides a voltage signal U pot proportional to the current angle of rotation.To measure this voltage, the middle pin of the potentiometer is connected to an analog input pin of the Arduino.By knowing the voltages at the two servomotor limits 0 • and 180 • , U pot can be mapped linearly to the rotation angle ϕ of the servomotor.At the end of the setup phase, a timer t is initialized and started before the program enters the main loop.
In the main loop, the Arduino continuously measures the amplified HFCT signal u L,amp (t) and monitors its THD value.If the THD value is greater than 1%, the rotation angle of the servomotor is reduced by 1 • to open the air gap.If the air gap is large enough, saturation does not occur, and the THD value is less than 1%.In this case, the rotation angle of the servomotor is increased by 1 • every 10 s to keep the air gap as short as possible, i.e., close to its optimum.Increasing the air-gap length has priority over decreasing it, since the air gap should rather be slightly too large than too short.The value of 10 s was chosen arbitrarily for the initial testing of the prototype.In a realistic environment, this time value depends on the rate of change of the amplitude of the power cable's operating current.This needs to be further investigated in the future.
5) Test: To check whether the servomotor control and thus the developed HFCT prototype works as planned, various measurements have been performed.Fig. 12 shows the results of an exemplary test run of about 13 min duration.For the test run, the HFCT is installed around a power cable carrying a 50 Hz current.This current is initially set to I 1,50 = 20 A and increases every 60 s, as can be seen by the blue line in Fig. 12.The red dashed line shows the optimal air-gap length d air,opt of the HFCT at the different current levels, calculated according to (1).The solid red line shows the actual air-gap length set by the servomotor control during the test run.The test run stops at a current of 180 A, because our current source has automatically switched off due to overload, so that higher currents could not be tested with the equipment used (Omicron CMC-256-6).
Comparing the red dashed line and the solid red line shows that the air-gap length set by the servomotor control is often a bit too long compared with the optimum and how the algorithm constantly tries to shorten the air gap every 10 s.Fig. 13.This test is similar to the one in Fig. 12, but over a much longer duration.The cyan curve shows the moving average of the air-gap length set by the servomotor's control algorithm.Fig. 14.Air-gap length set by the algorithm (red) is close to the calculated optimum (blue).The yellow curve shows the difference between the air-gap control algorithm and the optimal value.For further investigation, Fig. 13 shows the results of another similar test run with a much longer duration of about 47 min.Once again, the 50 Hz current starts at 20 A, but this time it increases only every 5 min.This makes it easier to observe the behavior of the servomotor control at the different current levels.To support the readability of Fig. 13, the cyan-colored line shows the moving average of the air-gap length set by the servomotor control.
It can be seen that the course of the moving average is similar to the calculated optimum plus an additional offset of about 0.2 mm at all times.So, the air-gap control works as intended, but the experiment shows a systematic and constant deviation from the optimal air-gap length.
We have observed this systematic deviation in all the test runs that we have performed over time.To better quantify the deviation, we averaged the measured air-gap length data of all our test runs.This gives the average air-gap length d air,set (I 1,50 Hz ), which is set by the servomotor control.The result is shown in Fig. 14 together with the optimal air-gap length function of our HFCT according to (1).The yellow curve shows the difference between both curves.
It can be clearly seen that the actual air-gap set by the servomotor is always slightly longer than the optimum, to be precise 0.1-0.2mm longer.This systematic deviation is mainly due to noise in the measured u L,amp (t) signal, which affects the calculated THD level (see Fig. 11).More noise leads to a higher THD content in the measurement.A higher THD level, in turn, leads the algorithm to set a longer air gap.
Two main sources of noise can be identified, first, general noise in the voltage signal u L,amp (t) and due to the measurement process.The level of this noise should be almost constant all the time and is compensated for by setting a THD Fig. 15.Relative error of the servomotor control.The calculation is based on the results shown in Fig. 14.The relative error decreases with longer air-gap lengths.The deviation is mainly due to mechanical vibrations, which are to be reduced by future design improvements.threshold greater than zero, for example, 1% in our laboratory (see Fig. 10).Second, and more importantly, we found that the moving part of our prototype tends to vibrate at a frequency of 50 Hz due to magnetic forces, especially at short air gaps d air < 1 mm.This vibration leads to additional noise in the measured voltage u L,amp (t), is not compensated by the THD threshold value, and is, thus, the main reason why the air-gap set by the servomotor's control algorithm is always 0.1-0.2mm longer than necessary (see Fig. 14).For air gaps longer than d air > 0.5 mm, the vibration intensity decreases, and the signal-to-noise ratio of u L,amp (t) improves, i.e., the absolute error reduces.
For further analysis, Fig. 15 shows the relative error of the servomotor control.The longer the air gap, the smaller the relative error.Thus, for higher currents I 1,50 Hz , the deviation between the set and optimal air-gap length becomes smaller.
To better avoid the vibrations and, thus, reduce the systematic deviation, the sensor design should be further improved in the future (mechanical redesign).Without vibrations, the absolute error should then be significantly lower.
By neglecting the systematic deviation in Fig. 14, the two curves are close to each other, proving that the algorithm is working correctly.The developed HFCT design and the servomotor control, thus, work as intended.
With the help of the developed control strategy, the air-gap length of the HFCT prototype is set close to optimal at all times, and the sensor can be used for online monitoring of power cables.Since no magnetic saturation occurs, the PD sensor always operates close to its highest possible sensitivity.

C. HF Measurement and PD Detection
To turn the HFCT into a PD sensor for online monitoring, the HF component of the HFCT output voltage must be continuously measured and monitored for PD signals.For this task, the HFCT output u L (t) is connected to a second microcontroller running a PD detection algorithm.In this section, our method for PD detection is explained in detail.
1) Analog Peak Detector: Before the HF component of the analog output signal of the HFCT u L (t) can be processed by a PD detection algorithm, it must first be digitized by an ADC.Since the spectrum of PD pulses contains signal components up to the HF range, the sampling frequency of the ADC must be very fast to avoid information loss.We have shown that successful online monitoring of power cables requires at least an HFCT bandwidth of 10 MHz to detect the majority of PDs [6].Therefore, the sampling frequency Analog peak detector circuit based on the OPA615 IC from Texas Instruments.The circuit of the OPA615 peak detector is based on the manufacturer's data sheet of the IC, but optimized for PD measurements [12].A high-pass filter is connected in front of the peak detector to suppress the 50 Hz component of u L (t). of the ADC must be at least higher than f s > 20 MHz (for accurate peak detection, it should be even higher).With the LPC4370 microcontroller, it is possible to measure u L (t) with a maximum sampling frequency of 80 MHz, but the amount of recorded data is then too large to process in real time, because the computing resources of the microcontroller are limited (CPU frequency of 204 MHz).
However, the sampling frequency can be significantly reduced if the analog signal u L (t) is preprocessed with an analog peak detector circuit before digitization; see Fig. 16.This circuit is based on an OPA615 IC from Texas Instruments, which can be used as peak detector for nanosecond pulses.Peak detection is performed by charging a capacitor via a diode.Because of the diode, only positive peak values can be measured with the circuit shown.The same circuit with reversed diodes can be used to measure negative pulses.To improve the response time of the circuit, Schottky diodes should be used, as they react much faster than conventional diodes.The Hold Control Pin 7 is set to 5 V (high) to enable continuous monitoring.
A high-pass filter is connected in front of the OPA615 IC to filter out any 50 Hz component from the HF measurement.The high-pass consists of a capacitor C = 330 nF and a resistor R = 4.7 k , resulting in a cutoff frequency of f cut ≈ 100 Hz.
Fig. 17 shows the operation of the analog peak detection circuit using an exemplary input signal u L (t) with six PD pulses of different amplitudes and pulsewidths (pulsewidths It can be seen that the output signal u L,peak (t) follows the highest value of the input voltage by charging the capacitor.In this way, the capacitor stores the pulse amplitude information of the input signal.This can be clearly seen in the zoomed-in view on the right-hand side of the figure.Over time, the capacitor discharges again and is ready to capture the next pulse.The choice of capacitor is a compromise between a small capacitance that can quickly follow the input signal and a larger capacitance that stores the information longer but responds more slowly.A capacitance of 27 pF is well suited for measuring nanosecond pulses.From the simulations, the self-discharge rate of the capacitor is about 23 (V/ms) or 23 000 (V/s).
The output signal u L,peak (t) is now much easier to digitize, since the signal bandwidth has been significantly reduced compared with u L (t).The ADC sampling frequency f s can, thus, be greatly reduced without losing much amplitude and time information of the PD pulses.Only the information about the exact pulse shape is lost due to signal preprocessing, but this is not a problem for pulse detection.
Fig. 18 shows the analog signal u L,peak (t) and the same signal sampled at two different frequencies, 4 and 2 MHz.It can be seen that both sampling frequencies are sufficient to digitize u L,peak (t) with good quality.Only the captured amplitudes are slightly lower than those of the original signal, which can be seen better in the zoomed-in view on the right-hand side of the figure.Sampling u L,peak with a frequency of f s = 2 MHz results in a maximum amplitude error of about 11 mV.Compared with 20 MHz, the sampling frequency can be reduced by a factor of 10, freeing up large processor resources that can be used for further signal evaluation instead.At f s = 4 MHz, the maximum amplitude error is in the range of 5 mV, and the sampling frequency is still a factor of five lower than without preprocessing.
2) PD Detection Algorithm: To achieve continuous PD monitoring, the output voltage of the analog peak detector circuit u L,peak (t) is connected directly to an ADC input channel of the LPC4370 board.The sampling frequency is set to f s,LPC = 2 MHz.The digitized signal is then processed in real time by the LPC4370 processor using a PD detection Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.algorithm.The algorithm is based on [13] and can be described with the following pseudocode: # U(t) is the measured vector sampled by the ADC # Settings lag = 16; # window length for moving mean/std.calc.threshold = 3.5; # peak if data is 3.5 std.away from mean influence = 0.01; # peak data has low influence on mean/std.# Initialize variables out = 0; # initialize output signal avgCalc = mean(U(1),...,U(lag)); # initial moving mean stdCalc = std(U(1),...,U(lag)); # initial moving std.
# Main loop for i=lag+1,...,t do if absolute(U(i) -avgCalc) > threshold * stdCalc then out = 1; # peak detected # reduce impact of peak on next mean/std.calc.U(i) = influence * U(i) + (1-influence) * U(i-1); else out = 0; # no peak detected end avgCalc = mean(U(i-lag+1),...,U(i)); # calc.moving mean stdCalc = std(U(i-lag+1),...,U(i)); # calc.moving std. end The algorithm is based on the statistical parameters mean and standard deviation.The moving average and the moving standard deviation of the ADC data stream are calculated based on the last 16 measured values.The window length for these calculations can be adjusted with the lag setting.Each time the ADC provides a new data sample, the main loop of the algorithm is executed once.At the beginning of the loop, it is checked whether the new data point is more than 3.5 standard deviations away from the moving average value.If yes, the output signal out is set to 1 (PD detected).Otherwise, out is set to 0. The sensitivity of the algorithm can be adjusted with the threshold setting.To make the algorithm more robust, the peak values should have only a small influence on the calculation of mean and standard deviation.Thus, when a peak is detected, the value of the corresponding data point is artificially reduced based on the influence setting.
3) Test: The algorithm has been tested with some example data created with LTSpice and MATLAB; see Fig. 19.The input data are similar to the pulse sequence shown in Fig. 17, but is additionally overlaid with noise.The signal-tonoise ratio is about 10.The absolute noise level is between 20 and 40 mV, which is a typical noise level for online PD measurements according to [14].It can be seen that the algorithm detects all five peaks of the input signal, i.e., all PD occurrences.The initial delay, threshold, and influence settings used for this test are determined by trial and error method.To improve algorithm performance, the three parameters should be statistically optimized in the future based on real PD measurement data.

IV. CONCLUSION
In this article, we have shown a concept to improve HFCT sensor technology for online PD monitoring of power cables.Therefore, we propose an improved HFCT sensor with the ability to self-adjust the length of the air gaps of its ferromagnetic split core.The air-gap length is controlled by a servomotor in such a way that magnetic saturation due to the power cable's operating current is avoided at all times.In this way, the PD sensor always reaches the highest possible sensitivity.
Our prototype has a simple and low-cost design, and all tests conducted to verify the proposed air-gap control strategy have been successful, proving that the concept works.However, there is still room for improvement.The mechanical design of all moving parts of the sensor has to be improved to better avoid vibrations due to magnetic forces.This will reduce the mechanically induced noise in the 50 Hz measurement and, thus, improve the quality of the air-gap control.Furthermore, the air-gap control has only been tested in our laboratory environment with low overall noise level.To adapt the air-gap control strategy to other environments, it will be necessary to introduce a dynamic THD threshold value that automatically adapts to the actual noise level.In addition, the parameters of our PD detection algorithm need to be optimized in the future based on data from real PD measurements on power cables.
It can be concluded that the developed prototype solves the saturation problem of HFCT during online monitoring in a simple but efficient way.As far as the authors are aware, no such HFCT exists to date.Thus, an improved version of our PD sensor prototype may be used by DSOs in the future to establish a condition-based maintenance strategy for all of their power cables.In this way, power outages could be prevented in time, but it remains to be analyzed whether such a monitoring system, consisting of hundreds or thousands of PD sensors, is economically viable.

Fig. 1 .
Fig. 1.Our optimized HFCT design for a measurement bandwidth of 0-10 MHz.The core is split and the length of each air gap d air can be adjusted (both air gaps are always of equal length).The core has the shape of a toroid to maximize its magnetic efficiency[5].

Fig. 3 .
Fig.3.CAD design of our HFCT with air-gap control.The left half of the split core can be moved via a servomotor.In this way, the length of the air gap d air can be adjusted in small steps between 0 and 12.4 mm.The motor is controlled by an Arduino microcontroller.

Fig. 4 .
Fig. 4. Photography of the manufactured prototype.The air gap is opened by a few mm.Most of the additional parts compared with Fig. 1 have been produced with a 3-D printer.

Fig. 7 .
Fig. 7.Output voltage of the HFCT prototype measured at increasing 50 Hz operating currents and, thus, at increasing levels of core saturation (while d air = 0 mm).At I 1,50 Hz = 2 A, the HFCT is not saturated, and u L is sinusoidal with f = 50 Hz (linear measurement).The other two measurements are not sinusoidal, indicating magnetic core saturation (nonlinear measurement).

Fig. 8 .
Fig. 8. Top: 50 Hz component of the HFCT output voltage u L (t) measured at three optimal operating points (linear measurement).The amplitudes of the measured sines ûL are in a range of about 35-60 mV.Bottom: Amplified HFCT output voltage u L,amp (t) measured at the same operating points.

Fig. 9 .
Fig. 9. Inverting amplifier to amplify the 50 Hz component of the HFCT output voltage u L (t) before it is digitized by the Arduino microcontroller.For a gain of about 25, the resistors are set to R 1 = 2.2 k and R 2 = 56 k .The coupling capacitor has a capacitance of C 1 = 50 µF.

Fig. 10 .
Fig. 10.Measurements of the amplified HFCT output voltage u L,amp (t) with the Arduino at different input currents I 1,50 Hz and air-gap lengths d air .The calculated THD values of the measurements are shown.The blue line indicates the optimal air-gap length function according to (1).

Fig. 11 .
Fig. 11.Flowchart of the Arduino program (air-gap control algorithm).Based on the THD value of the 50 Hz component of the HFCT output, the rotation angle ϕ of the servomotor is set.

Fig. 12 .
Fig. 12. Testing the HFCT prototype with increasing 50 Hz input current (blue).The air-gap length set by the servomotor's control algorithm is shown in comparison with the calculated optimum.

Fig
Fig. 16.Analog peak detector circuit based on the OPA615 IC from Texas Instruments.The circuit of the OPA615 peak detector is based on the manufacturer's data sheet of the IC, but optimized for PD measurements[12].A high-pass filter is connected in front of the peak detector to suppress the 50 Hz component of u L (t).

Fig. 17 .
Fig.17.Input and output voltage of the peak detection circuit.It can be seen how the peak value of the input signal is stored by the capacitor for a certain time.The storage effect can be better seen in the zoomed-in view on the right-hand side.The storage time is limited by the self-discharge rate of the capacitor.

Fig. 18 .
Fig. 18.Blue line shows the output voltage of the peak detection circuit.This voltage is digitized by an ADC.For the red line, the ADC sampling frequency is set to 4 MHz and for the yellow line to 2 MHz.Both sampling speeds are sufficient to digitize the signal with good quality.Only the pulse amplitude is a bit reduced.

Fig. 19 .
Fig. 19.Simulative test of the PD detection algorithm.Top: noisy input voltage (dark blue).Also shown are the moving average (cyan) and moving standard deviation (green) of the algorithm.Bottom: output of the algorithm that indicates where PDs are detected.