Magnetic Field Effects on Partial Discharges in Electrical Insulation Subjected to PWM Excitation

This article depicts an original measurement methodology and detection approach for determining the influence of a magnetic field on partial discharge (PD) dynamics in electrical insulation while subjected to pulsewidth modulated (PWM) excitation. Unlike conventional PD measurements that are only carried out in an electric field, it was demonstrated that the interplay of electric and magnetic fields enhances a PD's intensity. The quantitative effect of a magnetic field was captured by phase-resolved acquisition and visualization on time-sequence intensity diagrams. The increase in the PWM carrier frequency resulted in enhanced intensity and was also elevated by the effect of the magnetic field. The influence of the magnetic field on the PDs was associated with the elongation of the charged particle trajectory and effects that were caused by the Lorentz force. The presented study may contribute to PD measurement methodology in the power electronic environment in both electric and magnetic fields as well as a better understanding of the underlying physical mechanisms. Since the endurance and reliability of electrical insulation that is subjected to fast switching, PWM-modulated power electronic-based excitation is an actual topic in many segments, such as power grids, industry, and transportation; the awareness of PD-intensity modulation that originates from the presence of a magnetic field should be raised and investigated.


I. INTRODUCTION
T HE ubiquitous presence of power electronic devices (PE)   in power-conversion applications across various voltage levels poses a challenge -especially to medium-and highvoltage insulation systems.This refers to a broad application spectrum from the transportation segment (electric vehicles, rail, more-, or all-electric aircraft), power transmission, distribution and energy storage, renewable solar, wind, and hydrogen conversion up to even electrification in the space segment [1], [2], [3], [4], [5].Pulsewidth modulation (PWM) is a standard excitation pattern and strategy in power electronic applications.A high prevalence has been gained through the flexibility of control and hardware implementation.Unlike in sinusoidal driven systems, this approach brings additional stresses that are related to the The author is with the AGH University of Krakow, 30-059 Kraków, Poland (e-mail: marek.florkowski@ieee.org).
Color versions of one or more figures in this article are available at https://doi.org/10.1109/TPEL.2023.3334011.
Digital Object Identifier 10.1109/TPEL.2023.3334011ultrafast pulse transitions that are within a range of nanoseconds, with slew rates that are above 100 kV/µs in today's wideband gap GaN or SiC switches [6], [7], [8], [9], [10].Continuous research is devoted to electrical stresses in motors that are driven by variable frequency drives with increasing voltage levels and pulse slope transition times (slew rates) due to the application of fast switches [11], [12], [13].
The electrical insulation systems of all of the abovementioned sectors are prone to partial discharges (PD) and are usually investigated only in reference to applied voltage; i.e., electric field stress.However, magnetic fields are also present in all current-carrying devices; this is an additional modulation factor that influences PD dynamics [14], [15], [16], [17], [18], [19], [20], [21], [22].The novel aspect that is presented in this article specifically focuses on these effects under PWM stimuli; this refers to various classes of PE such as converters, power electronic components, and power modules but also to objects that are subjected to PD (motors, cables, power electronic transformers, and printed circuit boards) or power modules that contain semiconductor switches [1], [8], [23], [24], [25], [26].Power electronic modules often use solid polymeric or gel encapsulation to safeguard high-voltage (HV) insulation [27].
Increases in system voltage levels can be observed in all areas of power grids (including wind parks and string connectivity) as well as in the transportation segment.For example, the dc bus voltage in electric vehicles is currently at 800 V but is expected to go up to a few kV in the future; also, aircraft nowadays operate at voltages that are below 1 kV, but higher voltage levels are envisioned in future development [21].In the latter case, levels of even up to 6-10 kV have been revealed by NASA [28], [29], [30].In more-electric aircraft (MEA), high-altitude operation leads to a reduction in the PD-inception voltage due to the lower air pressure; for example, a pressure of 0.2 atm (corresponding to an altitude of 11 km) decreases it by 40% as compared to normal pressure [31].In high-current applications, laminated busbars are being considered in the power converters of MEA applications, replacing printed circuit boards.The insulation films in such a structure are exposed to both electric and magnetic fields.The impact on insulation integrity spreads here from the packaging of micro devices such as power modules (e.g., SiC-MOSFET, IGBT), through packed converter designs to insulation systems of electrical machines and cables [32], [33], [34], [35], [36], [37].In terms of harmonic spectra, more-complicated cases will concern PWM-modulated modular multilevel converters (MMCs) [38].However, higher numbers of levels (smaller step voltages) result in smaller magnitudes of partial discharges in MMCs [39], [40].The calculations of a magnetic field level in a modular multilevel converter in an HVdc application is shown in [41].During the normal operation of an HVdc converter, in the valve in bridge arms will flow a current with an amplitude of several kA, producing a magnetic field in the surrounding space (including the high-voltage insulation systems of the nearby exposed equipment).
The common trend in power electronics refers to the development of devices with high power densities.The primary challenges in medium-and high-voltage applications refer to losses and heat dissipation (hence, thermal management as well as electric insulation strength).The impact of PWM voltage waveforms on magnetic wire insulation and partial discharge development in SiC-based motor drives was analyzed in [42].In this context, the crucial element is a charge accumulation in tiny wire-coating insulation while exposed to a train of repetitive pulses.Reliable dielectric coatings are explored for corona-resistant magnet wires for electrical machines in aerospace applications [43].
For PD occurrence at PWM, the slew rates of the slopes are essential since the rise time impacts the inception level [44], [45], [46].Hence, ultrashort rise times lead to increased stresses in electrical insulation, which may result in PD development and accelerated failures.
This article presents the effect of a magnetic field on partial discharges in electrical insulation that is subjected to PWM excitation.The experiments were carried out on a designed twisted-pair helical-coil (TPHC).In this study, low-frequency PWM modulation was applied to reveal and separate the effects that originated from the magnetic field on the partial discharge dynamics.The effect of a magnetic field on PDs has been quantitatively illustrated in the time-sequence intensity diagrams.

II. MAGNETIC FIELD EFFECTS ON PARTIAL DISCHARGES
The electrical insulation of power devices that are connected to high-voltage sources is subjected to an electric field.In all current-carrying devices, a magnetic field will be simultaneously superimposed on the electric one.The partial discharge physics are usually analyzed with respect to only the electric field distribution; however, it has been observed that a magnetic field brings an additional modulation element to the PD's behavior, which can vary depending on the application and load current level [15], [16], [17], [18], [19], [20], [21], [22].The detected PD current pulses result from the propagation of charge carriers in an electric field that form a streamer [47].A visualization of an insulated enamel twisted-pair specimen in superposition of the magnetic B and electric E fields is shown in Fig. 1.It is assumed that one wire has high-voltage potential and the other is grounded.In a twisted-wire configuration, there are zones that contain tiny air gaps that are sources of discharges in case other conditions for discharge propagation are fulfilled.This refers to the level of the electric field and electron availability to start a discharge in the air.The kind of eyelet shape that is related to the mutual position of the wires results in various ranges of the directions of a local electric field E. This situation is denoted by the angular spread of the electric field that is represented by vectors E 1 and E 2 in Fig. 1.The magnetic field direction depends on the shape of the conductors.When the current flows through a wire, the field is circular in a perpendicular axis.The magnetic field in Fig. 1 is represented by two magnets, which also indicates the direction of induction vector B. The motion of charged particle position r in the superimposed electric E and magnetic fields B is determined by a Lorentz force and Newton's second law according to the following equation: where m is the particle mass, q -the particle charge, r -the particle position, and v -the particle velocity.In addition to the orientations of the E and B fields, the direction of charged particle velocity vector v influences the drift propagation, which can assume various trajectories that reflect helical, spiral, or cycloidal shapes, for example.A streamer partial discharge is characterized as the propagation of a self-channeling ionization in gas.In a twisted-pair arrangement, discharges occur in high-electric-field-prone zones.Streamer inception threshold field E str , which is controlled by the critical avalanche criterion, is defined according to [48] as follows: where E is an electric field, p -the pressure, a -the void radius, and (E/p) cr , A, and n -the ionization parameters.In the case of air, the parameters that charcterize the ionization process assume the following values: (E/p) cr = 25.2VPa −1 m −1 , A = 8.6 m 0.5 Pa 0.5 , and n = 0.5.Taking the additional effect of the magnetic field on the discharge propagation path, trajectory deflection, and elongation into account, the particle will assume stronger acceleration and will enhance the ionizations of the gas molecules.Since the number of particles is represented by the pressure in (2), it will be influenced by a magnetic field due to its impact on the free path trajectory; in this way, it influences the externally measured PD-inception voltage in collision probability.This effect on a symbolic pressure p can be denoted in crossed electric E and magnetic B fields as follows: The phase-resolved partial discharge (PRPD) acquisition is a technique, which allows for recording of PD event synchronously with respect to period of applied high voltage.Accumulating over a large number of periods allows one to obtain a PD pattern, which is characteristic for different types of discharges.In this way, PRPD images reveal simultaneously discharge phase position, magnitude, and intensity.One of the key attributes of PD is partial discharge inception voltage (PDIV).Apart from the availability of free electron to initiate discharge, the voltage level (i.e., electric field strength) must be above a certain threshold; it is a second condition, which must be fulfilled to trigger PD.The IEC standard [49] is the fundamental horizontal standard that provides the foundation for partial discharge measurement methods based on the apparent charge concept.Alternative methods, acoustic and electromagnetic ones using capacitors, high frequency current transformers, electric field sensors, and wideband antennas, are referenced in the technical specification [50].The partial discharge measurements in rotating electrical machines fed from voltage converters are described in [51].
In this article, the effect of PWM excition on partial discharge dynamics in the presence of a magnetic field was analyzed.Despite the high cutoff-detection frequency, the acquired PD images and time-sequence diagrams could also contain events that were related to the slopes of the excitation.However, their number was only related to the voltage excitation and was not influenced by the superimposed magnetic field effects (hence, the noticed surplus in the PRPD images and intensity diagrams referred decisively to the influence of the magnetic field on the PD dynamics).This methodology is graphically illustrated in Fig. 2. The block on the left symbolizes the high voltage PWM excitation applied to the sample.The middle block represents the detected and acquired PRPD image containing the PD pulses and remnants from high voltage PWM excitation.To analyze quantitatively the influence of magnetic field, the time-intensity diagrams (right block) were used.The number of recorded events is represented by number N (both PD and PWM remnants).It was depicted that those events that originated from the PWM excitation were not B-sensitive, whereas the PD patterns were prone to the magnetic field's effects.
The described effect has importance -both in PD-related research and in diagnostic applications that assess the condition of power equipment.

III. SIMULATIONS OF PARTICLE TRAJECTORY IN SUPERIMPOSED ELECTRIC AND MAGNETIC FIELDS
The intentions of the presented simulations were to visualize the influence of a superimposed magnetic field on PD trajectory in an energized twisted-pair specimen.The partial discharges that occurred in the high electric field exposed zones in the volume that was adjacent to the enameled wires.In practical windings, various mutual orientations between the electric and magnetic fields may be present.The diameter of the wires in this study was 1.4 mm.The introduced tiny distance between the wires was 30 µm at the point of their closest proximity.The simulations showed a hypothetical charged particle (electron) trajectory without interactions with other particles or molecules.The simulations were carried out in the twisted-pair geometry that is shown in Fig. 3 in the COMSOL Multiphysics framework [52].Motion (1) for a charged particle was solved in the superimposed magnetic and electric fields.The meshing was executed using tetrahedral elements.The simulations were carried out at a −1.2 kV voltage on an HV electrode.In the simulations, the dc condition was assumed, reflecting an instantaneous voltage on the PWM waveform.The boundary conditions refer to assumed potentials (i.e., HV on one wire, and ground on the second) as well as the freeze option that was set when the particle reached a wall.The particle source was placed on the HV electrode, and the initial mean kinetic energy of the electrons was 1 keV.The three cases that are shown in Fig. 3 highlight the trajectory deviation.The first case that is presented in Fig. 3(a) is a reference that was obtained without a magnetic field (B off state) with a straight trajectory that reflected the local electric field lines.The visualization was performed on the zy plane within a tiny airgap between the wires.Then, a low magnetic field (induction B = 60 mT) that was oriented along the x-axis was introduced, distinguishing the axial [see Fig. 3(b)] and opposite directions [see Fig. 3(c)].The particle-path deflection that was influenced by an additional Lorentz force magnetic component can be recognized in both cases.The magnetic field-originated force on a moving particle twists the original pathway and may be quantified in future research by a deflection angle depending on the interplay between both the electric and magnetic fields.
The presented qualitatively trajectory elongation will result in the discharge intensity variations (as will be presented further in the experimental section).

IV. SPECIMEN, SETUP, AND INSTRUMENTATION
The measurements were carried out in the original setup, which was well-suited for subjecting a specimen to combined electric and magnetic fields.Specifically, a rather weak magnetic field at a level of magnetic induction that was equal to 60 mT was superimposed to investigate its influence on the bottom line.The presented experiments were executed in the setup that is shown in Fig. 4.
It was important to safeguard those components that were exposed to the magnetic field in the experimental setup; therefore, they needed to be made of nonmagnetic materials.This especially applied to the electrodes, construction, and connections.The specimen was exposed to a static magnetic field that was provided by two permanent neodymium magnets that were positioned parallel to the axis of the twisted-pair coil on both sides of the arrangement at a mutual distance of 120 mm (thus forming a quasi-uniform magnetic field distribution in the gap).In this way, the magnetic field induction was at a level of 60 mT in the middle of the interspace (as measured by means of an SMS 102 meter with a Hall sensor).The background magnetic field was 46 µT, and the Earth's North Pole direction was perpendicular to the static field that was created by the magnets (as is depicted by the symbolic compass in Fig. 4).The stable positioning of the magnets was provided by a wooden construction.During the experiments, the magnets were placed and removed manually with high precision within their setup.
Twisted pair specimens are often used as representative samples for insulation tests and are especially relevant for electrical machines' turn insulation.Such specimens are relatively easy to manufacture, making them convenient for testing purposes.They consist of two insulated wires twisted together, which mimics the construction in real electrical winding.The twisted pair specimens provide a straightforward and controlled setup to measure the insulation integrity.Such specimens offer a uniform and consistent structure that allows for accurate and repeatable testing.This type of specimen has been widely accepted as a standard test sample in various industry standards and specifications, e.g., [51].This specimen setup (effect of discharges in air gap) has been selected on purpose in this work, since it can also be generalized to the other power electronics devices such as: power modules, printed circuit boards, and laminated busbar, where tiny inclusions in the form of voids or surface discharges may occur.The investigations were carried out on a specially designed specimen that consisted of twisted-pair wires that were additionally screwed to form a coil (as presented in Fig. 5).The main purpose of forming the twisted-pair helical-coil specimen was to extend the length of the twisted wires that were exposed to the magnetic field window; in this way, the effect was amplified.
In the experiments, the twisted-pair of enameled copper magnet wires with a diameter 1.4 mm and an enamel-coating thickness of 90 µm was formed (with a twist density of 0.8 twists/cm).Such a specimen mimicked a typical turn-to-turn motor-winding insulation system.The diameter of the coil was 30 mm, and the length along the main axis was 80 mm.The geometry of the twisted-wire coil is shown in Fig. 5(a).One wire was connected to the high-voltage potential, and the second was connected to the ground.Since the specimen took the form of a twisted-pair coil, there are a whole spectrum of angles between the vectors of magnetic field induction B and electric field strength E (from a parallel to perpendicular arrangement).A zoomed view on a contact spot between adjacent wires with an air gap is shown in Fig. 5(b).
The high-voltage sinusoidal (SIN), square (SQR), and PWM excitation was delivered from the high-voltage amplifier (Trek 20/20B) and controlled by a programmable generator (RIGOL).The high-frequency partial discharge loop was closed by a C c = 100 pF coupling capacitor that was located on a leg that was parallel to the sample [49].The voltage control and synchronization signal were taken from the high-voltage side by a TekProbe (Tektronix P6015A), which is represented by resistive divider R 1 and R 2 in Fig. 4. Its input impedance was 100 MΩ, and its division factor was equal to 1:1000.The measurements were carried out using a 100 MHz 1.25 Gs/s Tektronix scope (TSD 3014C).The following environmental conditions were present during the experiments: a temperature of 22 °C, a humidity level of 25%, and an atmospheric pressure Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
of 997 hPa.The PD acquisition was carried out in the wideband phase-resolved mode using an ICM-acquisition system by Power Diagnostix that was connected to a control computer using a GPIB interface.The sensitive PD detection was achieved by a wideband microstrip antenna that was characterized by high gain and a directional reception pattern.The bandwidth of the antenna was within an ultrahigh frequency range of 0.1-10 GHz.The antenna was connected to a battery powered (9 V) low-noise amplifier (LNA) with a bandwidth of 9 kHz to 3 GHz.The gain figure was +30 dB, the maximal power was 10 dBm, and the input impedance was 50 Ω.The lower corner cut-off frequency eliminated any low-frequency disturbances.The antenna was localized at a proximity of 30 cm from the stressed specimen.The amplitude spectrum (which is presented in the following section) was measured by means of a spectrum analyzer (Hewlett Packard HP8591E) that featured a bandwidth of 9 kHz-2 GHz.
The specimen was subjected to a two-level PWM-modulated waveform with a frequency of 50 Hz, a carrier that was within a range of 0.2-1.0kHz, and a voltage of up to 2 kV.The slew rate for the pulse edge was the same for the SQR and PWM as well as at the B on and B off stage.With regard to the control strategy, a low-frequency PWM modulation and carrier was intentionally applied in the experiments to reveal and separate the effects that originated from the superimposed magnetic field on the partial discharge dynamics.The fast pulse transition on the rising and falling slopes resulted in interference (whose spectrum often overlapped with the frequency bands that are characteristic of PDs).In such a situation, it is quite complicated to distinguish any interference that is induced by PWM excitation from partial discharge signals.In this context, various antennas are often applied for PD detection in order to safeguard the high-acquisition bandwidth and position the lower cut-off frequency above the upper band of the interference in the best way.However, the problem that was investigated in this article refers to the additional effects of PD intensity that are caused by magnetic fields.Therefore, assuming that a constant number of slopes that are caused by the rising and falling flanks of PWM stimuli in both magnetic field-free and field-present modes occurs in the predefined time window, the resulting variation in the number of discharges originates from the superposition of the magnetic field.

V. RESULTS AND DISCUSSION
The striking observations and investigations of the magnetic effects on PD dynamics in a PWM-driven application were done on twisted-pair helical coil specimens.For the sake of comparison, the measurements that were performed of the sinusoidal and square excitation are also presented.The experiments were carried out within a voltage range of 0.9-1.4kV.The discharges were recorded in the forms of PRPD patterns.The phase-synchronization signal was taken from the PWM sinusoidal modulation with a frequency of 50 Hz.The experiments were carried out for the following PWM carrier frequencies: 200 Hz, 500 Hz, and 1 kHz.The exemplary PWM waveform with a carrier frequency of 1 kHz and the PD pulses with the superimposed slope remnants are shown in Fig. 6.The remnants of PWM voltage switching are present in the detected patterns.However, it is important to underline that the focus in this article was on detection of the effect of the magnetic field, and the number of remnants from PWM voltage is constant.Hence, the observed effect of elevated number of events after switching on magnetic field can be solely attributed to the increased number of partial discharges.
For a visualization of the discharge dynamics (indicated by the number of PDs), time-intensity diagrams have been employed.The experiments were executed in predefined time intervals: 60 s in the PRPD acquisition, and 300 s in the time-intensity diagrams.The PD acquisition was carried out in one of two modes: 1) magnetic field-free and 2) with a static superimposed magnetic field with an induction B of 60 mT.Specifically, a rather low magnetic field was applied in order to reveal the partial discharge bottom-line effects.The PRPD patterns are shown for the B off state, since the main effect observed superimposing magnetic field was related to the PD intensity and therefore this is much better highlighted quantitatively in the time-intensity diagrams.
The experiments were performed in the setup that is shown in Fig. 4 on a TPHC specimen in air.PDIV was evaluated in the same way for SIN, SQR, and PWM.The PD were acquired in phase-resolved mode and while raising the voltage, the appearance of first stable pulses was attributed to inception level.However, it is much more difficult to identify the partial discharge inception level at PWM compared to SIN or SQR.The PD-inception voltage for the specimen varied with respect to the applied voltage waveform and was observed to be downgraded while applying the magnetic field.The PDs occurred above the PDIV, which was equal to 920 V (for the sinusoidal excitation in the magnetic-free case) and 880 V (when the magnetic field was turned ON).At the square-shaped waveform, the PDIV was lower (800 and 760 V for the B off and B on states, respectively).
In the case of the PWM excitation, it was noticed that the PDinception voltage was carrier frequency-dependent; however, it was very difficult to distinguish the difference between the B off and B on states at this threshold level at this initial stage due to the presence of the pulses that originated from the slopes.Therefore, in Table I, the same values were provided in case of PWM and B on and B off stage.The obtained values for the PWM carrier frequencies of 200 Hz, 500 Hz, and 1 kHz were 770, 820, and 870 V, respectively.The PDIV measurements for the different waveforms are listed in Table I.At higher voltages, above PDIV, the impact of the magnetic field was clearly distinguishable at PWM.The wideband PD detection was carried by means of a microstrip antenna that yielded directional signal reception.
A comparison of the amplitude spectrum that was within a range of 0.1-1.8GHz for the sinusoidal excitation with a frequency of 50 Hz and the PWM with a carrier frequency of 200 Hz with respect to the background spectrum is shown in Fig. 7.
The reference spectrum was obtained at a voltage that was below the PD inception [see Fig. 7(a)]; hence, only strong transmitters and disturbances were present.In the case of the sinusoidal stimulus at 1.2 kV (above the PDIV), the clearly distinguishable spectral ranges were recorded [as denoted by the arrows in Fig. 7(b)].The PD-originated spectrum at 1.2 kV (above the PDIV) was even denser at the PWM excitation [with a frequency of f c = 200 Hz -Fig.7(c)].

A. Sinusoidal Excitation
As a reference, the partial discharges were measured at the sinusoidal excitation within a voltage range of 0.9-1.4kV (PDIV = 920 V at 50 Hz).The exemplary PRPD image that was obtained at a voltage of 1.2 kV is shown in Fig. 8(a), while the diagram is shown in Fig. 8(b).
The PD-intensity elevation was noticed in the presence of the magnetic field.The two traces in the plot represent the positive and negative discharges (marked in red and blue, respectively).The average PD intensity is marked in the graph in both the B off and B on states.The intensity number corresponds to the recorded pulses within 300 s.

B. Square Excitation
In the following step, the square excitation was applied as an intermediate point to the PWM.The inception voltage dropped to 760 V at 50 Hz.The exemplary PRPD image that was recorded at a voltage of 1.2 kV is shown in Fig. 9(a), and the time-intensity sequence is shown in Fig. 9(b).The clear PD-intensity amplification was observed in the presence of the magnetic field.The average PD-intensity rises for the negative and positive discharges were 12.5 and 17.3%, respectively, switching from the B off state to the B on state.

C. PWM Excitation
The PDs at the PWM excitation were measured within a voltage range of 1.0-1.4kV.
The modulating frequency was set to 50 Hz, and the carrier frequency varied.As can be seen in the acquired PD images, the switching signals that originated from the rising and falling Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.slopes of the pulses are superimposed in the plots despite the high cutoff frequency that was determined by the antenna-detection system.Assuming a constant number of slopes in the modes without and with the presence of the magnetic field, however, the resulting difference in the numbers of acquired pulses refers strictly to the variation of the PDs.In this way, the time-sequence diagrams reflect the dynamics of the partial discharges that were influenced by the magnetic field.In addition, the impact of the carrier frequencies of 200 Hz, 500 Hz, and 1 kHz on the PD intensity in the presence of the magnetic field (B = 60 mT) was analyzed; the inception voltages for the carrier frequencies above were 770, 820, and 870 V, respectively.The PRPD images that were recorded at a voltage of 1.2 kV for those carrier frequencies are shown in Fig. 10.The time-intensity diagrams that were acquired at the 1.2 kV voltage while switching from the magnetic field-free B off state to the B on state for the PWM excitation on the TPHC specimen at carrier frequencies of 200 Hz, 500 Hz, and 1 kHz are shown in Fig. 11.Partial discharge-intensity amplification was observed in all of above cases when in the presence of the magnetic field.
The average PD-intensity rises at the applied voltage range of 1.0-1.4kV for the negative and positive discharges while switching from the B off state to the B on state were 22.6 and 23.9%, respectively (as is shown in Table II and illustrated in Fig. 12).As explained earlier in the experiment's methodology, the excess intensity was solely related to the magnetic field's effect.A comparison of the acquired numbers of pulses in the B off and B on states at different voltages within a range of 1.0-1.4kV at the PWM excitation is shown in Fig. 12.Three cases were distinguished that corresponded to the 200 Hz, 500 Hz, and 1 kHz carrier frequencies (as a reference, a sinusoidal instance was provided).The dotted lines in Fig. 12 represent the B off state, whereas the solid ones that are always positioned higher correspond to the presence of the magnetic field.Since the number of pulses also contained those impulses that originated from the excitation slopes, the difference between these two values revealed the excess that was caused by the magnetic field.
An illustration of the surplus number of pulses between the B on and B off states regarding the voltage dependence is shown in Fig. 13.These values can be attributed to the effect of the magnetic field, which yielded additional discharges.The intensity grew quite linearly with applied voltages within a range of 1.0-1.4kV, and the slope rose with increases in the carrier frequency (within a range of 0.2-1 kHz).The conditions for PD  occurrence depend on the electric field's strength in the micro air gap between the wires.The diameter of the wires particularly influence the electric field distribution in the nonhomogeneous areas.The PD mechanism is also impacted by the surface charge accumulation and the related memory effects, which lead to the distortion of instantaneous electric fields [53], [54].The elevated PD intensity that was revealed while switching ON the magnetic field may refer to the elongated free path trajectories of the charged particles-especially the electrons; in this way, it influenced the collision probability in the superimposed magnetic and electric fields.
The presented experimental results that were carried out on a twisted-pair helical coil at the PWM excitation indicated its sensitivity to a magnetic field and an amplification of the number of streamer channels.The underlying physical mechanism is a complex topic; hence, some hypotheses can be discussed at this stage.As shown in a previous section, a lower PD-inception voltage could be observed while switching ON the magnetic field.
While propagating between collisions, the electrons were subjected to increased driving forces by the additional Lorenz force component that resulted from the magnetic field; this led to a twisting effect (the straight drift paths in the electric-only field were altered to be more spiral-like) as well as enhanced acceleration as compared to the drifts that occurred only in the electric field.The stronger acceleration impacts the number of collisions between the free electrons and the gas molecules as well as the mean energy of the free electrons.The abovementioned effect resulted in the boosted ionizations of the gas molecules.The magnetic component is amplifying the space charge concentration in the whole interelectrode region, enlarging the possible ionization volume, thus increasing the collision probability with ions and gas molecules.It may also result in an increase in the number of streamer channels and, hence, a higher PD number.The longer trajectory also means a longer residence time for charges in the interelectrode space, especially electrons that cause successive ionization events.While analyzing the space charge that was created by the electrons and positive ions, an additional effect could be perceived; this was caused by the different polarities of the above charged particles that resulted in deflections in opposite directions.Hence, the promotion of the free electron paths between the collisions caused the local recombination rate to decline, resulting in an increased number of partial discharges.

VI. CONCLUSION
This article depicts an original measurement methodology and detection approach for determining the influence of a magnetic field on partial discharge dynamics in electrical insulation while being subjected to PWM excitation.The presented experiments illustrate the quantitative modulation of partial discharge intensity in a superimposed magnetic field.An intentionally low magnetic field (60 mT) was applied in order to investigate the effects that are driven by power electronic PWM-modulated converters in real power, industrial, or transportation highvoltage insulation.Unlike conventional PD measurements that are carried out only in an electric field, it was demonstrated that the interplay of electric and magnetic fields enhanced the PD intensity.The quantitative effect of the magnetic field was captured by the phase-resolved acquisition and visualization on time-sequence intensity diagrams.The number of surplus pulses between the magnetic field's "ON" and "OFF" states was attributed to the effect of the magnetic field on PD dynamics.Increasing the PWM carrier frequency resulted in enhanced intensities and was also elevated by the effect of the magnetic field.The influence of magnetic fields on PDs is associated with the elongation of the charged particle trajectories as well as the deflections that are caused by the Lorentz force in superimposed electric and magnetic fields.The presented study may contribute to the PD-measurement methodology in the power electronic environment in both electric and magnetic fields as well as aiding in understanding the underlying physical mechanisms.Since the endurance and reliability of electrical insulation that is subjected to fast-switching PWM-modulated power electronic-based excitation is an actual topic in many segments such as power grids, industry, and transportation (electric vehicles, rail, more-/allelectric aircraft, and maritime).An awareness of PD-intensity modulations that originate from the presence of magnetic fields should be raised and investigated.

Manuscript received 15
August 2023; revised 23 October 2023; accepted 12 November 2023.Date of publication 17 November 2023; date of current version 22 December 2023.Recommended for publication by Associate Editor F. Costa.

Fig. 1 .
Fig. 1.Visualization of insulated enamel twisted-pair specimen in superposition of magnetic B and electric E fields.

Fig. 2 .
Fig. 2. Detection methodology of magnetic field (B) influence on partial discharge dynamics at PWM excitation and time sequence diagram interpretation.

Fig. 3 .
Fig. 3. Visualization of influence of superimposed magnetic field on charged particle trajectory (red) in energized twisted-pair specimen airgap: (a) without magnetic field; with magnetic field in (b) x-axial direction and (c) x-axis opposite direction.

Fig. 7 .
Fig. 7. Comparison of amplitude spectrum at PD detector within range of 0.1-1.8GHz.(a) Background spectrum at sinusoidal excitation below PDIV containing signals from transmitters and disturbances.(b) Sinusoidal excitation at 1.2 kV with frequency of 50 Hz.(c) PWM with carrier frequency of 200 Hz (above PD-inception voltage).

Fig. 8 .
Fig. 8. (a) PD pattern acquired at 1.2 kV (B off ) for sinusoidal excitation on TPHC specimen.(b) Time-intensity sequence B off /B on of impact of magnetic field on PD dynamics (number N of negative and positive PD pulses denoted in blue and red, respectively).

Fig. 9 .
Fig. 9. (a) PD pattern acquired at 1.2 kV (B off ) for square excitation on TPHC specimen.(b) Time-intensity B off /B on sequence of impact of magnetic field on PD dynamics.

Fig. 11 .
Fig. 11.PD time-intensity diagrams acquired at 1.2 kV voltage while switching from magnetic field-free B off state to B on state for PWM excitation on TPHC specimen at following carrier frequencies.(a) 200 Hz.(b) 500 Hz.(c) 1 kHz.

Fig. 12 .
Fig. 12.Comparison of acquired numbers of pulses in B off and B on states within voltage range of 1.0-1.4kV at PWM excitation with carrier frequencies of 200 Hz, 500 Hz, and 1 kHz (sinusoidal stimulus is marked as reference): dotted lines -B off state; solid ones -B on state.

Fig. 13 .
Fig. 13.Number of surplus pulses between B on and B off states regarding voltage dependence that were attributed to effect of magnetic field on PD dynamics.

TABLE II NUMBER
OF PD PULSES AT VARIOUS PWM WAVEFORMS