Double-ring high-frequency common-mode switching oscillation current sensor for inverter-fed machine winding insulation monitoring

0 Introduction

With the establishment of the “carbon peak,carbon neutral” target,the path to green,low-carbon,and sustainable development has become an inevitable choice[1,2].Inverter-fed machines can improve the efficiency of energy conversion,and are widely used in industrial manufacturing,new energy generation,national defense,the military industry,and other vital fields.Unexpected failures of inverter-fed machines can result in significant downtime and economic losses,rendering their operation safe,reliable,and efficient.

As shown in Fig.1,stator winding insulation is one of the most fragile components in a drive system,accounting for approximately 40% of all failures [3,4].When an incipient fault arises in the motor-winding stator insulation,it escalates rapidly,potentially triggering severe accidents.The transient overvoltage induced by the high dv/dt rapid switching of the inverter can accelerate the aging process of the stator winding insulation.Consequently,real-time monitoring of the health status of inverter-fed machine insulation is pivotal for enhancing system reliability and mitigating operational and maintenance costs.

Fig.1 Distribution of motor failure causes[4]

In recent years,substantial attempts have been made to monitor the online insulation of inverter-fed machines [4-10].Among them,partial discharge methods can effectively indicate the health state of stator insulation.However,they are only applicable to medium-and high-voltage motors,and are susceptible to electromagnetic noise from inverters [5,6].Winding insulation capacitance is an important indicator of insulation degradation [7-9].It can evaluate the health status of the stator winding insulation by online monitoring of the capacitance and dissipation factor from the leakage current at multiples of the line frequency [10,11].Nonetheless,the impedance of insulation capacitors in low frequency bands (for example,50 Hz) is significantly high (MΩ-level),necessitating costly,high-sensitivity sensors for detecting slight changes in leakage current (µA-level) [11].

To improve the sensitivity of online insulation condition monitoring,efforts have been made to explore system highfrequency (HF) features,which can be roughly divided into the HF injection method [12,13] and inverter switching selfexcitation method [3],[14-19].The HF injection method[12,13] requires an additional HF excitation source that is intrusive to the inverter-fed machine system and may reduce efficiency and reliability.Conversely,the inverter selfexcitation method utilizes pulse-width modulation (PWM)voltage or switching transient processes as HF excitation sources,thereby eliminating the need for an additional source.According to the characteristic frequency bands,the inverter self-excitation method can be further divided into PWM frequency bands [14,15] and HF resonant frequency bands.In reference [14],the equivalent capacitance of the groundwall insulation was derived from the common-mode(CM) voltage and leakage current at the PWM frequency and/or their multiple harmonics.In reference [15],the groundwall and phase-to-phase insulation capacitances were extracted using CM and differential-mode (DM) voltages and PWM current harmonics.In the PWM frequency band,the CM impedance of the motor winding exhibits an advantage of exhibiting near-pure capacitance (with phase angle close to -90°,determined by the groundwall insulation capacitance) [14,15].This enables direct and effective monitoring of the ground wall insulation state by computing the equivalent capacitance to the ground.While the CM impedance of the machine in the PWM frequency band decreases significantly compared to that in the fundamental frequency band,it can still reach several thousand ohms.This necessitates a leakage current sensor with high accuracy and sensitivity.

To further improve sensitivity,there has been an increasing trend recently to exploit the HF characteristics from the switching transients of inverter-fed machine systems,that is,in the HF resonant frequency band.Highly sensitive detection of subtle variations in the insulation capacitance is achieved by utilizing HF resonance effects [3],[16-19].In reference [16],the switching transient current in the range of 50 kHz to 1 MHz was demonstrated to be sensitive to insulation degradation.In reference [17],the transient characteristics of the CM leakage current were analyzed,and the health state of groundwall insulation was effectively monitored using the amplitude,period,and attenuation time characteristics.In reference [18],insulation health monitoring was performed by evaluating the HF switching oscillation current.The CM characteristics of the HF switching oscillating current indicate the health state of the line-end coil insulation [3] and interturn insulation [19] in inverter-fed machines.In existing studies[14-19],researchers have broadly explored the HF CM characteristics in inverter-fed machine system for insulation online monitoring.however,the extracting process of HF CM current would be inevitably affected by the DM current.

Nevertheless,in the HF band,the motor winding exhibits an HF transmission-line effect with complex parasitic parameter coupling.These complexities cause the HF switching oscillating current to exhibit a multifrequency component [3],[19].The HF CM current is an effective index reflecting the insulation of the stator winding.Compared to the HF DM current,the HF CM current has a lower amplitude and frequency aliasing,which is difficult to separate.Interference of HF DM current on HF CM current extraction process introduces challenges in monitoring the insulation condition using the CM leakage current.

To address this challenge,this study presents an HF CM current sensor with a double ring.The inner ring acts as a magnetic shielding ring,and the magnetic field signals generated by the DM signals are regulated to cancel each other in the inner ring by placing a magnetic ring enclosing all three-phase cables.The outer ring was designed based on the Rogowski coil principle for HF CM current capture.The effectiveness of the sensor in improving the signal-to-noiseratio (SNR) is verified by magnetic field simulations and online insulation monitoring experiments.

1 High-frequency switching oscillation current in inverter-fed machine

In an inverter-fed machine system,the speed or torque of electric machine is controlled by a PWM inverter.Due to their efficiency and control capabilities,electrical machine fed with inverters have become prevalent in various industrial applications,such as electric vehicle,high-speed train.Inverter-fed machines can be classified according to their specific applications and configurations,e.g,inverterfed synchronous machines (SM),inverter-fed induction machine (IM).The inverter-fed machines offers several advantages,notably improved efficiency,energy savings,and reduced energy consumption[20].

In a real system,the aging process of insulation becomes complex when exposed to multiple stress factors.If the stator winding deteriorates owing to prolonged overheating,the high temperature triggers chemical reactions such as oxidation,leading to delamination and void formation.This resulted in a decrease in the insulation capacitance owing to the lower dielectric constant of air.In addition,the insulation parasitic capacitance is influenced by other degradation agents,such as oil contamination,moisture,electrical stress,and mechanical damage [21].Under moist conditions,the presence of water increases the average dielectric constant of the insulation,and consequently enhances its capacitance.When the end winding is contaminated with conductive pollutants,the ground potential of the stator core partly extends to the end winding,thereby effectively increasing the surface area and capacitance of the insulation.If the winding is energized with sufficiently high voltage,partial discharge occurs within the voids,“shorting out” and thereby increasing the capacitance through ionized gas.Therefore,the parasitic insulation capacitance serves as a reliable indicator of incipient degradation,typically showing a change of approximately 20%—50% [8,9],[12],[22].

The deterioration of the motor-winding insulation inherently alters the insulation capacitance.Fig.2 illustrates the HF transmission line model of the motor winding,which comprises a series of π-type equivalent circuits.In the HF band (above MHz),inductor branches with a large impedance can be ignored.The HF model of each phase winding of the motor can be simplified as an equivalent terminal capacitance Cg1 [23].The motor winding insulation is mainly determined by the equivalent parasitic capacitance of the first few coil insulations (including the main and turn insulations) connected to the motor inlet end in the switching-surge frequency band.

Fig.2 HF transmission line model of the motor

However,CM currents are prone to interference from the DM signals,which can disrupt their extraction of the CM currents.As illustrated in Fig.3,during the PWM switching transient,the motor-phase current contains multiple current components across different frequency bands.These include the low-frequency fundamental current,medium-frequency PWM ripple current,and HF switching oscillation current.Due to the presence of a capacitance at the line end to the ground [3],the HF switching oscillating current can be subdivided into the HF DM current and CM current.A high-frequency DM current flows from the phase-to-phase insulation capacitances.The CM current flows to the ground via the groundwall capacitance,which can effectively indicate the insulation state of the motor windings [3],[19].

Fig.3 Schematic of each current conduction path in the motor winding

As observed from the flow paths of the different mode currents shown in Fig.3,the DM current easily interferes with the extraction of the HF CM current.To reduce the interference of the DM current with multi-frequency components,this study proposes a double-ring HF CM current sensor based on the magnetic aggregation effect,as detailed in the next section.

2 Principle of the double-ring current sensor

2.1 Double-ring magnetic circuit model

A schematic of the proposed double-ring HF current sensor is shown in Fig.4.The sensor is configured to enclose all the three-phase cables at the end of the inverterfed machine,which is typically installed in a terminal box,as shown in Fig.4(a).The MXO with high permeability is selected as the core of the inner ring,which harnesses the magnetic aggregation effect to isolate the DM current magnetic field.To reduce the number of coils turns and improve the gain,the outer ring selects MXO with high permeability is also selected.And serves as the magnetic core of the Rogowski current sensor,enabling HF CM current monitoring.As shown in Fig.4(b),the inner radii of the inner and outer rings are a1 and a2,respectively;the outer radii are b1 and b2,respectively,and the heights are h1 and h2.

Fig.4 Diagram of double-ring sensor and measuring position

To prevent the unfiltered magnetic field from the inner ring affecting the detection of the outer ring,h2 should not exceed h1.The magnetic permeabilities of the inner and outer ring cores are μ1 and μ2,respectively.The secondary winding was uniformly wound on the outer-ring skeleton iron core,and the wiring was connected to a terminal resistor.Here,μ0 denotes the permeability of air,and is equal to 4π×10−7 H/m.

Compared with the single-ring current sensor,the inner ring of the double-ring current sensor harnesses the magnetic aggregation effect to isolate the DM current magnetic field,leading to a uniform magnetic field distribution outside the inner ring.The outer ring serves as the magnetic core of the Rogowski current sensor,enabling HF CM current monitoring.The double ring of the current sensor yielded higher resistance to the magnetic saturation,making it more appropriate for monitoring CM current signals in complex electromagnetic environments.In the following section,the operating principles of the inner and outer magnetic rings are analyzed.

2.2 Magnetic shield effect of inner ring

A magnetic field simulation analysis of the inner magnetic shielding ring was conducted to explore the magnetic field distribution after the introduction of the magnetic shield ring.Depending on the magnetic field distribution,it can be roughly divided into three regions∶inside,in the middle,and outside the ring.

The relative permeability of the media varied in each region.Based on the principles of electrodynamics,a vector magnetic potential equation in the space surrounding the magnetic shield ring was established and resolved using boundary conditions [23].When a single current-carrying conductor is placed eccentrically,the magnetic field strength along the Z-axis is zero owing to structural symmetry.Therefore,the magnetic field distribution is analyzed only on the r-φ plane,as shown in Fig.5.

Fig.5 Magnetic filter parameters and the magnetic field distribution on the r-φ plane

In reference [24],the equations of radial magnetic induction intensity Br3 and tangential magnetic induction intensity Bφ3 in region 3 are expressed as follows∶

where μ0 is the vacuum permeability,μ1 is the relative permeability of the magnetic ring,and I is the current amplitude of the current-carrying conductor.According to Eqs.(1) and (2),the magnetic field distribution in region 3 comprises two parts.The first part is the magnetic field generated by the conductor placed at the center with the same current value.The second part is the magnetic-field ripple,which is determined by the wire layout.When μ1 is significantly larger than μ0,the magnetic field ripples in Bφ3 and Br3 will approach zero.At this point,the magnetic field outside the magnetic ring exhibits an approximately uniform distribution.Based on the above analysis,the single conductor was extended to multiple conductors.Assuming that the magnetic ring contains k current-carrying conductors,the tangential magnetic induction intensity in region 3 is shown in equation (3)∶

When μ1 is significantly larger than μ0,the magnetic field in region 3 is also approximately evenly distributed.The magnetic fields generated by the DM current can be adjusted to the same path to cancel each other and achieve the separate detection of the CM current.The tangential component of the magnetic flux density measured in region 3 was approximated using Equation (4).

As shown in Equation (4),the tangential magnetic induction intensity of region 3 is positively related only to the CM current,and is not affected by the position of the measured wire.The radial magnetic induction Br3 tended to zero,indicating that the magnetic induction intensity in region 3 was tangential.This formed the foundation for the subsequent measurement of the CM current signal using an HF current sensor.

2.3 Design of HF CM current sensor at outer ring

Current sensors with magnetic cores designed based on the Rogowski coil principle have the advantages of high sensitivity,wide frequency response range,and non-contact,and are widely used in various fields.To capture the highfrequency switching oscillation current,the sensor must have a fast-transient response and MHz-class bandwidth with the -3 dB upper cut-off frequency fh(3 dB) higher than the frequency of the HF CM current.Moreover,the -3 dB lower cut-off frequency fl was higher than the frequency of the PWM ripple current.As shown in Section 2.2,when μ1 is significantly larger than μ0,the magnetic field ripples in Bφ3 and Br3 will approach zero.At this time,only the magnetic field generated by the CM current exists outside the inner ring.First,the parameters of the current sensor are designed.Based on the -3 dB bandwidth,the upper limit and lower limit cutoff frequencies are as follows∶

The upper and lower limits of the sensor satisfied the bandwidth of 50 kHz-20 MHz required in the experiment,and the self-inductance and distributed capacitance can be approximately calculated according to the following formula∶

where N is the number of winding turns and μ is the magnetic permeability of the sensor skeleton.ɛ is the relative permittivity of the skeleton.b,a, and h represent the outer diameter,inner diameter,and height of the skeleton,respectively.Sensor sensitivity is defined as the ratio of the output voltage to the current to be measured,and is expressed as follows∶

According to Equations (5)–(9),the sensor performance is determined by a combination of parameters.The sensor sensitivity and bandwidth were adjusted by varying the number of turns N and termination resistance Rt.

3 Analysis of HF electromagnetic performance of double-ring sensors

3.1 Design process of the proposed double ring sensor

Based on the theoretical analysis in Section III,the design process of the proposed double-ring current sensor was illustrated in Fig.6.The inner ring parameters were first determined by the relationship curves between inner ring parameters and SNR.Then,these parameters were applied to explore whether the magnetic field of the magnetic shield ring is distributed uniform through electromagnetic simulation.Finally,the parameters of outer ring were designed to meet the requirement of high gain and high bandwidth,designing an HF CM current sensor that is free from DM interference.

Fig.6 Design process of the proposed double ring sensor

3.2 Influence of magnetic ring parameters

To investigate the influence of the inner ring parameters on the SNR,the magnetic field distribution generated by the phase current was analyzed.The magnetic induction intensity of the differential mode current at any point outside the magnetic ring is expressed as Equation (10).

The magnetic induction intensity generated by the threephase CM current is simplified to three times that of the onephase CM current;thus,Equation (10) can be rewritten as

The effectiveness of the inner ring in filtering the DM signal is also explored.A specific inner ring is used as an example to verify the performance of the magnetic shielding ring.The inner ring parameters are listed in Table 1.The target function SNR was set as the ratio of the magnetic induction intensity generated by the CM signal to that generated by the DM signal,as defined in Equation (12).

Table 1 Initial parameter setting of inner and outer rings

Table 2 Comparison of the standard deviation of the resonant peak at different torque

Table 3 Comparison of standard deviation of HF CM resonant frequencies at different ΔCg1

The SNR was optimized as much as possible under the premise that the magnetic ring size met the practical requirements.The effects of the inner diameter,outer diameter,and permeability of the ring were analyzed.The initial inner and outer diameters of the inner ring were 19 and 31 mm,respectively,the height was 21 mm,and the relative permeability was 5000.The magnetic induction intensity and SNR generated by the common and DM currents at a point outside the ring can be calculated using Equations (10) and (12),respectively,as shown in Fig.7.

Fig.7 Relationship between the SNR

As illustrated in Fig.7,the SNR was negatively correlated with the inner diameter of the inner ring,positively correlated with the outer diameter of the inner ring,and positively correlated with the permeability of the inner ring.The selection of the magnetic ring parameters must be optimal for the inner ring parameters under the premise of satisfying engineering applications.Additionally,the outer ring was affected by the adjusted magnetic field range of the inner ring,and its height and permeability should not exceed those of the inner ring.The specific inner and outer ring parameters are listed in Table 1.

3.3 Simulation results of magnetic shielding performance

The magnetic field distribution generated by the DM current was simulated and analyzed to verify the effectiveness of the magnetic ring in shielding the DM current signal.First,the SolidWorks software was used to model the magnetic shielding ring.Then,a three-phase currents with a mutual 120-degree vector sum of zero was passed through the ring in the Maxwell.In this manner,the DM currents were simulated to investigate the actual effect of the magnetic shielding ring.The magnetic induction intensity distribution of the magnetic field is shown in Fig.8.

Fig.8 Spatial magnetic field distribution

The above experimental results show that when there is a magnetic shielding ring,the magnetic field generated outside the ring in space is uniformly and symmetrically distributed with the ring.In the absence of the magnetic shielding ring,the magnetic field was not evenly distributed outside the ring.This indicates that the magnetic ring can filter the magnetic field generated by the DM current such that the magnetic field outside the magnetic ring is evenly distributed.As shown in Fig.8(c),the magnetic induction intensity is consistent in the Z axis direction.It also shows that the magnetic induction intensity along the Z axis is 0.

The shielding effect of the inner ring on the DM signal was investigated;the simulation model is shown in Fig.9.Three current lines with a phase of 120 °to each other and a current magnitude of 10 A were used to simulate the three symmetrical DM currents.The magnetic induction intensity distribution of the DM currents in the ring was simulated by passing three current lines through the magnetic ring at any position.

Fig.9 Simulation model of mixed-state current magnetic field

The magnetic induction intensity generated by the threephase currents at a certain time at the center of the outer magnetic ring was extracted,and the variation curve of the magnetic induction intensity with the central path of the outer ring was obtained,as shown in Fig.10.

Fig.10 Changes of magnetic induction intensity in the center of the outer ring with the path

It can be seen from Fig.10 that the average value of the magnetic induction in the outer magnetic ring decreased by 53.9% in the double ring compared to that in the single ring.This indicates that the double ring can effectively filter out the DM and reduce the interference of the DM signal with the CM signal compared with the single ring.

4 Experimental study

Experiments were conducted to validate the feasibility and effectiveness of the proposed double-ring HF CM sensor for insulation monitoring in inverter-fed machines.The experimental setup is illustrated in Fig.15.The inverter-fed machine under test was a 380 V/3 kW permanent magnet synchronous motor with a rated current of 7.5 A and speed of 1500 rpm.The load motor was a 380 V/3 kW induction motor.The two drives,DeltaCH2000 and C2000,control the permanent magnet synchronous motor and induction motor in the speed and torque modes,respectively.The data acquisition unit was PICO 5444D.The HF voltage probe model was DP6150A (1500 V/100 MHz,accuracy 2%),and the HF current probe was CP8030B (30 A/50 MHz,accuracy 1%).The specific parameters of the double-ring sensors used in the experiment are shown in Table 1,and the coil turns of the outer ring high frequency current sensor are ten turns with a termination resistance of 20 Ω.

For a performance comparison,the machine CM currents were extracted from both the single-ring and double-ring sensors by enclosing the three-phase currents together,as shown in Fig.11.The PWM voltage and phase-current waveforms of the PMSM under normal operation are shown in Fig.12.The phase current of a PMSM contains multiple current components at different frequencies,including the fundamental current,PWM ripple current,and HF switching oscillating current.According to the conduction path,the HF switching oscillating current includes CM and DM currents.Moreover,a frequency-aliasing phenomenon exists in the switching oscillation currents.The frequency spectra of the HF switching oscillation current in different measurement modes are compared in Fig.13.An analysis of the single-phase and three-phase oscillating currents revealed a significant decrease in the HF DM current component at 9.5 MHz.The raw DM component in the motor phase current was as high as 0.171 A.After the use of a single-ring sensor enclosing three phases,the DM content was 0.025 A.Compared with the phase current DM content,the signal of the DM current magnetic field was reduced.After the use of the double-ring sensor enclosing the three phases,the DM content was 0.012 A,which is 52.0% lower than the result of the single-ring experiment.

Fig.11 Setup of electric machine winding groundwall insulation condition monitoring test rig

Fig.12 Waveforms of PWM voltage and phase current of PMSM during normal operation

Fig.13 Spectrum diagram under different measurement methods

As shown in Fig.14,100 segments of the switching oscillation current were captured and the relative changes in the content of the DM current were evaluated.The mean value of the HF DM current under the single-ring sensor is 0.0308 A,and the mean value of the HF DM current under the double-ring sensor is 0.0184 A.The double-ring sensor further filtered out 40.3% of the DM signal compared with the single-ring sensor,which corresponds to the simulation results.The experimental results shown in Fig.14 verify the effectiveness of the double ring in eliminating the DM interference.

Fig.14 Comparison of HF DM current component measured by single-ring and double-ring sensor

Additionally,the robustness of the HF CM current sensor in eliminating DM interference was tested under different operating conditions.A series of experiments were performed for different magnetic ring structures.As shown in Fig.15,the suppression effect of the double-ring sensor is stable under different torques by comparing the experimental results;the DM content is reduced by approximately 39.8%,and the standard deviation of 100 data points measured by the double-ring current sensor is reduced by approximately 20%.This indicates that the double ring has good stability under different operating conditions.

Fig.15 Comparison of HF DM current component at a variable torque

In practice,stator insulation failures often originate from localized weaknesses.For inverter-fed machines,the stator winding insulation at the machine terminal is more susceptible to failure under higher transient voltage stress[25].As shown in Fig.11,a configurable capacitor ΔCg1 is inserted in parallel between the machine terminal and ground to emulate the incipient terminal insulation degradation.As demonstrated in reference [3],the resonant frequency of the HF CM current is a reliable indicator of the winding terminal insulation state.The extracted insulation indicators of FHFCM using different current sensors are shown in Fig.16.Eighty data points were effectively extracted over a fundamental period at 30 Hz from the machine three-phase currents with a 4 kHz switching frequency of the VFD.It can be seen from Fig.16 that FHFCM decreases with increasing ΔCg1.When the inserted ΔCg1 is 220 pF,the standard deviation of FHFCM measured by the single-ring sensor is 60.10 kHz.The standard deviation of the FHFCM measured using the doublering sensor is 9.73 kHz.Compared to the single-ring current sensor,the standard deviation of 80 data points measured by the double-ring current sensor was reduced by 84%.This indicates that the results of the double-ring current sensor still have good consistency when measuring the HF CM current at different degrees of aging.

Fig.16 Comparison of HF CM current resonant frequencies measured at different aging degrees

This paper proposes a double-ring HF CM switching oscillation current sensor for inverter-fed machine winding insulation monitoring.The existing double-ring sensors are very rare and limited,which are primarily applied in fundamental frequency domains [26].The main advantage of the proposed double-ring sensor is its ability to filter DM interference.Compared to the experimental results of single-ring sensors,the proposed double-ring sensor exhibit improved consistency and accuracy of the target HF CM currents,which is beneficial for insulation monitoring.In practical applications,the proposed double-ring sensor in this study did not consider the fixation method of the double-ring and the mutual influence between the two rings.In the further work,an open-ended and/or flexible sensor is expected to be beneficial for practical applications.

5 Conclusions

Online monitoring of stator insulation health is essential to prevent unplanned downtime and minimize the associated economic losses,requiring accurate measurement of the HF CM current that reflects the winding insulation condition.To reduce the interference of the HF DM current in the HF CM current extraction process,a double-ring HF CM current sensor was designed.The following conclusions were drawn∶

(1) HF CM current can effectively reflect the inverterfed machine winding groundwall insulation condition,whose characteristics were mainly decided by the machine terminal capacitance.

(2) The magnetic ring can filter the magnetic field generated by the three-phase DM current signal,such that the magnetic field generated by the CM current is evenly distributed.

(3) A new double-ring HF current sensor is proposed for online insulation monitoring that can accurately extract the target HF CM current by eliminating the interference from DM signals.

The proposed sensor is expected to enhance the performance of online incipient insulation-degradation monitoring for inverter-fed machines.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 51907116,in part sponsored by Natural Science Foundation of Shanghai 22ZR1425400 and sponsored by Shanghai Rising-Star Program 23QA1404000.

Declaration of competing interest

The authors declare that they have no competing financial interests or personal relationships that may have influenced the work reported in this study.