Feature Extraction and Comprehension of Partial Discharge ... - MDPI

energies Article

Feature Extraction and Comprehension of Partial Discharge Characteristics in Transformer Oil from Rated AC Frequency to Very Low Frequency Zhongliu Zhou 1 Shaowei Guo 4 1

2 3 4

*

ID

, Yuanxiang Zhou 1,2, *, Xin Huang 1 , Yunxiao Zhang 1 , Mingyuan Wang 3 and

State Key Lab of Electrical Power System, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China; [email protected] (Z.Z.); [email protected] (X.H.); [email protected] (Y.Z.) School of Electrical Engineering, Xinjiang University, Urumqi 830047, China State Grid Jibei Electric Economic Research Institute, Beijing 100045, China; [email protected] North China Electric Power Research Institute Co., Ltd., Beijing 100045, China; [email protected] Correspondence: [email protected]; Tel.: +86-139-1109-7570

Received: 30 May 2018; Accepted: 26 June 2018; Published: 1 July 2018

Abstract: The reactive current can be reduced effectively by decreasing the frequency of the voltage in partial discharge (PD) test, especially for equipment with large capacitance. Thus, the cost and volume of the test power supply can be economized. To figure out the difference of PD characteristics in transformer oil between rated alternating-current (AC) frequency (50 Hz) and low frequency, tests are conducted from rated AC frequency to very low frequency (0.1 Hz) based on impulse current method. The results show that with the decrease of frequency, the inception voltage increases. The maximum and mean magnitude of discharge and pulse repetition rate first increase slightly, then decrease obviously. The main features of the variation of phase resolved PD (PRPD) patterns, discharge statistical patterns (phase distribution of maximum and mean discharge magnitude, pulse repetition rate qmax –φ, qmean –φ, n–φ; and number distribution of discharge magnitude n–q), and their characteristic parameters (skewness Sk + , Sk − ; kurtosis Ku + , Ku − ; asymmetry Asy ; and correlation coefficient Cc ) are depicted in detail, which should be paid attention to when using low frequency voltage. The inner mechanism for these variations is discussed from the aspects of the influence on electric field distribution and discharge process of frequency. Additionally, the variation trend of PD characteristics with the decrease of frequency can provide more information about insulation defect, which can be the supplement for discharge mode recognition. Keywords: partial discharge; low frequency voltage; PRPD; characteristic parameter; insulation defect diagnosis

1. Introduction To detect the defect in time and correctly avoid the serious faults of electrical equipment and interruption of power supply. One category of defect recognition methods is based on the operation condition, for example, the armature current of the direct-current (DC) generator [1], the current signal of three phase induction motor [2], sweep frequency response analysis to check the deformation [3], a simplified frequency-domain Volterra model to detect inter-turn faults [4], and so on. Another category of methods is based on the discharge information. Partial discharge is a kind of discharge that is restricted in the insulation defect region and does not form a complete breakdown damage. It is always accompanied by detectable phenomena such as electrical current [5], ultrasound [6], and light [7], which makes it an important indicator to check the insulation reliability of electrical Energies 2018, 11, 1702; doi:10.3390/en11071702

www.mdpi.com/journal/energies

Energies 2018, 11, 1702

2 of 17

equipment and discover early insulation hazards. Generally, PD detection is performed during a withstand test under the rated operating voltage even multiplied by a certain margin factor. Under the relatively high voltage defined by test standards, the demand for reactive power can be reduced by decreasing the voltage frequency as the equation depicts Q = U2 ωC [8], where Q (Var) is the reactive power, U (V) is the applied voltage, ω (1/s) is the angular frequency, and C (F) is the capacitance. Taking 0.1 Hz as an example, the reactive power can be reduced to 1/500 of that under rated alternating-current (AC) frequency. Thus, the volume, production cost, and transportation expense of test power supply can be economized, especially for the equipment with large capacitance. Also, there is consideration about substituting DC voltage for rated AC frequency voltage as the reactive current will be reduced to zero. However, the electric field under direct-current (DC) voltage obeys resistive distribution, which is far different from the capacitive distribution under actual operation conditions. Moreover, the waveform of DC voltage is not sinusoidal alternative and does not go across the zero point, which has a different influence on charge transportation after previous discharge from that of rated AC frequency [9]. Additionally, the space charge accumulated may cause unexpected damage to insulation during a DC withstand test. Above all, low frequency voltage is an appropriate option [10]. The first obstacle before the substitution of low frequency for rated AC frequency is how to evaluate the effectiveness of test results under low frequency, in other words, how to comprehend the test results because the traditional judging methods are not suitable. In 1961, Bhimani from the General Electric corporation proposed to use low frequency voltage to conduct a withstand test for reducing the capacity demand for test power supply, as the rotating machine to be checked has a large capacitance to the ground. His research shows that for PD in the void embedded in polyethylene sheets, the number of pulses under 0.1 Hz has the same order as that under 60 Hz. However, the difference becomes larger when the voltage decreases [11]. R. Miller points out that with the decrease of frequency, the magnitude of discharge in the void in epoxy resin decreases [12]. Because of the limitation of measurement technology, early research mainly focuses on whether there is a significant difference of discharge characteristics between rated AC frequency and low frequency, only for evaluating the effectiveness of a withstand test under low frequency [13–15]. With the increasing requirement for diagnosis accuracy, recent research begins to examine the details of the difference [16,17], for example, how the frequency affects the dissipation of discharge deposited from the previous half voltage cycle [18–20]. The existence of a statistical delay may lead to the difference of inception phase under different frequencies [21]. These studies, on the one hand, are necessary to grasp the discharge characteristics under low frequencies. On the other hand, they provide a new way to deepen the understanding of discharge mechanisms. The electrical strength of insulating oil is superior to that of compressed gas, which is equivalent to sulfur hexafluoride (SF6 ) at 0.3 MPa. For the electrode consisting of a sphere with the diameter of 12.5 mm, a plate with a diameter of 75 mm and a gap of 12.5 mm, the peak value of the breakdown voltage is about 90 kV [22]. Its heat dissipation capacity and substitutability are better than those of solid insulation. Thus, insulating oil is widely used in electrical equipment [23]. Because of the incorrect action during assembly of the transformers, protrusion of the metal may appear, which causes the inhomogeneous electric field and may lead to corona discharge in the insulating oil. For the ultra-high-voltage (UHV) AC transformers and converter transformers with large volumes, as shown in Figure 1, small deformation may occur during the load impact and the long journey from the manufactory to the substation, which may bring the protrusion of the metal. There have been some studies on the characteristics of corona discharge in oil under rated frequency AC and DC voltage, providing detailed information for insulation defect diagnosis and understanding discharge mechanism under the corresponding voltage [24–27]. However, research about the corona discharge in oil under low frequency is rarely reported. Analysis of the variation of discharge characteristics from rated AC frequency to low frequency has three main meanings. The first is to provide reference for insulation diagnosis under low frequency voltage, such as the PRPD in Section 3.2 and statistical

Energies 2018, 11, 1702

3 of 17

Energies 2018, 11, x FOR PEER REVIEW Energies 2018, 11, x FOR PEER REVIEW

3 of 17 3 of 17

patterns in Section 3.3.1. The second is to promote the understanding of corona discharge in insulating understanding of corona discharge in insulating oil, such as the discussion in Section 4. The third is oil, such as the discussion in Section 4. The third is to obtain the variation trend of discharge understanding of corona discharge in insulating oil, such as the discussion in Section 4. The third is to obtain the variation trend of discharge characteristics, which can be supplement for discharge characteristics, which can be supplement for discharge mode recognition, as the variation trend to obtain the variation trend which can be such supplement for discharge mode recognition, such as of the discharge variation characteristics, trend of statistical parameters in Section 3.1 and of statistical parameters in Section 3.1 and characteristic parameters in Section 3.3.2. mode recognition, such as the variation trend of statistical parameters in Section 3.1 and characteristic parameters in Section 3.3.2. characteristic parameters in Section 3.3.2.

(a) (a)

(b) (b)

Figure 1. Ultra‐high‐voltage (UHV) alternating‐current (AC) transformer and converter transformer. Figure 1. Ultra-high-voltage (UHV) alternating-current (AC) transformer and converter transformer. Figure 1. Ultra‐high‐voltage (UHV) alternating‐current (AC) transformer and converter transformer. (a) UHV AC transformer; (b) UHV converter transformer. (a) UHV AC transformer; (b) UHV converter transformer. (a) UHV AC transformer; (b) UHV converter transformer.

The main framework and approach of this research is shown in Figure 2. Firstly, a PD test and The main framework and approach of this research is shown in Figure 2. Firstly, a PD test and The main framework and approach of this research is shown in Figure 2. Firstly, a PD test and analysis system suitable for the applied voltage from rated AC frequency to very low frequency is analysis system suitable for the applied voltage from rated AC frequency to very low frequency is set analysis system suitable for the applied voltage from rated AC frequency to very low frequency is set up. Then, experiments are conducted under a series of frequencies to measure statistical up. Then, experiments are conducted under a series ofa frequencies to measure statistical parameters of set up. Then, experiments are PRPD, conducted under patterns, series and of frequencies to measure statistical parameters of discharge. Third, statistical their characteristic parameters are discharge. Third, PRPD, statistical patterns, and their characteristic parameters are obtained from the parameters of discharge. Third, PRPD, statistical patterns, and their characteristic parameters are obtained from the data acquired in the second step. Finally, we discuss the influence on discharge data acquired in the second step. Finally, we discuss the influence on discharge of frequency from the obtained from the data acquired in the second step. Finally, we discuss the influence on discharge of frequency from the aspects of the electric field distribution and discharge process. aspects of the electric field distribution and discharge process. of frequency from the aspects of the electric field distribution and discharge process.

Figure 2. Main framework and approach of this research. PD—partial discharge; PRPD—phase Figure 2. 2. Main Main framework framework and and approach approach of of this this research. research. PD—partial PD—partial discharge; discharge; PRPD—phase PRPD—phase resolved PD. Figure resolved PD. resolved PD.

2. Experimental Setup and Analysis Method 2. Experimental Setup and Analysis Method 2. Experimental Setup and Analysis Method 2.1. Test System, Procedure, and Sample Preparation 2.1. Test System, Procedure, and Sample Preparation 2.1. Test Procedure, Sample The System, PD test system and consists of Preparation three parts, as shown in Figure 3. The first part is a low The PD PD test test system consists of three parts, as shown in Figure 3. The part frequency is a low frequency voltage generator. The power amplifier Trek model 50/12 amplifies the small signal from The system consists of three parts, as shown in Figure 3. The first partfirst is a low frequency voltage generator. The power amplifier Trek model 50/12 amplifies the small signal from the output of the arbitrary waveform generator AFG 3011C to obtain the voltage required [28]. The voltage generator. The power amplifier Trek model 50/12 amplifies the small signal from the output of the output of the arbitrary waveform generator AFG 3011C to obtain the voltage required [28]. The frequency of the applied voltage can be adjusted from 50 Hz to very low frequency (0.1 Hz) [8,11], the arbitrary waveform generator AFG 3011C to obtain the voltage required [28]. The frequency of the frequency of the applied voltage can be adjusted from 50 Hz to very low frequency (0.1 Hz) [8,11], and the amplitude can be adjusted from 0 to 35 kV. The second part is the circuit of test electrode applied voltage can be adjusted from 50 Hz to very low frequency (0.1 Hz) [8,11], and the amplitude and the amplitude can be adjusted from 0 to 35 kV. The second part is the circuit of test electrode and measurement system. The radius of curvature of the needle electrode is about 3 μm, of which can be adjusted from 0 to 35 kV. The second part is the circuit of test electrode and measurement and measurement system. The radius of curvature of the needle electrode is about 3 μm, of which the tip is 2 mm away from the earth electrode. The earth electrode is a round plate with a diameter system. The radius of curvature of the needle electrode is about 3 µm, of which the tip is 2 mm away the tip is 2 mm away from the earth electrode. The earth electrode is a round plate with a diameter of 75 mm and covered by a piece of oil‐paper with thickness of 1 mm. One measurement impedance of 75 mm and covered by a piece of oil‐paper with thickness of 1 mm. One measurement impedance connected to the electrode is to acquire the discharge signals, another connected to the coupling connected to the electrode is to acquire the discharge signals, another connected to the coupling

Energies 2018, 11, 1702

4 of 17

from the earth electrode. The earth electrode is a round plate with a diameter of 75 mm and covered by 4 of 17 aEnergies 2018, 11, x FOR PEER REVIEW piece of oil-paper with thickness of 1 mm. One measurement impedance connected to the electrode is to acquire the discharge signals, another connected to the coupling capacitance is to acquire the capacitance is to acquire the applied voltage signal. The third part The is for data processing and applied voltage signal. The third part is for data processing and analysis. oscilloscope TDS 2024B The oscilloscope TDS accompanied 2024B is to monitor applied voltage accompanied the isanalysis. to monitor the applied voltage with the the high-voltage (HV) measuring probewith PVM-5. high‐voltage (HV) measuring probe PVM‐5. The PD analyzer MPD 600 transports the discharge The PD analyzer MPD 600 transports the discharge signals to the control unit MCU 500 by optical fiber signals to the control unit MCU 500 by optical fiber cable, which effectively reduces the interference. cable, which effectively reduces the interference. Some other actions are taken to avoid the unexpected Some other actions are taken to avoid the unexpected discharge in the test circuit, making the noise discharge in the test circuit, making the noise below 5 pC when the amplitude of applied voltage is below 5 pC when the amplitude of applied voltage is 35 kV. 35 kV.

Figure 3. PD test and analysis system from rated AC frequency to very low frequency. Figure 3. PD test and analysis system from rated AC frequency to very low frequency.

The electrode and its container were washed in the order of clean water, alcohol, and The electrode and its container were washed in the order of clean water, alcohol, and deionized deionized water, and then dried at 100 °C for 48 h [29]. The insulating oil was filtered, dried, and water, and then dried at 100 ◦ C for 48 h [29]. The insulating oil was filtered, dried, and the gas in it the gas in it was removed to ensure that its electrical strength, moisture content, gas content, and was removed to ensure that its electrical strength, moisture content, gas content, and acid value meet acid value meet the corresponding standards. The insulating paper is dried at 105 °C for 48 h and the corresponding standards. The insulating paper is dried at 105 ◦ C for 48 h and then impregnated then impregnated with insulating oil slowly at 40 °C in a vacuum oven. with insulating oil slowly at 40 ◦ C in a vacuum oven. The rising speed of the applied voltage in the experiments is 0.1 kV/step. PD inception voltage The rising speed of the applied voltage in the experiments is 0.1 kV/step. PD inception voltage (PDIV) is defined as the continuous and stable discharge pulses are firstly observed. The frequency (PDIV) is defined as the continuous and stable discharge pulses are firstly observed. The frequency selected is 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 5 Hz, 1 Hz, and 0.1 Hz. Discharge signals are recorded selected is 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 5 Hz, 1 Hz, and 0.1 Hz. Discharge signals are recorded and analyzed under constant voltage amplitude, that is, 16 kV, 20 kV, 24 kV, 26 kV, 30 kV, and 32 and analyzed under constant voltage amplitude, that is, 16 kV, 20 kV, 24 kV, 26 kV, 30 kV, and 32 kV. kV. The tests under each frequency and amplitude are repeated more than five times. The interval The tests under each frequency and amplitude are repeated more than five times. The interval of each of each test for the platform to be static is more than 15 min. test for the platform to be static is more than 15 min. 2.2. Analysis Method 2.2. Analysis Method The influence of frequency on PDIV, magnitude of discharge, and pulse repetition rate is The influence of frequency on PDIV, magnitude of discharge, and pulse repetition rate is demonstrated, which are direct indicators of the severity of discharge. Additionally, the influence demonstrated, which are direct indicators of the severity of discharge. Additionally, the influence on PRPD, discharge statistical patterns, and their characteristic parameters shown in Table 1 is also on PRPD, discharge statistical patterns, and their characteristic parameters shown in Table 1 is also depicted as reference for mode recognition under low frequency voltage. All the variations depicted as reference for mode recognition under low frequency voltage. All the variations mentioned mentioned above are in nature because of the influence on discharge process of frequency. above are in nature because of the influence on discharge process of frequency. In Table 1, qmax and qmean is the maximum and mean magnitude of discharge in the corresponding Table 1. Partial discharge (PD) statistical patterns and their characteristic parameters. phase window with the width of 1◦ . The unit of qmax and qmean is pC, and the unit of φ is phase Discharge Pattern Symbol Characteristic Parameters degree “◦ ”. The skewness Sk > 0 indicates that the distribution of discharge pattern is to the left of Phase distribution of maximum magnitude of discharge qmax–φ Sk+, Sk−, Kthe u+, K u−, Asy, Cc is normal distribution, and to the right on the contrary. The kurtosis Ku > 0 indicates distribution + − + −, Asy, Cc Phase distribution of mean magnitude of discharge qmean –φ Sk , Sk A , K sharper than normal distribution, and smoother on the contrary. The asymmetry 1 uindicates the syu >, K + − + Phase distribution of numbers of discharge n–φ that inSak , S k , Ku , K u−, A sy, Cc The distribution of discharge pattern in negative half cycle is higher than positive half cycle. Number distribution of discharge magnitude n–q Sk, Kuin a positive closer the correlation coefficient Cc is to 1, the more similar the outlines of the patterns In Table 1, qmax and qmean is the maximum and mean magnitude of discharge in the corresponding phase window with the width of 1°. The unit of qmax and qmean is pC, and the unit of φ is phase degree “°”. The skewness Sk > 0 indicates that the distribution of discharge pattern is to the left of normal distribution, and to the right on the contrary. The kurtosis Ku > 0 indicates the

Energies 2018, 11, 1702

5 of 17

and negative half cycle [30–32]. The superscripts “+” and “−” correspond to a positive and negative half cycle, respectively. The detailed calculation methods of each characteristic parameter can be found in our previous research [33]. Energies 2018, 11, x FOR PEER REVIEW 5 of 17 Table 1. Partial discharge (PD) statistical patterns and their characteristic parameters. distribution is sharper than normal distribution, and smoother on the contrary. The asymmetry A sy > 1 indicates the distribution of discharge pattern in negative half cycle is higher than that in a Discharge Pattern Symbol Characteristic Parameters positive half cycle. The closer the correlation coefficient Cc is to 1, the more similar the outlines of Sk + , Sk − , Ku + , Ku − , Asy , Cc Phase distribution of maximum magnitude of discharge qmax –φ the patterns in a positive and negative half cycle [30–32]. The superscripts “+” and “−” correspond Sk + , Sk − , Ku + , Ku − , Asy , Cc Phase distribution of mean magnitude of discharge qmean –φ to a positive and negative half ofcycle, respectively. The Phase distribution of numbers discharge n–φ detailed calculation Sk + , Sk − , Ku +methods , Ku − , Asy , Cof c each Number distribution of discharge magnitude n–q S , K u k characteristic parameter can be found in our previous research [33].

3. Experimental Results 3. Experimental Results 3.1. Statistical Parameters of Discharge 3.1. Statistical Parameters of Discharge

Partial discharge inception voltage (kV)

3.1.1. PDIV 3.1.1. PDIV With the decrease of frequency, PDIV in positive and negative half cycle both increases with a With the decrease of frequency, PDIV in positive and negative half cycle both increases with a faster rising rate below 5 Hz, as shown in Figure 4. Compared with that under rated AC frequency, faster rising rate below 5 Hz, as shown in Figure 4. Compared with that under rated AC frequency, PDIV increases by 26.93% under 5 Hz and by 139.82% under 0.1 Hz. PDIV in negative half cycle is PDIV increases by 26.93% under 5 Hz and by 139.82% under 0.1 Hz. PDIV in negative half cycle is higher than that in positive half cycle under each frequency involved. The difference between PDIV in higher than that in positive half cycle under each frequency involved. The difference between PDIV negative and positive half cycle increases, from 3.85 kV under 50 Hz to 5.93 kV under 1 Hz. in negative and positive half cycle increases, from 3.85 kV under 50 Hz to 5.93 kV under 1 Hz. 30 PDIV in positive half cycle PDIV in negative half cycle

25 20 15 10 5 0

50

45

40

35

30

25

20

15

10

Frequency of applied voltage (Hz)

5

0

Figure 4. PD inception voltage from rated AC frequency to very low frequency. PDIV—PD Figure 4. PD inception voltage from rated AC frequency to very low frequency. PDIV—PD inception voltage. inception voltage.

3.1.2. Maximum Magnitude of Discharge 3.1.2. Maximum Magnitude of Discharge Under voltage with relatively low amplitude, discharge below 5 Hz does not initiate. Under Under voltage with relatively low amplitude, discharge below 5 Hz does not initiate. voltage with relatively high amplitude, discharge above 5 Hz is so severe that the disperse noise Under voltage with relatively high amplitude, discharge above 5 Hz is so severe that the disperse noise from large discharge sometimes overlaps small discharge. Thus, the voltage amplitude and from large discharge sometimes overlaps small discharge. Thus, the voltage amplitude and frequency frequency is selected appropriately, as shown in Figure 5a. Discharge in positive cycle is more severe is selected appropriately, as shown in Figure 5a. Discharge in positive cycle is more severe than that than that in negative one, which is consistent with the results in previous research [34]. The reason is in negative one, which is consistent with the results in previous research [34]. The reason is that the that the positive streamer has a faster speed and is easier to develop than the negative streamer [35]. positive streamer has a faster speed and is easier to develop than the negative streamer [35]. With the decrease of frequency, the maximum magnitude of discharge in positive cycle Q max+ With the decrease of frequency, the maximum magnitude of discharge in positive cycle Qmax + first first increases slightly, and then decreases obviously with a faster descending rate under lower increases slightly, and then decreases obviously with a faster descending rate under lower frequency. frequency. When the amplitude is 20 kV, Q max+ under 5 Hz decreases by 42.26% compared with 50 When the amplitude is 20 kV, Qmax + under 5 Hz decreases by 42.26% compared with 50 Hz. When the + Hz. When the amplitude is 32 kV, Q max under 1 Hz decreases by 75.17% compared with 0.1 Hz. The amplitude is 32 kV, Qmax + under 1 Hz decreases by 75.17% compared with 0.1 Hz. The maximum maximum magnitude of discharge in negative −cycle Qmax− shows a continuous decreasing trend. magnitude of discharge in negative cycle Qmax shows a continuous decreasing trend. When the When the amplitude is 20 kV, Q max− under 5 Hz decreases by 93.44% compared with 50 Hz. − amplitude is 20 kV, Qmax under 5 Hz decreases by 93.44% compared with 50 Hz.

Energies 2018, 11, 1702

6 of 17

Energies 2018, 11, x FOR PEER REVIEW Energies 2018, 11, x FOR PEER REVIEW

6 of 17 6 of 17

16 kV 20 kV 16 kV

24 kV 26 kV 24 kV

30 kV 32 kV 30 kV

20 kV

26 kV

32 kV

40 30 20 10 5 1 Frequency of applied voltage (Hz) 40 30 20 10 5 1

1000 1000 750 750 500 500 250 250

Q in negative cycle (pC) in negative cycle (pC) Qmax max

Q in positive cycle (pC) in positive cycle (pC) Qmax max

30000 30000 25000 25000 20000 20000 15000 15000 10000 10000 5000 5000 0 50 0 50

0 0


(a) (a)

16 kV

20 kV

16 kV

24 kV

20 kV

24 kV

Increase sharply Increase sharply

75 75 50 50 25 25 0 50 0 50

Decrease slightly Decrease slightly

Decrease obviously Decrease obviously

40 30 20 10 5 Frequency of applied voltage (Hz) 40 30 20 10 5


(b) (b)

0 0

Figure 5. Maximum magnitude of discharge from rated AC frequency to very low frequency. (a) Figure 5. Maximum magnitude of discharge from rated AC frequency to very low frequency. (a) Qmax Figure 5. Maximum magnitude of discharge from rated AC frequency to very low frequency. (a) max in positive half cycle; (b) Qmax in negative half cycle. Q in positive half cycle; (b) Qmax in negative half cycle. Qmax in positive half cycle; (b) Qmax in negative half cycle. − under each frequency both With the increase of amplitude of applied voltage, Qmax++ and Qmax− With the increase of amplitude of applied voltage, Q Q under each frequency both With the increase of amplitude of applied voltage, Q max+and and Q max− under each frequency both max max increase. The increasing rate decreases with the increase of amplitude. Taking 5 Hz as an example, increase. The increasing rate decreases with the increase of amplitude. Taking 5 Hz as an example, increase. The increasing rate decreases with the increase of amplitude. Taking 5 Hz as an example, Qmax+ under 20 kV and 24 kV increases by 260.04% and 429.48% compared with 16 kV. + under 20 kV and 24 kV increases by 260.04% and 429.48% compared with 16 kV. + Q Qmax max under 20 kV and 24 kV increases by 260.04% and 429.48% compared with 16 kV.

3.1.3. Mean Magnitude of Discharge 3.1.3. Mean Magnitude of Discharge 3.1.3. Mean Magnitude of Discharge With the decrease of frequency, Qmean++ shows a decreasing trend with a faster descending rate With the decrease of frequency, Qmean shows a decreasing trend with a faster descending rate With the decrease of frequency, Q mean+ shows a decreasing trend with a faster descending rate under lower frequency, as shown in Figure 6a. When the amplitude is 20 kV, Qmean++ under 5 Hz under lower frequency, as shown in Figure 6a. When the amplitude is 20 kV, Q under 5 Hz mean under lower frequency, as shown in 50 Hz. Figure Q6a. When the amplitude is 20 relatively low kV, Q mean+ under 5 Hz decreases by 43.88% compared with mean−− decreases slightly under voltage, decreases by 43.88% compared with Hz. QQ decreases slightly under relatively low voltage, mean decreases by 43.88% compared with 50 50 Hz. mean− decreases slightly under relatively low voltage, while it decreases obviously under relatively high voltage. When the amplitude is 20 kV, Qmean−− while it decreases obviously under relatively high voltage. amplitude isis 2020 kV, Qmean while it decreases obviously under relatively high voltage. When When the the amplitude kV, Qmean− under 5 Hz decreases by 62.98% compared with 50 Hz. under 5 Hz decreases by 62.98% compared with 50 Hz. under 5 Hz decreases by 62.98% compared with 50 Hz. With the increase of amplitude, Qmean++ and Qmean− under each frequency both increase. Taking 1 − under each frequency both increase. Taking With the increase of +amplitude, Qmean and Qmean− under each frequency both increase. Taking 1 With the increase of amplitude, Q mean+ and Qmean Hz as an example, Q mean under 26 kV, 30 kV, and 32 kV increases by 42.91%, 86.16%, and 131.90% + 1Hz as an example, Q Hz as an example, Qmean under 26 kV, 30 kV, and 32 kV increases by 42.91%, 86.16%, and 131.90% + compared with 24 kV. mean under 26 kV, 30 kV, and 32 kV increases by 42.91%, 86.16%, and 131.90% compared with 24 kV. compared with 24 kV. 16 kV 20 kV 16 kV

24 kV 26 kV 24 kV

30 kV 32 kV 30 kV

20 kV

26 kV

32 kV

40 30 20 10 5 1 Frequency of applied voltage (Hz) 40 30 20 10 5 1 Frequency of applied voltage (Hz)

(a) (a)

100 100

Qmean in negative cycle (pC) Qmean in negative cycle (pC)

Qmean in positive cycle (pC) Qmean in positive cycle (pC)

15000 15000 12500 12500 10000 10000 7500 7500 5000 5000 2500 2500 0 50 0 50

0 0

16 kV 16 kV

80 80 60 60

20 kV

Decrease obviously

40 40

Decrease obviously

20 20 0 0

20 kV

Decrease slightly Decrease slightly

50 50

40

30

20

10

Frequency of applied voltage (Hz) 40 30 20 10 Frequency of applied voltage (Hz) (b)

5 5

0 0

(b)

Figure 6. Mean magnitude of discharge from rated AC frequency to very low frequency. (a) Qmean in Figure 6. Mean magnitude of discharge from rated AC frequency to very low frequency. (a) Q mean in mean in negative cycle. positive cycle; (b) Q Figure 6. Mean magnitude of discharge from rated AC frequency to very low frequency. (a) Qmean in positive cycle; (b) Qmean in negative cycle. positive cycle; (b) Qmean in negative cycle.

3.1.4. Pulse Repetition Rate 3.1.4. Pulse Repetition Rate + 3.1.4.With the decrease of frequency, the pulse repetition rate in positive and negative half cycle (R Pulse Repetition Rate + With the decrease of frequency, the pulse repetition rate in positive and negative half cycle (R −) both first increase slightly, and then decrease obviously, with a faster descending rate under and R With the decrease of frequency, the pulse repetition rate in positive and negative half cycle (R+ − and R−) both first increase slightly, and then decrease obviously, with a faster descending rate under + under 5 Hz decreases by lower frequency, as shown in Figure 7. When the amplitude is 20 kV, R and R ) both first increase slightly, and then decrease obviously, with a faster descending rate under + lower frequency, as shown in Figure 7. When the amplitude is 20 kV, R − + under 5 Hz decreases by 85.39% compared with 50 Hz. R under 5 Hz decreases by 96.33% compared with 50 Hz. lower frequency, as shown in Figure 7. When the amplitude is 20 kV, R under 5 Hz decreases by − under 5 Hz decreases by 96.33% compared with 50 Hz. 85.39% compared with 50 Hz. R + − under each frequency both increase. Taking 1 Hz as With the increase of amplitude, R 85.39% compared with 50 Hz. R− under+ and R 5 Hz decreases by 96.33% compared with 50 Hz. With the increase of amplitude, R and R− under each frequency both increase. Taking 1 Hz as + under 26 kV, 30 kV, and 32 kV increases by 93.68%, 257.13%, and 331.67% compared an example, R an example, R+ under 26 kV, 30 kV, and 32 kV increases by 93.68%, 257.13%, and 331.67% compared with 24 kV. with 24 kV.

Energies 2018, 11, 1702

7 of 17

With the increase of amplitude, R+ and R− under each frequency both increase. Taking 1 Hz as an example, R+ under 26 kV, 30 kV, and 32 kV increases by 93.68%, 257.13%, and 331.67% compared with 24 kV. Energies 2018, 11, x FOR PEER REVIEW 7 of 17 17.5 17.5 15.0 15.0 12.5 12.5 10.0 10.0 7.5 7.5 5.0 5.0 2.5 2.5 0.0 50 0.0 50

16 kV 20 kV 16 kV 20 kV

24 kV 26 kV 24 kV 26 kV

7 of 17 Repetition rate in negative cycle (pC) Repetition rate in negative cycle (pC)

Repetition rate in positive cycle (1/s) Repetition rate in positive cycle (1/s)

Energies 2018, 11, x FOR PEER REVIEW 60 60 50 50 40 40 30 30 20 20 10 10 3 32 21 10 50 0 50

30 kV 32 kV 30 kV 32 kV

40 30 20 10 5 1 0 Frequency of applied voltage (Hz) 40 30 20 10 5 1 0


(a) (a)

16 kV

20 kV

16 kV

20 kV

Increase slightly Increase slightly Decrease obviously Decrease obviously

40 30 20 10 5 0 Frequency of applied voltage (Hz) 40 30 20 10 5 0 Frequency of applied voltage (Hz)

(b) (b)

Figure 7. Pulse very low low frequency. frequency. (a) Figure 7. Pulse repetition repetition rate rate of of discharge discharge from from rated rated AC AC frequency frequency to to very (a) Figure 7. Pulse repetition rate of discharge from rated AC frequency to very low frequency. (a) Repetition rate in positive half cycle; (b) Repetition rate in negative half cycle. Repetition rate in positive half cycle; (b) Repetition rate in negative half cycle. Repetition rate in positive half cycle; (b) Repetition rate in negative half cycle.

3.2. PRPD 3.2. PRPD 3.2. PRPD PRPD is an intuitive indicator for mode recognition of insulation defect. PRPD of the defect in PRPD is an intuitive indicator for mode recognition of insulation defect. PRPD of the defect in this PRPD is an intuitive indicator for mode recognition of insulation defect. PRPD of the defect in research from rated AC frequency to 5 Hz is shown in Figure 8. The amplitude of applied this research research from frequency to to 5 Hz is shown in Figure 8. The8. amplitude of applied voltage this from rated rated AC AC frequency 5 Hz is shown in Figure The amplitude of applied voltage is 20 kV. There are some common features under each frequency. Discharge in positive half is 20 kV. There are some common features under each frequency. Discharge in positive half cycle is voltage is 20 kV. There are some common features under each frequency. Discharge in positive half cycle is more severe than that in negative half cycle. Discharge is distributed around the voltage more severe than that in negative half cycle. Discharge is distributed around the voltage peaks and cycle is more severe than that in negative half cycle. Discharge is distributed around the voltage peaks and appears like a mountain shape. With the decrease of frequency, the discharge magnitude, appears like a mountain shape. With the decrease of frequency, the discharge magnitude, the range of peaks and appears like a mountain shape. With the decrease of frequency, the discharge magnitude, the range of the discharge magnitude, and repetition rate all decrease, which makes the mountain the discharge magnitude, and repetition rate all decrease, which makes the mountain shape become the range of the discharge magnitude, and repetition rate all decrease, which makes the mountain shape become vague, as shown in Figure 8a–d. vague, as shown in Figure 8a–d. shape become vague, as shown in Figure 8a–d.

Magnitude of PD (pC) Magnitude of PD (pC)

100 0 45 90 135 180 225 270 315 360 0 45 90 135 Phase (°) 180 225 270 315 360 Phase (°)

(a) (a)

25000

20000 15000

400

45 45

90 90

100 0 135 180 225 270 315 360 0 Phase (°) 135 180 225 270 315 360 Phase (°)

(c) (c)

45 45

90 90

100 0 135 180 225 270 315 360 0 135 Phase (°) 180 225 270 315 360 Phase (°)

(b) (b)

25000

400

200 100

10000 5000

300 200

15000 10000

50000 0 0 0

400 300

20000 15000

200 100

10000 5000

50000 0 0 0

25000 20000

300 200

15000 10000

200 100

10000 5000

400 300

25000 20000

50000 0 0 0

300 200

15000 10000

200 100

10000 5000 50000 0 0 0

20000 15000

300 200

15000 10000

400 400 300


20000 15000

25000

25000 20000


400 400 300


25000

25000 20000

45 45

90 90

100 0 135 180 225 270 315 360 0 Phase (°) 135 180 225 270 315 360 Phase (°)

(d) (d)

Figure 8. PRPD from rated AC frequency to very 5 Hz with the voltage magnitude of 20 kV. (a) 50 Figure 8. PRPD from rated AC frequency to very 5 Hz with the voltage magnitude of 20 kV. (a) 50 Hz, (b) 30 Hz, (c) 10 Hz, and (d) 5 Hz. Figure 8. PRPD from rated AC frequency to very 5 Hz with the voltage magnitude of 20 kV. (a) 50 Hz, Hz, (b) 30 Hz, (c) 10 Hz, and (d) 5 Hz. (b) 30 Hz, (c) 10 Hz, and (d) 5 Hz.

Because discharger under 1 Hz and 0.1 Hz does not initiate under 20 kV, the amplitude Because discharger under 1 Hz and 0.1 Hz does not initiate under 20 kV, the amplitude selected for them is 32 kV. Under 1 Hz, the pattern in positive half cycle changes to closer to a half Because discharger under 1 Hz and 0.1 Hz does not initiate under 20 kV, the amplitude selected selected for them is 32 kV. Under 1 Hz, the pattern in positive half cycle changes to closer to a half mountain shape with only the left part, because the discharge termination phase is put forward, as for them is 32 kV. Under 1 Hz, the pattern in positive half cycle changes to closer to a half mountain mountain shape with only the left part, because the discharge termination phase is put forward, as shown in Figure 9a. More charge of the the discharge same polarity with high voltage electrode is produced shape with only the part, because termination phase is putelectrode forward,is asproduced shown in shown in Figure 9a. left More charge of the same lower polarity with high voltage during the left part of the mountain under frequency, which weakens the electric field Figure 9a. More charge of the same polarity with high voltage electrode is produced during the left during the left part of the part mountain under lower frequency, which weakens the electric field intensity during the right and suppresses the discharge there. The initial phase under lower part of the mountain under lower which weakens there. the electric field intensity during the intensity during the right part and frequency, suppresses the discharge The initial phase under lower frequency is put forward, which will be discussed in the following text. frequency is put forward, which will be discussed in the following text.

Energies 2018, 11, 1702

8 of 17

right part and suppresses the discharge there. The initial phase under lower frequency is put forward, which will be discussed in the following text. Energies 2018, 11, x FOR PEER REVIEW 8 of 17 Energies 2018, 11, x FOR PEER REVIEW

8 of 17

30000 24000 24000 18000 18000 12000 12000 6000 60000 0 0 0

45 90 135 180 225 270 315 360 45 90 135 Phase (°) 180 225 270 315 360 Phase (°)

(a) (a)

25000 25000 20000 20000 15000 15000 10000 10000 5000 5000 0 0 0 0



36000 36000 30000

45 90 135 180 225 270 315 360 45 90 135 Phase (°) 180 225 270 315 360 Phase (°)

(b) (b)

Figure 9. PRPD under 1 Hz and 0.1 Hz with the voltage magnitude of 32 kV. (a) 1 Hz and (b) 0.1 Hz. Figure 9. PRPD under 1 Hz and 0.1 Hz with the voltage magnitude of 32 kV. (a) 1 Hz and (b) 0.1 Hz. Figure 9. PRPD under 1 Hz and 0.1 Hz with the voltage magnitude of 32 kV. (a) 1 Hz and (b) 0.1 Hz.

3.3. Statistical Patterns and Characteristic Parameters 3.3. Statistical Patterns and Characteristic Parameters 3.3. Statistical Patterns and Characteristic Parameters

positive cycle negative cycle positive cycle negative cycle

12000 8000

100 80 80 60 60 40

8000 4000

mean

40 20 4000 20 0 0 0 40 80 120 160 200 240 280 320 360 0 0 Phase (°) 0 40 80 120 160 200 240 280 320 360

30000

Phase (°) (b) (b) positive cycle

12000 6000 60000 0 40 80 120 160 200 240 280 320 360 0 Phase (°) 0 40 80 120 160 200 240 280 320 360

Phase (°)

(d) (d)

mean

40 20 4000 20 0 0 0 40 80 120 160 200 240 280 320 360 0 0 Phase (°) 0 40 80 120 160 200 240 280 320 360

16000

mean

80 60 60 40

8000 4000

qmean cycle (pC) q in negative in negative cycle (pC)

12000 8000

100 100 80

Phase (°) (c) (c) positive cycle positive cycle

12000 8000

18000 12000

Phase (°)


16000 12000

positive cycle

24000 18000

16000

16000 12000

mean

4000 20 0 0 0 40 80 120 160 200 240 280 320 360 0 0 Phase (°) 0 40 80 120 160 200 240 280 320 360

qmean cycle (pC) q in positive in positive cycle (pC)

40 20

mean

mean

80 60 60 40

8000 4000

30000 24000

100

100 100 80

(e) (e)

8000 4000 4000 0 0 40 80 120 160 200 240 280 320 360 0 Phase (°) 0 40 80 120 160 200 240 280 320 360

mean

16000

16000 12000

12000 8000


Phase (°) (a) (a)




mean

4000 20 0 0 0 40 80 120 160 200 240 280 320 360 0 0 Phase (°) 0 40 80 120 160 200 240 280 320 360


40 20

16000

16000 12000

mean

80 60 60 40

8000 4000


12000 8000

100 100 80

mean



16000

16000 12000



3.3.1. Statistical Patterns 3.3.1. Statistical Patterns 3.3.1. Statistical Patterns qqmean–φ pattern under 50 Hz in positive and negative half cycle both appear like a rectangular –φ pattern under 50 Hz in positive and negative half cycle both appear like a rectangular mean qmean –φ pattern under 50 Hz in positive and negative half cycle both appear like a rectangular shape superimposed by a triangle shape on the top, as shown in Figure 10a. With the decrease of shape superimposed by a triangle shape on the top, as shown in Figure 10a. With the decrease of shape superimposed by a triangle shape on the top, as shown in Figure 10a. With the decrease of frequency, the peak value of the patterns decreases, from 17 nC under 50 Hz to 13 nC under 5 Hz in frequency, the peak value of the patterns decreases, from 17 nC under 50 Hz to 13 nC under 5 Hz in frequency, the peak value of the patterns decreases, from 17 nC under 50 Hz to 13 nC under 5 Hz in positive half cycle. Discharge in negative half cycle does not initiate below 1 Hz. Only the left part positive half cycle. Discharge in negative half cycle does not initiate below 1 Hz. Only the left part of positive half cycle. Discharge in negative half cycle does not initiate below 1 Hz. Only the left part of the triangle shape remains under 1 Hz. Several peaks appear in the pattern under 0.1 Hz. the triangle shape remains under 1 Hz. Several peaks appear in the pattern under 0.1 Hz. of the triangle shape remains under 1 Hz. Several peaks appear in the pattern under 0.1 Hz.

Phase (°)

(f) (f)

Figure 10. qmean–φ pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Figure 10. qmean–φ pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Figure 10. qmean –φ pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Hz, Hz, 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. Hz, 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV.

raterate in negative cycle(PDs/s) in negative cycle(PDs/s)

raterate in negative cycle(PDs/s) in negative cycle(PDs/s) rate in positive cycle(PDs/s) rate in positive cycle(PDs/s)

raterate in negative cycle(PDs/s) in negative cycle(PDs/s) rate in positive cycle(PDs/s) rate in positive cycle(PDs/s)

rate in positive cycle(PDs/s) rate in positive cycle(PDs/s)

n–φ pattern under 50 Hz in positive and negative half cycle both appear like a mountain shape, n–φ pattern under 50 Hz in positive and negative half cycle both appear like a mountain shape, as shown in Figure 11a. The peak value of positive half cycle is less than that of negative half cycle. n–φ pattern under 50 Hz in positive and negative half cycle both appear like a mountain shape, as shown in Figure 11a. The peak value of positive half cycle is less than that of negative half cycle. With the decrease frequency, peak decreases, from about 21 that PDs/s under 50 Hz cycle. to 6 as shown in Figureof 11a. The peakthe value ofvalue positive half cycle is less than of negative half With the decrease of frequency, the peak value decreases, from about 21 PDs/s under 50 Hz to 6 PDs/s under 5 Hz in positive half cycle. The pattern in negative cycle disappears below 1 Hz. The With the decrease of frequency, the peak value decreases, from about 21 PDs/s under 50 Hz to 6 PDs/s PDs/s under 5 Hz in positive half cycle. The pattern in negative cycle disappears below 1 Hz. The pattern appears several peaks under 0.1 Hz. under 5 Hz in positive half cycle. The pattern in negative cycle disappears below 1 Hz. The pattern pattern appears several peaks under 0.1 Hz. appears several peaks under 0.1 Hz. 90 90 90 35 35 35 In divided intopositive cycle two parts, the small discharge and large discharge 90part. positive cycledischarge is 90 positive cycle 90 35 35 35 30 n–q pattern, 30 30 75 75 75 negative cycle negative cycle negative cycle positive cycle positive cycle positive cycle 30 30 25 75 75 60 is 25 60 The boundary of the two parts is75601003025pC. The small discharge part mainly from the negative cycle negative cycle negative cycle negative cycle 25 25 25 20 20 20 60 60 60 45 45 45 and the 50 Hz, the small discharge45part 20 20 15 large discharge part is mainly 15from the positive cycle. Under20 15 45 45 30 30 30 15 15 15 10 10 10 decreases rapidly like a right-angled triangle. The large discharge3015part distributed widely like a turtle 30 30 15 15 105 105 105 15 15 15 50 50 0 0 a positive 0 back.50It indicates the different mechanism of the development of and negative streamer. 0 40 80 120 160 200 240 280 320 360 0 40 80 120 160 200 240 280 320 360 0 40 80 120 160 200 240 280 320 360 0 0 0 0 0 0 Phase(°) Phase(°) Phase(°) 0 40 80 120 160 200 240 280 320 360 0 40 80 120 160 200 240 280 320 360 0 40 80 120 160 200 240 280 320 360 The positive streamer has a faster speed, more complex structures, and more modes of development Phase(°) Phase(°) Phase(°) (a) (b) (c) (a) (b) (c)

(d)

(e)

(f)

Figure 10. qmean–φ pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Hz, 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV.

60 45

40

15

0 80 120 160 200 240 280 320 360

Energies 2018, 11, x FOR PEER REVIEW (d) (a) rate in positive cycle(PDs/s)

30 15

30 0 80 120 160 200 240 280 320 360

Phase(°) 40

45

Phase(°)

15 35 30 10 25 20 155 10 0 50 0 0

90 positive cycle negative cycle

75 60 45 30

40 40

80 120 160 200 240 280 32015 360 0 Phase(°) 80 120 160 200 240 280 320 360

Phase(°)

1.5 positive cycle

1.2

rate in negative cycle(PDs/s)

75

positive cycle

rate rate in positive cycle(PDs/s) in positive cycle(PDs/s)

positive cycle negative cycle

20 rate in negative cycle(PDs/s)

90

60

rate rate in positive cycle(PDs/s) in positive cycle(PDs/s)

75 rate in negative cycle(PDs/s)

5 0 0

positive cycle negative cycle

90 35 positive cycle 0.9 30 75 negative cycle 25 60 0.6 20 45 15 0.3 30 10 0.0 5 0 40 80 120 160 200 240 280 32015 360 Phase(°) 0 0 0 40 80 120 160 200 240 280 320 360

Phase(°)

(e) (b) rate in negative cycle(PDs/s)

30 25 35 20 30 15 25 10 20 155 1000

rate in negative cycle(PDs/s)

50 Hz in positive and negative half cycle both appear like a mountain shape, 9 of 17 as shown in Figure 11a. The peak value of positive half cycle is less than that of negative half cycle. With the decrease of frequency, the peak value decreases, from about 21 PDs/s under 50 Hz9 of 17 to 6 Energies 2018, 11, x FOR PEER REVIEW stage [35], resulting in a wide spread n–q pattern. Additionally, the small branches of the negative PDs/s under 5 Hz in positive half cycle. The pattern in negative cycle disappears below 1 Hz. The steamer may be suppressed by the main resulting in a regular n–q pattern. pattern 0.1 branch, Hz. 90 35 appears several peaks under rate in rate in positive cycle(PDs/s) positive cycle(PDs/s)

n–φ pattern Energies 2018, 11, 1702under

(f) (c)

9 of 17

45

rate in positive cycle(PDs/s)

60

20 15 10 5 0 0

rate in positive cycle(PDs/s)

Figure 11. n–φ pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Hz, 35 90 1.5 20 positive cycle 30 75 positive cycle positive cycle negative cycle 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. 25 1.2 15 10

0.9

In n–q pattern, discharge 30is divided into two parts, the small discharge and large discharge 0.6 15 5 0.3 part. The boundary of the two parts is 100 pC. The small discharge part is mainly from the negative 0 40 80 120 160 200 240 280 320 360 0.0 0 Phase(°) discharge part is cycle and the large cycle. 50 the small 0 40 Under 80 120 160 200Hz, 240 280 320 360 0 mainly 40 80 120 from 160 200 the 240 280positive 320 360 Phase(°) Phase(°) discharge part decreases rapidly like a right‐angled triangle. The large discharge part distributed (d) (e) (f) widely like a turtle back. It indicates the different mechanism of the development of a positive and

15

1 10

200 0100

0 5 100 5k 10k 15k 20k 25k 30k Magnitude of discharge (pC) 0 0 0 100 5k 10k 15k 20k 25k Magnitude of discharge (pC)

(e)

Number of large discharge

large discharge

0.8

600 500 400

0.6

small discharge large discharge

0.4

300

0 0

100 5k 10k 15k 20k Magnitude of discharge (pC)

3



large discharge

15

(f)

0.0 25k 5


0 25k

(a) (b) (c) Figure 12. n–q pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Hz, Figure 12. n–q pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Hz, 20 1.0 5 20 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. large discharge small20 discharge large discharge kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 4 32 kV. 0.8 80 kV; (c) 10 Hz, 15 60

20

0.2 10

200

0100

Number of large discharge Number of large discharge

20

0.6


2


300

3

Number of small discharge

0 25k

400

4


(d)


500



0 0


05 25k

large discharge 600


510

300 20 200 0 0 100

10 15



15 20


20



100

80 600 60 500 40 400

Number of large discharge Number of large discharge

Number of small discharge Number of small discharge

100



negative streamer. The positive streamer has a faster more complex and Figure 11. n–φ pattern from rated AC frequency to veryspeed, low frequency. (a) 50 Hz,structures, 20 kV; (b) 30 Hz,more Figure 11. n–φ pattern from rated AC frequency to very low frequency. (a) 50 Hz, 20 kV; (b) 30 Hz, modes of development stage [35], resulting in a wide spread n–q pattern. Additionally, the small 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. branches of the negative steamer may be suppressed by the main branch, resulting in a regular n–q pattern. In n–q pattern, discharge is divided into two parts, the small discharge and large discharge the frequency, of vertical anddischarge horizontal axisisofmainly two parts both decreases, With the decrease decrease of frequency, the range of small vertical and horizontal axis of two parts both part.With The boundary ofof the two partsthe is range 100 pC. The part from the negative as shown in Figure 12a–d. It is because of the aggravation of the weakening of the electric field by decreases, as shown in Figure part 12a–d. is because aggravation the weakening the cycle and the large discharge is It mainly from of thethe positive cycle. of Under 50 Hz, the of small residual space charge under lower frequencies. When the frequency continues to decrease, the left electric field by decreases residual space charge lower frequencies. frequency to discharge part rapidly like aunder right-angled triangle. TheWhen large the discharge partcontinues distributed part of large discharge turns to be like a right-angled triangle rather than a turtle back, as shown in decrease, the left part of large discharge turns to be like a right‐angled triangle rather than a turtle widely like a turtle back. It indicates the different mechanism of the development of a positive and Figure 12e.streamer. Under 0.1 Hz,positive the horizontal range shortens, as shown in Figure 12f. The back, as shown in Figure 12e. Under 0.1 Hz, the horizontal range of pattern shortens, as shown in negative The streamer hasofa pattern faster speed, more complex structures, andreason more is that with the decrease of dU/dt, the randomness and difference of discharge in positive cycle Figure 12f. The reason stage is that with the decrease of spread dU/dt, n–q the pattern. randomness and difference of modes of development [35], resulting in a wide Additionally, the tends small to be smaller. discharge in positive cycle tends to be smaller. branches of the negative steamer may be suppressed by the main branch, resulting in a regular n–q pattern. 600 600 600 20 20 20 With the small discharge decrease of frequency, the rangesmall discharge of vertical and horizontal axis of two parts both small discharge 500 500 500 15 15 15 large discharge large discharge 400 400 It is because 400 decreases, as large discharge shown in Figure 12a–d. of the aggravation of the weakening of the 300 300 300 10 10 10 electric field by residual space charge under lower frequencies. When the frequency continues to 200 200 200 5 5 decrease, the left part of large5 discharge turns to be like a right-angled 100 100 100triangle rather than a turtle 0 0 0 0 0 0in back,0 as100 shown Hz, of pattern 5k in 10k Figure 15k 20k12e. 25k Under 0.1 0 100 the 5k horizontal 10k 15k 20k range 25k 0 100shortens, 5k 10k as 15kshown 20k 25k Magnitude of discharge (pC) Magnitude of discharge (pC) Magnitude of discharge (pC) Figure 12f. The reason is that with the decrease of dU/dt, the randomness and difference of (a) (b) (c) discharge in positive cycle tends to be smaller. 5 1.0

10 3.3.2. Characteristic Parameters 2 0.4 40 Characteristic Parameters 3.3.2. 5 1 20 0.2 The variation trend of characteristic parameters is shown in Figure 13. With the decrease of parameters is shown 0 0 The variation trend of characteristic 0.0 of 0 in Figure 13. With the decrease 0 100 the 5k skewness 10k 15k 20k 25k 0then 100increases 5k 10k under 15k 20k 0.1 25kHz. 0 100 5k patterns 10k 15k 20kdecreases 25k 30k frequency, of all the statistical and Magnitude of discharge (pC) of all the statistical of discharge (pC) 0.1 Hz. Magnitude of discharge decreases (pC) frequency, the skewness patterns and thenMagnitude increases under Sk+(qmean–φ) decreases from −0.0232 under 50 Hz to −0.4283 under 1 Hz, which indicates the q mean–φ (d) (f) (e) pattern in positive half cycle shifts from a near normal distribution to a right bias distribution. Figure it 12.increases n–q patternto from rated AC frequency to very low frequency. (a) 50 Hz, trend, 20 kV; (b) 30 Hz, first However, −0.1525 under 0.1 Hz. With the same variation Sk+(n–φ) 20 kV; (c) 10 Hz, 20 kV; (d) 5 Hz, 20 kV; (e) 1 Hz, 32 kV; and (f) 0.1 Hz, 32 kV. decreases from 0.1706 under 50 Hz to −0.315 under 5 Hz, and then slightly increases to −0.04417

3.3.2. Characteristic Parameters

Energies 2018, 11, 1702

10 of 17

3.0

0.45

2.5 0.30

2.0

0.15

1.5

0.00

1.0

‐0.15 ‐0.30

0.5 S+k (qmean–φ)

S‐k (qmean–φ)

S+k (qmax–φ)

S‐k (qmax–φ)

S+k (n–φ)

S‐k (n–φ) Sk (n‐q)

‐0.45

Sk (n–q)

Sk (qmean–φ), Sk (qmax–φ), Sk (n–φ)

Sk + (qmean –φ) decreases from −0.0232 under 50 Hz to −0.4283 under 1 Hz, which indicates the qmean –φ pattern in positive half cycle shifts from a near normal distribution to a right bias distribution. However, it increases to −0.1525 under 0.1 Hz. With the same variation trend, Sk + (n–φ) first decreases10 of 17 from Energies 2018, 11, x FOR PEER REVIEW 0.1706 under 50 Hz to −0.315 under 5 Hz, and then slightly increases to −0.04417 under 0.1 Hz, approaching the normal distribution. The reason for the decrease is that more charge of the same under 0.1 Hz, approaching the normal distribution. The reason for the decrease is that more charge polarity with high voltage electrode under lower frequencyunder and suppresses the discharge of the same polarity with high accumulates voltage electrode accumulates lower frequency and on the right of the peak, as shown in Figure 10e. The reason for the slight increase under 0.1 Hz is that suppresses the discharge on the right of the peak, as shown in Figure 10e. The reason for the slight the variation rate of voltage decreases and the voltage waveform tends to be flat, which makes the increase under 0.1 Hz is that the variation rate of voltage decreases and the voltage waveform tends difference of each discharge smaller. to be flat, which makes the difference of each discharge smaller.

0.0 ‐0.5

50 45 40 35 30 25 20 15 10 5 Frequency of applied voltage (Hz)

‐1.0

0

K+u (qmean–φ)

1.0

+ u

0.5

K-u (qmean–φ) u

K (qmax–φ)

K (qmax–φ)

K+u (n–φ) Ku (n–q)

K‐u (n–φ)

10 8 6 4

0.0

2

‐0.5

Ku (n–q)

Ku (qmean–φ), Ku (qmax–φ), Ku (n–φ)

(a)

0

‐1.0 50 45 40 35 30 25 20 15 10 5 Frequency of applied voltage (Hz)

0

‐2

1.0

6

0.8

5 4

0.6 0.4 0.2

3 Asy (qmean–φ)

Cc (qmean–φ)

Asy (qmax–φ)

Cc (qmax–φ)

Asy (n–φ)

Asy(n–φ)

Asy (qmean, qmax–φ) ,Cc

(b)

2

Cc (n–φ)

1 0.0 50 45 40 35 30 25 20 15 10 5 Frequency of applied voltage (Hz)

0

(c) Figure 13. Characteristics parameters of statistical patterns from rated AC frequency to very low Figure 13. Characteristics parameters of statistical patterns from rated AC frequency to very low frequency. (a) Skewness Sk of statistical patterns from rated AC frequency to very low frequency, (b) frequency. (a) Skewness Sk of statistical patterns from rated AC frequency to very low frequency, kurtosis Ku of statistical patterns from rated AC frequency to very low frequency, and (c) asymmetry (b) kurtosis Ku of statistical patterns from rated AC frequency to very low frequency, and (c) asymmetry A and correlation coefficient Cc of statistical patterns from rated AC frequency to very low Asy sy and correlation coefficient Cc of statistical patterns from rated AC frequency to very low frequency. frequency.

Sk−(qmean–φ) decreases from 0.04764 under 50 Hz to −0.1859 under 10 Hz, shifting from a near normal distribution to a slightly right bias distribution. Sk(n–q) decreases from 2.5402 under 50 Hz to 0.7842 under 10 Hz, which means the degree of left bias decreases. Ku+(qmax–φ), Ku−(qmax–φ), Ku+(qmean–φ) and Ku−(qmean–φ) all show an increasing trend. Among them, Ku+(qmean–φ) increases from −0.8699 under 50 Hz to −0.3583 under 0.1 Hz, indicating the pattern gets

Energies 2018, 11, 1702

11 of 17

Sk − (qmean –φ) decreases from 0.04764 under 50 Hz to −0.1859 under 10 Hz, shifting from a near normal distribution to a slightly right bias distribution. Sk (n–q) decreases from 2.5402 under 50 Hz to 0.7842 under 10 Hz, which means the degree of left bias decreases. Ku + (qmax –φ), Ku − (qmax –φ), Ku + (qmean –φ) and Ku − (qmean –φ) all show an increasing trend. Among them, Ku + (qmean –φ) increases from −0.8699 under 50 Hz to −0.3583 under 0.1 Hz, indicating the pattern gets sharper but is always flatter than normal distribution. Under lower frequencies, with the decrease of dU/dt, the magnitude of more discharge tends to be close, which causes some large discharge to be distinct and finally makes the pattern sharper. Ku + (n–φ) does not show an obvious frequency dependence and is always smaller than zero. Ku (n–q) first increases from 5.2148 under 50 Hz to 6.1808 under 30 Hz, and then decreases to −0.7924 under 10 Hz. Under lower frequencies, it is more difficult for the discharge in negative cycle to develop. Thus, the small discharge part tends to be lower, which makes the n–q pattern become flatter, as shown in Figure 12a–d. The value of Asy (qmax –φ) and Asy (qmean –φ) under each frequency is near zero. Among them, Asy (qmean –φ) is less than 0.007, which indicates the discharge in negative half cycle is far smaller than that in positive half cycle. The reason is that the negative streamer has a lower speed and is more difficult to develop than the positive streamer. Asy (n–φ) decreases from 4.9765 under 50 Hz to 1.0506 under 10 Hz, indicating the difference between the distribution of n–φ in positive and negative cycle descends. This is because the decrease of pulse repletion rate in negative cycle is faster than that in positive cycle, as shown in Section 3.1.4. Discharge in negative cycle is more sensitive to the decrease of frequency. Cc (qmax –φ), Cc (qmean –φ), and Cc (n–φ) all decrease. Cc (qmean –φ) decreases from 0.7913 under 50 Hz to 0.5634 under 10 Hz, indicating the outlines of the qmean –φ pattern in positive and negative cycle become more different. 4. Discussion and Analysis 4.1. Influence on Electric Field Distribution of Frequency The insulating oil is weakly polar dielectric, and the fibre that makes up the insulating paper is polar dielectric. The capacitive property of them is mainly formed by dipole relaxation polarization. When the frequency of applied voltage decreases, the speed of the polar molecules turning its direction with the change of electric field becomes slower. Finally, the degree of polarization increases and the dielectric constant increases [36]. The distribution of the electric field will be affected by the variation of dielectric constant, which is simulated with the software Comsol Multiphysics. The governing equation of electric field is as follows, including the current continuity equation as Equation (1), the full current equation as Equation (2), and the relation equation of electric field intensity and potential as Equation (3) [37]. In the equations, J is the current density, σ is the conductivity, E is the electric field intensity, ω is the angular frequency of applied voltage, D is the displacement current, and V is the potential. ∇J = 0 (1) J = σE + jωD

(2)

E = −∇V

(3)

Besides the dimensions of the components given in Section 2.1, other dimensions are all defined according to the experimental electrode. The diameter of the insulating paper is 90 mm. The thickness of the plate electrode is 15 mm. The upper part of the needle is a cylinder with the diameter of 0.25 mm and the length of 10 mm. The angle of the needle tip is 60◦ . The diameter of the cylindrical conducting rod that connected to the needle is 9 mm and its length is 30 mm. To obtain a relatively accurate result, the part near the needle tip is divided into three refined meshing regions. The smallest unit size of the inner region is 0.0005 mm, which is 0.002 mm in the middle region and 0.02 mm in the outer region. The smallest unit size of other parts of the model is 0.1 mm. The dielectric constant of insulating oil

Frequency 50 Hz 30 Hz 10 Hz 5 Hz 1 Hz 0.1 Hz Insulating oil 2.182 2.183 2.197 2.230 2.365 3.782 Oil‐paper 4.566 4.574 4.596 4.616 4.715 5.137 Ratio of dielectric constant 2.0926 2.0953 2.0919 2.0700 1.9937 1.3581 Energies 2018, 11, 1702

12 of 17

The electric field intensity under each frequency decreases rapidly near the needle tip. The and oil impregnated paper under different frequencies is shown in Table 2, which is measured by the further from the tip, the slower the decline rate. The electric field is concentrated in the vicinity of Novolcontrol dielectric and impedance measurement system. The conductivity of insulating oil and the tip of about two to four times the radius of curvature, which is consistent with the hottest spot oil-paper is σ1 = 8.0 × 10−13 S/m and σ2 = 8.6 × 10−15 S/m. Figure 14 demonstrates the distribution demonstrated in research [38]. The decrease of potential in the oil gap under 50 Hz is slightly faster of potential and electric field underindicates 50 Hz and Hz. A comparison of the electric field along than that under 0.1 Hz, which a 0.1 higher electric field intensity under 50 intensity Hz. With the the gap under 50 Hz and 0.1 Hz is shown as Figure 15. Table 3 gives the electric field intensity at the decrease of frequency, the dielectric constant of insulating oil and oil‐paper both increase. Firstly, point 0.1 mm from the needle tip in the vertical direction toward the plate electrode from rated AC the rising rate of oil‐paper is larger than that of oil, then inversely, the latter is larger. Thus, the ratio frequency to very low frequency. of the dielectric constant of oil‐paper to oil first increases and then decreases, which dominates the electric field in the oil gap. The variation trend of electric field in the oil gap is consistent with the Table 2. Dielectric constant of insulating oil and oil impregnated paper under different frequencies. variation trend of maximum and mean magnitude of discharge and pulse repetition rate given in Section 3.1. The descending rare of the electric field becomes larger with the decrease of frequency, Frequency 50 Hz 30 Hz 10 Hz 5 Hz 1 Hz 0.1 Hz with the same characteristic of the descending rare of discharge statistical parameters. However, the Insulating oil 2.182 2.197different 2.230 2.365is relatively 3.782 small deviation ratio of electric field intensity to 2.183 50 Hz under frequencies Oil-paper 4.566 4.574 4.596 4.616 4.715 5.137 expect 0.1 Hz. There are still other factors that lead to the influence on discharge of frequency, Ratio of dielectric constant 2.0926 2.0953 2.0919 2.0700 1.9937 1.3581 which will be discussed in section 4.2.

(a)

(b)

(c)

(d)

Figure 14. Comparison of the potential and electric field distribution under 50 Hz and 0.1 Hz. (a) Figure 14. Comparison of the potential and electric field distribution under 50 Hz and 0.1 Hz. Potential distribution (50 Hz), (b) potential distribution (0.1 Hz), (c) electric field distribution (50 Hz), (a) Potential distribution (50 Hz), (b) potential distribution (0.1 Hz), (c) electric field distribution and (d) electric field distribution (0.1 Hz). (50 Hz), and (d) electric field distribution (0.1 Hz). Energies 2018, 11, x FOR PEER REVIEW 13 of 17 Table 3. Electric field intensity at the point 0.1 mm from the needle tip under different frequencies. 30

Electric field intensity (kV/mm)

Frequency 50 Hz 30 Hz 10 Hz 50 Hz5 Hz 1 Hz 0.1 Hz 25 Electric field intensity (kV/mm) 25.4078 25.4140 25.4068 0.1 Hz 25.3592 25.1886 23.2400 Deviation ratio to 50 Hz ‐ +0.0247% −0.0038% −0.1911% −0.8622% −8.5297% 20

Insulating oil

15

Insulating paper Interface

10 5 0 0.0 0.5 1.0 1.5 2.0 Distance away from the needle point (mm)

Figure 15. Comparison of the electric field intensity along the gap under 50 Hz and 0.1 Hz. Figure 15. Comparison of the electric field intensity along the gap under 50 Hz and 0.1 Hz.

4.2. Influence on Discharge Process of Frequency The electric field intensity increases with the increase of applied voltage. When it exceeds the withstand strength of the micro bubble near the tip, micro discharge occurs [39]. Energy produced by the discharge accelerates the ionization of liquid molecule. The charge generated enhances the

Energies 2018, 11, 1702

13 of 17

Table 3. Electric field intensity at the point 0.1 mm from the needle tip under different frequencies. Frequency

50 Hz

Electric field intensity (kV/mm) Deviation ratio to 50 Hz

25.4078 -

30 Hz

10 Hz

5 Hz

1 Hz

0.1 Hz

25.4140 25.4068 25.3592 25.1886 23.2400 +0.0247% −0.0038% −0.1911% −0.8622% −8.5297%

Energies 2018, 11, x FOR PEER REVIEW

13 of 17

Electric field intensity (kV/mm)

The electric field intensity under each frequency decreases rapidly near the needle tip. The further 30 from the tip, the slower the decline rate. The electric field is concentrated in the vicinity of the tip of 50 Hz 25 of curvature, which is consistent about two to four times the radius with the hottest spot demonstrated 0.1 Hz in research [38]. The decrease of potential in the oil gap under 50 Hz is slightly faster than that under 20 Insulating oil Insulating paper 0.1 Hz, which indicates a higher electric field intensity under 50 Hz. With the decrease of frequency, the dielectric constant of insulating oil and oil-paper both increase. Firstly, the rising rate of oil-paper 15 Interface is larger than that of oil, then inversely, the latter is larger. Thus, the ratio of the dielectric constant of oil-paper to oil first increases10and then decreases, which dominates the electric field in the oil gap. The variation trend of electric field in the oil gap is consistent with the variation trend of maximum 5 and mean magnitude of discharge and pulse repetition rate given in Section 3.1. The descending rare of the electric field becomes larger with the decrease of frequency, with the same characteristic of 0 0.0 0.5 1.0 1.5 2.0 the descending rare of discharge statistical parameters. However, the deviation ratio of electric field Distance away from the needle point (mm) intensity to 50 Hz under different frequencies is relatively small expect 0.1 Hz. There are still other Figure 15. Comparison of the electric field intensity along the gap under 50 Hz and 0.1 Hz. factors that lead to the influence on discharge of frequency, which will be discussed in Section 4.2. 4.2. Influence on Discharge Process of Frequency 4.2. Influence on Discharge Process of Frequency The electric field intensity increases with the increase of applied voltage. When it exceeds the The electric field intensity increases with the increase of applied voltage. When it exceeds the withstand strength of the micro bubble near the tip, micro discharge occurs [39]. Energy produced withstand strength of the micro bubble near the tip, micro discharge occurs [39]. Energy produced by accelerates the ionization of molecule. The by the the discharge discharge accelerates the ionization of liquid liquid molecule. The charge charge generated generated enhances enhances the the electric electric field field intensity intensity at at the the head head of of discharge discharge region, region, which which leads leads the the discharge discharge to to develop develop and and form a streamer channel. As shown in Figure 16, the electrons are attracted by the positive ions with form a streamer channel. As shown in Figure 16, the electrons are attracted by the positive ions with high density in front of the streamer channel and flow into it, which develops towards the opposite high density in front of the streamer channel and flow into it, which develops towards the opposite electrode. The electric field in the gap E is the combination of the Laplace electric field from applied electrode. The electric field in the gap E is the combination of the Laplace electric field from applied voltage field from space charge E2 . The space charge is ofis the samesame polarity of high voltage EE11 and and the the electric electric field from space charge E 2. The space charge of the polarity of voltage electrode and weakens the electric Thefield. frequency affects the affects generation and dissipation high voltage electrode and weakens the field. electric The frequency the generation and of space charge, resulting in influence on the discharge process. dissipation of space charge, resulting in influence on the discharge process.

Figure 16. Process of development of positive streamer in the insulating oil. Figure 16. Process of development of positive streamer in the insulating oil.

As shown in Figure 17, discharge occurs after a discharge delay τdelay when the applied voltage As shown in Figure 17, discharge occurs after a discharge delay τ delay when the applied voltage exceeds the theoretical discharge value. For u(t) = Umsin(2πft), where u(t) is the applied voltage and exceeds the theoretical discharge value. For u(t) = Um sin(2πft), where u(t) is the applied voltage Um is its peak value with the unit of kV, the initial time is shown in Equation (4). Under lower frequency, the voltage phase that τdelay occupies decreases, causing the initial phase to be put forward, as shown in Figure 8.

t1 

1 Ucr   delay arcsin 2 f Um

(4)

Energies 2018, 11, 1702

14 of 17

and Um is its peak value with the unit of kV, the initial time is shown in Equation (4). Under lower frequency, the voltage phase that τ delay occupies decreases, causing the initial phase to be put forward, as shown in Figure 8. Ucr 1 arcsin t1 = + τdelay (4) 2π f Um Energies 2018, 11, x FOR PEER REVIEW

14 of 17

Figure 17. Demonstration of the effective discharge time under different frequencies. Figure 17. Demonstration of the effective discharge time under different frequencies.

The effective effective discharge time teffect is proposed to demonstrate the when time the when the voltage applied The discharge time teffect is proposed to demonstrate the time applied voltage meets the discharge condition. t effect in a half cycle is shown as Equation (5). Although τ delay meets the discharge condition. teffect in a half cycle is shown as Equation (5). Although τ delay varies varies statistically, its order of magnitude is smaller than that of the first part of Equation (5). Thus, statistically, its order of magnitude is smaller than that of the first part of Equation (5). Thus, with the with the decrease of frequency, teffect increases. On the one hand, time will be for available for decrease of frequency, teffect increases. On the one hand, more timemore will be available discharge, discharge, which promotes the development of discharge. As shown in Section 3.1, the discharge which promotes the development of discharge. As shown in Section 3.1, the discharge statistical statistical parameters first increase in some frequencies. On the other hand, more space charge will parameters first increase in some frequencies. On the other hand, more space charge will accumulate accumulate in a half cycle, which aggravates the weakening of the electric field and suppresses the in a half cycle, which aggravates the weakening of the electric field and suppresses the development of development discharge. The the two effects is plays a result of which one Itplays discharge. The of final decision of thefinal two decision effects is aof result of which one a dominant role. can bea dominant role. It can be inferred from the experimental results that the second effect dominates inferred from the experimental results that the second effect dominates below 10 Hz. The termination below 10 Hz. The termination phase is put forward under lower frequency, which is more evidence phase is put forward under lower frequency, which is more evidence to show the aggravation of the to show the aggravation of the weakening of electric field by space charge. weakening of electric field by space charge. 1 1 1 Ucr teffect  1 (1  1arcsin U )   delay (5) cr teffect = f ( 2 − arcsinUm ) − τdelay (5) f 2 π Um The time interval between the termination of the previous half cycle and the inception of the successive half cycle is shown the as Equation (6). ofWith the decrease of frequency, tinterval increases. The time interval between termination the previous half cycle and the inception of the More time is available for the space charge from the previous half cycle to dissipate, which reduces successive half cycle is shown as Equation (6). With the decrease of frequency, tinterval increases. More the enhancement of the the space electric field from in the half cycle cycle. less seed time is available for charge thesuccessive previous half toAlso, dissipate, whichelectrons reduces will the remain for the successive half cycle. This is consistent with the increasing trend of PDIV. enhancement of the electric field in the successive half cycle. Also, less seed electrons will remain for 1 1 the increasing Ucr the successive half cycle. This is consistent of PDIV.   delaytrend tinterval with arcsin (6) f Um 11 Ucr tinterval = arcsin + τdelay (6) f π U m 5. Conclusions The characteristics of corona discharge in insulating oil are studied from rated AC frequency to 5. Conclusions very low frequency (0.1 Hz) based on the impulse current method. The main conclusions are as The characteristics of corona discharge in insulating oil are studied from rated AC frequency to follows. very low frequency (0.1 Hz) based on the impulse current method. The main conclusions are as follows. (1) Some fundamental characteristics remained, even the frequency decreases. Discharge in (1) Some fundamental characteristics remained, even the frequency decreases. Discharge in positive positive half cycle initiates earlier than that in negative half cycle. The magnitude of discharge half cycle initiates earlier that inlarger negative half cycle. The magnitude of discharge in positive in positive half cycle is than obviously than that in negative half cycle. Discharge in both half cycle is obviously larger than that in negative half cycle. Discharge in both cycle distributes cycle distributes in the vicinity of voltage peak. the the vicinity of voltage peak. (2) in With decrease of frequency, the inception voltage increases, which, under 0.1 Hz, is 2.4 times of that under rated AC frequency. The maximum and average magnitude of discharge and pulse repetition rate first increase slightly and then decrease obviously. For the voltage amplitude of 20 kV, Qmax+ under 5 Hz decreases by about 40% compared with 50 Hz. Qmean+ decreases by about 45%. R+ decreases by about 85%. (3) The range of the qmean–φ, n–φ, and n–q patterns shortens. The right side of the mountain shape

Energies 2018, 11, 1702

(2)

(3)

(4)

15 of 17

With the decrease of frequency, the inception voltage increases, which, under 0.1 Hz, is 2.4 times of that under rated AC frequency. The maximum and average magnitude of discharge and pulse repetition rate first increase slightly and then decrease obviously. For the voltage amplitude of 20 kV, Qmax + under 5 Hz decreases by about 40% compared with 50 Hz. Qmean + decreases by about 45%. R+ decreases by about 85%. The range of the qmean –φ, n–φ, and n–q patterns shortens. The right side of the mountain shape of qmean –φ pattern gradually disappears. The range of the vertical axis in positive cycle under 5 Hz decreases by about 25%. The n–φ pattern appears several peaks in positive cycle under 0.1 Hz. The range of the vertical axis in positive cycle under 5 Hz decreases by about 75%. The part of the large discharge in n–q pattern changes from a turtle back shape to a right-angled triangle. The range of horizontal axis under 5 Hz decreases by about 50%. The skewness of all of the statistical patterns decreases and then increases under 0.1 Hz. Sk + (qmean –φ) decreases from −0.0232 under 50 Hz to −0.4283 under 1 Hz, and then increases to −0.1525 under 0.1 Hz. Ku (qmax –φ) and Ku (qmean –φ) increase. The value of Asy (qmax –φ) and Asy (qmean –φ) under each frequency is near zero. Cc (qmax –φ), Cc (qmean –φ), and Cc (n–φ) decrease, indicating the similarity of the outlines of statistical patterns decrease.

The common features, as shown in (1), can still be the reference for mode recognition under low frequency. However, the differences of statistical parameters, statistical patterns, and characteristic parameters from that under rated AC frequency should be paid attention to in insulation defect diagnosis when using low frequency voltage, as shown in (2)–(4). If conditions permit, to measure the discharge information of equipment to be tested under multiple frequencies, rather than under a single frequency, and obtain the variation trends is beneficial to consolidate the insulation defect diagnosis. The variation trends above are caused by the combination of the influence on electric field and discharge process of frequency. Future research may concentrate on discharge information of insulating oil with different aging time under low frequency. Also, it is interesting to examine the discharge characteristics of other kinds of insulation defects under low frequency. Further, the simulation model proposed calculates the intrinsic electric field of applied voltage, some efforts are needed to consider the electric field of the space charge in future analysis [40]. Author Contributions: Z.Z. and Y.Z. conceived and designed the experiments. Z.Z., X.H., and Y.Z. performed the experiments. Z.Z. analyzed the data and prepared the manuscript. Y.Z., M.W., and S.G. helped to analyze the data and gave some valuable suggestions. Funding: This work is funded by the National Key R&D Program of China (2017YFB0902704) and the Science and Technology Project of SGCC (52018K160018). Acknowledgments: This work is supported by the National Key R&D Program of China (2017YFB0902704) and the Science and Technology Project of SGCC (52018K160018). Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2.

3.

4. 5.

Glowacz, A.; Glowacz, W.; Glowacz, Z. Recognition of armature current of DC generator depending on rotor speed using FFT, MSAF-1 and LDA. Eksploat. Niezawodn. Maint. Reliab. 2015, 17, 64–69. [CrossRef] Glowacz, A.; Glowacz, W.; Glowacz, Z.; Kozik, J.; Gutten, M.; Korenciak, D.; Khan, Z.F.; Irfan, M.; Carletti, E. Fault diagnosis of three phase induction motor using current signal, MSAF-Ratio15 and selected classifiers. Arch. Metall. Mater. 2017, 62, 2413–2419. [CrossRef] Gutten, M.; Korenciak, D.; Kucera, M.; Sebok, M.; Opielak, M.; Zukowski, P.; Koltunowicz, T.N. Maintenance diagnostics of transformers considering the influence of short-circuit currents during operation. Eksploat. Niezawodn. Maint. Reliab. 2017, 19, 459–466. [CrossRef] Lei, T.; Faifer, M.; Ottoboni, R.; Toscani, S. On-line fault detection technique for voltage transformers. Measurement 2017, 108, 193–200. [CrossRef] Zhu, L.; Feng, H.; Ji, S.; Rehman, H.; Wu, X. Primary Differential pulse method for partial discharge detection of oil-immersed inverted current transformers. IEEE Trans. Power Deliv. 2018, 33, 1492–1494. [CrossRef]

Energies 2018, 11, 1702

6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

19. 20. 21.

22. 23. 24. 25.

26.

27.

28.

16 of 17

Saravanakumar, N.; Sathiyasekar, K. Efficient method for location and detection of partial discharge in transformer oil by DOA estimation of circular array of ultrasonic sensors. J. Instrum. 2018, 13, P01026. [CrossRef] Ma, G.; Zhou, H.; Shi, C.; Li, Y.; Zhang, Q. Distributed partial discharge detection in a power transformer based on phase-shifted FBG. IEEE Sens. J. 2018, 18, 2788–2795. [CrossRef] Bhimani, B.V. Resistance and capacitance measurement on high-voltage insulation at very-low frequencies. Trans. Am. Inst. Electr. Eng. 1961, 80, 155–163. Fard, M.A.; Reid, A.J.; Hepburn, D.M. Analysis of HVDC superimposed harmonic voltage effects on partial discharge behavior in solid dielectric media. IEEE Trans. Dielectr. Electr. Insul. 2017, 24, 7–16. [CrossRef] Eager, G.S.; Katz, C.; Fryszczyn, B.; Densley, J.; Bernstein, B.S. High voltage VLF testing of power cables. IEEE Trans. Power Deliv. 1997, 12, 565–570. [CrossRef] Bhimani, B.V. Very-low-frequency high-potential testing. IEEE Trans. Power App. Syst. 1961, 80, 148–155. [CrossRef] Miller, R.; Black, I.A. Partial discharge measurements over the frequency range 0.1 Hz to 50 Hz. IEEE Trans. Electr. Insul. 1977, 12, 224–233. [CrossRef] Haga, K.; Yoneyama, M. Breakdown strength and dielectric characteristics of oil-impregnated paper cable insulation at very-low-frequencies. Electr. Eng. Jpn. 1968, 88, 39–48. Miller, R.; Black, I.A.; Gray, V.N. A variable low frequency high voltage generator using valves with fibre optic light guide control. J. Phys. E Sci. Instrum. 1975, 8, 748–750. [CrossRef] Miller, R.; Black, I.A. Partial discharge energy measurements on electrical machine insulation when energized at frequencies between 0.1 Hz and power frequency. IEEE Trans. Electr. Insul. 1979, 14, 127–135. [CrossRef] Bodega, R.; Morshuis, P.H.F.; Lazzaroni, M.; Wester, F.J. PD recurrence in cavities at different energizing methods. IEEE Trans. Instrum. Meas. 2004, 53, 251–258. [CrossRef] Wester, F.J.; Guilski, E.; Smit, J.J. Detection of partial discharges at different AC voltage stresses in power cables. IEEE Electr. Insul. Mag. 2007, 23, 28–43. [CrossRef] Illias, H.; Chen, G.; Lewin, P.L. Partial discharge behavior within a spherical cavity in a solid dielectric material as a function of frequency and amplitude of the applied voltage. IEEE Trans. Dielectr. Electr. Insul. 2011, 18, 432–443. [CrossRef] Forssen, C.; Edin, H. Partial discharges in a cavity at variable applied frequency part 1: Measurements. IEEE Trans. Dielectr. Electr. Insul. 2008, 15, 1601–1609. [CrossRef] Forssen, C.; Edin, H. Partial discharges in a cavity at variable applied frequency Part 2: Measurements and Modeling. IEEE Trans. Dielectr. Electr. Insul. 2008, 15, 1610–1616. [CrossRef] Fynes-Clinton, D.; Nyamupangedengu, C. Partial discharge characterization of cross-linked polyethylene medium voltage power cable termination defects at very low frequency (0.1 Hz) and power frequency test voltages. IEEE Electr. Insul. Mag. 2016, 32, 15–23. [CrossRef] Yang, Z.; Zhu, D. High Voltage and Insulation Technology, 2nd ed.; China Electric Power Press: Beijing, China, 2007. Zhang, L.; Zhao, L. Modeling of the partial discharge process in a liquid dielectric: Effect of applied voltage, gap distance, and electrode type. Energies 2013, 6, 934–952. Pompili, M.; Mazzetti, C.; Bartnikas, R. Phase relationship of PD pulses in dielectric liquids under ac conditions. IEEE Trans. Dielectr. Electr. Insul. 2000, 7, 113–117. [CrossRef] Swati, K.; Yadav, K.S.; Sarathi, R.; Vinu, R.; Danikas, M.G. Understanding corona discharge activity in titania nanoparticles dispersed in transformer oil under AC and DC voltages. IEEE Trans. Dielectr. Electr. Insul. 2017, 24, 2325–2336. [CrossRef] Beroual, A.; Khaled, U.; Noah, P.S.M.; Sitorus, H. Comparative study of breakdown voltage of mineral, synthetic and natural oils and based mineral oil mixtures under AC and DC voltages. Energies 2017, 10, 511. [CrossRef] Korobeynikov, S.M.; Bychkov, A.L.; Chimitova, E.V.; Demin, V.A. Statistical analysis of partial discharge characteristics in transformer oil at the “point-plane” electrode at alternating voltage. Probl. Reg. Energ. 2017, 2, 36–44. Florkowski, M.; Florkowska, B.; Furgal, J.; Zydron, P. Impact of high voltage harmonics on interpretation of partial discharge patterns. IEEE Trans. Dielectr. Electr. Insul. 2013, 20, 2009–2016. [CrossRef]

Energies 2018, 11, 1702

29.

30. 31. 32. 33.

34. 35.

36. 37. 38. 39.

40.

17 of 17

Deng, J.; Wang, M.; Zhou, Y.; Zhou, Z.; Zhang, Y.; Zhang, L.; Liu, X. Partial discharge characteristics of uniform gap in oil-impregnated paper insulation under switching impulse voltage. IEEE Trans. Dielectr. Electr. Insul. 2017, 23, 3584–3592. [CrossRef] Tang, J.; Wang, J.; Li, J.; Tan, Z. Statistical parameter method for PD pattern recognition. High Volt. Eng. 2002, 28, 4–6. Gulski, E.; Kreuger, F.H. Computer aided recognition of discharge sources. IEEE Trans. Dielectr. Electr. Insul. 1992, 27, 82–92. [CrossRef] Candela, R.; Mirelli, G.; Schifani, R. PD recognition by means of statistical and fractal parameters and a neural network. IEEE Trans. Dielectr. Electr. Insul. 2000, 7, 87–94. [CrossRef] Zhou, Y.; Zhou, Z.; Zhang, L.; Zhang, Y.; Mo, Y.; Sun, J. Characterization and comprehension of corona partial discharge in air under power frequency to very low frequency voltage. Plasma Sci. Technol. 2017, 20, 054016. [CrossRef] Liao, R.; Duan, L.; Wang, K.; Yang, L.; Yuan, L.; Guo, C. Partial discharge characteristics of point-plane model in oil-paper insulation under AC voltage. High Volt. Eng. 2014, 40, 648–654. Beroual, A.; Zahn, M.; Badent, A.; Kist, K.; Schwabhe, A.J.; Yamashitica, H.; Yamashitica, K.; Danikas, M.; Chadband, W.G.; Torshin, Y. Propagation and structure of streamers in liquid dielectrics. IEEE Electr. Insul. Mag. 1998, 14, 6–17. [CrossRef] Liang, X.; Zhou, Y.; Zeng, R. High Voltage Engineering, 3rd ed.; Tsinghua University Press: Beijing, China, 2015. Feng, C.; Ma, X. Introduction of Engineering Electromagnetic Field; Higher Education Press: Beijing, China, 2000. Schmidt, W.F. Electronic conduction processes in dielectric liquid. IEEE Trans. Electr. Insul. 1984, EI-19, 389–418. [CrossRef] Borsi, H.; Gockenbach, E.; Schroder, U.; Schilier, G. Contribution to the clarification of partial discharge behaviour in insulating liquids using the schlieren technique. Int. Trans. Electr. Energy Syst. 1991, 1, 271–279. [CrossRef] Velasco, J.; Frascella, R.; Albarracín, R.; Burgos, J.C.; Dong, M.; Ren, M.; Yang, L. Comparison of positive streamers in liquid dielectrics with and without nanoparticles simulated with finite-element software. Energies 2018, 11, 361. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Feature Extraction and Comprehension of Partial Discharge ... - MDPI

Feature Extraction and Comprehension of Partial Discharge ... - MDPI

Suggest Documents

Partial Discharge Feature Extraction Based on Ensemble ... - MDPI

Feature Selection for Partial Discharge Diagnosis - CiteSeerX

Partial Erosion-Based Feature Extraction ... - Semantic Scholar

Entropy-Based Feature Extraction for Electromagnetic ... - MDPI

EXTRACTION, PARTIAL CHARACTERIZATION AND ...

Deep Region of Interest and Feature Extraction Models for ... - MDPI

Comparison of sEMG-Based Feature Extraction and Motion ... - MDPI

Fractal Feature Analysis and Information Extraction of ... - MDPI

Hospital Discharge Instructions: Comprehension and Compliance ...

Classification of Partial Discharge Signals by Combining ... - MDPI

partial discharge monitoring of turbogenerators

measurement and analysis of partial discharge

Feature-Extraction and Feature-Selection for ...

Feature-Extraction and Feature-Selection for ...

by Using a Rogowski Coil in Partial Discharge Measurements - MDPI

Defect Pattern Recognition Based on Partial Discharge ... - MDPI

Partial Discharge Recognition with a Multi-Resolution ... - MDPI

Magnetic Field Feature Extraction and Selection for Indoor ... - MDPI

Magnetic Field Feature Extraction and Selection for Indoor ... - MDPI

Feature Extraction and Selection for Myoelectric Control Based ... - MDPI

Physical Extraction and Feature Fusion for Multi-Mode Signals ... - MDPI

Feature Surface Extraction and Reconstruction from Industrial ... - MDPI

Water Feature Extraction and Change Detection Using ... - MDPI

EXTRACTION, PARTIAL CHARACTERIZATION AND ... - Alice