Yingbo YU (于營波) and Zhongjian KANG (康忠健)

Institute of New Energy, China University of Petroleum Huadong-Qingdao Campus, Qingdao 266580,People’s Republic of China

Abstract High voltage fracturing technology was widely used in the field of reservoir reconstruction due to its advantages of being clean, pollution-free, and high-efficiency.However, high-frequency circuit oscillation occurs during the underwater high voltage pulse discharge process,which brings security risks to the stability of the pulse fracturing system.In order to solve this problem,an underwater pulse power discharge system was established, the circuit oscillation generation conditions were analyzed and the circuit oscillation suppression method was proposed.Firstly, the system structure was introduced and the charging model of the energy storage capacitor was established by the state space average method.Next, the electrode high-voltage breakdown model was established through COMSOL software,the electrode breakdown process was analyzed according to the electron density distribution image, and the plasma channel impedance was estimated based on the conductivity simulation results.Then the underwater pulse power discharge process and the circuit oscillation generation condition were analyzed, and the circuit oscillation suppression strategy of using the thyristor to replace the gas spark switch was proposed.Finally, laboratory experiments were carried out to verify the precision of the theoretical model and the suppression effect of circuit oscillation.The experimental results show that the voltage variation of the energy storage capacitor, the impedance change of the pulse power discharge process,and the equivalent circuit in each discharge stage were consistent with the theoretical model.The proposed oscillation suppression strategy cannot only prevent the damage caused by circuit oscillation but also reduce the damping oscillation time by 77.1%,which can greatly improve the stability of the system.This research has potential application value in the field of underwater pulse power discharge for reservoir reconstruction.

Keywords: underwater high voltage pulse discharge, circuit oscillation suppression, state space average method, pulse power thyristor

1.Introduction

Reservoir reconstruction plays an important role in enhancing oil and gas recovery, and the reservoir improvement techniques consist mainly of multistage hydrofracturing [1-3], high energy gas fracturing [4-6], the ultrasonic method [7, 8], and electrical explosion method[9-11],etc.High voltage pulse fracturing plays a more and more important role in the process of reservoir reconstruction due to its advantages of high efficiency, being environmentally friendly, and easy operation.Therefore, it was widely used in the applications of oil plug removal [12], coal fracturing[13],permeability enhancement[14,15],and shale gas stimulation [16], and it would have a better effect if combined with frequency resonance technology [17].

However, there generates high-frequency oscillation during the high voltage discharge process, which brings security risks to the stability of the system.The high-power oscillation current reduces the service life of the energy storage capacitor, and the peak oscillation voltage also puts forward higher requirements for the withstand voltage of the energy storage circuit,but we often neglect the importance of oscillation suppression in improving the characteristics of pulse discharge.

For example,the pulse power switch is very important in pulse fracturing technology, and the characteristics and performance of the pulse power switch directly affect the efficiency of pulse power discharge and the reservoir fracturing effect.The gas spark switch was the most widely used [18]due to its simple structure and high-power breakdown capability, though it has the disadvantages of low repetition rate and serious switch corrosion.Scholars solve its weakness by improving the recovery rate of hold-off voltage through adding airflow between electrodes [19], decreasing electrode space [20], injecting different gases between electrodes[21, 22] and changing switch geometry structure [23].These improvements increase switching power and repetition rate,which is of positive significance for repeated pulse fracturing,but the problem of electrode corrosion and high-frequency circuit oscillation has not been solved.Electrode corrosion leads to inconsistent breakdown voltage[24],which makes it difficult to accurately control the discharge time interval,resulting in a poor reservoir resonance effect.The peak high voltage and the pulse current generated by high-frequency circuit oscillation can cause the system over-voltage and overtemperature, and the lifetime of the high voltage film capacitor decreases sharply under such circumstances [25], leading to irreversible damage to the energy storage capacitor and peripheral circuits.

In order to suppress the potential threat caused by highfrequency circuit oscillation,a pulsed power discharge system based on a gas spark switch was established in this work.The equivalent charge-discharge circuit model was built, the impedance change tendency of the discharge electrode during the breakdown process was simulated by using COMSOL software, and the current-voltage characteristics of underwater high voltage pulse discharges were analyzed.The generation conditions of electrical pulse discharge oscillation were analyzed through the RLC equivalent circuit, and the strategy of using pulse power thyristors to suppress reverse current was proposed.

2.Simulation model analysis and modeling of energy storage system

In order to analyze the high voltage pulse discharge oscillation process, the equivalent circuit of a pulse power system based on a gas spark switch was studied,and the time-varying energy storage circuit was simplified based on the state space averaging method.

2.1.Equivalent circuits of each part of the system

The high-voltage pulse fracturing system includes a control module, rectifier inverter module, high-voltage armored cable,and energy transducer.The control module and rectifier inverter module were arranged on the ground, and the transducer was placed in the underground mine.The high-voltage cable was connected with the transducer,and the cable length was up to 3 km, enabling the transducer to perform highvoltage pulse fracturing work at any perforation position in the mine within 3 km depth.Each module of the pulse fracturing system and its equivalent circuit are shown in figure 1.In figure 1, the three-phase AC voltage source is the power input of the system, and the rectifier inverter module receives control signals from the control system.The length of a high-voltage armored cable is more than 3 km,which can be equivalent to a series circuit of resistance and inductance,where the resistance and inductance are 93 Ω and 250 μH,respectively.The transducer is mainly composed of an energy storage structure,pulse power switch,and discharge structure,and it works in an underground mine full of water.The energy storage structure was a fourfold voltage rectifier circuit consisting of four 10 μF high-voltage polymer film capacitors and four high-voltage silicon stacks.The pulse power switch was two-electrode self-breakdown gas spark switch, and the discharge structure was a threaded cylindrical electrode,whose material was copper tungsten alloy resistant to high temperature and oxidation corrosion.The shell was made of high tensile strength metal with good sealing characteristics,which can isolate the energy storage circuit and power switch in the shell to avoid external water erosion and discharge pulse impact.Besides, the shell was connected to the ground and slotted at the tail to form an energy transmission channel.

2.2.Equivalent model of nonlinear time-varying circuit

The voltage on the energy storage capacitor in the voltage doubling rectifier circuit presents a nonlinear time-varying relationship, therefore, it is necessary to model the timevarying circuit for better analysis.The input voltage is a threephase AC voltage source, which can be expressed as

where ua, ub, and ucare the three items of three-phase voltages,and the controller adjusts the rectifier voltage amplitude by controlling the conduction angle α of the rectifier bridge,and the relationship between the control angle α and the output rectifier voltage Ureccan be expressed as

Figure 1.Equivalent circuit of high-voltage pulse fracturing system.

Figure 2.System equivalent circuit simplification.(a) The complex AC time-varying circuit and (b) the simplified circuit.

The inverter module converts the rectifier voltage to AC square wave voltage with a duty cycle of 50%,then the boost transformer enlarges the AC voltage by nine times.Therefore,at the input of the high-voltage cable, the relationship between the input voltage Uacand rectifier control angle α was obtained

The control module and the rectifier inverter module were equivalent to the controlled AC source, and the system equivalent circuit is shown in figure 2(a).The circuit in figure 2(a)was still a complex AC time-varying circuit,and it was necessary to be further equivalent to the circuit displayed in figure 2(b)for better analysis of the pulse power discharge process.

In figure 2, figure 2(a) is a voltage doubling rectifier circuit, which belongs to a complex AC time-varying circuit,and it is necessary to convert figure 2(a) to the DC circuit shown in figure 2(b) for better analyzing the circuit characteristics.

The state-space averaging method has been widely applied for nonlinear time-varying circuits analysis [26, 27]due to its ability to convert time-varying circuits into linearity circuits [28], so this method was adopted for figure 2(a) circuit simplification.The AC power supply in figure 2(a) was divided into positive and negative stages according to voltage direction, and the simplified circuit for each stage was illustrated in figure 3.

In figure 3,upand unare the amplitudes of AC source in positive and negative voltage directions, Ipand Inare the positive and negative flowing currents, respectively.In addition, the RL series circuit was used to represent the armored cable impedance.In the circuit corresponding to the positive voltage stage, the loop voltage relations of meshes 1 and 2 can be listed as

Figure 3.Positive voltage stage (a) and negative voltage stage (b)simplified circuit.

where equations (4) and (5) are the voltage relationship of meshes 1 and 2 in figure 3, respectively.Besides, uc1-uc4denote the voltages of capacitors C1-C4, respectively.As an energy storage element,the capacitor C1 keeps absorbing the energy of the power supply upfor the first half cycle.In the meanwhile, the potential on C3 was moved to C2 to realize potential balance.The voltage on inductor L would increases linearly in a very short time according to the theory of the small signal model [29], so, if the rising voltage on L was noted as vg(t), the following expression can be obtained

where vg(t)can be equivalent to the voltage increase value on the inductance at every moment, which was far less than the value of Ripin equation (4), so the value of L(dip/dt) can be neglected, and equation (4) can be overwritten as

Therefore, the voltage variation trend on capacitor C1 can be expressed as

The same analysis can also be applied to the circuit corresponding to the negative voltage stage, and the loop voltage relations of meshes 3 and 4 can be listed as

where equations (9) and (10) are the voltage relationship of meshes 3 and 4 in figure 3, respectively.Different from the previous stage, capacitor C1 plays the role of the voltage source in this stage, and the capacitor C2 was charged by unand C1 for another half cycle.During this period, the potential on C4 was moved to C3 to realize potential balance.Noting the voltage on C1 as u0, the voltage on C1 and C2 as u1and the relationship between u0and u1satisfies

where u0can be replaced with the following expression(referring to equation (8))

Since there exists the relationship up=un(referring to equation (3)), the voltage on capacitor C1 was noted asuc1′,and its voltage expression in a single cycle can be expressed as

where T and τ are the single period time and time constant,respectively, and the full cycle voltage change tendency on C1 can be estimated by using the state space average method according to circuit time constant τ.The value of T in this design is 0.5 ms, and substituting the value into equations (11)-(13), then we obtain the time constant value τ=0.0233.As is known to all,the value of the time constant τ is equivalent to the value of Ceqmultiplied by Reqin figure 2(b), and the Ceqcan be calculated according to the principle of energy conservation, the storage energy and discharge energy satisfy

where the storage energy value of the voltage doubling circuit is on the left of the equation and the discharge energy is on the right,besides,the value of C is 10 μf,and there exists the relationship uc4=uc3=uc2=2uc1.Finally, we obtain the circuit parameters in figure 2(b)

Furthermore, the theoretical expressions of discharge voltage and energy storage voltage are obtained

where udand ucrepresent the discharge voltage and energy storage voltage, respectively, and ufis the reverse voltage after the discharge process.

3.Analysis of electrode breakdown process

The impedance changes dramatically when the electrode gap was broken down by high voltage, and it is difficult to observe the plasma channel formation process as well as impedance changing tendency since the electrode is wrapped by an insulation medium.The structure of the gas spark switch and discharge electrode was introduced in this section,and the high voltage discharge simulation was carried out by COMSOL software, then the plasma channel formation process and impedance changing tendency were analyzed based on simulation modeling results.

3.1.Gas spark switch and discharge electrode structure

The main components of the gas spark switch and discharge electrode are made of copper tungsten alloy resistant to high temperature and oxidation corrosion, and their structures are depicted in figure 4.

Figure 4.The structure of gas spark switch (a) and discharge electrode (b).

In figure 4, there is a ceramic wall wrapped around the gas switch, which plays a key role in heat isolation and high voltage insulation.Besides, the electrode plate in the gas switch is made of copper, which has good conductivity and heat dissipation ability, and there are small threaded holes distributed around the middle big threaded hole in the plate,the middle threaded hole is used to fix the electrode and the around smaller holes are designed to fix ceramic tubes for electrode plate supporting function.The electrodes in gas switch as well as in discharge structure are made of copper tungsten alloy with high strength and oxidation corrosion resistance.In addition, the electrode structure is designed as cylindrical with thread,which is not only convenient to adjust the electrode gap but also conducive to replacement and maintenance.The working environment of the discharge electrode is a water-filled underground mine, and the outer wall of the discharge electrode is a metal shell with high tensile strength and good sealing characteristics,the shell was connected to ground and slotted at the tail to form an energy transmission channel.

3.2.High voltage breakdown process of electrode

The main components of gas spark switch and discharge structure are copper tungsten alloy electrodes, and there are some similarities between gas spark discharge and pulsed arc electrohydraulic discharge.When the electrode discharges in gas,the high voltage directly breaks through the gas to form a plasma channel.In the process of pulsed arc electrohydraulic discharge, there are both the collision ionization of charged particles and the expansion and development of hot bubbles,and the electron avalanche develops along the bubble holes[30-32], and finally completes the whole process of pulsed electrohydraulic discharge.

In this work, COMSOL 6.0 multi-physical field simulation software was used to simulate the electrode breakdown process with argon as the gas between the electrode gaps.In the simulation software, the electrode material was set as copper tungsten alloy, and the electrode diameter and electrode gap were 32 mm and 10 mm, respectively.To simplify the simulation model, the closed space inside the bubble is chosen as the simulation domain,and the hydrate interference factors around the bubbles are removed.The electrode breakdown process can be observed through the development of electron density on the electrode surface.Two-dimensional axisymmetric modeling was adopted, and its simulation circuit and modeling graphics are exhibited in figure 5.

In figure 5,Vinis the external DC voltage,which was set to 15 000 V, and in the external RC series circuit, R and C were set to 120 Ω and 8.1 μF, respectively.In order to make the initial environment universal,the electron density value in the simulation domain is set to 1013m-3with reference to many studies [17, 33, 34], and the electron density variation during the electrode breakdown process was shown in figure 6.

In figure 6, figure 6(a) was the original electron density,the space electrons gradually move to the anode under the influence of the applied electric field and finally converge to the anode tip, and the electron migration process can be seen from figures 6(b)and(c),corresponding to the time of 0-1.58 μs.As electrons gather at the anode tip, the electrons were emitted from anode to cathode to form a plasma channel during the period of 1.67-2.18 μs, and the electrode breakdown process can be seen from the development of electron density referring to figures 6(d)-(f).The electron density increases sharply at this stage,and the whole breakdown time was within 0.6 μs.

Figure 5.The structure of simulation circuit.

Figure 6.Electron density distribution during electrode breakdown process.

Figure 7.Conductivity variation under different currents.

Figure 8.The RLC equivalent discharge circuit.

Figure 9.Capacitor voltage variation characteristics in different RLC parameters.

3.3.Analysis of impedance characteristics of plasma channel

In order to study the impedance variation characteristics in the process of electrode breakdown, the plasma channel current was set based on the variation trend of the actual oscillation current from 10 to 610 A,and the conductivity changes under different currents as displayed in figure 7.

As shown in figure 7, the conductivity shows an increasing tendency with the increase of current, and the maximum conductivity value increases from 5.65 × 103to 9.45 × 103S m-1.In addition, the plasma channel radius would expand with the increase of conduction current,and the radius of the plasma channel was distributed from 1.5 to 3 mm when the current varies from 10 to -610 A.The equivalent resistance Rplsof plasma channel can be calculated based on the conductivity S using the following equation

where L represents the gap length of the electrode and r represents the cross-section radius of the plasma channel.The equivalent resistance was distributed in the range of 0.037-0.35 Ω after substituting data into the calculation.

It can be seen from the simulation results that the high voltage breakdown time of the electrode is very short(within 1 μs), and the equivalent resistance gradually decreases with the increase of the plasma channel current,and the equivalent resistance changes in a certain range to form a relatively stable state.The circuit oscillation conditions can be analyzed in detail through the impedance change trend.

4.Underwater pulse power discharge process analysis

4.1.Discharge equivalent circuit analysis

The discharge circuit of the energy storage capacitor in the process of pulse power discharge can be equivalent to the RLC series circuit, and the schematic illustration is in figure 8.

In figure 8, R, L, and C represent plasma channel equivalent resistor,circuit inductance,and a storage capacitor,respectively, and the circuit relationship can be described as follows.

Figure 10.Equivalent circuit and corresponding voltage and current on electrode.

where UL, UC, and i represent inductance voltage, discharge voltage, and circuit current, respectively.The relationship between voltage variation characteristics of the energy storage capacitor and R, L, C parameters was shown in figure 9.

It can be seen from figure 9 that, when R ＜ 2(L/C)1/2,the system exhibits underdamped oscillation, and the peak oscillation will cause great damage to the system.When the electrode breaks down in the discharge process, the system meets the damping oscillation condition according to the simulation results, which were also consistent with the relevant research [35, 36].When circuit oscillation occurs, the capacitor voltage and current satisfy

where A and K are constants,φ and β are angles,the capacitor voltage and the current show oscillation attenuation trend.

4.2.Circuit equivalence in different discharge stages

The gas spark switch and the discharge structure meet the circuit oscillation condition during the high voltage breakdown process according to previous study.Therefore, the discharge process was divided into four stages according to the circuit oscillation characteristics, namely, the gas spark switch breakdown stage, the discharge electrode pre-breakdown stage, the electrode discharge stage, and the damping oscillation stage.The equivalent circuit of each stage and corresponding discharge voltage and current on the electrode are exhibited in figure 10.

In figure 10, the gas spark switch breakdown stage(marked 1) and electrode discharge stage (marked 3) have something in common,the impedance of both stages changes dramatically in a very short time, resulting in a high-quality factor to generate an oscillation peak.In the discharge electrode pre-breakdown stage (marked 2), due to the fact that hydrate filled between two discharge electrodes and it took some time for liquid gasification and ionization to produce an electro-hydraulic effect, during this stage, the discharge electrode presents a resistance character and shows a zero input response in equivalent discharge circuit.In the damping oscillation stage (marked 4), the impedance of plasma channels formed in previous stages (marked 1 and 3) varies with the current in a small range showing a relatively stable characteristic, resulting in an oscillation attenuation trend.

4.3.Improvement strategy

The gas spark switch and the discharge structure can generate high-frequency circuit oscillation during the high voltage breakdown process,and the values of peak oscillation voltage and current are much larger than the average discharge voltage and current,which brings great potential safety hazards to the circuit insulation and components voltage endurance.This kind of oscillation harm is particularly obvious to the energy storage capacitor,in the case of high-frequency discharge,the multiple cycle oscillation peak pulse current can make the capacitor heat up, resulting in the service life decrease of the energy storage capacitor due to over-voltage and over-temperature working conditions.In order to improve the discharge process without loss of discharge strength, the most effective method is to suppress the reverse current.

The thyristor has a high switching power characteristic and the ability to pass through ultra-high surge current,which has been widely used in many high-power applications [37],in addition, its reverse current automatic shutdown characteristic was very suitable for reverse oscillation current suppress in underwater pulse power discharges.If the gas spark switch was replaced by a pulse power thyristor, the oscillation of electrode discharge voltage and current waveform can be well improved, and the waveform theoretical improvement can be displayed in figure 11.

In figure 11,the original high-frequency oscillation in the high-voltage breakdown process of the gas spark switch would completely disappear since the gas spark switch was replaced by thyristors.In the electrode discharge stage, the voltage energy on the energy storage capacitor was so high that the reverse oscillation voltage cannot make the thyristor current flow backward,and the current flow direction was still dominated by the energy storage voltage.Therefore, in this stage, the reverse oscillation current can be suppressed without turning off the thyristor.

In the damping oscillation stage, the voltage of the energy storage capacitor decreases,and the reverse oscillation voltage would be higher than that of the energy storage capacitor, so, at this time, the current flow direction was dominated by the oscillation voltage.However, when the current reverse oscillation occurs,the thyristor would be shut down due to the reverse current automatic shutdown characteristic, and the damping oscillation process will be terminated in advance after only half a cycle,which greatly reduces the discharge time.

Figure 11.Electrode discharge waveform theoretical improvement.(a)The original discharge waveform and(b)the discharge waveform after oscillation suppression.

5.Underwater pulse power discharge process analysis

5.1.Introduction to experimental device

In order to study the underwater pulse power discharge process of a gas spark switch as the pulse power switch and verify the thyristor suppression effect on pulse power discharge oscillation,the experimental platform was designed as shown in figure 12.

In figure 12, the control unit (marked 1) can adjust the voltage of the energy storage capacitor (marked 2) by controlling the rectifier angle, and the storage capacitor and discharge electrode (marked 5) were connected at both ends of the two-electrode gas spark switch(marked 3)to form a series connection.In addition, the electrode was immersed in the cuboid water cylinder and fixed on the metal frame connected to the ground, and the pulse power thyristor (marked 4) was the comparison test component.

Figure 12.Experimental platform for underwater pulse power discharge.

5.2.Energy storage experiment

The charging voltage is adjusted by the control unit,when the voltage of the energy storage capacitor reaches the gas spark switch self-breakdown voltage and the pulse power discharge condition is reached.However, there will be reverse voltage ufafter the pulse power discharge, and the actual charging waveform was compared with the theoretical charging waveform as depicted in figure 13.

It can be seen from figure 13 that the theoretical modeling curve almost overlaps with the simulation curve, and it also shows a good consistency compared with the actual charging curve.The error between theoretical calculation and actual charging waveform was calculated, and the results were that the average error, absolute error and mean square deviation were 2.69%, 4.02%, and 7.27%, respectively.The error is small, which indicates that the theoretical modeling can accurately reflect the circuit characteristics of the charging circuit.

Figure 13.Comparison between actual charging curve and theoretical modeling.

5.3.Underwater pulse power discharge experiment

5.3.1.Typical waveform of pulse power discharge.When the voltage of the energy storage capacitor reaches the discharge voltage, the electrode produces discharge action after the gas spark switch breakdown by high voltage, the voltage-current characteristic curves on the discharge electrode and energy storage capacitor were recorded by oscilloscope DL350,three sets of typical curves were selected,as exhibited in figure 14.In figure 14, it can be seen from figures 14(a1) and (b1)that the gas spark switch breakdown stage, discharge electrode pre-breakdown stage, electrode discharge stage,and damping oscillation stage were distinguished clearly, the oscillation peak voltage was more than two times higher than the discharge voltage,and the damping oscillation attenuation time is about 175 ms for 5-6 cycles.It seems that the gas spark switch breakdown stage was missing in figures 14(a2)and(b2),this is because the digital oscilloscope sampling time is 1 μs (DL350 sample rate is 1 M), which is larger than the electrode breakdown time (0.6 μs in simulation), and based on this reason, the oscillation process of electrode discharge stage was often missing in the recording curve, which was also suitable for gas spark switch breakdown stage.Therefore,the record maximum oscillation peak value was often smaller than the actual value.When the time of discharge electrode pre-breakdown stage is very short, there will be two highfrequency oscillation waveforms suspected to be connected together, as shown in figures 14(a3) and (b3).

5.3.2.Parameter identification of damping oscillation.In the discharge electrode pre-breakdown stage, the circuit is equivalent to the RC series circuit shown in figure 10, and the discharge electrode voltage satisfies zero input response,the relationship can be expressed as

where Udrepresents the electrode voltage, U represents the voltage before attenuation, R and C represent the values of equivalent resistance of the electrode and energy storage capacitor, respectively.The equivalent resistance can be calculated by substituting a two-point value in the prebreakdown stage, and after averaging multiple calculations,the resistance value satisfies R=220 Ω.

In the damping oscillation stage, the voltage and current relation satisfies equation (21).For the oscillation current,when the condition satisfiesωt+β=and there will besin (ωt+β)= 1,these points are the vertexes of the current damping oscillation curve, which decay exponentially, and can be expressed as

The time difference between two adjacent vertices is exactly a period T, when the value of current damping oscillation between two adjacent vertices and the time between two points are known, the values of R and L can be obtained by the following formula

The average period of damped oscillation is 35 μs measured in figure 14, and the values of R and L were calculated as R=0.1515 Ω,L=3.787 μH.The peak voltage of circuit oscillation is related to the quality factor Q, the higher the quality value Q, the higher the peak oscillation voltage, and the expression of quality factor Q satisfies

In the gas spark switch breakdown stage and electrode discharge stage, because of the large breakdown current, the equivalent resistor satisfies R ＜ 0.1515.Assuming that the inductance value remains unchanged,and the quality factor Q was calculated as expressed Q ＞ 4.5, therefore, high peak circuit oscillation will be formed in the two stages.

The electrode discharge voltage waveform in the same test was selected, and the calculation parameter was substituted into the equivalent circuit, the comparison between the actual waveform and equivalent circuit waveform is illustrated in figure 15.

Figure 14.Typical voltage-current characteristic curves on discharge electrode(a1),(a2)and(a3)and energy storage capacitor(b1),(b2)and(b3).(a1) and (b1) is a set of the typical voltage-current characteristic curve on the discharge electrode and energy storage capacitor,respectively, (a2) and (b2), (a3) and (c3) are another two sets.

In figure 15, the actual discharge waveform in the prebreakdown stage and damping oscillation stage is consistent with the equivalent circuit model of the theoretical analysis,besides, the calculated plasma channel resistance and inductance values are within the theoretical calculation range of the simulation model, indicating that the theoretical modeling build by COMSOL software can accurately reflect the impedance variation characteristics during the discharge process.

5.4.Improvement strategy based on thyristor

In order to verify the oscillation suppression effect of using thyristors as a pulse power switch, the pulse power thyristor 5STP6500 was selected to replace the gas spark switch for the comparison test.The pulse power discharge comparison waveform in a single cycle was shown in figure 16.

In figure 16,there are oblivious peak oscillation voltages on the inserted figure in the original discharge waveform,while such oscillation is not found in the insert figure in the waveform after oscillation suppression,indicating that reverse turn-off characteristics of the thyristor can effectively suppress the peak voltage caused by high-frequency oscillation.In addition, the voltage and current of the energy storage capacitor will experience the damping oscillation attenuation process in the damping oscillation stage on the original discharge waveform, which lasts for more than 175 ms, and during this period, the energy storage capacitor will experience 5 to 6 times charging and discharging process.The life of a high-voltage film capacitor is often measured by the number of charging and discharging cycles, therefore, multiple charging and discharging in a short time will make the capacitor life decay faster [25].In the waveform after oscillation suppression, the current damping oscillation process only maintains half a cycle, and the oscillation time was reduced to 40 ms, which is 77.1% lower than that before suppression.In addition, the energy storage capacitor only charges and discharges one cycle in a single discharge process,which improves the life of the energy storage capacitor.

Through comparative tests, it is concluded that using thyristors as a pulse power switch to replace the traditional gas spark switch cannot only prevent the damage of continuous high-frequency oscillation current to the energy storage capacitor, but also greatly reduce the voltage requirements of components, and reduce the discharge time,which can significantly improve the oscillation characteristics of underwater pulse discharge circuit.

Figure 15.Comparison between actual waveform and equivalent circuit waveform.

Figure 16.Comparison between original discharge waveform(a)and the waveform after oscillation suppression(b).The insert picture was repeated discharge waveform on storage capacitor.

6.Conclusions

An underwater pulsed power discharge system was established,the conditions of circuit oscillation were analyzed based on the theoretical model,and the circuit oscillation suppression method by using pulse power thyristors to replace the gas spark switch was proposed.The method was verified by experiment, and the results show that the high-frequency oscillation was significantly suppressed, and the damping oscillation time was reduced by 71%.Thyristor has the advantages of low cost, small volume,large conduction power, and high surge current, which was widely used in high voltage rectification and high voltage direct current transmission (HVDC), however, it is rarely used in the field of underwater pulse power discharge.As a semi-controlled device, the thyristor has the characteristic of automatic turn-off under reverse current, therefore, it can suppress the circuit oscillation process by blocking the reverse current and reduce the oscillation time by cutting off the circuit,which was suitable for the application of underwater pulsed power discharge.The series diode in the discharge circuit can also suppress the reverse current, which seems to be a simple method.In fact, the ultra-high voltage high-current diode is expensive and has a large volume and uncontrollable factors, it would not turn off when experiencing the reverse current,and the circuit would still experience a long period of oscillation.Compared with fully controlled devices such as IGBT and MOSFET,thyristor has the advantages of higher withstand voltage,higher switching power,and a stronger anti-interference ability for current signal control, and the automatic turn-off characteristics under reverse current make it easier to control the discharge process by focusing only on the driving signal.This study has a potential application value in the field of stability improvement of pulse power discharge equipment.

Acknowledgments

This work was financially supported by the National Science and Technology Major Project (No.2016ZX05034004).