1408 B. Feng et al.: Thermal Characteristics of All-Film Pulsed Capacitors in Application of Repetitive Pulse Discharge Thermal Characteristics of All-Film Pulsed Capacitors in Application of Repetitive Pulse Discharge Bingyang Feng, Yuansheng Li and Mengbing He State Key Laboratory of Advanced Electromagnetic Engineering and Technology Huazhong University of Science and Technology, Wuhan, China ABSTRACT Temperature rise is one of the major causes for all-film pulsed capacitor (AFPC) failure under high repetitive high-voltage pulse discharge operations. To study the thermal characteristics, a thermal simulation model is established. In this model, the actual operation conditions of capacitors are applied. The practical internal structure and heat production transfer of the AFPC are considered. The validation of the model is proved by the simulation and the experimental results. Based on the finite element method (FEM), the overall temperature field distribution of the AFPC, and the mathematical model between discharge voltage, frequency and temperature rise can be calculated. This model is capable of evaluating the temperature rise characteristics of an AFPC in repetitive high-voltage pulse discharge and can provide certain instructive suggestions for the safe operation and the optimal design of AFPC. Index Terms — all-film pulsed capacitor (AFPC), repetitive high-voltage pulse discharge, thermal characteristic, finite element method (FEM), frequency 1 INTRODUCTION THE development of high repetition rate pulsed power devices has become an important research direction in pulsed power technology in recent years [1–3]. High power pulse capacitor plays an important role in energy storage and discharge. In order to achieve certain stringent requirements, including short rise time, high power and high repetitive frequency, capacitors must be able to reach certain levels of high voltages, high currents, have low inductance, long lifetime, and good thermal conductivity. The all-film pulsed capacitors (AFPC) have the characteristics of small size, light weight, low loss, low-temperature rise, and excellent partial discharge performance, so they are widely used in the highvoltage output of pulse sources [4, 5]. The lifetime of the capacitor is one of the key factors restricting the continuous operation of the pulse power system . The failure of AFPC is often manifested as a sudden breakdown, which directly causes the system to stop operating. Thermal aging is one of the major factors causing breakdown [7, 8]. In repetitive discharge applications, heat will accumulate inside the capacitor causing the internal temperature to rise. The temperature rise will accelerate the aging rate of the insulating material, which may cause the dielectric material to decompose and produce certain forms of by-products, such as gas or carbon particles. These by-products will reduce the insulation performance and aggravate the aging process of the Manuscript received on 4 January 2021, in final form 15 May 2021, accepted 16 June 2021. Corresponding author: M. He. dielectric. Moreover, if the capacitor exceeds a certain temperature, it will directly cause thermal breakdown of the insulating material. Therefore, studying the temperature rise and distribution characteristics is of great significance to the optimal design of the capacitor and the maintenance of the system. At present, there have already been some numerical studies on the thermal characteristics of capacitors. Gualous et al  adopted computational fluid dynamics to establish and solve the temperature field model of supercapacitors. But there is a big difference between supercapacitors and pulse capacitors, and the solution procedure was complex. Liu et al  assumed the temperature of the capacitor shell to be a certain value, and obtained the estimation formula of the highest temperature between the shell and the interior of the capacitor according to the heat balance equations. However, the temperature distribution inside the capacitor was not obtained, and the formula was inaccurate because of the simplified calculation. Liang et al  established a 3-D finite volume method temperature calculation model for the power capacitor. The temperature distribution and the internal maximum temperature of the power capacitor have been simulated. The validation of the numerical model was also verified by tests. Nevertheless, the heat generation of the power capacitor is mainly due to the dielectric loss, while the pulse capacitor is due to the electrode heat loss. Li et al  investigated the temperature rise of the metallized film capacitor (MFC) based on the repetition pulse lifetime test platform. However, the rated voltage of MFC is relatively low, and there are distinctive differences between DOI: 10.1109/TDEI.2021.009567 Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. IEEE Transactions on Dielectrics and Electrical Insulation Vol. 28, No. 4; August 2021 MFC and AFPC in structure and failure mechanism. Therefore, the model for MFC cannot be applied in temperature simulations for AFPC. This paper takes the AFPC operating under high-voltage repetitive pulse discharge conditions as the research object, analyzes the internal structure of the capacitor and the process of heat generation and transfer, and establishes a simulation model. The validation of the model has been accomplished by comparing the simulation and experimental results, which have shown a good agreement with each other. By using the finite element method (FEM) to calculate the temperature field, crucial data have been obtained, such as the temperature field distribution of the whole capacitor, the temperature rise of both the internal and the external shell, etc. At the same time, according to different pulse waveform parameters, the mathematical model between discharge voltage, frequency and stationary temperature rise is established. These have certain guiding significance for the prediction of temperature rise and safe operation of AFPC under high-voltage repetitive frequency discharge conditions. 2 CAPACITOR STRUCTURE AND HEAT TRANSFER PROCESS 2.1 THE STRUCTURE OF AFPC The target capacitor in this research is composed of core elements, insulating shell, impregnant, etc. The dielectric dissipation factor of the capacitor is about 0.0002. The core element is the most important unit of the capacitor, which is wound by aluminum foil electrode and dielectric film. The schematic diagram of the structure is shown in Figure 1. The dielectric film adopts polypropylene film with low dissipation factor (~10-4) and high dielectric strength (~600 MV/m at capacitor level) , whose structure is simple, temperature rise is low, and short-term electrical breakdown performance is excellent. The multilayer film structure is adopted to avoid the influence of the local electrical weakness of the film. The aluminum foil electrode adopts a convex foil structure and a hemming process to improve the electric field distribution . 1409 series-connected cores into the insulating shell, and after vacuuming, inject the Benzyl Toluene impregnant to complete the assembly of the capacitor. Table 1 shows the dimension of the capacitor. Table 1. Dimension of the capacitor. Structural parameter Value Structural parameter Value Shell length (mm) 244 element length (mm) 137 Shell width (mm) 151.4 element width (mm) 90.1 Shell height (mm) 105.1 element height (mm) 17.8 Shell thickness (mm) 6.5 element number 10 2.2 HEAT PRODUCTION AND TRANSFER PROCESS Understanding the heat generation and transfer process of the AFPC is the premise of modeling and analysis. Under high-voltage pulse discharge conditions, the heat is mainly generated by the pulse current flowing on the aluminum foil of the capacitor core component, which is conducted from the inside to the outside; the impregnant near the core transfers heat to the inner surface of the shell through convection heat dissipation; the heat from the inner surface of the shell is transferred to the outer surface through thermal conduction; finally, all the heat is lost to the air environment by convection and radiation. The heat transfer process is shown in Figure 2. Figure 2. The heat transfer process in AFPC. When the total heating power inside the capacitor is equal to the total heat dissipation power of the shell, the capacitor reaches the thermal equilibrium state, and the temperature distribution of the capacitor remains stable. 3 SIMULATION MODELING OF THERMAL CHARACTERISTICS Figure 1. The structure of the AFPC core element. Several core components are connected in series by soldering tin and lead-out pieces on the side. Each capacitor component has an encapsulation gasket to provide insulation. Then put the 3.1 HEAT CALCULATION The heat of the AFPC in the high-voltage pulse discharge condition is mainly generated by the large current flowing through the aluminum foil electrode. According to [15, 16], the AFPC film structure, shown in Figure 1, can be divided into n equal infinitesimals along the film width direction, which is equivalent to a two-dimensional RC circuit network model, shown in Figure 3a. The Cn is the capacitance for each infinitesimal film and Rn is the resistance for each infinitesimal electrode. Since the current in in each infinitesimal is almost equal, according to Kirchhoff’s Current Law, the current is distributed Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. 1410 B. Feng et al.: Thermal Characteristics of All-Film Pulsed Capacitors in Application of Repetitive Pulse Discharge linearly in the electrodes, shown in Figure 3b, where the x-axis is the direction in which current flows from the lead-out end of the electrode convex foil to the clear margin of the dielectric film . So, the current i(t) is at the maximum value near the lead-out end of the electrode and at the minimum about zero near the clear margin. The heat under the action of a pulse discharge can be calculated as: 2 b x i(t ) RAl (t ) dtdx 0 0 b Q t b (1) where b is the effective width between electrode and dielectric film, as shown in Figure 3b, t is the pulse current action time, i(t) is the amplitude of the pulse current flowing through the electrode terminal, and RAl(t) is the varying resistance of the aluminum foil electrode due to the temperature variation during discharge. The convection heat transfer process of the impregnant is more complicated and needs to meet the conservation of mass, momentum, and energy. Certain simplifications are made in the analysis, and the partial differential equation of convection heat transfer is obtained as: T T T T 2T 2T 2T +u + +w = + ( + ) (3) t x y z CP x2 y 2 z 2 where u, ν, and w are the velocity of the fluid in x, y, and z directions, respectively. When the capacitor temperature reaches a stable value, the heat transferred to the shell must be balanced with the heat dissipation of the case through radiation and convection. Therefore, the surface heat dissipation is used as the boundary condition on the shell when calculating the coupled field: (b) Figure 3. (a) Equivalent RC circuit network model and (b) linear distribution of current in aluminum foil electrode. 3.2 FLUID-SOLID-THERMAL COUPLING FIELD There are solid and liquid materials inside the capacitor, so the temperature model is the calculation of the fluid-solidthermal coupling field. The FEM has become one of the most popular methods for calculating fluid-solid-thermal coupling field due to its high accuracy, multiple numerical algorithms, and multi-grid support . The temperature distribution of the fluid-solid-thermal coupling field should satisfy the corresponding governing equations. The forms of heat transfer in the capacitor include the conduction and convection of the internal medium and the radiation and convection of the shell and the air. The partial differential equation of heat conduction in the Cartesian coordinate system is: T 2T 2T 2T =div( gradT )+ ( 2 2 2 ) t x y z =hext (Text T ) (Text 4 T 4 ) (4) where Γ is the capacitor shell, Text is the temperature of the environment, T is the temperature of the shell, hext is the heat dissipation coefficient of the shell, n is the unit vector of the outer normal direction on the shell, σ is the Stefan-Boltzmann Constant, σ = 5.67 × 10-8W/(m2ꞏK4), and ε is the radiation coefficient of the shell. Because the value of σ is small, it can usually be ignored. (a) CP T n 3.3 SIMULATION MODEL ESTABLISHMENT For the convenience of modeling and calculation, the core element made of polypropylene film, aluminum foil and Benzyl Toluene impregnant are equivalent to a whole. Calculate the equivalent density and specific heat according to the thickness of aluminum foil, polypropylene film, and Benzyl Toluene d Al Al d PP PP d BT BT = d Al d PP d BT C = d Al Al CAl d PP PPCPP d BT BT CBT d Al Al d PP PP d BT BT (5) where ρ is the equivalent density and C is the equivalent specific heat, ρA1, ρPP, ρBT are the densities of aluminum foil, polypropylene film, and Benzyl Toluene impregnant, respectively, and CA1, CPP, CBT are the specific heats of them, respectively. The dAl, dPP, dBT are the thicknesses of the media with the value of 10 μm, 32 μm, and 1 μm. The equivalent thermal conductivity of the element shows the anisotropic nature , as shown in Figure 4. (2) where ρ, CP, and T are the density, specific heat capacity, and temperature of the micro-element, respectively, t is the time, λ is the thermal conductivity, and Φ is the heat power per unit volume. In this model, the core elements are set as the heat source. Figure 4. Anisotropy of element heat conduction. Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. IEEE Transactions on Dielectrics and Electrical Insulation Vol. 28, No. 4; August 2021 1411 In x and y directions, the internal heat conduction of the element is parallel, which means the multi-layer dielectric conducts heat at the same time. In z-direction, the internal heat conduction is in series, which means the multi-layer dielectric conducts heat sequentially. So, the thermal conductivity in different directions can be described as: d Al Al d PP PP d BT BT x =y = d Al d PP d BT d Al d PP d BT = z d Al Al d PP PP d BT BT where λA1, λPP, and λBT are the thermal conductivities of aluminum foil, polypropylene film, and Benzyl Toluene impregnant, respectively. Table 2 shows the property parameters of various materials in the capacitor. According to the above analysis and the parameters in Table 1 and Table 2, a simulation model is established in the FEM software. Mesh division is the key to FEM. The quality of the mesh is directly related to the simulation time and the accuracy of the simulation results, so finer mesh division is used to ensure the quality. The overall model of the AFPC and the mesh division result are shown in Figure 5. Table 2. Material property parameters. Material Specific heat (J/(gꞏ°C)) Density (g/cm3) Aluminum foil Polypropylene film Benzyl toluene Insulated shell 0.89 1.9 1.6 2.3 2.7 0.89–0.91 0.98 0.84 (a) (6) Thermal conductivity (W/mꞏK) 238 0.22 0.12 0.33 (b) Figure 6. Determination of heat dissipation coefficient: (a) the AFPC prototype heated in the chamber with a constant temperature and (b) comparison of experimental surface temperature and simulation in the cooling process. The results indicate that the experimental data matches well with the simulation, which has a heat dissipation coefficient of 7.5 W/(m2·K). Therefore, the heat dissipation coefficient of the capacitor shell is chosen as 7.5 w/(m2·K). This parameter contains the heat loss caused by convection and radiation. 4 RESULTS AND DISCUSSION 4.1 COMPARISON OF SIMULATION AND EXPERIMENTAL RESULTS The repetitive frequency high-voltage pulse discharge platform is shown in Figure 7. Adopting the burst repetition frequency mode, the primary energy storage capacitor is charged by the high-voltage charging power supply. The discharge of the primary capacitor is controlled by the thyristor in parallel with the reverse diode, and the energy is transferred to the AFPC in the form of the pulse transformer. Through the switch-on of the self-trigger gap, the AFPC discharges to the load. Figure 5. Capacitor simulation model and mesh division. 3.4 DETERMINATION OF HEAT DISSIPATION COEFFICIENT To obtain the heat dissipation coefficient of the capacitor shell surface, the AFPC prototype is placed in a thermostat with constant temperature and heated, as shown in Figure 6a, then placed in air for cooling while recording the surface temperature in the center of the surface. Meanwhile, three heat dissipation simulations with different heat dissipation coefficients are set, and the heat dissipation curves obtained by the simulation are compared with the actual data. The results are shown in Figure 6b. Figure 7. High voltage repetitive frequency pulse discharge platform. Based on the experimental platform, the repetitive discharge experiment was conducted on the AFPC at the discharge Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. 1412 B. Feng et al.: Thermal Characteristics of All-Film Pulsed Capacitors in Application of Repetitive Pulse Discharge voltage of 30 kV. 5 identical capacitors of the same manufacture batch are adopted and operating under the same experimental conditions. Through the measurement of the oscilloscope, the typical voltage and current waveforms of a single discharge are shown in Figure 8. Under the repetitive pulse discharge conditions, the pulse platform discharges 5 times per second, which means the frequency is 5 Hz. Each discharge time is 5 μs, and the cooling time is about 0.2 s. Figure 10. The AFPC surface temperature rise result of simulation and experiment. is appropriate to use this model to simulate and predict the thermal characteristics of the AFPC in actual conditions. Figure 8. Typical voltage and current waveform of HV pulse discharge. The temperature data of the different external surfaces measured by the Fluke TiS60+ Thermal Imager are shown in Figure 9. At the same time, according to the typical discharge waveform, shown in Figure 8, the transient temperature rise calculation is performed in the model at the same condition. According to Equation (1), the heat of a single pulse is 2.3662 J calculated by MATLAB. By the calculation and comparison of the energy at different times, the heat generated on the aluminum foil electrode at each discharge is turned out to be approximately uniform, and the electrode in the experimental condition can be considered as a stable heat source. The temperature of the environment in the simulation is set to 23 ℃, which is consistent with the experimental environment. The results of the experiment and simulation are compared in Figure 10. It can be seen that the curves fit well, which means that it 4.2 THE TEMPERATURE DISTRIBUTION OF THE AFPC Considering that in actual application, the high-voltage repetitive pulse discharge platform needs to run continuously, the duration of repetitive pulse discharge operation is set to 600 min in the simulation model. After the simulation is completed, the temperature field distribution diagrams of AFPC at different times are shown in Figure 11. It can be seen that the distribution of the temperature field is not uniform, and there are partial hottest points. Figure 11. Temperature field distribution of AFPC at different times. (a) (b) (c) (d) Figure 9. The temperature of the different external surfaces: (a) the front surface, t = 30 min, (b) the front surface, t = 110 min, (c) the side surface, t = 50 min and (d) the side surface, t = 110 min. By using a probe to measure the temperature of the hottest point inside the capacitor and three different external surfaces, the temperature rise curves obtained are shown in Figure 12. When the repetitive pulse discharge duration is about 600 minutes, the curves tend to be flat, indicating that the heat production and dissipation of the capacitor are basically in balance. The maximum temperature of the capacitor is inside the element, which indicates the temperature of the dielectric. It is 11.24 ℃ higher than the front surface, 16.52 ℃ higher than the side surface, and 18.21 ℃ higher than the top surface. The difference in surface temperature is mainly due to the structure of the core elements and the anisotropy of thermal conductivity. According to the Law of Arrhenius, the high temperature will deteriorate the performance of the dielectric material. It has Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. IEEE Transactions on Dielectrics and Electrical Insulation Vol. 28, No. 4; August 2021 1413 (a) Figure 12. Temperature rise curves at different locations. been indicated that the breakdown strength of the dielectric film is independent of temperature up to 40 °C and drops linearly as a function of temperature by almost 10% between 40 °C and 80 °C due to the enhanced thermal aging mechanism [20, 21]. Therefore, the maximum allowable temperature of the internal dielectric medium of AFPC is usually 80 °C. Taking the temperature of the dielectric as the evaluation object, the temperature tends to stabilize after 600 minutes, as shown in Figure 12, and the maximum temperature of the dielectric is less than 80 ℃, indicating that the capacitor can operate safely for a long time under this condition. 4.3 THE MATHEMATICAL MODEL BETWEEN DISCHARGE VOLTAGE, FREQUENCY, AND TEMPERATURE RISE In the application of repetitive pulse discharge, voltage and frequency are indicators that need lots of attention. Therefore, to study the effect of voltage and frequency on temperature rise, calculations at different frequencies and different discharge voltages are set to obtain the highest temperature rise curve, as shown in Figure 13. It can be seen in Figure 13a that the temperature rise of the capacitor is very small and basically remains constant at 1 Hz. At 5 Hz and 10 Hz, the capacitor can operate continuously and stably for a long time. But at 15 Hz, after about 212 min, the highest temperature of dielectric exceeds 80 ℃. Also, as shown in Figure 13b, the capacitor can operate continuously and stably at 15 kV, 30 kV, and 45 kV. But at 60 kV, after about 128 min, the highest temperature exceeds 80 ℃. In this state, the probability of thermal aging of the dielectric medium and internal breakdown of the capacitor is greatly increased, which is very likely to cause the sudden failure of the capacitor and affect the continuous operation ability of the discharge platform. Based on the stationary temperature of the hottest spot of the dielectric inside capacitor, the relationship between the highest temperature rise and frequency at different voltages, and the relationship between the highest temperature rise and voltage at different frequencies are obtained, as shown in Figure 14. (b) Figure 13. (a) The highest temperature rise curves at different frequencies and (b) the highest temperature rise curves at different voltages. Through the method of fitting analysis, the regression equations between stationary highest temperature rise, discharge voltage, and frequency are obtained as: Tmax =Text k f U 2.0068 0.9979 Tmax =Text kU f (7) where Tmax is the highest temperature of the dielectric inside the capacitor, Text is the temperature of the environment, U is the amplitude of the pulse voltage in kV, f is the discharge frequency in Hz, kf is the model coefficient related to the capacitor model, and frequency, and kU is the model coefficient related to the capacitor model and voltage. From Equation (7), there are reasons to believe that within an appropriate range, there is a mathematical relationship between stationary highest temperature rise, voltage, and frequency. So, after enough calculations, the surface model of the relationship between them is obtained, as shown in Figure 15. Through the method of nonlinear surface fitting analysis, the mathematical model between stationary temperature rise, discharge voltage, and frequency can be summarized as: T m a x T ext A f 0 .9 9 7 9 U 2 .0 0 6 8 B f 0 .9 9 7 9 C (8) where A is the model coefficient, which is 0.00557, B is the model coefficient, which is 0.00571 with a root mean squared Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. 1414 B. Feng et al.: Thermal Characteristics of All-Film Pulsed Capacitors in Application of Repetitive Pulse Discharge (a) (b) Figure 14. (a) The relationship between the stationary highest temperature rise and voltage at different frequencies and (b) the relationship between the stationary highest temperature and frequency at different voltages. Figure 15. The surface model between discharge voltage, frequency, and stationary highest temperature rise. error of 0.00716, and C is the model coefficient, which is 0.0218 with a root mean squared error of 0.04718. 4.4 DISCUSSION It can be found that the thermal field distribution of the AFPC is not uniform, and there are partial high temperatures appear during repetitive pulse operations. The highest temperature showed up inside the capacitor, which indicated the maximum temperature of the dielectric. The temperature on each surface was different due to the structure of the core and the anisotropy of thermal conductivity. The model based on Equation (8) indicates that there is a mathematical relationship between stationary temperature rise, discharge voltage, and frequency. Since the measurement of dielectric temperature inside the capacitor is usually not convenient, by using such the simulation and mathematical model, the stationary temperature of the whole AFPC under the practical application of repetitive pulse discharge can be calculated and predicted before the operation, and the security state of the system can be guaranteed within an appropriate range of voltage and frequency. Therefore, considering from improving the thermal characteristics and reducing the maximum temperature rise of dielectric inside the AFPC in the application of repetitive pulse discharge, the capacitor can be installed vertically or horizontally to obtain a larger heat dissipation area. At high voltages and frequencies, it is necessary to install cooling equipment in the repetitive pulse power system because there will be an unacceptable temperature rise after a period of continuous operation. Besides, the structure of the AFPC needs to be optimized. For example, adopting insulating shell materials with high heat dissipation performance can ensure that the capacitor transfers enough heat to the external environment during the pause of discharge, and the highfluidity impregnant can ensure the internal thermal field distribution of the capacitor relatively uniform. 5 CONCLUSIONS This paper focuses on the thermal characteristics of the AFPC at the high-voltage output of the pulse source in the application of high-voltage repetitive pulse discharge, analyzes the internal structure of the AFPC and the heat production and transfer process. The temperature rise analysis model is established and validated by comparison with experiments, and the temperature rise of AFPC under different discharge frequencies and pulse voltages are obtained based on the FEM method. The results show that the internal temperature rise of dielectric inside the capacitor is the highest after a period of operation. The temperature distribution of each surface of the capacitor is different, while the top and side surfaces are lower. Therefore, the capacitor can be installed vertically or horizontally. The mathematical model of the relationship between temperature, frequency, and voltage is obtained by the fitting method. This model can be used to calculate and predict the temperature rise of the AFPC under different conditions to ensure safe operation. At high voltages and frequencies, the temperature rise of the capacitor is higher and the heat generation is faster. It is necessary to add additional heat dissipation equipment or improve the structure and thermal characteristics of the AFPC, such as the adoption of insulating shell materials with high heat dissipation performance and impregnant with high fluidity. In order to make the simulation model more consistent with the actual application, the temperature distribution of the Authorized licensed use limited to: Huazhong University of Science and Technology. Downloaded on January 13,2022 at 09:12:36 UTC from IEEE Xplore. Restrictions apply. IEEE Transactions on Dielectrics and Electrical Insulation Vol. 28, No. 4; August 2021 surrounding environmental airflow field can be taken into consideration in the next step. REFERENCES                 Y. Mi et al, “An MMC-based modular unipolar/bipolar high-voltage nanosecond pulse generator with adjustable rise/fall time,” IEEE Trans. Dielectr. Electr. Insul., vol. 26, no. 2, pp. 515–522, Apr. 2019. Z. Li et al, “A novel drive circuit with overcurrent protection for solid state pulse generators,” IEEE Trans. Dielectr. Electr. Insul., vol. 26, no. 2, pp. 361–366, Apr. 2019. H. Li et al, “Study on the lifetime characteristics of pulsed capacitors based on the theory of space charge,” IEEE Trans. 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Ind. Appl., vol. 38, no. 3, pp. 713–718, May/Jun. 2002.  H. Li et al, “Electric Field and Temperature Dependence of Electrical Conductivity in Biaxially Oriented Polypropylene Films,” IEEE Trans. Plasma Sci., vol. 42, no. 11, pp. 3585–3591, Nov. 2014.  S. Qin et al, “Implications of the anisotropic thermal conductivity of capacitor windings,” IEEE Elect. Insul. Mag., vol. 27, no. 1, pp. 7–13, Jan./Feb. 2011. Bingyang Feng was born in China. He received his B.Eng. degree in electrical engineering and automation from Huazhong University of Science and Technology, Wuhan, China, in 2017. Currently, he is working toward a Ph.D. degree in electrical engineering at Huazhong University of Science and Technology, Wuhan, China. His research interests include design and analysis of high-voltage and high-power pulse source, and high-frequency and highvoltage conversion technology. Yuansheng Li was born in China. He received his M.Eng. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2018. Currently, he is working toward a Ph.D. degree in electrical engineering at Huazhong University of Science and Technology, Wuhan, China. His research interests include gas switch, high power pulse source and high voltage pulse discharge crushing technology. Mengbing He was born in China. He received his M.Sc. degree from Wuhan University, Wuhan, China, in 1998, and a Ph.D. degree from Huazhong University of Science and Technology, Wuhan, China, in 2003. Currently, he is a professor at Huazhong University of Science and Technology. His research interests are gas switch and high voltage capacitor for pulse power technology, high power pulse source, pulse electric dust removal technology, high voltage pulse discharge crushing technology and application of solid-state switch in pulse power technology. 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