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Discussion on Minimum Precharged Voltage and Energy of the Counter-Current Capacitor in ICCOS Xukun Liu, Student Member, IEEE, Xinjie Yu, Member, IEEE, Rui Ban, Student Member, IEEE, and Zhen Li Member, IEEE

Abstract— Because it possesses higher current turn-off capability, the inverse current commutation with semiconductor devices (ICCOS) is a better option for the opening switch of an inductive pulsed power supply than the integrated gate commutated thyristor. This paper investigates the counter-current capacitor, which is the key component that determines the turn-off result and the volume of the counter-current branch. The major contributions of this paper include the following: 1) deriving an analytical expression for the minimum precharged capacitor voltage that can reliably turn off the main switch; 2) verifying this expression through a series of experiments within a current range of 0 to 4000 A and an energy range of 0 to 50 kJ; 3) giving an approximate expression for the optimal capacitance that minimizes the precharged energy; and 4) investigating the variation trends of the optimal capacitance and the corresponding optimal precharged energy with varying inductor current. Index Terms— Counter-current capacitor, inductive pulsed power supply (IPPS), inverse current commutation with semiconductor devices (ICCOS), main switch, opening switch.

I. I NTRODUCTION

T

HE inductive pulsed power supply (IPPS) has become a promising option for electromagnetic launching power supplies [1]–[5]. At present, current commutation is a difficult technical problem that restricts the energy level of a single module [6]–[10]. Specifically, unlike capacitors that can hold energy by themselves for a relatively long time, inductors need a loop to maintain current. Therefore, an opening switch with proactive current turn-OFF capability is needed to commute inductor current from the prime source to the load. One option is to use a fully controlled semiconductor device, such as the integrated gate commutated thyristor (IGCT). However, IGCTs possess limited (kilo-ampere level) current turn-OFF capability, which restrains the inductor current [11]. Moreover, compared with thyristors, IGCTs are more vulnerable in practical and more expensive. An alternative option is to adopt inverse current commutation with semiconductor devices (ICCOS) [6]. The working principle of this technique

Manuscript received January 3, 2017; revised April 18, 2017 and May 12, 2017; accepted May 13, 2017. Date of publication May 31, 2017; date of current version July 7, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 50877039 and in part by Tsinghua University Initiative Scientific Research Program under Grant 20121087927. (Corresponding author: Xinjie Yu.) The authors are with the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China, and also with the State Key Laboratory of Power System, Beijing 100084, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2017.2705190

Fig. 1. Three placement methods for the counter-current branch in the single-stage XRAM circuit and the meat grinder circuit.

is elaborated in Section II-A. In brief, a fast thyristor with sufficient current conducting capability and voltage withstanding capability acts as the main switch. A counter-current branch consisting of a pulsed capacitor (i.e., the countercurrent capacitor) and a fast thyristor (i.e., the counter-current thyristor) is introduced to generate a counter-current pulse and to thus turn OFF the main switch. Under this circumstance, the main switch possesses remarkable current turn-OFF capability. The XRAM and the meat grinder are two basic circuits used for almost all IPPS circuits [3], [5], [12], [13]. In terms of applying ICCOS in these two circuits (as well as the improved circuits based on them), there are three placement methods for the counter-current branch [14]–[19], as shown in Fig. 1. The counter-current path for the first method is counter-current branch → main switch; that of the second method is countercurrent branch → main switch → prime source → load; that of the third method is counter-current branch → main switch → prime source. Different counter-current paths result in different performance. A qualitative and comprehensive performance comparison is presented based on the following three aspects. A. Voltage Stress of the Main Switch In the second method, the load is included in the countercurrent path. Thus, the load current increases with increasing counter-current pulse, which occurs relatively slow. In the first

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and third methods, the load is not included in the countercurrent path. Therefore, the load current increases extremely rapid when the inductor current is commuted from the countercurrent branch to the load, i.e., when the load diode is turned ON and the counter-current thyristor is turned OFF . As a result, for the first and third methods, the voltage stress of the main switch, i.e., the commutation voltage caused by the load inductance, is larger than that of the second method [6], [14]. However, because the load inductance is generally small (microhenry level), these voltages are relatively low.

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 45, NO. 7, JULY 2017

TABLE I P ERFORMANCE C OMPARISON OF THE T HREE P LACEMENT M ETHODS

B. Full Use of the PreCharged Capacitor Energy For all three methods, generating the counter-current pulse does not consume much energy. After the current of the main switch crosses zero, the remaining capacitor energy will be fed to the inductor. The difference between the first method and the other two methods is the final state. Specifically, for the second and third methods, (approximately) when the capacitor voltage crosses zero, the inductor current will decrease, turning on the load diode. Then, the inductor current will be commuted from the counter-current branch to the load, forcing the current of the counter-current thyristor to decrease rapidly. When this current crosses zero, the counter-current thyristor is turned OFF . At this moment, the capacitor voltage is approximately zero. However, this situation is slightly different for the first method. In the first method, the counter-current thyristor is turned OFF not after the capacitor voltage crosses zero but after the total voltage of the prime source and the countercurrent capacitor crosses zero. As a result, the final voltage of the capacitor will be approximately the negative value of the prime source voltage. Considering that the final energy of the capacitor essentially originates from the precharged capacitor energy, similar to the first method, the precharged capacitor energy is not fully fed to the inductor [6], [14] but remains substantially in the form of a negative voltage in the capacitor. C. Precharged Capacitor Voltage In the second and third methods, the prime source is included in the counter-current paths; thus, generating the counter-current pulse requires the capacitor voltage to overcome the prime source voltage [6]. As a result, the precharged capacitor voltage will be higher for these two methods that for the first method. Moreover, for the second method, the load is included in the counter-current path; thus, the total path inductance will be much greater. As a result, to achieve the same-amplitude counter-current pulse, the precharged capacitor voltage should be even higher [6], [14]. Table I presents a brief summary of the above comparison. Our research mainly focuses on meat grinder circuits. Moreover, the counter-current capacitor in the third method can be used to recapture the leakage flux energy of the inductors [20], [21]. Therefore, in this paper, we adopt the third placement method for further study. The research approach would be the same for the other two methods. The capacitance C and the precharged voltage UC of the counter-current capacitor are two key parameters for

Fig. 2. Equivalent circuit for the charge stage, the counter-current stage, and the continuing-charge stage.

the counter-current branch. From the perspective of turn-OFF reliability, the larger the C is and the higher the UC is, the longer the duration of the counter-current pulse will be, and the higher the turn-OFF reliability of the main switch will be [20] and [21]. However, from the perspective of energy density, the larger theC is and the higher the UC is, the higher the precharged energy will be; the larger the capacitor volume will be; and the lower the energy density of the IPPS module will be [20] and [21]. In other words, the turn-OFF reliability and the energy density provide contradictory requirement for C and UC . The main focus of this paper is to investigating the minimum UC that can turn OFF the main switch and the optimal value of C for minimizing the precharged energy. II. M INIMUM P RECHARGED VOLTAGE In this section, we first derive the analytical expression for the minimum precharged voltage of the counter-current capacitor that can reliably turn OFF the main switch. Then, we verify the general validity of this expression through a series of experiments within the current range of 0 to 4000 A and the energy range of 0 to 50 kJ. A. Theoretical Analysis The XRAM circuit and the meat grinder circuit have the same first three stages of their working processes, i.e., the charge stage, the counter-current stage, and the continuingcharge stage [13], [14]. Fig. 2 shows the equivalent circuit for these three stages, where U S is the prime source, which is a dc source; and i S is its current; T1 is the main switch, which has a triggering time of tT1 ; T2 is the counter-current thyristor, which has a triggering time of tT2 ; C is the countercurrent capacitor; and i C , u C , UC , and E C are the current, voltage, precharged voltage, and precharged energy of the

LIU et al.: DISCUSSION ON MINIMUM PRECHARGED VOLTAGE AND ENERGY

capacitor, respectively; L C is the parasitic inductance in the counter-current branch; L is the energy storage inductor; and R, i L , and I L are the resistance, current, and maximum current (i.e., the value of i L when T1 is about to be turned OFF) of the inductor, respectively. 1) Charge Stage: The starting event of the charge stage is the triggering of T1 . During this stage, L is charged by U S . When i L reaches its expected value, i.e., i L , T2 is triggered, and this stage ends. 2) Counter-Current Stage: The starting event of the counter-current stage is the triggering of T2 . During this stage, a counter-current pulse is generated by C, forcing i S to decrease rapidly. When i S crosses zero, this stage ends. From the perspective of circuit analysis, this stage can be approximately solved as follows. Compared with that of the charge stage (tens of milliseconds), the duration of this stage is negligible (tens of microseconds). Thus, i L can be considered constant during this stage, i.e., I L . In addition, the variation in u C is much smaller than those in U S and UC . Thus, i C varies approximately linear, and the rate of increase can be expressed as UC − U S di C = . dt LC Then, i C can be expressed as UC − U S i C (t) = (t − tT2 ) . LC Then, the duration of this stage can be expressed as

(1)

(2)

IL L C . (3) UC − U S Using the u−i integral relation of the capacitor, the variation in u C during this stage can be expressed as tT 2 +t2 I L2 L C i C (t) u C = dt = − . (4) − C 2C(UC − U S ) tT 2 t2 =

Thus, the value of u C at the end of this stage can be expressed as u C-2end = UC + u C .

(5)

3) Continuing-Charge Stage: The starting event of the continuing-charge stage is when i S crosses zero. During this stage, L is continuously charged by C until all the precharged capacitor energy is released. In addition, T1 withstands an inverse voltage of approximately U S − u C . If the duration of this negative voltage is longer than the reverse recovery time tq of T1 , then T1 is reliably turned OFF. Because tq is generally short (tens of microseconds), i L can be considered constant during this period as well, i.e., I L . Using the u − i integral relation of the capacitor, the variation in u C during this short period (not the full stage) can be expressed as I L tq δu C = − . (6) C Then, the above condition for the reliable turn-OFF of the main switch can be expressed as u C-2end + δu C ≥ U S .

(7)

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By substituting (4)–(6) into (7), the inequality can be rewritten as (UC − U S )2 −

I 2 LC I L tq (UC − U S ) − L ≥ 0. C 2C

(8)

As shown in (8), C, UC , I L , and U S determine the turn-OFF result of the main switch. For conciseness, C and UC are collectively called the counter-current parameters; and I L and U S are collectively called the turn-OFF conditions. With determined C, I L , and U S , the minimum UC that can reliably turn OFF the main switch can be obtained by solving (8) and is expressed as UC-min

IL = US + C

1 2 1 tq + t + 2L C C . 2 2 q

(9)

B. Experimental Verification In the theoretical analysis of Section II-A, the thyristors are treated as ideal devices. Neglecting the dynamic characteristics of the thyristors and using the approximations made in the derivation, will to some degree affect the accuracy of (9). Thus, a series of experiments are conducted to verify the general validity of this expression. A brief description of our experimental platform is presented here. For availability and implementation restrictions, a 103.8-mF pulsed capacitor acts as the prime source. The counter-current capacitor is one of four pulsed capacitors with capacitance values of 404.9, 604.8, 803.6, and 1007 μF. The parasitic inductance in the counter-current branch is estimated as 0.8 μH. The energy storage inductor is a 6.75-mH custom inductor with the air-core flat spirals of a strip coil structure [22], [23]. The KK-2500A-3000V and KK-1000A-3500V fast thyristors from ShengTang Corporation are used as the main switch and the counter-current thyristor, respectively, and they both possess a rated reverse recovery time of 55 μs. The CWT-150R Rogowski current transducer from PEM Corporation and the OIDP-100 high-voltage differential probes from Oltek Corporation are used to measure i L , u C , and the prime capacitor voltage, respectively. Equation (9) is also relevant when the prime source is a capacitor. In this case, U S in (9) is replaced by the prime capacitor voltage at the end of the charge stage. For conciseness, this voltage is represented by US−off . With tT 1 , tT 2 , and the initial voltage U S0 of the prime capacitor given, US−off can be easily acquired by solving the charge stage, which is an RLC (resistor–inductor–capacitor) second-order oscillation process. The specific expressions are omitted due to the limited paper length. Our experiments are divided into two groups. In the first group, the fixed parameters are I L and US−off ; the variable is C; and the research aim is to verify the validity of (9), especially as C varies. In the second group, the fixed parameter is C; the variable is I L (as well as US−off ); and the research aim is to verify the expansibility of (9), with varying inductor current and energy.

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Fig. 3. Results of the experiments with a fixed I L and US−off and the corresponding theoretical analysis. The blue circles and the red crosses represent the experimental cases in which the main switch can or cannot be turned OFF, respectively. The dashed black line represents the theoretical results of (9).

1) Experiments Under Determined Turn-Off Conditions: In the first set of experiments, U S0 , tT 1 , and tT 2 are fixed at 1000 V, 0 ms, and 35 ms, respectively; under this circumstance, I L and US−off are fixed at 2620 A and 390 V, respectively; the corresponding inductor energy is 23.2 kJ; C varies from 400 to 1000 μF; and UC varies from 400 to 1000 V. The results of the experiments and theoretical analysis are shown in Fig. 3. As shown in Fig. 3, the results of the experiments and theoretical analysis generally coincide. Moreover, as for certain turn-OFF conditions, UC−min is negatively correlated with C, which coincides with the expectations from (9). 2) Experiments With Variable Inductor Energy: In the second set of experiments, C is fixed at 1007 μF; UC varies from 200 to 1000 V; U S0 varies from 400 to 1400 V; tT 1 and tT 2 are fixed at 0 and 35 ms, respectively; I L and US−off are then determined by U S0 and tT 2 − tT 1 . The relationships between I L , US−off , and U S0 are shown in Fig. 4, and the results of experiments and theoretical analysis are shown in Fig. 5. As shown in Fig. 4, the inductor energy range is from 0 to 50 kJ. As shown in Fig. 5, the results of the experiments and theoretical analysis generally coincide. Based on the above experimental results, (9) can be concluded to be generally valid, at least within a current range of 0 to 4000 A and an energy range of 0 to 50 kJ. According to our experience, 1.2 times the theoretical result of (9) can guarantee reliable turn-OFF of the main switch.

Fig. 4. Relationships between I L , US−off , and US0 . The blue and red points represent the measured data in the experiments. (However, the different colors are only meaningful in Fig. 5.) The dashed black lines represent the results of the theoretical analysis of the charge stage. In addition, the inductor energy is indicated with numbers.

Fig. 5. Results of the experiments with a fixed C and the corresponding theoretical analysis. The blue circles and the red crosses represent the experimental cases in which the main switch can or cannot be turned OFF, respectively. The dashed black line represents the theoretical results of (9).

In this section, we first discuss the design of C that achieves optimal E C for determined turn-OFF conditions (i.e., I L and U S ). Then, we investigate the variation trends of the optimal C and E C when the turn-OFF conditions vary. For conciseness, the optimal C and E C are represented by Copt and E C−opt , respectively. The prime source in this section is the same as that in Section II-A, which is a dc source. A pulsed capacitor was used as the prime source in Section II-B as a compromise due to availability and implementation restrictions.

III. M INIMUM P RECHARGED E NERGY On the basis of (9), further research can be conducted. This section focuses on the precharged energy E C of the countercurrent capacitor, which directly determines the volume of the counter-current branch and is expressed is EC =

1 CUC2 . 2

(10)

A. Copt and UC−opt for the Determined Turn-Off Conditions For the determined C, U S , and I L , the minimum E C that can reliably turn OFF the main switch can be acquired by substituting (9) into (10) 2 1 IL 1 1 2 tq + E C-min = C U S + tq + 2L C C . (11) 2 C 2 2

LIU et al.: DISCUSSION ON MINIMUM PRECHARGED VOLTAGE AND ENERGY

Fig. 6. Variation trend of E C−min with varying C. The optimal point is indicated by a diamond symbol. I L and U S are 2620 A and 390 V, respectively. The blue circle and the red cross represent the 404.9-μF and 805.2-V and the 404.9-μF and 704.9-V data points in Fig. 3, respectively.

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Fig. 7. Variation trend of Copt with varying I L . The black, red, and blue lines represent the values of U S of 500, 1000, and 1500 V, respectively.

TABLE II C OMPARISON OF PARAMETER S WEEP AND A PPROXIMATE E STIMATION

For constant turn-OFF conditions, E C−min will vary with C. The minimum value of E C−min for all C values is the value of E C−opt that we are searching for. However, the expression of E C−min is so complex that the analytical expressions of Copt and E C−opt cannot be directly derived. Therefore, parameter sweep is applied to (11) to search for Copt and E C−opt . I L and U S are set as 2620 A and 390 V, respectively, and C varies from 400 to 1000 μF, which are the same values as those used in Section II-B1. The results are shown in Fig. 6. As shown in Fig. 6, with increasing C, E C−min first decreases and then increases. When C is 355.3 μF, E C−min achieves the optimal value of 117.2 J. The experiments indicate that E C−opt is between 100.6 and 131.3 J, which verifies the theoretical results of the parameter sweep to some extent. By neglecting the 2L C C term in (11) and conducting further derivation, an approximate expression for estimating Copt can be obtained I L tq Copt = . (12) US Table II compares the parameter sweep and the approximate estimation results for Copt and E C−opt . The error between these values is within engineering tolerance, which is acceptable. B. Variation Trends of Copt and UC−opt With Varying Turn-Off Conditions The turn-OFF conditions undoubtedly influence Copt and E C−opt . This section addresses the variation trends of Copt and E C−opt . I L varies from 0 to 4000 A, and U S is set

Fig. 8. Variation trend of E C−opt with varying I L . The black, red, and blue lines represent the values of U S of 500, 1000, and 1500 V, respectively.

as 500, 1000, or 1500 V, which corresponds to three circumstances, i.e., three problems. The solution method is parameter sweep, specifically, two-layer (i.e., C and I L ) nested loops, and the results are shown in Figs. 7 and 8. As shown in Fig. 7, Copt is directly proportional to I L and negatively correlated with U S , which coincides with the expectation from (12). As shown in Fig. 8, E C−opt is directly proportional to I L . In addition, the lower the U S is, the lower the E C−opt will be. Because the current in the experiments in Section II-B varies from 0 to 4000 A, we have strong confidence in the validity of these conclusions within this current range. IV. C ONCLUSION This paper focuses on the minimum precharged voltage and energy of the counter-current capacitor in ICCOS. The analytical expression of the minimum precharged capacitor voltage UC−min that can turn OFF the main switch is shown in (9), and the validity of this equation is experimentally verified. For determined turn-OFF conditions (i.e., the maximum inductor current I L and the prime source voltage U S ), (12) gives the approximate expression of the optimal capacitance Copt

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that achieves optimal precharged energy E C−opt . For variable turn-OFF conditions, both Copt and E C−opt are directly proportional to I L and are negatively and positively correlated with U S , respectively. In this paper, the thyristors are treated as ideal devices in the theoretical analysis. In other words, the ON–OFF state of the thyristors is more important than their dynamic characteristics, such as the reverse recovery process. Neglecting these characteristics will somewhat affect the accuracy of the circuit solution and (9) and (12), especially when the inductor current is very high. Moreover, the reverse recovery time of the main switch is treated as a constant. In practice, this parameter will be influenced by many factors, such as the ON-state current, the ON -state duration, the rate of decrease of the ON -state current, and the rate of increase of the OFF-state voltage. We will consider these characteristics and factors in the future studies, as using a thyristor circuit model that is closer to reality will provide a more accurate theoretical analysis. In addition, whether conclusions of this paper can be extended to higher current and energy levels needs further verification, which is another important goal of our future research. R EFERENCES [1] I. R. McNab, “Pulsed power options for large EM launchers,” IEEE Trans. Plasma Sci., vol. 43, no. 5, pp. 1352–1357, May 2015. [2] I. R. McNab, “Large-scale pulsed power opportunities and challenges,” IEEE Trans. Plasma Sci., vol. 42, no. 5, pp. 1118–1127, May 2014. [3] O. Liebfried, “Brief review of inductive pulse power generators for railguns,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [4] O. Liebfried and V. Brommer, “A four-stage XRAM generator as inductive pulsed power supply for a small-caliber railgun,” IEEE Trans. Plasma Sci., vol. 41, no. 10, pp. 2805–2809, Oct. 2013. [5] X. Yu and X. Liu, “Review of meat grinder circuits for railguns,” IEEE Trans. Plasma Sci., to be published, doi: 10.1109/TPS.2017.2705164. [6] P. Dedie, V. Brommer, and S. Scharnholz, “ICCOS countercurrentthyristor high-power opening switch for currents up to 28 kA,” IEEE Trans. Magn., vol. 45, no. 1, pp. 536–539, Jan. 2009. [7] S. Scharnholz, V. Brommer, G. Buderer, and E. Spahn, “High-power MOSFETs and fast-switching thyristors utilized as opening switches for inductive storage systems,” IEEE Trans. Magn., vol. 39, no. 1, pp. 437–441, Jan. 2003. [8] A. Sitzman, D. Surls, J. Mallick, and E. Dierks, “Operational limits of a commercial gate turn-off thyristor for inductive-store systems,” IEEE Trans. Plasma Sci., vol. 39, no. 1, pp. 316–321, Jan. 2011. [9] W. Jiang, K. Nakahiro, K. Yatsui, J. H. Kim, and N. Shimizu, “Repetitive pulsed high voltage generation using inductive energy storage with static-induction thyristor as opening switch,” IEEE Trans. Dielectrics Electr. Insul., vol. 14, no. 4, pp. 941–946, Aug. 2007. [10] W. Jiang et al., “Compact solid-state switched pulsed power and its applications,” Proc. IEEE, vol. 92, no. 7, pp. 1180–1196, Jul. 2004. [11] ABB Switzerland Ltd. Asymmetric Integrated GateCommutated Thyristor 5SHY 55L4500, accessed on Apr. 18, 2013. [Online]. Available: https://library.e.abb.com/public/5d6d8847ef6bf67483257b510047d998 /5SHY%2055L4500_5SYA1243-06April%2013.pdf [12] X. Liu, X. Yu, R. Ban, and Z. Li, “Analysis of the meat grinder with SECT circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [13] X. Liu, X. Yu, R. Ban, and Z. Li, “Analysis of the capacitor-aided meat grinder circuits for inductive pulsed power supply,” IEEE Trans. Plasma Sci., to be published, doi: 10.1109/TPS.2017.2705179. [14] O. Liebfried, V. Brommer, and S. Scharnholz, “Development of XRAM generators as inductive power sources for very high current pulses,” in Proc. 19th IEEE Int. Pulsed Power Conf., Jun. 2013, pp. 1–6. [15] P. Dedié, V. Brommer, and S. Scharnholz, “Twenty-stage toroidal XRAM generator switched by countercurrent thyristors,” IEEE Trans. Plasma Sci., vol. 39, no. 1, pp. 263–267, Jan. 2011.

[16] P. Dedié, V. Brommer, and S. Scharnholz, “Experimental realization of an eight-stage XRAM generator based on ICCOS semiconductor opening switches, fed by a magnetodynamic storage system,” IEEE Trans. Magn., vol. 45, no. 1, pp. 266–271, Jan. 2009. [17] X. Yu, R. Ban, X. Liu, and Z. Li, “The meat grinder with SECT circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [18] X. Yu and X. Chu, “Stretch meat grinder with ICCOS,” IEEE Trans. Plasma Sci., vol. 41, no. 5, pp. 1346–1351, May 2013. [19] H. Wang, L. Xie, G. Zhang, X. He, and Z. Chen, “A 50 kJ inductive– capacitive storage module with solid-state high-power opening switch based on counter-current thyristor,” IEEE Trans. Plasma Sci., vol. 43, no. 8, pp. 2658–2662, Aug. 2015. [20] X. Liu, X. Yu, R. Ban, and Z. Li, “Parameter analysis of the countercurrent branch in the STRETCH meat grinder with ICCOS circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [21] X. Liu, X. Yu, R. Ban, and Z. Li, “Parameter selection of the energy transfer capacitor in the meat grinder with SECT circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [22] X. Liu, X. Yu, and Z. Li, “Inductance calculation and energy density optimization of the tightly coupled inductors used in inductive pulsed power supplies,” IEEE Trans. Plasma Sci., to be published. [23] Z. Li, X. Yu, S. Ma, and Y. Sha, “Structural parameter optimization of inductors used in inductive pulse power supply,” IEEE Trans. Plasma Sci., vol. 43, no. 5, pp. 1456–1461, May 2015.

Xukun Liu (S’15) was born in Jiangxi, China, in 1993. He received the B.S. degree in electrical engineering and automation from Tsinghua University, Beijing, China, in 2014, where he is currently pursuing the Ph.D. degree in electrical engineering with the Department of Electrical Engineering. His current research interests include pulsed power supply.

Xinjie Yu (M’01) was born in Guizhou, China, in 1973. He received the B.S. and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1996 and 2001, respectively. He is currently an Associate Professor with the Department of Electrical Engineering, Tsinghua University. His current research interests include pulsed power supply, current sensors, and computational intelligence.

Rui Ban (S’15) was born in Shaanxi, China, in 1992. He received the B.S. degree in electrical engineering and automation from Tsinghua University, Beijing, China, in 2015, where he is currently pursuing the M.S. degree with the Department of Electrical Engineering. His current research interests include inductive pulsed power supply.

Zhen Li (M’12) was born in Shandong, China, in 1982. He received the B.S. degree in electrical engineering and automation from Beijing Technology and Business University, Beijing, China, in 2004, and the M.S. degree in electrical engineering from Tsinghua University, Beijing, in 2008. He is currently an Engineer with the Department of Electrical Engineering, Tsinghua University, Beijing. His current research interests include pulsed power supply.

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Discussion on Minimum Precharged Voltage and Energy of the Counter-Current Capacitor in ICCOS Xukun Liu, Student Member, IEEE, Xinjie Yu, Member, IEEE, Rui Ban, Student Member, IEEE, and Zhen Li Member, IEEE

Abstract— Because it possesses higher current turn-off capability, the inverse current commutation with semiconductor devices (ICCOS) is a better option for the opening switch of an inductive pulsed power supply than the integrated gate commutated thyristor. This paper investigates the counter-current capacitor, which is the key component that determines the turn-off result and the volume of the counter-current branch. The major contributions of this paper include the following: 1) deriving an analytical expression for the minimum precharged capacitor voltage that can reliably turn off the main switch; 2) verifying this expression through a series of experiments within a current range of 0 to 4000 A and an energy range of 0 to 50 kJ; 3) giving an approximate expression for the optimal capacitance that minimizes the precharged energy; and 4) investigating the variation trends of the optimal capacitance and the corresponding optimal precharged energy with varying inductor current. Index Terms— Counter-current capacitor, inductive pulsed power supply (IPPS), inverse current commutation with semiconductor devices (ICCOS), main switch, opening switch.

I. I NTRODUCTION

T

HE inductive pulsed power supply (IPPS) has become a promising option for electromagnetic launching power supplies [1]–[5]. At present, current commutation is a difficult technical problem that restricts the energy level of a single module [6]–[10]. Specifically, unlike capacitors that can hold energy by themselves for a relatively long time, inductors need a loop to maintain current. Therefore, an opening switch with proactive current turn-OFF capability is needed to commute inductor current from the prime source to the load. One option is to use a fully controlled semiconductor device, such as the integrated gate commutated thyristor (IGCT). However, IGCTs possess limited (kilo-ampere level) current turn-OFF capability, which restrains the inductor current [11]. Moreover, compared with thyristors, IGCTs are more vulnerable in practical and more expensive. An alternative option is to adopt inverse current commutation with semiconductor devices (ICCOS) [6]. The working principle of this technique

Manuscript received January 3, 2017; revised April 18, 2017 and May 12, 2017; accepted May 13, 2017. Date of publication May 31, 2017; date of current version July 7, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 50877039 and in part by Tsinghua University Initiative Scientific Research Program under Grant 20121087927. (Corresponding author: Xinjie Yu.) The authors are with the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China, and also with the State Key Laboratory of Power System, Beijing 100084, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2017.2705190

Fig. 1. Three placement methods for the counter-current branch in the single-stage XRAM circuit and the meat grinder circuit.

is elaborated in Section II-A. In brief, a fast thyristor with sufficient current conducting capability and voltage withstanding capability acts as the main switch. A counter-current branch consisting of a pulsed capacitor (i.e., the countercurrent capacitor) and a fast thyristor (i.e., the counter-current thyristor) is introduced to generate a counter-current pulse and to thus turn OFF the main switch. Under this circumstance, the main switch possesses remarkable current turn-OFF capability. The XRAM and the meat grinder are two basic circuits used for almost all IPPS circuits [3], [5], [12], [13]. In terms of applying ICCOS in these two circuits (as well as the improved circuits based on them), there are three placement methods for the counter-current branch [14]–[19], as shown in Fig. 1. The counter-current path for the first method is counter-current branch → main switch; that of the second method is countercurrent branch → main switch → prime source → load; that of the third method is counter-current branch → main switch → prime source. Different counter-current paths result in different performance. A qualitative and comprehensive performance comparison is presented based on the following three aspects. A. Voltage Stress of the Main Switch In the second method, the load is included in the countercurrent path. Thus, the load current increases with increasing counter-current pulse, which occurs relatively slow. In the first

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and third methods, the load is not included in the countercurrent path. Therefore, the load current increases extremely rapid when the inductor current is commuted from the countercurrent branch to the load, i.e., when the load diode is turned ON and the counter-current thyristor is turned OFF . As a result, for the first and third methods, the voltage stress of the main switch, i.e., the commutation voltage caused by the load inductance, is larger than that of the second method [6], [14]. However, because the load inductance is generally small (microhenry level), these voltages are relatively low.

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 45, NO. 7, JULY 2017

TABLE I P ERFORMANCE C OMPARISON OF THE T HREE P LACEMENT M ETHODS

B. Full Use of the PreCharged Capacitor Energy For all three methods, generating the counter-current pulse does not consume much energy. After the current of the main switch crosses zero, the remaining capacitor energy will be fed to the inductor. The difference between the first method and the other two methods is the final state. Specifically, for the second and third methods, (approximately) when the capacitor voltage crosses zero, the inductor current will decrease, turning on the load diode. Then, the inductor current will be commuted from the counter-current branch to the load, forcing the current of the counter-current thyristor to decrease rapidly. When this current crosses zero, the counter-current thyristor is turned OFF . At this moment, the capacitor voltage is approximately zero. However, this situation is slightly different for the first method. In the first method, the counter-current thyristor is turned OFF not after the capacitor voltage crosses zero but after the total voltage of the prime source and the countercurrent capacitor crosses zero. As a result, the final voltage of the capacitor will be approximately the negative value of the prime source voltage. Considering that the final energy of the capacitor essentially originates from the precharged capacitor energy, similar to the first method, the precharged capacitor energy is not fully fed to the inductor [6], [14] but remains substantially in the form of a negative voltage in the capacitor. C. Precharged Capacitor Voltage In the second and third methods, the prime source is included in the counter-current paths; thus, generating the counter-current pulse requires the capacitor voltage to overcome the prime source voltage [6]. As a result, the precharged capacitor voltage will be higher for these two methods that for the first method. Moreover, for the second method, the load is included in the counter-current path; thus, the total path inductance will be much greater. As a result, to achieve the same-amplitude counter-current pulse, the precharged capacitor voltage should be even higher [6], [14]. Table I presents a brief summary of the above comparison. Our research mainly focuses on meat grinder circuits. Moreover, the counter-current capacitor in the third method can be used to recapture the leakage flux energy of the inductors [20], [21]. Therefore, in this paper, we adopt the third placement method for further study. The research approach would be the same for the other two methods. The capacitance C and the precharged voltage UC of the counter-current capacitor are two key parameters for

Fig. 2. Equivalent circuit for the charge stage, the counter-current stage, and the continuing-charge stage.

the counter-current branch. From the perspective of turn-OFF reliability, the larger the C is and the higher the UC is, the longer the duration of the counter-current pulse will be, and the higher the turn-OFF reliability of the main switch will be [20] and [21]. However, from the perspective of energy density, the larger theC is and the higher the UC is, the higher the precharged energy will be; the larger the capacitor volume will be; and the lower the energy density of the IPPS module will be [20] and [21]. In other words, the turn-OFF reliability and the energy density provide contradictory requirement for C and UC . The main focus of this paper is to investigating the minimum UC that can turn OFF the main switch and the optimal value of C for minimizing the precharged energy. II. M INIMUM P RECHARGED VOLTAGE In this section, we first derive the analytical expression for the minimum precharged voltage of the counter-current capacitor that can reliably turn OFF the main switch. Then, we verify the general validity of this expression through a series of experiments within the current range of 0 to 4000 A and the energy range of 0 to 50 kJ. A. Theoretical Analysis The XRAM circuit and the meat grinder circuit have the same first three stages of their working processes, i.e., the charge stage, the counter-current stage, and the continuingcharge stage [13], [14]. Fig. 2 shows the equivalent circuit for these three stages, where U S is the prime source, which is a dc source; and i S is its current; T1 is the main switch, which has a triggering time of tT1 ; T2 is the counter-current thyristor, which has a triggering time of tT2 ; C is the countercurrent capacitor; and i C , u C , UC , and E C are the current, voltage, precharged voltage, and precharged energy of the

LIU et al.: DISCUSSION ON MINIMUM PRECHARGED VOLTAGE AND ENERGY

capacitor, respectively; L C is the parasitic inductance in the counter-current branch; L is the energy storage inductor; and R, i L , and I L are the resistance, current, and maximum current (i.e., the value of i L when T1 is about to be turned OFF) of the inductor, respectively. 1) Charge Stage: The starting event of the charge stage is the triggering of T1 . During this stage, L is charged by U S . When i L reaches its expected value, i.e., i L , T2 is triggered, and this stage ends. 2) Counter-Current Stage: The starting event of the counter-current stage is the triggering of T2 . During this stage, a counter-current pulse is generated by C, forcing i S to decrease rapidly. When i S crosses zero, this stage ends. From the perspective of circuit analysis, this stage can be approximately solved as follows. Compared with that of the charge stage (tens of milliseconds), the duration of this stage is negligible (tens of microseconds). Thus, i L can be considered constant during this stage, i.e., I L . In addition, the variation in u C is much smaller than those in U S and UC . Thus, i C varies approximately linear, and the rate of increase can be expressed as UC − U S di C = . dt LC Then, i C can be expressed as UC − U S i C (t) = (t − tT2 ) . LC Then, the duration of this stage can be expressed as

(1)

(2)

IL L C . (3) UC − U S Using the u−i integral relation of the capacitor, the variation in u C during this stage can be expressed as tT 2 +t2 I L2 L C i C (t) u C = dt = − . (4) − C 2C(UC − U S ) tT 2 t2 =

Thus, the value of u C at the end of this stage can be expressed as u C-2end = UC + u C .

(5)

3) Continuing-Charge Stage: The starting event of the continuing-charge stage is when i S crosses zero. During this stage, L is continuously charged by C until all the precharged capacitor energy is released. In addition, T1 withstands an inverse voltage of approximately U S − u C . If the duration of this negative voltage is longer than the reverse recovery time tq of T1 , then T1 is reliably turned OFF. Because tq is generally short (tens of microseconds), i L can be considered constant during this period as well, i.e., I L . Using the u − i integral relation of the capacitor, the variation in u C during this short period (not the full stage) can be expressed as I L tq δu C = − . (6) C Then, the above condition for the reliable turn-OFF of the main switch can be expressed as u C-2end + δu C ≥ U S .

(7)

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By substituting (4)–(6) into (7), the inequality can be rewritten as (UC − U S )2 −

I 2 LC I L tq (UC − U S ) − L ≥ 0. C 2C

(8)

As shown in (8), C, UC , I L , and U S determine the turn-OFF result of the main switch. For conciseness, C and UC are collectively called the counter-current parameters; and I L and U S are collectively called the turn-OFF conditions. With determined C, I L , and U S , the minimum UC that can reliably turn OFF the main switch can be obtained by solving (8) and is expressed as UC-min

IL = US + C

1 2 1 tq + t + 2L C C . 2 2 q

(9)

B. Experimental Verification In the theoretical analysis of Section II-A, the thyristors are treated as ideal devices. Neglecting the dynamic characteristics of the thyristors and using the approximations made in the derivation, will to some degree affect the accuracy of (9). Thus, a series of experiments are conducted to verify the general validity of this expression. A brief description of our experimental platform is presented here. For availability and implementation restrictions, a 103.8-mF pulsed capacitor acts as the prime source. The counter-current capacitor is one of four pulsed capacitors with capacitance values of 404.9, 604.8, 803.6, and 1007 μF. The parasitic inductance in the counter-current branch is estimated as 0.8 μH. The energy storage inductor is a 6.75-mH custom inductor with the air-core flat spirals of a strip coil structure [22], [23]. The KK-2500A-3000V and KK-1000A-3500V fast thyristors from ShengTang Corporation are used as the main switch and the counter-current thyristor, respectively, and they both possess a rated reverse recovery time of 55 μs. The CWT-150R Rogowski current transducer from PEM Corporation and the OIDP-100 high-voltage differential probes from Oltek Corporation are used to measure i L , u C , and the prime capacitor voltage, respectively. Equation (9) is also relevant when the prime source is a capacitor. In this case, U S in (9) is replaced by the prime capacitor voltage at the end of the charge stage. For conciseness, this voltage is represented by US−off . With tT 1 , tT 2 , and the initial voltage U S0 of the prime capacitor given, US−off can be easily acquired by solving the charge stage, which is an RLC (resistor–inductor–capacitor) second-order oscillation process. The specific expressions are omitted due to the limited paper length. Our experiments are divided into two groups. In the first group, the fixed parameters are I L and US−off ; the variable is C; and the research aim is to verify the validity of (9), especially as C varies. In the second group, the fixed parameter is C; the variable is I L (as well as US−off ); and the research aim is to verify the expansibility of (9), with varying inductor current and energy.

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Fig. 3. Results of the experiments with a fixed I L and US−off and the corresponding theoretical analysis. The blue circles and the red crosses represent the experimental cases in which the main switch can or cannot be turned OFF, respectively. The dashed black line represents the theoretical results of (9).

1) Experiments Under Determined Turn-Off Conditions: In the first set of experiments, U S0 , tT 1 , and tT 2 are fixed at 1000 V, 0 ms, and 35 ms, respectively; under this circumstance, I L and US−off are fixed at 2620 A and 390 V, respectively; the corresponding inductor energy is 23.2 kJ; C varies from 400 to 1000 μF; and UC varies from 400 to 1000 V. The results of the experiments and theoretical analysis are shown in Fig. 3. As shown in Fig. 3, the results of the experiments and theoretical analysis generally coincide. Moreover, as for certain turn-OFF conditions, UC−min is negatively correlated with C, which coincides with the expectations from (9). 2) Experiments With Variable Inductor Energy: In the second set of experiments, C is fixed at 1007 μF; UC varies from 200 to 1000 V; U S0 varies from 400 to 1400 V; tT 1 and tT 2 are fixed at 0 and 35 ms, respectively; I L and US−off are then determined by U S0 and tT 2 − tT 1 . The relationships between I L , US−off , and U S0 are shown in Fig. 4, and the results of experiments and theoretical analysis are shown in Fig. 5. As shown in Fig. 4, the inductor energy range is from 0 to 50 kJ. As shown in Fig. 5, the results of the experiments and theoretical analysis generally coincide. Based on the above experimental results, (9) can be concluded to be generally valid, at least within a current range of 0 to 4000 A and an energy range of 0 to 50 kJ. According to our experience, 1.2 times the theoretical result of (9) can guarantee reliable turn-OFF of the main switch.

Fig. 4. Relationships between I L , US−off , and US0 . The blue and red points represent the measured data in the experiments. (However, the different colors are only meaningful in Fig. 5.) The dashed black lines represent the results of the theoretical analysis of the charge stage. In addition, the inductor energy is indicated with numbers.

Fig. 5. Results of the experiments with a fixed C and the corresponding theoretical analysis. The blue circles and the red crosses represent the experimental cases in which the main switch can or cannot be turned OFF, respectively. The dashed black line represents the theoretical results of (9).

In this section, we first discuss the design of C that achieves optimal E C for determined turn-OFF conditions (i.e., I L and U S ). Then, we investigate the variation trends of the optimal C and E C when the turn-OFF conditions vary. For conciseness, the optimal C and E C are represented by Copt and E C−opt , respectively. The prime source in this section is the same as that in Section II-A, which is a dc source. A pulsed capacitor was used as the prime source in Section II-B as a compromise due to availability and implementation restrictions.

III. M INIMUM P RECHARGED E NERGY On the basis of (9), further research can be conducted. This section focuses on the precharged energy E C of the countercurrent capacitor, which directly determines the volume of the counter-current branch and is expressed is EC =

1 CUC2 . 2

(10)

A. Copt and UC−opt for the Determined Turn-Off Conditions For the determined C, U S , and I L , the minimum E C that can reliably turn OFF the main switch can be acquired by substituting (9) into (10) 2 1 IL 1 1 2 tq + E C-min = C U S + tq + 2L C C . (11) 2 C 2 2

LIU et al.: DISCUSSION ON MINIMUM PRECHARGED VOLTAGE AND ENERGY

Fig. 6. Variation trend of E C−min with varying C. The optimal point is indicated by a diamond symbol. I L and U S are 2620 A and 390 V, respectively. The blue circle and the red cross represent the 404.9-μF and 805.2-V and the 404.9-μF and 704.9-V data points in Fig. 3, respectively.

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Fig. 7. Variation trend of Copt with varying I L . The black, red, and blue lines represent the values of U S of 500, 1000, and 1500 V, respectively.

TABLE II C OMPARISON OF PARAMETER S WEEP AND A PPROXIMATE E STIMATION

For constant turn-OFF conditions, E C−min will vary with C. The minimum value of E C−min for all C values is the value of E C−opt that we are searching for. However, the expression of E C−min is so complex that the analytical expressions of Copt and E C−opt cannot be directly derived. Therefore, parameter sweep is applied to (11) to search for Copt and E C−opt . I L and U S are set as 2620 A and 390 V, respectively, and C varies from 400 to 1000 μF, which are the same values as those used in Section II-B1. The results are shown in Fig. 6. As shown in Fig. 6, with increasing C, E C−min first decreases and then increases. When C is 355.3 μF, E C−min achieves the optimal value of 117.2 J. The experiments indicate that E C−opt is between 100.6 and 131.3 J, which verifies the theoretical results of the parameter sweep to some extent. By neglecting the 2L C C term in (11) and conducting further derivation, an approximate expression for estimating Copt can be obtained I L tq Copt = . (12) US Table II compares the parameter sweep and the approximate estimation results for Copt and E C−opt . The error between these values is within engineering tolerance, which is acceptable. B. Variation Trends of Copt and UC−opt With Varying Turn-Off Conditions The turn-OFF conditions undoubtedly influence Copt and E C−opt . This section addresses the variation trends of Copt and E C−opt . I L varies from 0 to 4000 A, and U S is set

Fig. 8. Variation trend of E C−opt with varying I L . The black, red, and blue lines represent the values of U S of 500, 1000, and 1500 V, respectively.

as 500, 1000, or 1500 V, which corresponds to three circumstances, i.e., three problems. The solution method is parameter sweep, specifically, two-layer (i.e., C and I L ) nested loops, and the results are shown in Figs. 7 and 8. As shown in Fig. 7, Copt is directly proportional to I L and negatively correlated with U S , which coincides with the expectation from (12). As shown in Fig. 8, E C−opt is directly proportional to I L . In addition, the lower the U S is, the lower the E C−opt will be. Because the current in the experiments in Section II-B varies from 0 to 4000 A, we have strong confidence in the validity of these conclusions within this current range. IV. C ONCLUSION This paper focuses on the minimum precharged voltage and energy of the counter-current capacitor in ICCOS. The analytical expression of the minimum precharged capacitor voltage UC−min that can turn OFF the main switch is shown in (9), and the validity of this equation is experimentally verified. For determined turn-OFF conditions (i.e., the maximum inductor current I L and the prime source voltage U S ), (12) gives the approximate expression of the optimal capacitance Copt

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that achieves optimal precharged energy E C−opt . For variable turn-OFF conditions, both Copt and E C−opt are directly proportional to I L and are negatively and positively correlated with U S , respectively. In this paper, the thyristors are treated as ideal devices in the theoretical analysis. In other words, the ON–OFF state of the thyristors is more important than their dynamic characteristics, such as the reverse recovery process. Neglecting these characteristics will somewhat affect the accuracy of the circuit solution and (9) and (12), especially when the inductor current is very high. Moreover, the reverse recovery time of the main switch is treated as a constant. In practice, this parameter will be influenced by many factors, such as the ON-state current, the ON -state duration, the rate of decrease of the ON -state current, and the rate of increase of the OFF-state voltage. We will consider these characteristics and factors in the future studies, as using a thyristor circuit model that is closer to reality will provide a more accurate theoretical analysis. In addition, whether conclusions of this paper can be extended to higher current and energy levels needs further verification, which is another important goal of our future research. R EFERENCES [1] I. R. McNab, “Pulsed power options for large EM launchers,” IEEE Trans. Plasma Sci., vol. 43, no. 5, pp. 1352–1357, May 2015. [2] I. R. McNab, “Large-scale pulsed power opportunities and challenges,” IEEE Trans. Plasma Sci., vol. 42, no. 5, pp. 1118–1127, May 2014. [3] O. Liebfried, “Brief review of inductive pulse power generators for railguns,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [4] O. Liebfried and V. Brommer, “A four-stage XRAM generator as inductive pulsed power supply for a small-caliber railgun,” IEEE Trans. Plasma Sci., vol. 41, no. 10, pp. 2805–2809, Oct. 2013. [5] X. Yu and X. Liu, “Review of meat grinder circuits for railguns,” IEEE Trans. Plasma Sci., to be published, doi: 10.1109/TPS.2017.2705164. [6] P. Dedie, V. Brommer, and S. Scharnholz, “ICCOS countercurrentthyristor high-power opening switch for currents up to 28 kA,” IEEE Trans. Magn., vol. 45, no. 1, pp. 536–539, Jan. 2009. [7] S. Scharnholz, V. Brommer, G. Buderer, and E. Spahn, “High-power MOSFETs and fast-switching thyristors utilized as opening switches for inductive storage systems,” IEEE Trans. Magn., vol. 39, no. 1, pp. 437–441, Jan. 2003. [8] A. Sitzman, D. Surls, J. Mallick, and E. Dierks, “Operational limits of a commercial gate turn-off thyristor for inductive-store systems,” IEEE Trans. Plasma Sci., vol. 39, no. 1, pp. 316–321, Jan. 2011. [9] W. Jiang, K. Nakahiro, K. Yatsui, J. H. Kim, and N. Shimizu, “Repetitive pulsed high voltage generation using inductive energy storage with static-induction thyristor as opening switch,” IEEE Trans. Dielectrics Electr. Insul., vol. 14, no. 4, pp. 941–946, Aug. 2007. [10] W. Jiang et al., “Compact solid-state switched pulsed power and its applications,” Proc. IEEE, vol. 92, no. 7, pp. 1180–1196, Jul. 2004. [11] ABB Switzerland Ltd. Asymmetric Integrated GateCommutated Thyristor 5SHY 55L4500, accessed on Apr. 18, 2013. [Online]. Available: https://library.e.abb.com/public/5d6d8847ef6bf67483257b510047d998 /5SHY%2055L4500_5SYA1243-06April%2013.pdf [12] X. Liu, X. Yu, R. Ban, and Z. Li, “Analysis of the meat grinder with SECT circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [13] X. Liu, X. Yu, R. Ban, and Z. Li, “Analysis of the capacitor-aided meat grinder circuits for inductive pulsed power supply,” IEEE Trans. Plasma Sci., to be published, doi: 10.1109/TPS.2017.2705179. [14] O. Liebfried, V. Brommer, and S. Scharnholz, “Development of XRAM generators as inductive power sources for very high current pulses,” in Proc. 19th IEEE Int. Pulsed Power Conf., Jun. 2013, pp. 1–6. [15] P. Dedié, V. Brommer, and S. Scharnholz, “Twenty-stage toroidal XRAM generator switched by countercurrent thyristors,” IEEE Trans. Plasma Sci., vol. 39, no. 1, pp. 263–267, Jan. 2011.

[16] P. Dedié, V. Brommer, and S. Scharnholz, “Experimental realization of an eight-stage XRAM generator based on ICCOS semiconductor opening switches, fed by a magnetodynamic storage system,” IEEE Trans. Magn., vol. 45, no. 1, pp. 266–271, Jan. 2009. [17] X. Yu, R. Ban, X. Liu, and Z. Li, “The meat grinder with SECT circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [18] X. Yu and X. Chu, “Stretch meat grinder with ICCOS,” IEEE Trans. Plasma Sci., vol. 41, no. 5, pp. 1346–1351, May 2013. [19] H. Wang, L. Xie, G. Zhang, X. He, and Z. Chen, “A 50 kJ inductive– capacitive storage module with solid-state high-power opening switch based on counter-current thyristor,” IEEE Trans. Plasma Sci., vol. 43, no. 8, pp. 2658–2662, Aug. 2015. [20] X. Liu, X. Yu, R. Ban, and Z. Li, “Parameter analysis of the countercurrent branch in the STRETCH meat grinder with ICCOS circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [21] X. Liu, X. Yu, R. Ban, and Z. Li, “Parameter selection of the energy transfer capacitor in the meat grinder with SECT circuit,” presented at the 18th Symp. Electromagn. Launch Technol., Wuhan, China, Oct. 2016. [22] X. Liu, X. Yu, and Z. Li, “Inductance calculation and energy density optimization of the tightly coupled inductors used in inductive pulsed power supplies,” IEEE Trans. Plasma Sci., to be published. [23] Z. Li, X. Yu, S. Ma, and Y. Sha, “Structural parameter optimization of inductors used in inductive pulse power supply,” IEEE Trans. Plasma Sci., vol. 43, no. 5, pp. 1456–1461, May 2015.

Xukun Liu (S’15) was born in Jiangxi, China, in 1993. He received the B.S. degree in electrical engineering and automation from Tsinghua University, Beijing, China, in 2014, where he is currently pursuing the Ph.D. degree in electrical engineering with the Department of Electrical Engineering. His current research interests include pulsed power supply.

Xinjie Yu (M’01) was born in Guizhou, China, in 1973. He received the B.S. and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1996 and 2001, respectively. He is currently an Associate Professor with the Department of Electrical Engineering, Tsinghua University. His current research interests include pulsed power supply, current sensors, and computational intelligence.

Rui Ban (S’15) was born in Shaanxi, China, in 1992. He received the B.S. degree in electrical engineering and automation from Tsinghua University, Beijing, China, in 2015, where he is currently pursuing the M.S. degree with the Department of Electrical Engineering. His current research interests include inductive pulsed power supply.

Zhen Li (M’12) was born in Shandong, China, in 1982. He received the B.S. degree in electrical engineering and automation from Beijing Technology and Business University, Beijing, China, in 2004, and the M.S. degree in electrical engineering from Tsinghua University, Beijing, in 2008. He is currently an Engineer with the Department of Electrical Engineering, Tsinghua University, Beijing. His current research interests include pulsed power supply.