Modelling and simulation on a novel meat grinder circuit for the dynamic pulsed power load

Compared with the capacitive pulsed power supply (CPPS), the inductive pulsed power supply (IPPS) is considered to have broader prospects because of its theoretically higher energy densities. Most recent researches focus on characteristics of the IPPS with a fixed load, which is rather different from practical applications from the engineering point of view. In this paper, with the purpose of preliminarily verifying the IPPS’s feasibility, the performance of the novel meat grinder circuit with a dynamic load model is presented and analysed under PSpice environment. The analysis model is based on the parameters of the four-module IPPS and the pulsed power load built in Institute of Electrical Engineering. Finally, the comparison between the IPPS and the CPPS with same initial energy is carried out.


Introduction
The pulsed power supply (PPS) requires power in gigawatt range and mega-ampere currents which should be maintained for several milliseconds [1][2][3]. Because of higher energy densities, the inductive pulsed power supply (IPPS) attracts interest [4,5].
Researches on derived circuits of two basic topologies, the XRAM and the meat grinder, last for years [6][7][8]. In terms of the meat grinder, the Slow TRansfer of Energy Through Capacitive Hybrid (STRETCH) meat grinder is proposed by Institute for Advanced Technology [9,10]. Besides, both STRETCH meat grinder with SECT and STRETCH meat grinder with ICCOS are developed by Tsinghua University [11,12].
As shown in Fig. 1, a novel meat grinder circuit is proposed by Institute of Electrical Engineering (IEE) [13]. Compared with STRETCH meat grinder, the main switches are replaced by IGBTs in order to obtain better load current waveforms and lower voltage stress on the opening switch. Note that the direction of diode in the parallel of IGBT 2 is opposite to the diode with the same position in the STRETCH meat grinder circuit.
The IPPS designed by IEE comprises four novel meat grinder modules. With a fixed 0.4-mΩ resistance, the experimental load current reached 30.40 kA with a 1.7-ms pulse width, which basically meets the requirement of a small-scale pulse high-current launcher. In this paper, the mathematical model of the pulse high-current launcher is presented, and the dynamic load model including the velocity and displacement of the armature is used to replace the fixed load under PSpice environment. The efficiency of the system consisting of the four-module IPPS and the pulse high-current launcher is calculated. The comparison between the IPPS and the CPPS with same initial energy is carried out in order to reveal any further research possibilities for its improvements.

Establishment of dynamic model for the pulse high-current launcher
As shown in Fig. 3(a), the structure of one kind of the pulse high-current launcher consists of four parallel rails and a sliding armature. The process of launching is the interaction of multiple physical fields. As shown in Fig.  3 (b), the electrical equivalent model is established to describe its complex physical phenomena.

Rail inductance and resistance
The inductance of the rail rail ( ) L x and the resistance of the rail rail ( ) R x increase linearly by the displacement of the armature. Both of them are given by where x is the displacement of the armature, ' L and ' R are inductance gradient and resistance gradient of the rail respectively, 0 L and 0 R are initial inductance and resistance of the rail respectively.

Contact velocity skin effect
During the process of launching, contact and interface physics must be considered because of its great impact on the loss of system energy. Based on the theory of contact velocity skin effect (VSEC), this performancelimiting effect represents as an equivalent resistance VSEC R [14]. The equivalent resistance VSEC R is given by where VC R is the proportional coefficient, v is the velocity of the armature.

Back-electromotive force
The motion of armature causes the back-electromotive force EMF u , which is given by where rail i is the current flowing through the rail.

Friction force
In the practical situation, the contact pressure C F at the rail-armature interface consists of the mechanical stress Cmech F and the electromagnetic force Cem F . As the current rises, the electromagnetic force Cem F becomes an overwhelming force over the contact pressure C F . The contact pressure C F and a simplified friction force f are given by where wing l is the length of the armature's wing, s is the distance between inner rails, and 2 μ is the friction coefficient.

Calculation module for the velocity and displacement of the armature
The driving force generated in the armature and the acceleration of the armature are given by where m is the mass of the armature, wing l is the length of the armature's wing. Compared with the acceleration of the armature without considering the friction force, the equivalent inductance gradient ' eq L is given by The velocity of the armature is given by  1 1 ) and ( ) L i t , the current of the inductor cal L , is given by where 0 i is the initial current of the inductor cal L .
With the definition of ' cal = 2 eq L m L and 0 (10) and (12) are consistent, which means ( ) L i t represents the velocity of the armature.
Based on the above analysis, the calculation module for the velocity and displacement of the armature is presented in Fig. 4.

Performance of the novel meat grinder with the pulse high-current launcher
Most discharge characteristics of derived meat grinder circuits have two current peaks. In order to realize a large scale IPPS system to meet the requirement from the engineering point of view, a novel meat grinder is proposed [13]. As shown in Fig. 5, both the novel meat grinder and the STRETCH meat grinder in the simulation use same parameters of the four-module IPPS with the fixed load of a 0.4-mΩ resistance and a 1-μH inductor. From the results of simulation and experiment, the novel meat grinder circuit has better load currents waveforms and higher peak current, which means it is more easily to be shaped for superposition.
The parameters of the four-module IPPS and the pulse high-current launcher is presented in Table 1.
It is noteworthy that the operation of IGBTs affects the performance of the novel meat grinder circuit. The principle is that the conduction of IGBT 2 must precede the turn-off of IGBT 1 . Otherwise the delay of conduction on IGBT 2 leads to higher voltage stress on the opening switch IGBT 1 . In this paper, the operation of IGBTs is as the same as the operation in the experiment with a 0.4-mΩ resistance. Namely, the turn-on of IGBT 2 is 0.2-ms earlier than the turn-off of IGBT 1 , and L t , the pre-charge time of the primary inductor 1 L and the secondary inductor 2 L , is 12.2 ms. To achieve a higher current peak, four modules of the novel meat grinder are triggered simultaneously. As shown in Fig. 6, the performance of the four-module IPPS including the voltage of the primary capacitor S C and the energy transfer capacitor 1 C , the current through the inductors 1 L and 2 L , the current through the rail, the velocity and the displacement of the armature is presented.  According to the simulation, the initial energy of IPPS system is given by 68.107 kJ 2 2 The energy of charging to the inductors 1 L and 2 L is given by The efficiency of charging is given by ( 1 5 ) The muzzle energy is given by The efficiency of discharging and the whole system are given by

Comparison between the IPPS and the CPPS
From the engineering point of view for pulse highcurrent launchers, the novel meat grinder, or other PPSs, must drive the projectile at rather higher muzzle velocity than the projectile launched by gas dynamic launchers. Unfortunately, the IPPS with mature technologies has not been developed up to now. Meanwhile, the CPPS has proven its reliability and usability in most researches [2,4,15]. Therefore, it is necessary to draw a comparison between the novel meat grinder circuit and the CPPS. The simulation and analysis in this paper is the basis for improvements and the definite construction for full-scale demonstration.
In order to access the performance of the IPPS and reveal further possibilities for its improvements, the CPPS with same initial primary energy is simulated as well. The parameters of the CPPS in IEE is shown in Table 2. Considering that the IPPS is trigged simultaneously, the triggering method of the CPPS is the same. The comparison between the IPPS and the CPPS is shown in Table 3. According to the comparison, the efficiency of the CPPS is 5.36 times higher than the efficiency of the IPPS.
Note that the capacitors S C and 1 C store a certain mount of energy after launching. The residual energy of the capacitors S C in the IPPS is 15.655 kJ, which is 22.986 % of the initial energy. The residual energy of the capacitors S C in the IPPS is 10.347 kJ, which is 15.192 % of the initial energy. Both of them comprise a considerable propotion of the initial energy, which means great potential for efficiency improvement. Further researches would be needed for any feasibilities, methods and actual ratio for the muzzle energy of the residual energy recovery.

Conclusion
With the purpose of verifying the feasibility of the IPPS and revealing its further improvement, the dynamic model for the pulse high-current launcher is established in this paper. Based on the practical parameters of the novel meat grinder circuit and the launcher built by IEE, the performance of the four-module IPPS is simulated and analysed.
With the initial energy of 68.107 kJ, the muzzle velocity and the muzzle energy are 450.570 m/s and 1.523 kJ, respectively. According to the calculation, the efficiency of charging and discharging are 36.560 % and 6.115 %, respectively. The system efficiency of the IPPS is 2.236 %, which is much lower than the CPPS with same initial energy. The reason of low efficiency in the IPPS is a considerable amount of residual energy stored in the primary capacitor S C and the energy transfer capacitor 1 C . Further researches will focus on the residual energy recovery to improve the efficiency of the IPPS.