Neural Network-Based Limiter with Transfer Learning

Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic methods.et al.in J Comput Phys 367:166-191.,2018;Veiga et al.in European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,pp.2525-2550.ECCM.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galer-kin(RKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard limiter.Furthermore,we describe a strategy to transfer the shock-indicator to a residual distribution(RD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured meshes.We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both RKDG and RD schemes.

Study on the formation of arc plasma on the resistive wall liquid metal current limiter

Due to its significant attributes,the liquid metal current limiter(LMCL)is considered a new strategy for limiting short-circuit current in the power grid.A resistive wall liquid metal current limiter(RWLMCL)is designed to advance the starting current-limiting time.Experiments are performed to investigate the dynamic behaviors of liquid metal,and the influence of different currents on the liquid metal self-shrinkage effect is compared and analyzed.Furthermore,the liquid metal self-shrinkage effect is mathematically modeled,and the reason for the formation of arc plasma is obtained by simulation.The laws of arc plasma formation and the current transfer in the cavity are revealed,and the motion mechanisms are explained by physical principles.The simulations are in accordance with the test data.It is demonstrated that the sudden change of the current density at both ends of the wall causes the liquid metal to shrink and depress under the electromagnetic force,and the current starts to transfer from the liquid metal path to the wall resistance path.The RWLMCL can effectively advance the starting current-limiting time.

On High-Resolution Entropy-Consistent Flux with Slope Limiter for Hyperbolic Conservation Laws

This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy production,a third-order differential term deduced from the previous work of Ismail and Roe[11].The corresponding dissipation term is added to the original Roe flux to achieve entropy consistency.The new,resultant entropy-consistent(EC)flux has a general and explicit analytical form without any corrective factor,making it easy to compute and a less-expensive method.The inequality constraints are imposed on the standard piece-wise quadratic reconstruction to enforce the pointwise values of bounded-type numerical solutions.We design the new minmod slope limiter as combining two separate limiters for left and right states.We propose the EC-Limited flux by adding this reconstruction data method to the primitive variables rather than to the conservative variables of the EC flux to preserve the equilibrium of the primitive variables.These resulting fluxes are easily applied to general hyperbolic conservation laws while having attractive features:entropy-stable,robust,and non-oscillatory.To illustrate the potential of these proposed fluxes,we show the applications to the Burgers equation and the Euler equations.

A novel fault current limiter topology design based on liquid metal current limiter

The liquid metal current limiter(LMCL)is regarded as a viable solution for reducing the fault current in a power grid.But demonstrating the liquid metal arc plasma self-pinching process of the resistive wall,and reducing the erosion of the LMCL are challenging,not only theoretically,but also practically.In this work,a novel LMCL is designed with a resistive wall that can be connected to the current-limiting circuit inside the cavity.Specifically,a novel fault current limiter(FCL)topology is put forward where the novel LMCL is combined with a fast switch and current-limiting reactor.Further,the liquid metal self-pinch effect is modeled mathematically in three dimensions,and the gas-liquid two-phase dynamic diagrams under different short-circuit currents are obtained by simulation.The simulation results indicate that with the increase of current,the time for the liquid metal-free surface to begin depressing is reduced,and the position of the depression also changes.Different kinds of bubbles formed by the depressions gradually extend,squeeze,and break.With the increase of current,the liquid metal takes less time to break,but breaks still occur at the edge of the channel,forming arc plasma.Finally,relevant experiments are conducted for the novel FCL topology.The arcing process and current transfer process are analyzed in particular.Comparisons of the peak arc voltage,arcing time,current limiting efficiency,and electrode erosion are presented.The results demonstrate that the arc voltage of the novel FCL topology is reduced by more than 4.5times and the arcing time is reduced by more than 12%.The erosions of the liquid metal and electrodes are reduced.Moreover,the current limiting efficiency of the novel FCL topology is improved by 1%–5%.This work lays a foundation for the topology and optimal design of the LMCL.

Investigation on the Arc Ignition Characteristics and Energy Absorption of Liquid Metal Current Limiter Based on Self-Pinch Effect

The GaInSn liquid metal current limiter based on the fluid pinch effect has broad application prospects due to its particular properties. However, the limited rated current and abil- ity of power dissipation are the critical problems for its wide application. Firstly, the temperature distribution of the liquid metal current limiter （LMCL） was obtained by experiments with a rated current of 1 kA and the arc ignition phenomenon was observed with 1.5 kA, which indicates that the rated current is mainly limited by the arc rather than the high temperature compared to the traditional switchgears. Furthermore, an improved method is proposed by adding the paralleled pure resistance, impedance or another LMCL element to protect the setup from the fault energy concentration in the setup. The problem of a slower arc voltage increasing rate can be solved by adding a paralleled impedance with suitable parameters. Finally, the current limiting properties based on the improved method were investigated and the alternating oscillating current was found between two paralleled LMCL elements owing to their deviation of arc ignition in reality.

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory （WENO） schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin （DG） method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.

Plasma Limiter Based on Surface Wave Plasma Excited by Microwave

A novel plasma limiter, in which the plasma is excited by surface wave, is presented. The breakdown time of some gases filled in the limiter were calculated as a function of gas pres- sure, ionization degree and density of seed electrons under low pressure （0.01 -1 Torr） and high pressure （10 -1000 Torr） cases. The results show that the limiter filled with Xe with a pressure of 0.9 Torr, seed electron density of 10^16 m^-3, and ionization degree of 10^-4, has a breakdown time of approximate 19.6 ns.

Evidence of vapor shielding effect on heat flux loaded on flowing liquid lithium limiter in EAST

A lithium(Li)vapour layer was formed around a flowing liquid Li limiter to shield against the plasma incident power and reduce limiter heat flux in the EAST tokamak.The results revealed that after a plasma operation of a few seconds,the layer became clear,which indicated a strong Li emission with a decrease in the limiter surface temperature.This emission resulted in a dense vapour around the limiter,and Li ions moved along the magnetic fleld to form a green shielding layer on the limiter.The plasma heat flux loaded on the limiter,measured by the probe installed on the limiter,was approximately 52%lower than that detected by a fast-reciprocating probe at the same radial position without the limiter in EAST.Additionally,approximately 42%of the parallel heat flux was dissipated directly with the enhanced Li radiation in the discharge with the liquid metal infused trenches(LIMIT)limiter.This observation revealed that the Li vapour layer exhibited an excellent shielding effect to liquid Li on plasma heat flux,which is a possible beneflt of liquid-plasma-facing components in future fusion devices.

Study of the Fast-Closing Switch Used for Fault Current Limiters in Power System

This paper presents a new type of fault current limiter (FCL) based on fast closing switch, which is composed of a capacitor bank and a reactor in series. The main control component is a fast closing switch connected in parallel with the capacitors, which is driven by the electromagnetic repulsion force. It can response the order within 1 ms. When fault occurs, the switch closes and the capacitors are bypassed, and the fault current is limited by the reactor. Simulation analysis and experiment show that the electromagnetic repulsion force actuator can meet the demand of fast closing switch, it is feasible to develop the FCL with low cost and high reliability.

The application of limiter target electrostatic measurement system in J-TEXT tokamak

The limiter target electrostatic measurement system including limiter grounding current sensors and Langmuir probes have been newly developed for the measurement of the limiter target area on the Joint-Texas Experimental tokamak (J-TEXT). Current sensors fixed between graphite limiters and the vacuum vessel walls are used to measure the currents between limiters and vessel wall. Simultaneously, a rectangular poloidal array containing 54 Langmuir probes is embedded in the graphite tiles of limiters for a more localized measurement. Based on this system, the effect of both the plasma’s inherent behavior, including plasma motion and the 2/1 tearing mode, and the electrode biasing on probe and sensor signals have been observed and analyzed in the experiments.

Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.

Numerical Investigation of Heat Deposition Patterns on the Surface of HT-7 Actively Cooled Toroidal Limiter

Two water cooled toroidal limiters were used in HT-7 to exhaust power effectively since the spring campaign of 2004. The heat flux deposition pattern on their surfaces both in steady state and transient state, caused only by plasma displacement, were studied with ANSYS code. The ripple of the toroidal magnetic field was taken into account. The heat flux deposition appeared to be periodic. The ripple and the relative location of the limiter to the toroidal field （TF） coils, as well as the shift of the center of the last closed flux surface （LCFS）, had a vital influence upon the heat flux profile. The location with maximum temperature didn＇t coincide with that for the maximum heat flux in a transient state. The shift of the center of LCFS, caused by plasma displacement, made the heat flux on the limiter more uneven. The heat flux deposition pattern concerning the real shift of the center of LCFS at a transient state calls for further research.

Placement optimization of Multi-Type fault current limiters based on genetic algorithm

The fault current limiter(FCL)is an effective measure for improving system stability and suppressing short-circuit fault current.Because of space and economic costs,the optimum placement of FCLs is vital in industrial applications.In this study,two objectives with the same dimensional measurement unit,namely,the total capital investment cost of FCLs and circuit breaker loss related to short-circuit currents,are considered.The circuit breaker loss model is developed based on the attenuation rule of the circuit breaker service life.The circuit breaker loss is used to quantify the current-limiting effect to avoid the problem of weight selection in a multi-objective problem.The IEEE 10-generator 39-bus system in New England is used to evaluate the performance of the proposed genetic algorithm(GA)method.Comparative and sensitivity analyses are performed.The results of the optimized plan are validated through simulations,indicating the significant potential of the GA for such optimization.

Suppression of runaway current by electrode biasing and limiter biasing on J-TEXT

The avoidance of runaway electrons(REs) generated during plasma disruption is of great concern for the safe operation of tokamak devices.Experimental study on the suppression of runaway current by electrode biasing(EB) and limiter biasing(LB) has been performed on the J-TEXT tokamak,which could be an alternative way to suppress the runaway current.The experimental results show that the higher the voltage value,the smaller the runaway current in both EB and LB experiments.The runaway current can be completely suppressed at an electrode biased voltage of +450 V and a limiter biased voltage of +300 V.The comparison of the energy spectra during the runaway plateau phase shows that the maximum energy max(E_(RE)) and radiation temperature T_(HXR)hard x-rays(HXRs)are significantly reduced after the application of +200 V limiter biased voltage.The electric field generated by the biased voltage may be the key factor to suppress the runaway current,and the measured radial electric field increases obviously after the voltage is applied.This may result in an increase in the loss of REs to realize the suppression of runaway current.

Magnetic configuration effects on the edge heat flux in the limiter plasma on W7-X measured using the infrared camera and the combined probe

Controlling the heat and particle fluxes in the plasma edge and on the plasma facing components is important for the safe and effective operation of every magnetically confined fusion device.This was attempted on Wendelstein 7-X in the first operational campaign,with the modification of the magnetic configuration by use of the trim coils and tuning the field coil currents,commonly named iota scan.Ideally,the heat loads on the five limiters are equal.However,they differ between each limiter and are non-uniform,due to the（relatively small） error fields caused by the misalignment of components.It is therefore necessary to study the influence of the configuration changes on the transport of heat and particles in the plasma edge caused by the application of error fields and the change of the magnetic configuration.In this paper the upstream measurements conducted with the combined probe are compared to the downstream measurements with the DIAS infrared camera on the limiter.

Modelling of carbon erosion and re-deposition for the EAST movable limiter

e movable limiter at the mid-plane of the Experimental Advanced Superconducting Tokamak （EAST） with carbon coatings on the surface was exposed to edge plasma to study the material erosion and re-deposition.After the experiments,the carbon erosion and re-deposition is modelled using the 3D Monte Carlo code ERO.The geometry of the movable limiter,3D configuration of the plasma parameters and electromagnetic fields under both limiter and divertor configurations have been implemented into the code.In the simulations,the main uncertain parameters such as carbon concentration ρc in the background plasma and cross-field transport coefficient D⊥ in the vicinity of surface according to the ‘funneling model＇,have been studied in comparison with experiments.The parameter ρc mainly influences the net erosion and deposition profiles of the two sides of the movable limiter,while D ⊥ mostly changes the profiles on the top surface.

Simulation Study of Heat Flux Deposition Pattern on the Surface of HT-7 Toroidal Limiters

The heat flux deposition pattern on the toroidal limiters installed in HT-7 was simulated with ANSYS code. The simulation model was established with the ripple of the magnetic field. The heat deposition pattern and temperature distribution on the surface of the toroidal linfiters were obtained. A comparison of the results obtained with and without the shaped tiles, used to reduce the heat flux on the leading edge of the limiters, was made. The maximum heat load allowed at the leading edge was about 1.8 MW/m2 because of the poor power removing capacity on the ends of the limiters. This approach can also be applied to other devices with a limiter configuration in a circular cross-section shape.

NUMERICAL ANALYSIS AND CONSTRUCTION OF LIMITER OF HIGH RESOLUTION DIFFERENCE SCHEME

In the paper, based on the theory of the remainder effects of difference schemes, some typical limiters are analysed and compared. For different limiters, the different strength of numerical dissipation and dispersion of schemes is the reason why the schemes show obvious different characteristics. After analysing and comparing the numerical dissipation and dispersion of various schemes, a new kind of limiter is proposed. The new scheme has high resolution in sharp discontinuities, and avoids the 'distortion' due to the stronger numerical dispersion in the relatively more smooth region. Numerical experiments show that the scheme has good properties.

Research on a Fast-Closing Switch Based Fault Current Limiter with Series Compensation

A new type of fault current limiter (FCL) with series compensation based fast-closing switch is proposed. It is composed of a capacitor bank and a reactor in series. The main control component is a fast-closing switch connected in parallel with the capacitors, which is driven by the electromagnetic repulsion force. When fault occurs, the switch closes and bypasses the capacitors, and the fault is limited by the reactor then. Simulated analysis and experiments show that it is feasible to develop the FCL with low cost and high reliability. The effectiveness of transient stability for power system is evaluated by digital simulation.

Effect of New Suggested Ferroresonance Limiter on the Stability Domain of Chaotic Ferroresonance in the Power Transformer with Linear Core Model

This Paper studies the effect of new suggested ferroresonance limiter on controlling ferroresonance oscillations in the power transformer. It is expected that this limiter generally can control the ferroresonance. For studying these phenomena, at first ferroresonance is introduced and a general modeling approach is given. A simple case of ferroresonance in a three phase transformer is used to illustrate these phenomena. Then, effect of new suggested ferroresonance limiter on the onset of chaotic ferroresonance and control of these oscillations in a power transformer including linear core losses is studied. Simulation is done on a three phase power transformer while one of its phases is opened, and effect of varying input voltage on occurring ferroresonance overvoltage is studied. Results show that connecting the ferroresonance limiter to the transformer exhibits a great controlling effect on the ferroresonance overvoltage. Phase plane diagram, FFT analysis along with bifurcation diagrams are also presented. Significant effect on occurring chaotic ferroresonance, the range of parameter values that may lead to overvoltage and magnitude of ferroresonance overvoltage is obtained, showed and tabulated.