Research on AC Electronic Load with Energy Recovery Based on Finite Control Set Model Predictive Control

Nowadays,AC electronic loads with energy recovery are widely used in the testing of uninterruptible power supplies and power supply equipment.To tackle the problems of control difficulty,strategy complexity,and poor dynamic performance of AC electronic load with energy recovery of the conventional control strategy,a control strategy of AC electronic load with energy recovery based on Finite Control Set Model Predictive Control(FCSMPC)is developed.To further reduce the computation burden of the FCS-MPC,a simplified FCS-MPC with transforming the predicted variables and using sector to select expected state is proposed.Through simplified model and equivalent approximation analysis,the transfer function of the system is obtained,and the stability and robustness of the system are analyzed.The performance of the simplified FCS-MPC is compared with space vector control(SVPWM)and conventional FCS-MPC.The results show that the FCS-MPC method performs better dynamic response and this advantage is more obvious when simulating high power loads.The simplified FCS-MPC shows similar control performance to conventional FCS-MPC at less computation burden.The control performance of the system also shows better simulation results.

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

FINITE TIME BLOW UP OF THE SOLUTIONS TO BOUSSINESQ EQUATION WITH LINEAR RESTORING FORCE AND ARBITRARY POSITIVE ENERGY

Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Mechanistic insights into homogeneous electrocatalytic reaction for energy storage using finite element simulation

The application of homogeneous electrocatalytic reactions in energy storage and conversion has driven surging interests of researchers in exploring the reaction mechanisms of molecular catalysts.In this paper,homogeneous electrocatalytic reaction between hydroxymethylferrocene(HMF)and L-cysteine is intensively investigated by cyclic voltammetry and square wave voltammetry for which,the secondorder rate constant(k_(ec))of the chemical reaction between HMF^(+)and L-cysteine is determined via a 1D homogeneous electrocatalytic reaction model based on finite element simulation.The corresponding k_(ec)(1.1(mol·m^(-3))^(-1)·s^(-1))is further verified by linear sweep voltammograms under the same model.Square wave voltammetry parameters including potential frequency(f),increment(Estep)and amplitude(ESW)have been comprehensively investigated in terms of the voltammetric waveform transition of homogeneous electrocatalytic reaction.Specifically,the effect of potential frequency and increment is in accordance with the potential scan rate in cyclic voltammetry and the increase of pulsed potential amplitude results in a conspicuous split oxidative peaks phenomenon.Moreover,the proposed methodology of k_(ec)prediction is examined by hydroxyethylferrocene(HEF)and L-cysteine.The present work facilitates the understanding of homogeneous electrocatalytic reaction for energy storage purpose,especially in terms of electrochemical kinetics extraction and flow battery design.

The Continuum Stored Energy for Constitutive Modeling Finite Deformations of Polymeric Materials

With symmetries measured by the Lie group and curvatures revealed by differential geometry, the continuum stored energy function possesses a translational deformation component, a rotational deformation component, and an ellipsoidal volumetric deformation component. The function, originally developed for elastomeric polymers, has been extended to model brittle and ductile polymers. The function fits uniaxial tension testing data for brittle, ductile, and elastomeric polymers, and elucidates deformation mechanisms. A clear distinction in damage modes between brittle and ductile deformations has been captured. The von Mises equivalent stress has been evaluated by the function and the newly discovered break-even stretch. Common practices of constitutive modeling, relevant features of existing models and testing methods, and a new perspective on the finite elasticity-plasticity theory have also been offered.

Exciting Forces for a Wave Energy Device Consisting of a Pair of Coaxial Cylinders in Water of Finite Depth

二同轴的垂直柱体一个是骑空柱体和其它在在一个透不过的水平底部上面的某距离的更大的半径的稳固的柱体，被考虑。由这二柱体的衍射的这个问题，被看作一个浮标和一个圆形的盘子的理想化，能被看作一台波浪精力设备。被这台设备创造并且转的波浪能量能适当地代替常规能量在许多应用被使用。变量的分离的方法被用来在四个清楚地识别的区域为使衍射的潜力获得分析表情。由沿着在这些区域之间的三条虚拟边界使用适当匹配条件，线性方程的一个系统被获得，它为未知系数被解决。潜力允许我们获得对两柱体起作用的令人激动的力量。令人激动的力量的集合为柱体的不同半径并且为在柱体之间的不同差距被获得。在半径和差距的变化在力量上有重要效果，这被观察。它主要被发现那令人激动的力量在更低的频率仅仅是重要的。令人激动的力量几乎消失在更高的频率。这个问题也为没有板安排的基础案例被调查，即，有仅仅漂浮的柱体的案例拴住到海床。为两安排的力量的比较被执行。以便由于巨浪运动，相应的增加的团和抑制系数照顾柱体的放射因为两柱体也被计算。所有结果图形地并且与可得到的结果相比被描绘。

Finite Element Analysis on a Square Canister Piezoelectric Energy Harvester in Asphalt Pavement

A novel square canister piezoelectric energy harvester was proposed for harvesting energy from asphalt pavement. The square of the harvester was of great advantage to compose the harvester array for harvesting energy from the asphalt pavement in a large scale. The open circuit voltage of the harvester was obtained by the piezoelectric constant d33 of the piezoelectric ceramic. The harvester is different from the cymbal harvester which works by the piezoelectric constant d31. The finite element model of the single harvester was constructed. The open circuit voltage increased with increase of the outer load. The finite element model of the single harvester buried in the asphalt pavement was built. The open circuit voltage, the deformation difference percent and the stress of the ceramic of the harvester were obtained with different buried depth. The open circuit voltage decreased when the buried depth was increased. The proper buried depth of the harvester should be selected as 30 - 50 mm. The effects of structure parameters on the open circuit voltage were gotten. The output voltage about 64.442 V could be obtained from a single harvester buried under 40 mm pavement at the vehicle load of 0.7 MPa. 0.047 mJ electric energy could be gotten in the harvester. The output power was about 0.705 mW at 15 Hz vehicle load frequency.

Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation

In this paper,two fourth-order compact finite difference schemes are derived to solve the nonlinear fourth-order wave equation which can be viewed as a generalized model from the nonlinear beam equation.Differing from the existing compact finite difference schemes which preserve the total energy in a recursive sense,the new schemes are proved to per-fectly preserve the total energy in the discrete sense.By using the standard energy method and the cut-off function technique,the optimal error estimates of the numerical solutions are established,and the convergence rates are of O(h^(4)+τ^(2))with mesh-size h and time-step τ.In order to improve the computational efficiency,an iterative algorithm is proposed as the outer solver and the double sweep method for pentadiagonal linear algebraic equations is introduced as the inner solver to solve the nonlinear difference schemes at each time step.The convergence of the iterative algorithm is also rigorously analyzed.Several numerical results are carried out to test the error estimates and conservative properties.

Numerical Verification of Transition’s Energies of Excitons in Quantum Well of ZnO with the Finite Difference Method

This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated using the finite difference method. In that way, the one-dimensional Schrödinger equation has been solved by using the BLAS and LAPACK libraries. The numerical results are in good agreement with the experimental ones.

Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system

The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge- Kutta （RK） method is an important part of the former, and the continuous finite element method （CFEM） belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms --the regular method. Finally, numerical experiments are given to verify the theoretical results.

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

VARIATIONAL PRINCIPLES OF ASYMMETRIC ELASTICITY THEORY OF FINITE DEFORMATION

In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation energy is derived and the physical meaning is clarified. The power variational principle and the complementary power variational principle for finite deformation mechanics are supplemented and perfected.

Finite element analysis of stress and strain distributions in InAs/GaAs quantum dots

In this paper, we perform systematic calculations of the stress and strain distributions in InAs/GaAs truncated pyramidal quantum dots （QDs） with different wetting layer （WL） thickness, using the finite element method （FEM）. The stresses and strains are concentrated at the boundaries of the WL and QDs, are reduced gradually from the boundaries to the interior, and tend to a uniform state for the positions away from the boundaries. The maximal strain energy density occurs at the vicinity of the interface between the WL and the substrate. The stresses, strains and released strain energy are reduced gradually with increasing WL thickness. The above results show that a critical WL thickness may exist, and the stress and strain distributions can make the growth of QDs a growth of strained three-dimensional island when the WL thickness is above the critical value, and FEM can be applied to investigate such nanosystems, QDs, and the relevant results are supported by the experiments.

Finite Element Formulation and Analysis of Fracture Resistance Effected by Near-Tip Nonlinearities in Piezoelectric Solids

Comsidering the fact there are no systematic study on crack effected by large-scale near--tip nonlinearitiesup to now, a nonlinear finite element formulation accounting for nonlinearities and elasticity coupled with piezoelectricity is derived and a finite element program is developed. Numerical examples are presented to show the effect of nonlinear fracture characteristics on fracture resistance. It is found that an electric field may give a negative driving forceto prevent crack propagation.

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.

A NEW HIGH-ORDER MULTI-JOINT FINITE ELEMENTFOR THIN-WALLED BAR

A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.

NONLINEAR QUASI-CONFORMING FINITE ELEMENT METHOD

The nonlinear quasi-conforming FEM is presented based on the basic concept of the quasi- -conforming finite element. First, the incremental principle of stationary potential energy is discussed, Then, the formulation process of the nonlinear quasi-conforming FEM is given. Lastly, two computational examples of shells are given.