Monte Carlo simulations of nanometric devices beyond the “mean-field” approximation

For nanoscale electron devices, the role of a single-electron (or a single-impurity) can have a large impact on their electrical characteristics. A new method for introducing the long-range and short-range Coulomb interaction in semiconductor semi-classical Monte Carlo simulations is presented. The method is based on directly dealing with a many-particle system by solving a different Poisson equation for each electron. The present work shows the numerical viability of this alternative approach for nanoscale devices with few (<100) electrons. The method is compared with the traditional “mean-field” Monte Carlo simulations. It is shown, numerically, that the “mean-field” approximation produces important errors for aggressively-scaled devices.     

An efficient numerical approach to studying impact ionization in sub-micrometer devices

A positive feedback model is introduced to facilitate numerical calculations of the impact-ionization current gain in sub-micrometer devices. Demonstrations of this model’s applicability are done through Monte Carlo simulations to fit the experimental data of short p-i-n diodes. It is shown from the simulations’ results that the phonon-collision broadening effect and the intra-collisional field effect play an important role in the II process in deep sub-micrometer devices. It is also shown, for the first time, that the impact-ionization rates at very low energies can be extracted from the measured current gain in short p-i-n diodes.     

Variable order and variable step-size integration method fortransient analysis programs

A variable-order and variable-step-size integration method using the backward differentiation formulas (VOVS-BDF) is introduced to optimize numerical integration orders and step sizes for power transient analysis. The basic concept and the numerical stability of the VOVS-BDF are discussed and shown for efficient computer-aided power transient analysis. A new searching method for break points is proposed to adjust the step-sizes. The VOVS-BDF is validated through analysis examples of an instantaneously controlled inverter circuit and a single-conductor line system. The procedures for the necessary program changes are also described     

Distributed fusion white noise deconvolution estimators

The white noise deconvolution or input white noise estimation problem has important applications in oil seismic exploration, communication and signal processing. By combining the Kalman filtering method with the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, new distributed fusion white noise deconvolution estimators are presented by weighting local input white noise estimators for general multisensor systems with different local dynamic models and correlated noises. The new estimators can handle input white noise fused filtering, prediction and smoothing problems, and are applicable to systems with colored measurement noise. Their accuracy is higher than that of local white noise deconvolution estimators. To compute the optimal weights, the new formula for local estimation error cross-covariances is given. A Monte Carlo simulation for the system with Bernoulli-Gaussian input white noise shows their effectiveness and performance.     

系统状态空间分割法在电力系统可靠性评估中的应用

目前电力系统可靠性评估方法无法避免对无故障状态子空间的抽样,为此提出了系统状态空间分割法。该方法将系统状态空间分割为无故障状态子空间和各阶故障状态子空间,并根据各阶故障状态子空间特点分别采用解析法和蒙特卡洛法进行分析。该方法不需要对无故障状态子空间抽样,并可对各故障状态子空间的抽样次数进行最优分配。同时提出了仅需要少量...     

基于自适应蒙特卡洛法的磁场辐射发射测量不确定度评定

针对测量不确定度评定中测量不确定度表示指南法（GUM）不适用于输入输出变量关系非线性或输出变量非正态分布的情况,提出采用自适应蒙特卡洛法（AMCM）评定25 Hz～100 kHz磁场辐射发射（RE101）测试的测量不确定度。首先阐述蒙特卡洛法（MCM）和AMCM评定测量不确定度的计算步骤,其次分别用AMCM和GUM法评定RE101测量不确定度,在相同的包含概率下比较两种方法的覆盖区间差值与数值允差,表明AMCM的评定结果可靠性更高,适用于RE101测量不确定度评定。AMCM可以推广到其他电磁兼容测试项目的不确定度评定中,将有效提高不确定度评定的可靠性。     

基于逆向蒙特卡罗法的煤粉炉内辐射能传递计算

针对求解煤粉炉内辐射能传递方程时遇到的大辐射源小接收体现象所带来的时间复杂度问题，提出使用三维逆向蒙特卡罗法来提高求解精度和收敛速度。通过从炉内混合介质到辐射能传感器的辐射投影强度的逆向模拟计算，求解了炉内介质的辐射特性参数，并分析了炉内介质辐射特性的变化与辐射能之间的对应关系，计算结果表明该方法能够节省计算时间并提高计算精度。辐射能传递计算的结果给出了300MW煤粉炉内辐射能信号光谱分布曲线，并显示了炉内辐射能随介质物理特性的变化关系曲线，为基于辐射能信号的锅炉燃烧诊断研究提供了理论依据。     

A linear response Monte Carlo algorithm for inversion layers and magnetotransport

Certain simulation problems require the solution of the Boltzmann equation for small driving forces. Due to the bad signal to noise ratio of the standard Monte Carlo algorithm in the linear regime these simulations are extremely CPU intensive. A linear response Monte Carlo algorithm is proposed which is orders of magnitude faster than the standard approach. It is used to extract transport parameters from magnetotransport measurements and to match semiempirical inversion layer models to experimental data.     

一种基于OpenMP和MPI的非序贯蒙塔卡罗暂态稳定评估的动态混合并行化方法

为了提高暂态稳定性分析中非序贯蒙塔卡罗串行算法的计算效率,提出并实现了一种基于OpenMP和MPI的风险评估混合动态并行算法。利用动态规划规则将蒙塔卡罗抽样样本点以MPI方法分配给计算机集群上的多个PC进程,再在各进程内采用多线程的并行计算模式对系统故障的分析处理的循环部分进行OpenMP并行分解。大量实验模型的测试和数据分析表明,在保证准确度的前提下,算法取得了理想的并行效率,普通集群最高达到了3.28倍的加速比,混合集群最高达到了5.06倍的加速比。     

水源地地下水综合补给量频率分析的方法

如何解决水源地地下水综合补给量的频率分析计算问题 ,采用解析法、数值法、物理实验以及经验频率都存在着各种困难 ,运用蒙特卡罗方法会使此类问题迎刃而解。蒙特卡罗方法是用数学的方式在属性概率模型控制下 ,产生足够多的伪随机变量 ,构成大容量样本 ,形成分布来求解的。经过理论和实践说明蒙特卡罗方法能在水资源量评价中发挥重要的作用。     

多谐波源同次谐波叠加计算方法

在相角未知条件下,国家标准中采用系数估算的方法进行谐波叠加计算,效果往往并不理想。在谐波叠加理论分析的基础上,文中构造了基于核密度估计与重要抽样的蒙特卡洛方法,用以计算多谐波源的同次谐波叠加电流。首先,运用核密度估计法可以计算谐波电流相角的概率密度函数,且通过重要抽样方法可对其进行抽样并得到核样本数据。再利用蒙特卡洛方法结合核样本数据对谐波叠加的交叉项进行估算,最终确定出谐波叠加电流的计算公式。仿真分析与实际算例表明,所提算法可获得更为精确的谐波叠加电流估计量,并可以简单高效地应用于多谐波源系统的谐波叠加中。     

大型电力系统可靠性评估中的马尔可夫链蒙特卡洛方法

提出大型电力系统可靠性评估的一种新的蒙特卡洛模拟方法-马尔可夫链蒙特卡洛方法(Markov chain Monte Carlo, MCMC)。MCMC方法是一种特殊的蒙特卡洛方法,它将随机过程中的马尔可夫过程引入到蒙特卡洛模拟中,实现动态蒙特卡洛模拟。该方法通过重复抽样,建立一个平稳分布与系统概率分布相同的马尔可夫链,从而得到系统的状态样本。由于MCMC方法考虑了系统各个状态间的相互影响,相比于随机采样的蒙特卡洛方法所得到的独立样本序列,更准确模拟了电力系统运行实际情况。IEEE-RTS 24节点算例表明,该算法可快速收敛,节省计算时间,提高计算速度。同时,由于每条马尔可夫链均收敛于同一个分布,即所谓平稳分布,所以算法具有良好的稳定性。对西北330 kV电网的可靠性评估再次表明了该方法的正确性和有效性以及该方法用于大型电力系统的可靠性评估的优越性和潜力。     

可靠性评估中随机模拟的精度控制

采用Monte Carlo模拟法，在提出了随机模拟系统状态及其转移过程的概率方法的基础上， 首次实现了对结果精度的定量控制。实例计算结果表明预测结果能满足精度要求，证明了将 该方法应用于电力系统可靠性的评估是切实可行的。     

相关性条件下合成不确定度的MC方法

本文研究了在相关性条件下测量不确定度合成的蒙特卡罗方法,讨论了相关系数对计算结果的影响,给出了改进的MC算法,并以实例验证了该算法能够提高蒙特卡罗方法合成不确定度的计算精度.     

Monte Carlo computation of power generation production costs underoperating constraints

This paper highlights the need for considering the stochastic processes associated with the frequency and duration of generating unit outages for assessing the mean and variance of production costs under operating constraints. A numerical example based on a Markov model is given to show that Monte Carlo estimates of these quantities may be incorrect if only the forced outage rates are used in place of the stochastic parameters underlying the outage frequency and duration. Additionally it describes a variance reduction procedure whereby the Monte Carlo estimates can be obtained with a much smaller sample size than would be required otherwise. A numerical example is given for a small system     

Monte Carlo methods in an introductory electromagnetic course

Although the pedagogical value of introducing numerical methods such as finite-element methods, finite-difference methods, and moment methods in an introductory electromagnetics (EM) course has been recognized, no similar attempt has been made to introduce Monte Carlo methods. An attempt is made to fill this gap by presenting Monte Carlo procedures in simple terms that can be presented in an introductory EM course. The statistical method is specifically applied to potential problems. Typical illustrative examples are provided     

Two-point estimate method for quantifying transfer capability uncertainty

A two-point estimate method is proposed in this paper to assess the power transfer capability uncertainty. This paper assumes that the uncertainty of the line parameters and bus injections involved in transfer capability calculations can be estimated or measured and shows how to estimate the corresponding uncertainty in the transfer capability. Instead of using a large number of simulations as required in the Monte Carlo approach, for a system with n uncertain parameters, the two-point estimate method uses 2n calculations of transfer capability to quantify the uncertainty. The proposed method uses a numerical method to calculate the moments of the transfer capability. The moments are then used in the probability distribution fitting. Using the obtained transfer capability uncertainty information and a desired level of reliability, an adequate transmission reliability margin can be determined for each transmission service. The proposed method can be used directly with a deterministic computer program and it does not require derivatives of the transfer capability. Test results of the proposed method are compared with those obtained from the Monte Carlo simulations and a truncated Taylor series expansion method.     

Wigner Function-Based Simulation of Quantum Transport in Scaled DG-MOSFETs Using a Monte Carlo Method

Source-to-drain tunneling in deca-nanometer double-gate MOSFETs is studied using a Monte Carlo solver for the Wigner transport equation. This approach allows the effect of scattering to be included. The subband structure is calculated by means of post-processing results from the device simulator Minimos-NT, and the contribution of the lowest subband is determined by the quantum transport simulation. By separating the potential profile into a smooth classical component and a rapidly varying quantum component the numerical stability of the Monte Carlo method is improved. The results clearly show an increasing tunneling component of the drain current with decreasing gate length. For longer gate lengths the semi-classical result is approached.     

A Monte Carlo Method Seamlessly Linking Quantum and Classical Transport Calculations

A Monte Carlo method for carrier transport is presented, which simultaneously takes into account quantum interference and dissipation effects. The method solves the space-dependent Wigner equation including semi-classical scattering through the Boltzmann collision operator. To this equation a particle model is assigned, which interprets the non-local potential operator as a generation term for numerical particles of positive and negative statistical weight. A numerical technique to control the avalanche of numerical particles is discussed. Since the Wigner equation simplifies to the Boltzmann equation in classical device regions, the solutions of the quantum kinetic equation and the classical one are linked in a natural way. This approach allows the simulation of a quantum region embedded in an extended classical region. Results of this approach are demonstrated for a resonant tunneling diode.     

异步电机不对称运行时电容值的确定

借助网络图论，用回路电流法列写了便于计算机辅助分析计算的网络方程，计算了单相电源供电的三相异步电机稳态运行时的各支路电流。基于支路电流，推导了对应于正序与逆序旋转磁场的正序与逆序等效电流。以逆序电流有效值与正序电流有效值之比作为不对称运行异步电机运行状态的判据，该判据最小为优化的目标函数，运行电容值为一维变量，用黄金分割法求出某一转差率下的理想运行电容值。算例的计算结果表明，在运行范围内理想电容值变化不大，这为选择一合理的固定运行电容值提供了理论依据。