Fourier approach to semiconductor device modelling

A novel procedure for the numerical modelling of current transport in semiconductor devices is presented. The method is based on high-order trigonometric expansions (Fourier series) of the solution. The expansion coefficients are calculated in a Galerkin-type algorithm. The method offers infinite-order accuracy regardless of the number of spatial dimensions of the model. Well-conditioning and diagonal dominance of the discrete equations render the numerical procedure stable and effective. Significant advantages are expected, particularly for the solution of strongly non-linear multidimensional device models. Properties of the algorithm are demonstrated on standard semiconductor devices.     

非线性系统的线性化

由于非线性系统线性化时采用泰勒展开式可能会得出错误的结果,指出了系统的线性化应该是在方程式推导过程中同时进行.对磁悬浮系统,在拉格朗日方程建立过程中求取相应的偏导数从而得出系统的线性化方程.给出了用Simulink的非线性系统仿真方法,并用非线性系统在小偏差下的仿真结果与线性化系统的结果进行对比.结果表明,这样的求取过程物理概念清楚、简单,有助于正确列写系统的方程式.     

基于光滑非线性互补函数的电力市场动态研究

为了模拟电力市场中发电商的有限理性博弈行为,提出了考虑输电网约束的有限理性古诺博弈动态模型,即内嵌社会效益最大化问题的差分动态模型。借助数学理论中的非线性互补方法,利用光滑的非线性互补函数将这一数学结构复杂的模型转换为常见的差分?代数方程,从而为进一步开展有限理性古诺博弈动态演化的定量分析奠定了基础。最后针对3寡头古诺博弈进行数值仿真,计算得出不同市场参数下的市场动态行为,并着重探讨了当市场参数超出均衡点稳定域时出现了周期甚至混沌的动态行为。     

非线性控制理论在电力系统中应用综述

综述了非线性控制方法在电力系统中的应用。分别对基于微分几何理论的反馈线性化方法（包括输入对状态反馈线性化和输入输出反馈线性化方法）、直接反馈线性化方法、非线性变结构控制和基于Lyapunov综合方法等几种主要方法在电力系统非线性控制中的应用加以讨论。最后指出了仍然存在的技术难题,展望了有价值的研究方向。     

双轴励磁同步发电机的微分反馈非线性最优励磁控制

本文在微分几何理论的基础上，提出了更简明、更适合工程用的面向多输入系统的微分反馈补偿物理精确线性化方法，解决了电力系统控制设计中的强非线性问题及鲁棒性问题，并据此推导了双轴励磁同步发电机的微分反馈非线性最优励磁控制规律。仿真结果表明，所设计的控制方式能较大幅度地提高系统的动态稳定性和暂态稳定性。     

汽轮机组的数学机械化建模与算法分析

对于大型汽轮发电机组,描述系统运行状态的微分方程相对复杂且维数很高,为对其进行解析分析,首先应用模态综合法建模得到降阶后的微分方程组,经代数变换后应用数学机械化方法进行解析建模分析。由于参加消元的节点位移变量均是线性变量,故消元时可保留油膜力表达式的非线性成分不变,这样就得到了维数相对较低且等式右端含有非线性油膜力表达式的代数方程组。为实现具有上述特点的代数方程组的求解,提出了既不同于解析法又与经典数值算法不完全相同的微分控制算法思想,据此实现对复杂汽轮发电机组转子系统的建模及对节点位移响应的分析与预测。     

混合交直流电力系统的非线性调制策略

针对大扰动情形，文中提出了一种用于改善多机交直流混合电力系统（有多条直流线路落点于其中）暂态稳定性的非线性控制方法，该方法基于微分几何理论，地直流输电系统等效为两个分别连接在整流侧和逆变侧的变导纳支路，在推导出直流输电系统的等效变导纳与各发电机输出电磁功率间的解析关系后，传统的发电机动态方程可被表示成仿射非线性的形式，因而可应用全局线性化方法来求得其控制变量，本文方法的主要特点在于，所求得的调制功率是一个交流系统状态的自适应和非线性函数，它可通过局部的反馈信号和少量来自其它发电机的信号来实现，文中以一个双馈入直流输电系统为测试对象，给出了所提控制器的设计过程和基于测试系统的仿真结果。     

Boost变换器精确反馈线性化滑模变结构控制

利用非线性系统的微分几何理论,在Boost变换器仿射非线性模型基础上,推导出对应的非线性坐标变换矩阵和状态反馈表达式,得到Boost变换器状态反馈精确线性化模型。在此线性化模型基础上,选取线性切换函数和指数趋近律,设计滑模变结构控制器。研究对比表明,所提出的精确反馈线性化滑模变结构控制策略具有良好的动态响应调节和稳态误差调节特性,同时克服了现有精确反馈线性化控制策略固有的对精确数学模型依赖性的缺点,表现出更强的鲁棒性,从而具有一般性理论和实际意义。     

A space-domain preconditioned spectral method for non-linear boundary value problems

A novel spectral procedure for the numerical solution of non-linear boundary value problems is presented. The discrete spectral equations are solved by an iterative algorithm using space-domain preconditioning. The preconditioning operator is obtained by spatial weighting (or windowing) of the exact differential operator. Convergence behaviour of the iterative solution is investigated using an eigenvalue analysis. Theoretical estimates for the convergence rate and accuracy are compared with that achieved in a numerical application—a non-linear boundary value problem from semiconductor device modelling. The method combines the infinite-order exponential accuracy of spectral discretizations with the sparse structure of finite difference equations. This offers numerical advantages in comparison to previously developed Fourier–Galerkin algorithms, particularly important for physically ill-conditioned and strongly non-linear problems. The tradeoff of achievable accuracy versus computer time is easily controlled, thus making essential speed-ups possible for moderate accuracy requirements.     

直流变换器并联系统动态均流的非线性控制

基于微分几何理论，该文针对并联直流变换器提出了一种新颖的非线性动态均流控制策略。文章首先利用开关脉冲分段函数建立了两相交错并联变换器两输入两输出仿射非线性模型，推导出对应的非线性坐标变换矩阵和非线性状态反馈规律表达式，得到状态反馈精确线性化模型。接着文章利用二次型最优控制对线性化模型进行动态均流控制设计，得到精确线性化的状态反馈规律，建立了一种基于微分几何理论的非线性均流控制策略。研究表明，两相并联直流变换器通过状态反馈精确线性化得到的非线性均流控制策略，比现有PID均流控制有更好的动态均流特性，同时具有较好的动态和稳态品质。     

CCM Buck变换器的状态反馈精确线性化的非线性解耦控制研究

基于非线性系统的微分几何理论，应用脉冲模型积分法建立CCM(电流连续型)Buck变换器的非线性仿射模型，推导出对应的非线性坐标变换矩阵和非线性状态反馈表达式，得到了Buck变换器状态反馈精确线性化模型，由此提出了电感电流和输出电容电压解耦控制策略。研究结果表明，Buck变换器通过状态反馈实现精确线性化得到的非线性控制策略，比现有的PI控制有更好的动态响应调节和稳态误差调节特性。同时说明状态反馈精确线性化能对Buck变换器这类分段线性系统实现完全解耦控制，从而具有一般性理论和实际意义。     

计算机代数在电力系统非线性控制中应用

阐述了精确线性化的原理,讨论了非线性系统状态反馈精确线性化的计算机代数设计方法,采用Matlab完成了相应软件包的开发,并使用该软件包对电力系统中汽轮发电机组汽门开度的非线性控制实例进行了仿真研究。仿真结果表明,引入了设计得到的非线性控制量后,电力系统的稳定性得到了有效提高。     

基于输入对状态反馈线性化的非线性励磁控制

将输入对状态反馈线性化的思想应用于发电机励磁控制系统,得出了一套实用的发电机非线性励磁控制规律,应用此方法和采用状态反馈精确线性化的方法推导出的非线性控制规律具有一致性,且比基于微分几何理论的状态反馈精确线性化方法更加简单实用。仿真证明该文提出的非线性励磁控制器在系统发生大扰动时比常规的AVR+PSS更能抑制系统的振荡,对增强系统稳定性具有一定作用。     

Model order reduction of coupled circuit‐device systems

We consider model order reduction of integrated circuits with semiconductor devices. Such circuits are modeled using modified nodal analysis by differential‐algebraic equations coupled with the nonlinear drift‐diffusion equations. A spatial discretization of these equations with a mixed finite element method yields a high dimensional nonlinear system of differential‐algebraic equations. Balancing‐related model reduction is used to reduce the dimension of the decoupled linear network equations, whereas the semidiscretized semiconductor model is reduced using proper orthogonal decomposition. Because the computational complexity of the reduced‐order model through the nonlinearity of the drift‐diffusion equations still depends on the number of variables of the full model, we apply the discrete empirical interpolation method to further reduce the computational complexity. We provide numerical comparisons that demonstrate the performance of the presented model reduction approach. Copyright © 2012 John Wiley & Sons, Ltd.     

A frequency‐domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential‐algebraic equations

A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential‐algebraic form. The method is based on the harmonic balance (HB) technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the HB equations for the determination of the periodic steady state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to the study of the dynamics of the limit cycle of a Colpitts oscillator. Copyright © 2007 John Wiley & Sons, Ltd.     

磁集成电压调整模块中磁路耦合的反馈精确线性化解耦控制

试图利用微分几何理论实现磁集成电压调整模块非线性解耦控制.首先分析集成磁心磁路的耦合关系和等效磁路,由此建立了磁集成电压调整模块两输入两输出仿射非线性模型,并基于微分几何理论推导出对应的非线性坐标变换矩阵和非线性反馈规律表达式,得到变换器的状态反馈精确线性化模型.实验表明,磁集成电压调整模块非线性控制策略克服了磁集成中磁路耦合的影响,比现有非解耦PI控制有更好的动态品质和稳态特性,同时容易实现各相电流均流控制和磁路集成的控制解耦.     

计算非线性时变涡流场的有限元方程频域算洁

本文提出了一种计算时变非线性涡流场的有限元方程频域算法，该方法在时域内确定非线性单元各时刻的磁阻率，利用离散付立叶变换在频域内求解有限元方程，并用直接解法与逐次松驰因子迭代法相结合的方法处理频域方程组的非线性问题。文中还用一算例验证了本法的有效性。     

含STATCOM装置的凸极式发电机励磁稳定控制设计

针对单机无穷大系统,采用凸极式发电机(xd′≠xq)模型,建立了包含静态同步补偿器(STATCOM)的系统方程,并利用微分几何线性化方法,实现了凸极式发电机励磁与STATCOM的协调控制,克服了以往的STATCOM模型需要假设STATCOM输出电压矢量在d轴的强约束条件。该设计方法进一步推广了微分几何线性化理论和控制器的应用范围,并提高了STATCOM与励磁协调控制的实用性。仿真结果表明文中所提出的模型和协调控制方法的合理性和有效性。     

A fast numerical algorithm for transient stability studies of power systems

A fast numerical solution of a technique for improving the speed of the transient stability solution of power systems is presented in this paper. The system is described by a set of first-order differential equations which consist of both linear and nonlinear parts. The linear set of equations is considered separately and is solved by modal analysis using closed-form solutions. The nonlinear part of the equations is solved by a numerical method. As explicit solutions are available for the linear part of the equations, the solution time is considerably reduced. The proposed technique is employed for computing the transient stability of a sample power system represented in detail. A comparison is made with a conventional solution procedure.     

On some optimal control problems for electrical circuits

Some optimal control problems for linear and nonlinear ordinary differential equations related to the optimal switching between different magnetic fields are considered. The main aim is to move an electrical initial current by a controllable voltage in shortest time to a desired terminal current and to hold it afterwards. Necessary optimality conditions are derived by Pontryagin's principle and a formal Lagrange technique. In the case of a linear system, the principal structure of time‐optimal controls is discussed. The associated optimality systems are solved by a one‐shot strategy using a multigrid software package. Various numerical examples are discussed. Copyright © 2013 John Wiley & Sons, Ltd.