Self-heating in a coupled thermo-electric circuit-device model

The self-heating of a coupled thermo-electric circuit-semiconductor system is modeled and numerically simulated. The system consists of semiconductor devices, an electric network with resistors, capacitors, inductors, and voltage sources, and a thermal network. The flow of the charge carriers is described by the energy-transport equations coupled to a heat equation for the lattice temperature. The electric circuit is modeled by the network equations from modified nodal analysis coupled to a thermal network describing the evolution of the temperatures in the lumped and distributed circuit elements. The three subsystems are coupled through thermo-electric, electric circuit-device, and thermal network-device interface conditions. The resulting system of nonlinear partial differential-algebraic equations is discretized in time by the 2-stage backward difference formula and in space by a mixed finite-element method. Numerical simulations of a one-dimensional ballistic diode and a frequency multiplier circuit containing a pn-junction diode illustrate the heating of the semiconductor device and circuit resistors.     

高速互连线耦合串扰分析

推导并求解了最差情况下分布参数互连线耦合串扰所满足的微分方程。化简表达式以计算任意输入下耦合串扰波形。实验结果证明该方法有较高地计算效率和精度。     

采用旋转因子法的同步电机模型

提出了一种新的适用于电力系统机网暂态过程数值仿真的有阻尼绕组同步电机模型。通过采用“旋转因子法”对同步电机的电压方程组进行差分化，成功地消除了因旋转电势引起的，存在于同步电机直轴电压方程和交轴电压方程之间的耦合，导出了相互解耦的直轴和交轴瞬态等值电路。文末的算例通过比较该模型与EMTP模型的仿真结果，证明这种新模型是正确的，其仿真算法比常用的EMTP算法更精确、更稳定。     

机网暂态过程数值仿真中的同步电机模型

提出了一种新的适用于电力系统机网暂态过程数值仿真的无阻尼组同步电机模型,通过采且“先求通解,再用梯形法求积”的方法对同步电机的电压方程组进行差分化,成功地消除了因旋转电势引起的、存在于同步电机直轴电压方程和交轴电压方程之间的耦合,导出了相互解耦的直轴和交轴瞬态等值电路。通过算例比较了该模型与ＥＭＴＰ模型的仿真结果,证明这种新模型是正确的,其仿真算法比ＥＭＴＰ算法更精确、更稳定。     

Pinning control and adaptive control for synchronization of linearly coupled reaction‐diffusion neural networks with mixed delays

This paper focuses on the pinning control and adaptive control for synchronization of an array of linearly coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. Firstly, the asymptotical synchronization of coupled semilinear diffusion partial differential equations with mixed time delays is achieved by employing pinning control scheme. The pinning controller is obtained by using Lyapunov‐Krasovskii functional stability theory. The stability condition is represented by linear matrix inequality. The controller gain matrix is easy to be solved. Secondly, the adaptive synchronization condition of an array of linearly coupled reaction‐diffusion neural networks with mixed delays is obtained by using adaptive control scheme. Finally, two numerical examples of coupled semilinear diffusion partial differential equations with mixed time delays are given to illustrate the correctness of the obtained results.     

Monitoring of automation and telemechanical components for railroads in the event of parametric faults

A monitoring circuit is proposed for microprocessor-based automation and telemechanical systems for railroads. This circuit takes the form of a nonlinear quadrupole, and may be investigated by numerical solution of a system of differential equations. The monitoring circuit is simulated with parametric faults of its components.     

Numerical modeling of near corona wire electrohydrodynamic flow in a wire-plate electrostatic precipitator

Numerical modelling of the flow velocity fields for the near corona wire electrohydrodynamic (EHD) flow was conducted. Solutions of the steady, two-dimensional momentum equations have been computed for a wire-plate type electrostatic precipitator (ESP). The equations were solved in the conservative finite-difference form on a fine uniform rectilinear grid of sufficient resolution to accurately capture the momentum boundary layers. The numerical procedure for the differential equations was used by SIMPLEST algorithm. The CFD code coupled with Poisson's electric field, ion transport equations and the momentum equation with electric body force, was used for the numerical simulation with the Chen-Kim k-epsiv turbulent model. The numerical results show that EHD secondary flow was clearly visible in the downstream regions of the corona wire despite the low Reynolds number for the electrode (Re _cw=12.4). Secondary flow vortices caused by the EHD increases with increasing discharge current or EHD number, hence pressure drop of ESP increases     

汽轮发电机定子冷却水路堵塞时的温度场分析与计算

水氢氢汽轮发电机定子冷却水系统发生堵塞的事故时有发生,对定子温度进行监测是诊断冷却系统故障的重要手段之一,因此掌握冷却系统的故障状态和电机中温度分布的对应规律是非常必要的.为此,根据流体力学和传热学的基本原理,结合水氢氢汽轮发电机的结构特点,提出了汽轮发电机定子线棒冷却水路发生堵塞时定子温度场的数学模型.采用热平衡方程对定子温度场的偏微分方程进行离散化处理,与冷却系统中水温及氢温的计算相耦合,形成联立方程组.在此基础上研究了定子线棒冷却水路发生堵塞时对发电机定子温度场的影响,分析总结了空心股线堵塞的严重程度与定子线棒出水口温度以及定子槽检温计温度之间的变化规律,为发电机发生水路堵塞时的故障诊断提供了理论依据.     

A minimum five‐component five‐term single‐nonlinearity chaotic jerk circuit based on a twin‐jerk single‐op‐amp technique

A minimum 5‐component 5‐term single‐nonlinearity chaotic jerk circuit is presented as the first simplest chaotic jerk circuit in a category that a single op‐amp is employed. Such a simplest circuit displays 5 simultaneous advantages of (1) 5 minimum basic electronic components, (2) 5 minimum algebraic terms in a set of 3 coupled first‐order ordinary differential equations (ODEs), (3) a single minimum term of nonlinearity in the ODEs, (4) a simple passive component for nonlinearity, and (5) a single op‐amp. The proposed 5‐term single‐nonlinearity chaotic jerk circuit and a slightly modified version of an existing 6‐term 2‐nonlinearity chaotic jerk circuit form mirrored images of each other. Although both mirrored circuits yield 2 different sets of the ODEs, both sets however can be recast into a pair of twin jerk equations. Both mirrored circuits are therefore algebraically twin 5‐component chaotic jerk circuits, leading to a twin‐jerk single‐op‐amp approach to the proposed minimum chaotic jerk circuit. Two cross verifications of trajectories of both circuits are illustrated through numerical and experimental results. Dynamical properties are also presented.     

Complex vector model of the squirrel-cage induction machineincluding instantaneous rotor bar currents

In this paper, a new detailed mathematical derivation of the squirrel-cage induction machine d-q model is introduced. The model is based on coupled magnetic circuit theory and complex space-vector notation and takes into account the actual nonsinusoidal rotor bar distribution. It is shown for the first time that, given the structural symmetry of the induction machine, both stator and rotor circuits can be modeled by the simple set of only four coupled differential equations, i.e., the d-q model. More importantly, the number of equations does not depend on the number of rotor bars, and the model is valid even if the number of bars per pole is not an integer number. This enormous simplification is achieved without loss of generality nor loss of any information contained in the full set of equations, and it is valid for any operating condition. The actual n rotor bars and end-ring currents are fully included in the model, and they are obtained directly by using a simple vector transformation. In addition, the three-phase rotor equivalent parameters are obtained. Second-order effects, such as skin effect in the rotor bars, can be taken into account by simply modifying the bar and end-ring resistance values. An equivalent circuit based on the model is also derived     

Extremum seeking-based observer design for reduced order models of coupled thermal and fluid systems

We present an extremum seeking (ES)-based robust observer design for thermal-fluid systems, pursuing an application to efficient energy management in buildings. The model is originally described by Boussinesq equations which is given by a system of two coupled partial differential equations (PDEs) for the velocity field and temperature profile constrained to incompressible flow. Using proper orthogonal decomposition, the PDEs are reduced to a set of nonlinear ordinary differential equations. Given a set of temperature and velocity point measurements, a nonlinear state observer is designed to reconstruct the entire state under the error of initial states, and model parametric uncertainties. We prove that the closed loop system for the observer error state satisfies an estimate of L₂ norm in a sense of locally input-to-state stability with respect to parameter uncertainties. Moreover, the uncertain parameters estimate used in the designed observer are optimized through iterations of a data-driven ES algorithm. Numerical simulation of a two-dimensional Boussinesq PDE illustrates the performance of the proposed adaptive estimation method.     

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.     

A novel linear equivalent circuit of a transformer winding considering the frequency-dependence of the impedances

A new methodology for the representation of a transformer winding or any set of magnetically coupled coils by means of an equivalent circuit is presented in this paper. This circuit is suitable for the representation of the frequency-behavior of a system of coils at high frequencies and it consists of RL coupled circuit elements. The frequency-behavior representation of the actual impedances is accomplished by means of additional RL loops. Therefore, the circuit synthesis theory takes a step beyond the RL Foster or Cauer equivalent circuits, which were developed to represent only a single inductive element. Starting from the proposed equivalent circuit, the matrix equation of the system of coupled inductive branches is derived and their equivalence with the characteristic equations of the real system is proved. Finally, the method is applied to the modeling of transformer windings.     

On stochastic modelling of linear circuits

In this paper, the deterministic modelling of linear circuits is replaced by stochastic modelling by including variance in the parameters (resistance, inductance and capacitance). Our method is based on results from the theory of stochastic differential equations. This method is general in the following sense. Any electrical circuit that consists of resistances, inductances and capacitances can be modelled by ordinary differential equations, in which the parameters of the differential operators are the functions of circuit elements. The deterministic ordinary differential equation can be converted into a stochastic differential equation by adding noise to the input potential source and to the circuit elements. The noise added in the potential source is assumed to be a white noise and that added in the parameters is assumed to be a correlated process because these parameters change very slowly with time and hence must be modelled as a correlated process. In this paper, we model a series RLC circuit by using the proposed method. The stochastic differential equation that describes the concentration of charge in the capacitor of a series RLC circuit is solved. Numerical simulations in MATLAB are obtained using the Euler–Maruyama method. Copyright © 2008 John Wiley & Sons, Ltd.     

Linearization of a heat-transfer system model with approximation of transport time delay

A method is proposed for linearizing the nonlinear model of a heat-transfer facility the state variables of which at equilibrium points are determined by numerically solving the initial bilinear system of differential equations for a stationary position of the control valve equipped with a constant-speed electric drive. The considerable transport time delay resulting from the distributed design of the heat-transfer system secondary circuit is approximated by a limited number of first-order inertial sections for obtaining a mathematical model in the Cauchy form. The proposed linearization method is tested on an operating hot-water supply heat-transfer system, and the study results are presented in the form of transient curves.     

A practical guide to multidimensional wave digital algorithms using an example of fluid dynamics

The wave digital concept for numerical integration of partial differential equations leads to algorithms with highly advantageous features as robustness, full localness and massive parallelism. However, the required synthesis of an internally multidimensionally passive reference circuit, from which the algorithm is derived, usually demands an in‐depth knowledge of circuit theory and a high level of intuition. In this practical guide, a step‐by‐step approach for the synthesis of such reference circuits is introduced to relax these requirements, using the nonlinear fluid dynamic equations as a nontrivial example. General implementation issues for the wave digital algorithm are discussed as well as applying arbitrary passive linear multistep methods in place of the commonly used trapezoidal rule. As an example, we take the well‐known numerically critical shock tube problem, the solution of which is problematic when the trapezoidal rule is used as unwanted oscillations occur. These oscillations are suppressed when using the second‐order accurate Gear method instead. Copyright © 2010 John Wiley & Sons, Ltd.     

Computational solution of the atomic mixing equations: special methods and algorithm of IMPETUS II

The IMPETUS II code simulates the atomic mixing and particle emission that occurs when a solid is bombarded by energetic particles (as in SIMS or SNMS). The underlying model consists of a system of partial differential equations that are solved by a finite difference method (FDM). Special techniques are also employed to model thin layers and sharp interfaces, to deal efficiently with wide homogeneous layers (when the solution is tending to a steady state), to model linear diffusion in order to smooth the sharp interfaces before they enter to domain of the FDM. In this paper the special techniques are described in detail. Results from test problems, demonstrating these techniques, are shown. An algorithm that describes the way the IMPETUS II code is structured is given. © 1998 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.     

三相半波可控整流电路的计算机仿真

在三相半波可控整流电路物理模型的基础上，根据晶闸管的导通条件，建立了在不同条件下整流电路中物理量所适应的常微分方程组，在此基础上利用MATLAB语言对整流器进行模拟仿真，并对其仿真结果进行分析。