An efficient algorithm for finding all DC solutions of piecewise‐linear circuits

An efficient algorithm is proposed for finding all DC solutions of transistor circuits where characteristics of transistors are represented by piecewise‐linear (PWL) convex monotone functions. This algorithm is based on a simple test (termed the linear programming, LP, test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem by surrounding component PWL functions by rectangles. Then the dual simplex method is applied, by which the number of pivotings per region becomes very small. In this letter, we propose a new LP test using the dual simplex method and triangles. The proposed test is not only efficient but also more powerful than the conventional test using the simplex method or rectangles. Copyright © 2008 John Wiley & Sons, Ltd.     

Formulating hybrid equations and state equations for nonlinear circuits using SPICE

Hybrid equations are often used in the theoretical study of nonlinear resistive circuits because they have an easy‐to‐analyze structure. They are also advantageous in the numerical analysis of nonlinear resistive circuits because they are separable and consist of a relatively small number of variables. However, the hybrid equations are seldom used in practical applications because their formulation is complicated. In this letter, we propose a simple method for formulating the hybrid equations using SPICE. In the proposed method, we only perform the transient analysis of SPICE on a linear circuit that is obtained through a small modification to the original circuit. It is also shown that state equations for nonlinear dynamic circuits can also be formulated by using the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

General circuit equation formulation method for simulation of a power electronic system

This paper proposes a general circuit equation formulation method by generalizing the conventional modified nodal analysis (MNA) method. The method consists of two equation types; one is conversation equations which express a conservation law in each physical system like Kirchhoff's law for an electrical system and the other is constraint condition equations, for example, signal flow relations in a control system. Therefore it is possible to analyze a mixed physical system generally by formulating equations simultaneously with node variables of systems and necessary constraint equations. MNA has special features such that it can express contributions of each element or component to the equations simply and clearly by a so‐called stamp. This paper derives how to express the contributions and get a stamp for the equations. A stamp is flexible and not unique and dependent on purposes. It is possible to select a stamp for each element to be compatible with ones by the tableau method. A prototype simulation program is developed and validated for four application examples which are selected to show how the proposed method works. It is possible to simulate a power electronic system generally by developing such a simulator which can handle general stamps from input data information flexibly. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(2): 58–65, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20048     

一种分析双凸极电机非线性磁路的新方法

提出了双凸极电机非线性磁路的简化分析方法,即1/4回路磁通法。该方法可以在任意转子位置、任意励磁电流和电枢电流下求得各支路的磁通。与变网络等效磁路法相比,该方法形成非线性方程组维数少,节省计算时间。与有限元法计算结果和实验结果比较表明该算法具有较高的精度。     

LW4—220型断路器压气特性优化设计及分析

本文对剪刀式传动系统进行分析并推导出传动比计算式及液压环形间隙缓冲计算式;在压气特性优化设计中采用了正交设计法及目的规划法;最后对进行过的几次断流试验作了简单的分析小结。     

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

An efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10³⁰⁰, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.     

Selecting printed circuit board parameters using swarm intelligence to minimize crosstalk between adjacent tracks

The purpose of this paper is to provide a numerical tool for designers in order to help reduce the unwanted coupling between nearby transmission lines on printed circuit boards. This is accomplished using particle swarm optimization technique, where the coupling factor between adjacent lines is used as the fitness function. The coupling factor is computed based on conformal mapping equations of capacitances for even and odd modes of different types of transmission lines, including microstrip and strip lines. Anisotropic, isotropic, asymmetric, and symmetric coupled lines are considered. The S‐parameters of the optimized and unoptimized configurations are computed from the conformal mapping equations and also using the full‐wave electromagnetic simulator IE3D, which is based on the method of moments, where an agreement can be observed between the two results. Different examples are presented here that show the effectiveness of this method in reducing the coupling factor. A Matlab program is written to harness particle swarm optimization to find optimum solutions. Copyright © 2014 John Wiley & Sons, Ltd.     

短路限流器的配置与优化

讨论了电力系统短路电流计算方程,在此基础上建立了由系统短路电流限值确定限流器阻抗的数学模型。对于单组限流器,该模型为线性方程组,具有唯一解,对于多组限流器则为线性不定方程组,存在多解情况。运用广义逆方法和优化方法,直接从线性不定方程组的相容解集合中求得符合要求的优化解,在系统短路电流不超限条件下实现多组限流器的配置和优化。算法具有非常良好的收敛特性和较快的计算速度,适合大系统应用。许多情况下使用单组限流器不能满足要求,而使用多组限流器则可以有效地将系统短路电流抑制在要求范围内。工程实例验证了算法的有效性和实用性。     

Circuit analysis by a new multirate method

This paper proposes a new multirate analysis method which selects a proper numerical integration step size for each variable in analyzing a circuit which has subcircuits with different rates. First a formulation technique of multirate circuit equations is derived. Then a rate classification technique is derived from the error estimation formula of the backward differentiation formula (BDF). Further a step‐size adjustment technique at a breakpoint is explained. Finally the proposed method is applied to a basic filter and a dc–dc converter circuit shows the efficiency of the method. © 1999 Scripta Technica, Electr Eng Jpn, 126(4): 55–62, 1999     

An interval algorithm for finding all solutions of non‐linear resistive circuits

In this letter, an efficient algorithm is proposed for finding all solutions of non‐linear (not piecewise‐linear) resistive circuits. This algorithm is based on interval analysis, the dual simplex method, and the contraction methods. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500–700 non‐linear circuit equations in acceptable computation time. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

水轮发电机的风路和数值解法

对水轮发电机的典型通风系统结构进行了分析,绘出相应的等效风路图。并根据等效风路图列出压力平衡方程和流量守恒方程。采用高斯消去法和欠松弛迭代法并应用计算机对这些方程进行数值求解,从而计算出各支路的流量。     

Modeling and Diagnosing Eccentricity Fault Using Three-dimensional Magnetic Equivalent Circuit Model of Three-phase Squirrel-cage Induction Motor

This article presents the three-dimensional modeling of an induction motor using a magnetic equivalent circuit. The main goal of introducing the three-dimensional model is to include axial fluxes in the machine equations. Furthermore, enhancement of the precision of teeth flux estimation and air-gap permeances, as the most important and dominant factors, is another achievement of this model compared to that of the two-dimensional model. This increases the accuracy of the estimated torque. Although it is possible to include the impact of the bar skew in the two-dimensional modeling using a magnetic equivalent circuit, this can be included more precisely in the three-dimensional model due to the three-dimensional nature of the bar skew. Therefore, the three-dimensional model as an efficient method with rapid computations and suitable precision is used for modeling various types of eccentricity. It is shown that the three-dimensional model results are closer to the experimental results compared to that of the two-dimensional model. This confirms the merit of the three-dimensional model. Also, this method can be a proper substitution to the finite-element method in modeling a machine under fault and fault diagnosis.     

基于多目标线性规划的模拟电路软故障诊断方法

阐述了一种新的容差条件下基于多目标线性规划理论的模拟电路软故障诊断方法。通过灵敏度分析建立电路测试节点电压增量方程,并以元件参数变化量与标称值的百分比作为故障判据。采用多目标线性规划方法求解测试节点方程组来估算电路中各元件在一定故障情况下的参数变化百分比,将方程组的解与各元件容差范围相比较来定位故障元件。仿真结果表明,该方法兼顾故障元件的定位和故障元件参数变化量的估算,可以有效地实现模拟电路元件参数在一定容差范围内变化条件下的软故障诊断。     

可控移相器对系统不对称短路电流的影响研究

以可控移相器在电力系统中得到广泛应用为研究背景,以研究可控移相器接入系统后对不对称短路电流的影响为目标,提出了基于可控移相器的不对称短路电流实用计算方法。首先根据可控移相器的结构与原理建立其正序、负序以及零序模型。然后基于对称分量法建立含可控移相器系统的各序分量网络方程,进而提出含可控移相器系统的各类型不对称短路电流实用计算方法,并分析影响短路电流的因素。最后基于三机九节点系统,运用上述实用计算方法进行不对称短路电流计算,算例仿真结果表明该方法具备有效性。通过对比分析可知移相器的移相角和短路点位置是影响短路电流的因素,而影响情况需通过具体计算得出。     

考虑电动斥力的低压直流断路器动力学仿真及应力分析

以多体系统动力学为基础,建立低压直流断路器的动力学模型。将机械运动方程和电路、电磁场方程耦合求解,从而实现考虑电动斥力的断路器分断过程仿真。通过有限元分析软件Ansys与多体动力学分析软件ADAMS的协同仿真,建立断路器的刚一柔耦合动力学模型,完成关键零件在断路器短路故障分断过程中的强度分析,为断路器设计中关键零件的设计和优化提供一条有效的途径。     

3/12相双绕组发电机交直流同时突然短路研究

根据3／12相双绕组发电机的基本磁链和电压方程以及等效电路，该文用解析分析和电路模型仿真两种方法详细研究了交直流同时突然短路的过渡过程，得出了定转子短路时间常数和交流侧短路电流的完整表达式，通过适当的近似，进一步给出了适合工程应用的交流侧短路电流的近似和简明表达式以及直流侧最大短路电流的估算公式。另外，还研究了线路电阻对短路电流的影响，结果表明：在分析和测试交直流同时突然短路时，线路电阻，尤其是直流侧线路电阻必须考虑，仿真和实验验证了该文所得数学模型及分析方法的准确性。     

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.     

断路器传动机构的动力学分析及研究

推出了具有理想约束的平面多环多自由度多刚体系统的计及摩擦的动力学方程组,采用了迭代方法使摩擦计算线性化,并运用解大型稀疏线性方程组的技巧提出了动力学分析方法。在此基础上建立了ZN4—10/1000—16型真空断路器的动力学方程,运用上述动力学分析方法编制了程序对其分、合闸过程进行了分析,并将计算结果与实验曲线进行了比较。     

全桥LLC电路时域模型及其分析

传统LLC电路分析基于频域分析方法,采用只考虑基波分量的基波近似法(FHA)进行等效。传统分析方法忽略了高次谐波对功率转换的影响,是对谐振变换的一种近似,而不是准确模型。根据全桥LLC电路实际电压、电流波形,首先给出了LLC谐振变换器全时域的分析方法及步骤,列出了非线性时域方程组。然后基于时域方程绘制了包含全部信息的增益曲线,分析LLC电路整个工作频段的增益,并与FHA进行了比较。最后,在20kW电动汽车充电模块电路上对所述时域模型和增益分析进行了实验验证。