Analysis of Nonlinear Electrical Circuits Using Bernstein Polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.

Nonlinear Resistance Circuit Subsection Linearity Decomposition Fitting Analysis

The analysis of circuits is frequently required in the electricity of physics. When analyzing circuits, the general idea is to study the issues related to nonlinear resistance circuits based on commonly used physical and electrical theory. Generally, circuits can be divided into linear resistance circuits and nonlinear resistance circuits. However, for some nonlinear resistance circuit, a small part of them are decomposed through subsection linearity while most of them are adopted the form of hieroglyph combination for subsection decomposition fitting analysis. For the following contents, the author will adopt curve layout method to analyze nonlinear resistance element and relation characteristics of voltage and current;to state the characteristics and nature of common electronic elements in our life, and concepts of concave resistance and convex resistance;to analyze the characteristics of nonlinear resistance circuits through electrical circuit analysis method based on the electrical theorem of physics;finally, to analyze referring to actual cases, study the veracity, verify the feasibility and scientificity of the adopted analytical approach, apply image graphics of the resistance circuits in the convenient way to solve complicated design problems among actual electrical problems.

Wavelet neural network based fault diagnosis in nonlinear analog circuits

The theories of diagnosing nonlinear analog circuits by means of the transient response testing are studled. Wavelet analysis is made to extract the transient response signature of nonlinear circuits and compress the signature dada. The best wavelet function is selected based on the between-category total scatter of signature. The fault dictionary of nonlinear circuits is constructed based on improved back-propagation（BP） neural network. Experimental results demonstrate that the method proposed has high diagnostic sensitivity and fast fault identification and deducibility.

Dynamical analysis and circuit simulation of a new three-dimensional chaotic system

This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in the third equation. Basic dynamic properties of the new system are investigated by means of theoretical analysis, numerical simulation, sensitivity to initial, power spectrum, Lyapunov exponent, and Poincar~ diagrams. The dynamic properties affected by variable parameters are also analysed. Finally, the chaotic system is simulated by circuit. The results verify the existence and implementation of the system.

Investigation of the compact torus plasma motion in the KTX-CTI device based on circuit analyses

Compact torus(CT)injection is one of the most promising methods for the central fuelling of next-generation reactor-grade fusion devices due to its high density,high velocity,and selfcontained magnetised structure.A newly compact torus injector(CTI)device in Keda Torus e Xperiment(KTX),named KTX-CTI,was successfully developed and tested at the University of Science and Technology in China.In this study,first,we briefly introduce the basic principles and structure of KTX-CTI,and then,present an accurate circuit model that relies on nonlinear regression analysis(NRA)for studying the current waveform of the formation region.The current waveform,displacement,and velocity of CT plasma in the acceleration region are calculated using this NRA-based one-dimensional point model.The model results were in good agreement with the experiments.The next-step upgrading reference scheme of the KTX-CTI device is preliminarily investigated using this NRA-based point model.This research can provide insights for the development of experiments and future upgrades of the device.

基于非线性分析的无线通信识别系统优化研究

为了进一步提升插秧机的通信效率及整机作业效率,以无线通信识别模块为研究对象,基于非线性分析控制理论展开优化研究。结合插秧机的作业环境特征和各组件协调作业特点,从通信信号的非线性处理和保证抗干扰能力角度入手,建立通信识别系统的非线性控制器模型,并针对系统的输入输出和接口模块完成电路控制与程序优化布局。同时,进行插秧作业通信监测验证试验,结果表明:此非线性分析应用机理下,插秧机作业的智能性与精准性得到显著提高,通过非线性控制实现了细致有效的数据计算分析,通信传输效率相对提升了5.69%,插秧深度合格率可达96.78%,满足智能插秧设计要求。

An Exponential Chaotic Oscillator Design and Its Dynamic Analysis

After years of development, chaotic circuits have possessed many different mathematic forms and multiple realization methods. However, in most of the existing chaotic systems, the nonlinear units are composed of the product terms. In this paper, in order to obtain a chaotic oscillator with higher nonlinearity and complexity to meet the needs of utilization, we discuss a novel chaotic system whose nonlinear term is realized by an exponential term. The new exponential chaotic oscillator is constructed by adding an exponential term to the classical Lüsystem. To further investigate the dynamic characteristics of the oscillator, classical theoretical analyses have been performed, such as phase diagrams, equilibrium points, stabilities of the system,Poincaré mappings, Lyapunov exponent spectrums, and bifurcation diagrams. Then through the National Institute of Standards and Technology(NIST) statistical test, it is proved that the chaotic sequence generated by the exponential chaotic oscillator is more random than that produced by the Lü system. In order to further verify the practicability of this chaotic oscillator, by applying the improved modular design method, the system equivalent circuit has been realized and proved by the Multisim simulation. The theoretical analysis and the Multisim simulation results are in good agreement.

Analysis of Electromagnetic Environment Effect Using TDIE-FDTD-MNA Hybrid Algorithm

It is important but difficult to analyze the electromagnetic environment effect(E3) in the designing of modern airborne,sea,space,and ground systems.Thus a hybrid algorithm of time domain integral equation,finite difference time domain and modified nodal analysis(TDIE-FDTD-MNA) is developed to analyze the E3 of complex systems with cables and nonlinear circuit structures.The plane wave time domain(PWTD) enhanced TDIE method is adopted to solve field problems.The higher order FDTD(2,4) is adopted to solve cable problems.The MNA is adopted to obtain the response of complex circuits(with nonlinear structures).Numerical examples demonstrate the effectiveness of the proposed algorithm.

电路及谐振子参数对YIG调谐振荡器相位噪声的影响

利用单一变量法,详细分析了某型YIG调谐振荡器不同电路参数(如基极反馈电感、负压电阻等)及谐振子参数(耦合环大小、小球饱和磁化强度等)对振荡器相位噪声的影响。结果表明,振荡器相位噪声随基极反馈电感的增大而增高,高频端的相位噪声相对低频端随负压电阻的增大改善更大;而对于YIG小球铁磁共振线宽ΔH,相对于高频端来说,相位噪声随ΔH的增大在低频端增高更多。总之,降低YIG调谐振荡器的相位噪声是根据各指标需求综合优化振荡器电路各参数的结果。

电力系统中压电网谐振关键元器件评估

模态分析法可以获得最丰富的谐振信息,现有灵敏度分析方法可以得到每种元器件对谐振影响程度的排序,但无法明确辨别谐振关键元件和谐振电路。首先,通过推导对各参与因子的物理意义进行了解释,归纳了现有的2种灵敏度分析方法;然后,考虑不同属性元器件取值范围的差异性及逆变器外特性的影响,提出了一种适用于配电网谐振关键元件和电路的识别方法;最后,通过算例分析和PSCAD仿真结果,验证了所得谐振关键元器件的准确性。该方法可以较为准确地识别出系统固有谐振的关键元器件,为研究谐波谐振问题及其抑制、事故调查分析等提供参考。

水中脉冲放电振荡特性分析及抑制方法研究

水中脉冲功率放电过程中产生的电路振荡,会延长放电时间,降低储能电容寿命。为了对电路振荡进行抑制,首先根据脉冲功率放电装置工作环境,利用COMSOL仿真软件,建立了二维轴对称高压放电模型,模拟了11 kV下电极间隙为4 mm下的高压击穿过程,并分析了等离子通道电导率变化趋势。然后建立等离子通道二维阻抗模型,对电极上的实际放电波形进行了非线性回归分析,得到其电阻和电感分别为0.439Ω和19.8729μH。最后根据负载特性提出了用脉冲功率晶闸管来抑制电路振荡的策略,并进行了脉冲功率放电实验。实验表明,通过理论阻抗计算得到的电极电压与实际放电电压相符合,且使用晶闸管脉冲功率开关可有效地抑制电路振荡,使振荡时间由220μs降低到36μs,降低了83.6%。

NEW EFFICIENT ALGORITHM FOR NONLINEAR CIRCUIT SYSTEM

A new efficient algorithm is given for calculation of the steady-state response of non-linear circuit driven by multifrequency signals, which are possibly made up of incommen-surable frequencies. The algorithm is particularly useful when the steady state responseis not periodic. The algorithm is much more efficient than numerical integration methods for circuitscontaining only a few nonlinear elements, compared with the number of inductors andcapacitors. It is based on a combined application of the "harmonic balancen" and "leastsquare approach", and does not require any transient analysis. The algorithm can be usedin a microcomputer.

高压直流输电系统非线性变结构控制器的设计

为了进一步改善高压直流 ( HVDC)输电系统的性能 ,采用在逆变侧定无功电流控制方式代替传统的定熄弧角控制 ,并将现代控制理论中非线性系统的状态反馈精确线性化方法与线性系统的变结构控制理论相结合 ,设计了非线性变结构控制器。仿真结果表明 ,所设计的新型控制器能够改善直流系统的性能 。

东北、华北和华东电网联网方案研究

研究了2015年我国东北、华北和华东三个大区电网的联网方案,针对不同联网方案下系统的低频振荡特性进行了分析和比较,证明了在系统中的主要大型发电厂配置电力系统稳定器(Power System Stabilizer,PSS)可以改善低频振荡的阻尼特性,并验证了所配置的PSS的有效性。文章还对系统负荷的阻尼特性进行了灵敏度分析,最后对各种交流和直流故障下系统的暂态稳定特性进行了研究。初步结果表明,将三个大区电网互联为一个大同步电网在技术上是可行的。

电力系统基频铁磁谐振谐波平衡分析

应用谐波平衡法分析了典型铁磁谐振电路基频谐振及其影响因素,确定了该电路的基频谐振区域。该法能较全面的分析非线性电路基频铁磁谐振,也能用于分频、倍频铁磁谐振分析。在电力系统设计时,可先用该法找出系统运行的安全区和谐振区,合理选择系统参数,使系统运行在安全区域内以抑制铁磁谐振。

比例放大器驱动电路特性分析及控制器设计

由于"反接卸荷"式驱动电路电流的非线性特性,当采用传统比例积分控制器进行电磁铁电流闭环控制时存在零位滞后现象,为了解决这一问题,建立"反接卸荷"式驱动电路的非线性数学模型.通过实验验证了该模型的有效性,分析非线性对电流控制器的设计影响.基于分析结论,提出新型的电流控制器设计方案.该方案的主要特征是通过采用死区跨越和抗饱和控制思路,使控制器快速跨越驱动电路的非线性区域.试验结果表明,该控制器能够有效地消除零位滞后现象.

基于灵敏度理论的逆变器并网系统谐振特性分析

针对逆变器并网系统的串、并联谐振分析,采用灵敏度分析理论,得到特定次谐波谐振的元件参与度、谐振回路构成情况等信息。在模态分析的基础上,通过求解网络矩阵特征值对系统元件的偏导值,分别给出了系统各元件在谐振频率下的串、并谐振归一化灵敏度求解公式,得到系统元件对特定次频率谐振的参与度。建立了四节点并网测试系统,对各元件进行灵敏度分析,得了到各元件谐振参与度。同时灵敏度分析结果说明,串联谐振与并联谐振在同一谐振频率下参与元件不完全相同。仿真和实验结果证明了灵敏度分析的有效性。

面向系统动态分析的场路网耦合时步有限元模型

为了在分析系统扰动条件下机网相互影响问题时,能够更准确地考虑发电机的非线性,建立了适合不同网络结构、扰动类型以及不同计算任务的系统动态分析场-路-网耦合时步有限元通用性模型,进而详细推导了单机无穷大系统、两机系统以及三机系统的具体计算格式。在此基础上为使该模型适合更多的网络结构和不同任务的动态分析,引入了相应的控制变量,用于对方程本身、机网接口以及时步有限元计算参数进行控制与调整。模型与算法为深入研究动态过程机-网相互影响,并进一步获得发电机的简化模型提供了新的计算工具。

非线性电路暂态仿真中消除数值振荡的改进方法

在电力系统的电磁暂态数字仿真中,非线性元件的非线性特性将导致数值计算中产生数值振荡。引入一种新的离散方法—改进的节点分析法,对非线性元件进行处理,离散化得到等效伴随电路,然后求解。通过Matlab软件仿真得到等效后的电压波形,与ATP和PSCAD模型比较,所提算法可以有效消除数值振荡,并不会出现'毛刺'现象,适合非线性元件的仿真。

大容量变压器线圈短路状态下非线性稳定性与动力稳定性

针对大容量变压器在短路状态下线圈的机械稳定性问题,采用三维计算模型,选取空间梁单元模式,应用大位移小应变理论,选用Budiansky-Roth准测判断失稳临界状态,对线圈结构的非线性动静态稳定性进行有限元分析。