Steady state analysis of electronic circuits by cubic and exponential splines

Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady state of RF circuits. HB is based on a Fourier expansion of the unknown waveforms and is state-of-the-art. Unfortunately, trigonometric polynomials exhibit poor convergence properties in cases where the signal is not quasi-sinusoidal which leads to a prohibitive run-time even for small circuits. Moreover, the approximation of sharp transients leads to the well-known Gibbs phenomenon, which cannot be reduced by an increase of Fourier coefficients. In this paper, we present an alternative approach based on alternatively cubic or exponential splines for a (quasi-) periodic steady state analysis. Unlike trigonometric basis function, a spline basis solves for a variational problem, i.e., the cubic spline minimizes the curvature. Because of their compact support, spline bases are better suited for waveforms with sharp transients. Furthermore, we show that the amount of work for coding of splines is negligible if an implementation of HB is available. In general, designers are mainly interested in spectra and not in waveforms. Therefore, a method for calculating the spectrum from a spline basis is derived too.     

DC tolerance analysis of electronic circuits by polyhedral circuits

Real equilibrium solutions of electronic circuits are affected by deviation of real characteristics of devices from their nominal values, producing the displacement of solution points from their nominal position. In this paper, a method to determine all the equilibrium regions in which real equilibrium points may fall is presented. The analysis is based on the introduction of the so‐called strip characteristics that represent the characteristics of devices affected by tolerances. They are modeled by polyhedral characteristics. Different situations may occur as tolerances grow. A nominal solution point may disappear, or on the other end, some solution point not present with nominal characteristics may appear. These possible events call for a classification of the equilibrium regions in either certain or uncertain, depending on the existence or not of an equilibrium point for any choice of real characteristics. The algorithm adopts linear programming techniques and a clustering algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

A discrete-time approach to the steady state analysis and optimization of non-linear autonomous circuits

In this paper a method for the steady state analysis and optimization of non-linear autonomous circuits is described. After discretizing the linear part of the circuit, a system of non-linear algebraic equations is obtained. the final formulation is written entirely in the discrete-time domain, making it unnecessary to repeatedly take direct and inverse DFTs during the solution process. Furthermore, it is shown that the resulting formulation may be viewed as a generalization of the harmonic balance equations. an analytic method for computing the exact partial derivatives of the resulting equations with respect to the samples of the variables, the oscillation period and the circuit element values is described, making the proposed approach efficient for both analysis and optimization. Different globally convergent techniques for solving the non-linear system of equations are described, with emphasis on an algorithm based on fast simulated diffusion. Selected application examples are provided to validate the proposed approach.     

Equivalent circuits for transient and steady state calculations in coaxial tubes

Contents Transient field and current have been calculated in coaxial tubes for a given applied voltage wave form. The boundary value problem of the diffusion equation has been solved. The solution lead to equivalent circuits i.e. circuits with lumpedL, R elements which can describe the impedance behaviour as accurately as required. This method could well be applied to find short circuit currents and steady state losses in cables, bus bars and gas insulated transmissions.

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Ersatzschaltbilder zur Berechnung von transienten und stationären Zuständen in koaxialen rohrförmigen Leitern

Übersicht Transiente Felder und Ströme werden in koaxialen Zylinderanordnungen bei eingeprägter Spannung berechnet. Das entsprechende Randwertproblem aus der Maxwellschen Theorie wird gelöst. Die Lösung führt zu einem equivalenten Ersatzschaltbild mit konzetrierten Elementen. So kann das Impedanzverhalten beliebig genau beschrieben werden. Diese Methode kann für die Berechnung von Kurzschlußströmen und stationären Verlusten in Kabeln, Sammelschienen und gasisolierten Übertragungstrecken von Bedeutung sein.

     

Computer-aided analysis of power electronic circuits by stepwise topological identification

A new approach for the time-domain simulation of power electronic circuits is developed. The methodology is based on stepwise identification of circuit topology. The simulation process automatically looks for a valid topology in every step. At each simulation instant, the circuit topology is transformed into a resistive network, giving another superior feature of this method: the avoidance of solving complicated s-domain or differential formulas. No small-signal approximation is assumed. Parasitic resistance of the reactive element is included in the circuit model. Several examples illustrating the generality and computational efficiency of this new method are presented. The simulated results are favourably verified with experimental measurements and available literature. © 1997 John Wiley & Sons, Ltd.     

一种描述电力电子电路状态转换的新方法

在开发采用集成芯片控制的电力电子系统时,电力电子电路研究人员与嵌入式软件编制人员之间缺乏简单有效的沟通方法.通过对电力电子电路特点的分析,得到相对于控制器出口"可见"部分电路状态集的组成形式.定义了扩展有限状态机EFSM(Extended Finite State Machine)模型,提出基于EFSM的电力电子电路状态转化的描述方法.以带饱和电感的移相式软PWM逆变电路为实例,用EFSM模型进行了描述.实例模型体现了电路状态之间转换的连续直观和系统的完整性.此方法简洁有效.     

Curve-search algorithm for DC analysis of non-linear electronic circuits

The solution of the original DC analysis problem is reformulated as a search for a certain point in functional space which belongs to the curve in the same space. the generalized matrix equation of the hyperplane normal to this curve is easily derived and a new iterative algorithm is presented. Some critical situations arising in non-linear circuit simulation and the behaviour of the new approach in these cases are considered. Six application examples are given.     

进相试验中凸极同步发电机静态稳定限制的数值分析

为研究凸极同步发电机进相试验中进相无功及功角的限值问题,建立了两种不同进相试验条件下凸极同步发电机静态稳定功率方程。通过对两个功率方程的数值分析,揭示了凸极同步发电机静态稳定极限功率和极限功角随试验电压及电气参数的变化规律,以及发电机饱和对静态稳定的影响。研究结果表明,凸极发电机低负荷时的进相深度主要取决于其q轴电抗;相同条件下d、q电抗越小发电机允许的进相无功和其极限功角越大;进相试验电压对极限无功影响较大,但对极限功角影响很小;利用发电机不饱和参数计算出极限无功和功角比较保守,以此为依据进行进相深度的控制可以保障机组的运行安全。     

A spice-based approach to steady state circuit analysis

A new SPICE-based approach for steady state circuit analysis is presented which uses SPICE computational capabilities and a master programme to carry out the periodic response. the master programme implements a suitable method for steady state analysis and is linked with SPICE only via I/O SPICE files. This allows the use of all SPICE analyses together with the new one simply by adding a new statement in the input SPICE file. In this paper the bases of this technique, including the chosen steady state method and the whole system structure, are discussed. Simulation results produced by this technique have been compared, by means of two meaningful examples, with those obtained both by SPICE and by a dedicated simulator for steady state analysis working in the frequency domain.     

Periodic steady state analysis using shooting and wave-form-newton

This paper describes a method of determining the forced periodic steady state response of non-linear circuits. the method is closely related to the work of Aprille and Trick Proc. IEEE, 60 , 108-114 (1972) and also to the finite difference method for solving a boundary value problem. The new approach is a shooting method in the sense that in every iteration an initial value problem is solved. It is, however, also a relaxation method, because in every iteration a periodic wave-form is obtained. This is achieved by solving in each step a linear time-dependent differential equation whose solution can be easily transformed into a periodic solution satisfying this linear equation. Because the iteration takes place on wave-forms rather than initial values and every solution satisfies the boundary conditions, the method is robust. It will be shown that for a causal approximation of the time derivatives the iterated wave-forms are equal to those found using the finite difference methods.     

Power system steady state security analysis using vector processingcomputers

The main difficulties encountered in applying a vector processor to the solution of a power flow is the sparsity of the power flow matrices which results in very short vectors when the nonzero terms are gathered into a packed vector format. The authors describe a steady-state security analysis code which overcomes the problem of very short vectors. The length of the list of outages is the major problem in security analysis since it usually includes at least each individual piece of equipment taken one at a time, and a large number of cases with multiple outages. The use of contingency selection and screening has opened the way to reducing this burden, but a very large number of individual cases must be run to satisfy the need to be sure that no cases have gone unchecked. The efforts described have extended the computational speed with which this can be accomplished, and the implementation of very high performance security analysis codes has been made possible     

Envelope analysis of nonlinear electronic circuits based on harmonic balance method

We propose here a Spice‐oriented envelope analysis based on the HB (harmonic balance) method, where Fourier coefficients are assumed to be slowly varying. The Fourier expansions of nonlinear devices are executed by MATLAB in the symbolic forms. In this time, the nonlinearities need to be approximated by the polynomial functions. The determining equation of the HB method is formulated as Sine–Cosine circuit in the form of schematic diagram using ABMs (analog behavior models) of Spice. Each sub‐circuit corresponding to the higher harmonic component is almost the same circuit topology as the original one and has dynamic elements such as capacitors and inductors. The Sine–Cosine circuit can be solved by the transient analysis of Spice. Thus, our method is rather a symbolic approach in the meaning that the HB determining equation is given by the schematic diagram of Spice. Our method can be easily applied to the analysis of middle order of nonlinear communication circuits such as mixers and amplitude modulators and to the analysis of interesting phenomena in the nonlinear oscillations. After many simulation experiments, the results show that our envelope analysis is about 50 times faster than the direct transient analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

On the steady state analysis of a current fed induction motor

Contents The performance equations of an induction motor operating on a current source inverter are derived using a stationary reference frame of two of the three phases. The equations are well suited for simulation of a current controlled inverter fed induction motor on a digital computer using well known numerical methods of integration. A method is presented for the steady state analysis via state transition signal flow graph. This method is found to offer several advantages over the methods available in the literature using state space techniques. The steady state solution of the equations can be used to show that the rotor flux varies sinusoidally and it induces a sinusoidal voltage in the stator phases accompanied with voltage spikes during commutation.

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Über das stationäre Verhalten eines Asynchronmotors mit eingeprägtem Strom

Übersicht Für einen Asynchronmotor, der über einen Umrichter mit eingeprägtem Strom arbeitet, werden die Gleichungen in einem auf zwei Strangachsen bezogenen Koordinatensystem aufgestellt. Diese sind für die Simulation des Motors unter Benutzung bekannter Integrationsmethoden auf einen Digitalrechner gut geeignet. Es wird eine Methode zur Untersuchung des stationären Zustands mit Hilfe von Signalflußdiagrammen vorgelegt. Diese Methode weist gegenüber der Darstellung im Zustandsraum einige Vorteile auf. Anhand der Lösungen wird gezeigt, daß der Fluß sich sinusförmig ändert und in den Ständersträngen sinusförmige Spannungen mit überlagerten Spitzen induziert.

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Nomenclature i _A,i _B,i _C Stator phase currents - i _a,i _b,i _c rotor phase currents - l _d D. C. link current - L _g mutual inductance between stator and rotor phases (L _m=3/2L _g) - L _s,L _r leakage inductance of stator and rotor windings per phase - L _s,L _r self inductances of stator and rotor windings - P pairs of poles - R _s,R _r stator and rotor resistances per phase - T _cl electromagnetic torque developed - u _A,u _B,u _C stator phase voltages - u _a,u _b,u _c rotor phase voltages - _A , _B , _C stator flux linkages - _a , _b , _c rotor flux linkages - 1–L _m ² /(L _s L _r)=leakage coefficient - electrical angle between the axes of the stator and rotor phases - d/dt=angular speed of the rotor     

Envelope simulation by SPICE-compatible models of linear electriccircuits driven by modulated signals

SPICE-compatible equivalent circuits were developed to facilitate the analysis and envelope simulation of electric circuits driven by modulated signals. The circuits are based on a novel complex phasor-domain transformation. The proposed method facilitates simulation of any general linear circuit driven by a modulated signal such as amplitude modulation, frequency modulation, or phase modulation. Simulation time by the proposed envelope simulation is much faster than the full cycle-by-cycle simulation of the original circuit and excitation     

基于小波分析及网络的电力电子电路故障诊断方法

针对电力电子电路故障,结合小波多分辨分析,将信号的特征提取作为网络的第一层,用小波函数代替普通神经网络中的S函数,提出了函数型和权值型两种不同的4层小波神经网络方法,给出了相应的数学模型和学习算法。以三相整流桥电路为例,建立了小波神经网络的输出与故障元之间的对应关系,实现了电路的故障诊断,并与用普通BP网络诊断的结果进行了比较。仿真结果验证了两种方法的正确性。     

静态同步串联补偿器稳态特性分析与详细数学模型的建立

通过数学推导得出了静态同步串联补偿器（SSSC）的功率传输特性及包含交直流系统的详细数学模型。数学模型对SSSC的交流部分和直流部分分别进行分析和数学建模，并通过交、直流侧功率守恒将二者联系在一起。利用EMTDC提供的元件库，搭建了含单机无穷大系统及SSSC装置的仿真系统。SSSC装置包括二电平、六脉冲电压源逆变器及其SPWM脉冲发生回路。利用EMIDC中的控制模块构建了典型的PI控制回路，实现对线路潮流的实时控制。仿真结果验证了SSSC功率传输特性及其数学模型的正确性。     

标准遗传算法的收敛性分析及其趋近稳态的速度估计

应用齐次Ｍｒｋｏｖ链仔细分析了标准遗传算法（ＳＧＡ）趋近于稳态的过程,给出其稳态分配的具体表示形式;同时得到了更广泛和严格意义上的与ＳＧＡ控制参数相联系的到达稳态的速度估计,其结果对于其他全局收敛ＧＡ的收敛性和收敛速度研究都有借鉴意义。