Considerations on the equivalence between non‐uniform transmission lines

We investigate the relation of equivalence between non‐uniform lossless transmission lines (LC lines or lines, for short) with sectionally smooth distributed parameters (series inductance L(x) and shunt capacitance C(x) per unit length, x being the spatial variable). The equivalence condition is derived by heuristic and well‐grounded inference. The condition provides us with the basis on which we can generate by rote a line equivalent to a fixed original line according to a specified change of spatial variable (elasticity function). The concept of intermediary lines between a pair of equivalent lines is introduced to enhance precise understanding of the condition and the procedure to generate equivalent lines. In addition, fused parameters are defined as a generalization of distributed parameters, in terms of which the argument and formulas are developed in a brief and inclusive manner. It is shown to be possible, on generating equivalent lines, to preassign a fused parameter of the equivalent line or one of the associated intermediary lines instead of specifying the elasticity function. Equivalent lines thus obtained are called conditioned equivalent lines. We discuss how to get conditioned equivalent lines as well as equivalency tests of arbitrarily given pair of LC lines to present some comprehensible and promising methods involving a versatile, graphical technique. We also refer to such interesting topics as a normalization of LC lines, a kind of conservation law of fused parameters between equivalent lines and the scope of realizable characteristics by LC lines conditioned in an arbitrary way. Some formerly known equivalence conditions are located appropriately in the context of our theory. Further, the equivalence condition is shown to be not only sufficient but also necessary for LC lines whose distributed parameters may have a finite number of points of discontinuity by invoking a theorem for an inverse scattering problem. Copyright © 2005 John Wiley & Sons, Ltd.     

Composition dependent electrocaloric behavior of (SrxBa1-x)Nb2O6 ceramics

This article presents electrocaloric effect in (Sr_xBa_1-x)Nb₂O₆ ceramics (where x = 0.25, 0.50 and 0.75) using an indirect approach based on Maxwell's relations. Here, we have calculated various parameters of electrocaloric effect like temperature change (ΔT), entropy change (ΔS) and heat carrying capacity (ΔQ) of material due to the change in polarization under two different electric fields of 30 kV/cm and 20 kV/cm. (Sr_xBa_1-x)Nb₂O₆ ceramics is well known pyroelectric material, where by increasing Sr/Ba ratio the ferroelectric behavior turns towards relaxor behavior. While in terms of electrocaloric effect performance (temperature change ΔT) is increase as the Sr/Ba ratio increases. Additionally, maximum ΔT (0.30 K) was found for (Sr_xBa_1-x)Nb₂O₆ ceramic having x=0.75 molar concentration under the electric fields of 30 kV/cm.     

TRANSIENT STABILITY OF SERIES AND SHUNT COMPENSATED SCHEMES FOR AC TRANSMISSION SYSTEMS

ABSTRACT

Transient stability of a system transferring power through a long EHV AC transmission line with various series and shunt compensation schemes is determined and compared. The general 2-port, 4-terminal network model of a transmission line and compensation is used. The extended equal area criterion is reformulated in terms of the ABCD constants rather than the transfer admittance to determine the critical clearing angle. The critical clearing time is then determined by estimating the faulted angle through the Taylor series expansion. Effects of various factors, such as degree of series and shunt compensations, line length and the load power and power factor, on transient stability are studied. A comparison of critical clearing time for different transmission line models (distributed and lumped parameters) is also made.     

Structure,nonlinearity, and system theory

The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more ‘constructive’ as re system perception and possible structural generalizations, is considered, supported by arguments related to the classification of switched circuits as linear and nonlinear. The point of the distinction is mainly that when solving dx/dt = F(x,u,t), one immediately dwells into the analytical problems related to pure mathematics, whereas for dx/dt = [A(t,x)]x + [B(t,x)]u(t), considering first a constant matrix [A], one introduces the system's physical structure and considering then [A(x)] sees the nonlinearity of the system as a dependence of the structure on the processes in it or on system's input. (This might be named structural response). The thinking in terms of structure better observes the engineering and physical degrees of freedom, which are relevant regarding applications. Some electronic systems and physical systems (e.g., hydrodynamic) are considered in these terms. The logical side is always the focus, and the pedagogical (even philosophical) side is not ignored. Copyright © 2013 John Wiley & Sons, Ltd.     

Determining the periodic response of nonlinear systems by a gradient method

For systems of differential equations of the form ? = f(x) or x = f(x, t) , a periodic response may be identified by the requirement that x(kT) = x(0) , where k = 1, 2, … and T is the period, x(0) = x₀ being the initial-condition vector. We describe a gradient method for finding this x₀ vector by minimizing the square magnitude of the ‘discrepancy vector’ δ(x₀) = x(T)–x₀. The gradient of the scalar function P(x₀) = δ^t(x₀)δ(x₀) with respect to x₀ is calculated by one full-period forward integration of the original differential equation to obtain δ(x₀), and then one full-period backward integration of the adjoint variational equations, using δ(x₀) as the initial-condition vector. The gradient of P(x₀) is then twice the adjoint discrepancy vector. We use Fletcher's method of optimization to minimize P(x₀) .     

An accurate time‐domain model of transmission lines with frequency‐dependent parameters

Linear lossy two‐conductor transmission line can be modelled as dynamic two ports in the time domain, via the describing input and transfer impulse responses. This convolution technique is very effective when dealing with networks composed of transmission lines with frequency‐dependent parameters and non‐linear and/or time‐varying circuits. The paper carries out an accurate analysis of this model, in the most general case of lines with frequency‐dependent parameters. For such lines it is not possible to evaluate analytically the impulse responses, nor is it possible to catch them numerically, due to the presence of irregular terms, such as Dirac pulses, terms that numerically behave as Dirac pulses, and functions of the type 1/t^ρ with 0 < ρ <1. A simple method is proposed to evaluate exactly all the irregular terms of the impulse responses: once these irregular parts have been extracted, the regular remainders are easily evaluated numerically. This method is applied to analyse lines with frequency‐dependent parameters of practical interest, such as superconductor transmission lines, power lines above a finite conductivity ground, lines with frequency‐dependent dielectric losses and lines with normal and anomalous skin‐effect. Numerical simulations are carried out for illustration. Copyright © 2000 John Wiley & Sons, Ltd.     

Design,Analysis, Fabrication,and Testing of Laboratory Model of Transmission Line

This article presents a procedure for the development of a scaled-down laboratory model of a transmission line based on per unit. values of a true line. The X/R ratio of the model is kept same as that of the true line, as then only their performance can be compared. The current-carrying capacity of the scaled-down model is closer to 20 A to enhance its utility with different flexible AC transmission systems devices. A scaled-down model of a true line for which parameters are available in the open literature is fabricated, and a case study of its simulation and validation is presented. These studies show that the laboratory model is able to emulate closely the true line, and therefore, it can be fruitfully used for the dynamic study of the transmission line embedded with flexible AC transmission systems and hardware-in-loop simulation studies.     

Structural and Dielectric Properties of Ca Doped Barium Iron Niobate

Ceramic materials with high dielectric constant are being used in many electric and electro-optics applications. Ca substituted barium iron niobate with general formula (Ba_1-xCa_x) (Fe_0.5Nb_0.5)O₃ with x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0 were prepared by conventional solid state reaction method. Structural properties were investigated using X-ray diffraction and scanning electron microscope. Two types of phases were observed for 0.4 ≤ x ≤ 08. Dielectric constant and loss tangent were measured using impedance analyzer in the frequency range of 20 Hz–1 MHz at room temperature. Dielectric constant and loss tangent were found to decrease with increasing the frequency. A relatively good combination of dielectric constant and loss tangent was obtained for x = 0.2 (?_r = 1441 and tan δ = 0.19) at 10 KHz.     

Design of multi-band multi-section transmission line transformer using particle swarm optimization

The design of N _t -section matching transformer operating at N _t arbitrary frequencies using the particle swarm optimization (PSO) method is presented. Although analytical methods based on standard transmission line theory can be used in such designs, however, the analysis becomes cumbersome if N _t exceeds two, and numerical methods should be used to solve the resulting nonlinear equations. The design using the PSO, however, is much easier, and gives the same results as the analytical methods. Different examples are presented and compared with published literature.     

Performance enhancement of two-degree-of-freedom controllers via adaptive techniques

This paper generalizes earlier results on adaptive disturbance estimate (innovations) feedback regulation to the case of adaptive tracking, refining some of the techniques and formulations in the process. The adaptations proposed search within the class of all stabilizing two-degree-of-freedom controllers for a nominal plant and minimize a reference signal/disturbance rejection measure. The emphasis in the paper is on issues relevant to the tracking task and simulation results to demonstrate the effectiveness of the approach. The adaptive scheme is based on results concerning the convenient characterization of the class of all stabilizing two-degree-of-freedom controllers in terms of an arbitrary filter Q with a stable proper transfer function matrix Q(s). The fact that the closed-loop transfer matrices are affine in Q(s) permits a straightforward on-line least-squares update of the parameters of the filter Q on-line. The theory for the class of stabilizing controllers is used to set up appropriate signal preprocessing. The direct adaptive schemes proposed turn out to be recursive prediction error schemes which have local convergence properties. When convergent, they ensure enhancement of the performance of a fixed controller in other than the nominal plant case.     

Nonlinear boundary-value problem for cylindrical corona discharge

Contents Closed-form (one-dimensional) solutions are derived for the electric fieldE(r) and potentialV(r) in a positive ion discharge between a stressed wire anode atr=a and a coaxial cylinder cathode atr=b. It is shown that this system sustains two different corona discharge modes, namely with radially (i) decreasing (k<1) and (ii) increasing (k>1) electric field strengthE(r), wherek=E _I /E _a is the crucial discharge number. E_I = (I/2₀)^1/2 [V/m] is given in terms of the discharge currentI [A/m], whereas the electric fieldE _a [V/m] at the anode depends on currentI and ion temperatureT _i at the cathode. The physical properties of these discharge modes are discussed analytically.

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Nichtlineares Randwertproblem der zylindrischen Korona-Entladung

Übersicht Geschlossene (eindimensionale) Lösungen werden abgeleitet für das elektrische FeldE(r) und PotentialV(r) in einer positiven Ionen-Entladung zwischen einer Hochspannungsanode mit Radiusr=a und einer koaxialen Zylinderkathode mit Radiusr=b. Es wird gezeigt, daß in diesem System zwei verschiedene Typen von Korona-Entladungen existieren können, nämlich mit radial (i) abnehmender (k<1) und (ii) zunehmender (k>1) elektrischer Feldstärke, wobeik=E _I /E _a der kritische Entladungsparameter ist. E_I = (I/2₀)^1/2 [V/m] ist durch den EntladungsstromI [A/m], während das elektrische FeldE _a [V/m] an der Anode durch StromI und IonentemperaturT _i an der Kathode bestimmt ist. Die physikalischen Eigenschaften dieser Entladungstypen werden analytisch diskutiert.

     

An expanded dalton-cameron method: DC decay testing method at an arbitrary rotor position

The Dalton-Cameron method is a well-known method for determining direct and quadrature axis subtransient reactance (x′_d and x′_q) by standstill response testing. This method entails calculating x′_d and x′_q from the voltage and current measured when a rated-frequency single-phase voltage is applied to each armature winding (U-V, V-W, and W-U) in turn. The authors have developed a new method to calculate x′_d, x′_q and the impedance loci by applying a dc voltage instead of a single-phase voltage. This method was named the expanded Dalton-Cameron method. The method is a small-capacity standstill test, and is carried out by using the following three steps. The first is to short-circuit the U and V terminals while a dc current flows between these terminals, to measure the voltage and current (V_DC and I_DC) when the dc current flows between these terminals and to record the dc decay current (i(t)) after these terminals are short-circuited. This same procedure is also performed for the V-W and W-U terminals in turn. The second step is to draw the impedance loci from the measured V_dc, I_dc and i(t) by means of Fourier transformation and to divide it into the direct-axis and quadrature-axis impedance loci (Z_d(js), Z_q(js)). The third step is to calculated the values of x′_d and x′_q from Z_d(js) and Z_q(js) and the starting performance on the basis of the two-reaction theory. Experimental and calculated results on starting performance, as well as a comparison with calculated results of x′_d and x′_q by the Dalton-Cameron method, clearly show that this method is very useful. © 1998 Scripta Technica, Electr Eng Jpn, 123(2): 53–60, 1998     

Protection relaying scheme based on fault reactance operation type

The theories of operation of existing relays are roughly divided into two types: the current differential type based on Kirchhoff's first law and the impedance type based on Kirchhoff's second law. We can use Kirchhoff's laws to rigorously formulate fault phenomena, so the circuit equations are represented as nonlinear simultaneous equations whose variables are the fault point k and the fault resistance R_f. This method has two defects: (1) a heavy computational burden in iterative calculation by the N‐R method and (2) the relay operator cannot easily understand the principle of numerical matrix operation. The new protection relay principles proposed in this paper focus on the fact that the reactance component at the fault point is close to zero. The reactances X_f(S) and X_f(R) at the ends of the branch are calculated by solution of linear equations. If the signs of X_f(S) and X_f(R) are not the same, it can be inferred that the fault point is located in the branch. This reactance X_f corresponds to the difference in branch reactance between the actual fault point and an imaginary fault point. Thus, the relay engineer can understand the fault location in terms of the concept of “distance.” Simulation results using this new method indicate that it can provide much more precise estimation of fault locations than those obtained by inspection of operating transmission lines. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 168(1): 29–40, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20720     

The dynamics of a non-linear discrete oscillator

The dynamic behaviour of a simple second-order discrete system with a single non-linear factor, specified by (x, y)- (Ax + B(y + sin(2π(x +y))), x), (A, B) ? D = {(A, B): A, B ≥ 0, A + B < 1} - is studied. the parameter subspace of D is analysed in detail. the bifurcation sets of the system are found. the existence of chaos in the system is proved by applying Marotto's theorem. the result of computer simulation agrees well with its analytical counterpart, and confirms that the single non-linear factor ? = sin(2π(x + y)) is indeed the crucial point of a very complicated dynamic behaviour, including the alternative emergence of periodic, quasi-periodic and chaotic phenomena, of this simple second-order oscillator.     

三相不对称T型输电线路参数测量方法研究

传统的T型输电线路参数测量方法基于线路的三相参数对称,没有考虑线路三相不对称对参数测量的影响,而现有的不对称输电线路参数测量方法不适用于含T型接线的特殊输电线路。提出了三相不对称T型输电线路参数测量方法,应用Levenberg-Marquardt(简称L-M)优化算法求解输电线路非线性参数方程组的参数。通过PSCAD软件对单回不对称线路参数测量方法的仿真,验证了用L-M算法计算非线性方程组参数的可行性。然后对所提出的不对称T型输电线路参数测量方法进行了仿真,验证了所提出的不对称T型输电线路参数测量方法是正确可行的。     

Mobile defect contribution to the dielectric non-linearity of PZT ferroelectric thin films

Abstract

Effect of the speed of bias voltage variation v on the dielectric non-linearity of metal-PZT-metal thin film capacitors has been studied. A distance ΔV between two maxima of C-V dependence on the voltage scale, characteristic for ferroelectric phase, as a function of the v value was investigated. It was established that decreasing vvalue led to ΔV decrease: ΔV = 1.8–2.0 V when v = 1.6x10⁴ V/s, and ΔV ? 1.0 V when v = 6.5x10^?2 V/s. The ΔV(v) dependence can be explained by the decreasing of the coercive field of the film due to the migration of charged mobile defects such as the doubly ionized oxygen vacancies, and the formation of space charge regions near the electrodes. Using the experimental data some parameters of the migration process were evaluated: the concentration of oxygen vacancies and their mobility were found to be about 10²⁴ m^?3 and 10^?11 m²/Vs, respectively. These values are close to the data published in the literature obtained using the alternative methods of investigation.     

Use of lossless transmission‐line segments and shunt resistors for TLM diffusion modelling

In diffusion modelling by means of the transmission‐line matrix (TLM) method, a nodal arrangement of using lossless transmission‐line segments and series resistors is almost exclusively adopted and is currently considered as a standard approach. In this paper, the use of shunt resistors instead of series resistors is shown to represent an equally valid configuration. As a starting point, we have derived the telegrapher's equation in its most general form for TLM modelling of diffusion processes. A general algorithm based on the shunt‐resistor TLM model for implementing a numerical solution of the diffusion equation in multiple dimensions is given. Fundamental analysis and calculated examples confirm that the alternative shunt‐resistor configuration does not exhibit the unwanted absorption effects suggested by a recent paper (Internat. J. Numerical Model.: Electronic Networks, Devices and Fields 2002; 15 :261). Copyright © 2003 John Wiley & Sons, Ltd.     

基于抽样盲数的线路N-1静态安全评估

为了研究负荷和新能源出力不确定性对线路静态安全分析结果的影响,提出了一种基于抽样盲数的线路静态安全评估方法。首先介绍了将持续负荷曲线和新能源持续出力曲线抽象成为抽样盲数的抽样方法,并将负荷抽样盲数和新能源出力抽样盲数的样本进行相互组合得到多个待分析场景。在此基础上,分析每个场景下发生线路N-1时是否有其余线路或元件过载,计算发生过载情况的场景概率之和便可得到所研究网络不满足N-1准则的概率。最后,对这些存在不满足N-1准则风险的线路依据风险概率进行排序得到所研究电网薄弱环节。结合7节点交直流电网算例对所提出的方法进行了详细说明,计算结果表明抽样盲数方法可用于线路N-1静态安全评估,从而实现对电网的多维度评价。     

Compact arbitrary terminated power divider with bandwidth-enhanced negative group delay characteristics

A novel compact arbitrary terminated power divider with bandwidth-enhanced negative group delay (NGD) characteristics is proposed. The NGD characteristics are controlled by characteristic impedances of transmission lines and the coupled line between two output ports. Flat and wide NGD bandwidth is produced by using the combination of a series resistor and short-circuited coupled-line section. The complete closed-form equations are presented. For experimental demonstration, a prototype is designed and fabricated at f₀ of 2.14 GHz. The measured results indicate that the proposed power divider is able to realize wide NGD bandwidth and good NGD flatness.     

Characteristic analysis of a wideband balun transformer having a delay line element for phase compensation

The balanced‐unbalanced transformer (balun) is extensively used in radio communication and measuring instruments. In recent years, with the development of television and portable telephones, wideband transformers tend to be miniaturized. In this paper, the wideband transformer is analyzed in terms of distributed coupled‐line theory. A main result of the analysis is that the balance and unbalance transmission characteristics of the balun are markedly improved in the high‐frequency range by using a delay line element for compensation. If the connection point S_w between the coil winding and delay line is off the ground, the balance transmission band is about doubled in the low‐frequency range. If the point S_wis grounded and if the impedance ratio m² is small, a higher degree of unbalance attenuation can be obtained. Better balance transmission characteristics can be obtained when the matching factor K approaches half the optimum. In addition, we show that an in‐phase or anti‐phase transformer can be made on the basis of our isolation wideband transformer. The equivalent circuits of in‐phase and anti‐phase wideband n:1 transformers are obtained from our theoretical analysis and these can be formed by the same transformer. The transmission characteristics of in‐phase and anti‐phase wideband transformers are analyzed and improved characteristics are obtained in the high‐frequency range. The theoretical and experimental values agree well over the wide frequency range of 100 KHz to 1000 MHz. ©1998 Scripta Technica, Electr Eng Jpn, 126(2): 1–14, 1999