The realization of complex impedance standard

The objective of this paper is to present an approach for isolating the harmonic contents in both voltage and current waveforms of the montage feeder of Gharb Talkha substation (60/11 KV). A novel technique using Discrete Wavelet transform (DWT) for the analysis of the waveforms harmonics content At the beginning the substation is simulated using Simulink toolbox in Matlab program with and without the presence of capacitor bunk. The obtained voltage and current waveforms are compared to the actual data. The proposed model is used to study the effect of replacing the capacitor bank with single tuned parallel passive filter. The resulting current and voltage waveforms are analyzed using the proposed DWT technique. The analysis showed that the Total Harmonic Distortion (THD) of both voltage and current waveforms is improved as well as the power factor.

Pantograph arcing with AC supply generates transients, cause asymmetries and distortion in supply voltage and current waveforms and can damage the pantograph and the overhead contact line. The asymmetry generates a net dc component and harmonics, which propagate within the traction power and signalling system and causes electromagnetic interference. Unlike DC-fed systems (Part I), the arcing in ac supply is complex because of the zero crossing of currents and voltages. In this paper, we discuss the mechanisms of sliding contact and arcing between pantograph-contact wire using the experimental setup described in Part I. Influences of various parameters and test conditions on arcing phenomenon and their signature patterns on the supply voltage and current waveforms are presented. It is shown how the arcing mechanism and corresponding asymmetry in the voltage and current waveforms are governed by line speed, current, supply voltage, inductive load, and pantograph material. The asymmetry in the current waveform is mainly due to the difference in the duration of successive zero-current regions and uneven distortion of the waveshapes. This, in turn, creates the asymmetry in the voltage waveform. The findings presented in this paper could be beneficial for coming up with appropriate mitigation techniques from the electromagnetic interference due to pantograph arcing in AC traction systems.

An experimental investigation of a TRAPATT diode with its oscillator circuit is presented. The measurements of current and voltage waveforms were made with a sampling oscilloscope (3 dB bandwidth, 14 GHz)and an improved capacitive voltage-divider probe. Design information is given for this type of probe which can have an almost unlimited bandwidth. Voltage and current waveforms across the semiconductor chip are presented for a diode that oscillated at 1 GHz with an efficiency of 49%. It is shown that the mode of operation and the waveforms are explained well by a simple theoretical model that has been developed.

In this chapter, we shall discuss techniques used to fit faulted current and voltage waveforms, each to a sinusoidal waveform containing a fundamental component, a decaying/constant direct current (DC) component and/or harmonics.These techniques use the least squares (LSQ) method to minimise the fitting error, and all have the common goal of extracting the fundamental components of voltage and current waveforms, to calculate the impedance to the fault or the comparison of current-based signals in digital differential protection.

Voltage source inverter (VSI) had been used in dc traction power substation to deliver the trains braking energy back to the utility grid. To mitigate low order harmonics components, pulse-width-modulation (PWM) technique is commonly used in VSI controlled. As a result, the ac voltage and current waveforms may contain high frequency ripples. This paper proposes to mitigate the high frequency harmonics using LCL-filter with series <em>R</em>-damper. This filter offers good attenuation on harmonics with smaller size compare to other passive filter topologies. Theoretical analysis and simulation verification are conducted in designing the proposed filter. System level simulation had also been carried out. Sinusoidal grid current and voltage waveforms are recorded (THD<2%). This paper also includes damping losses analysis in conjunction with resonance peak suppression in designing the <em>R</em>-damper.

When the soil invaded by water as the grounding medium in green power generation sites near river basins, on the coast, is dominantly characterized in terms of its resistivity, the characteristics of the voltage and current waveforms on transient discharges such as the soil can be experimentally investigated using the liquid gap, reproducing the resistivity of the soil. The transient discharge characteristics is available information on the surge withstand rating of surge protective devices used in the green power generation sites. Experimental results on the behaviour of lightning impulse discharges in a tap-water gap are reported; these results show that the resistivity of tap water is nearly equal to those of a river and cultivated and marshy land. Further, (1) the discharge voltage and current waveforms indicate the periodic attenuated waveforms for one period, and the voltage waveforms indicate amplitude distortions; (2) the discharge impedance obtained using the fitting curves to the discharge waveforms ranges from 1 to 2.5 times that of the tap-water resistance, i.e., 80Ω, and from 8 to 3.2 times that for positive and negative rod discharges.

The experimental study of a low-frequency sinusoidal two-phase generator with digital waveform synthesis is presented, whose main purpose is improving the stability and accuracy of the complex ratio between the output voltages. The improved performance is obtained by means of a filtering technique with low phase shift and an original automatic control based on an auxiliary generator which interlocks the two out-of-phase voltages through the ratio windings of a composite transformer. With a bandwidth of 5 mHz, a reduction of the rms instability to levels ranging from a few parts to below one part in 107 has been achieved, for different dynamic settings of the control.

The paper describes a class of nonlinear binary sequences which possess cyclic and multiple-state occurrence properties. Such sequences are null or cyclic, preceded by either a zero or finite transient phase.The sequences are realised by controlling the individual transfer between successive stages of a primaryregister by the states of a corrupting-register, which itself may be cyclic in behaviour.By considering a specific example the paper demonstrates that a pseudo-random binary sequence may be modified in this way. Two practical applications are discussed, namely the generation of vehicle travelling times used in traffic simulation studies of signalised intersections, and digital waveform synthesis

The present methods used to calibrate an active power or energy meter device under test (DUT) under nonsinusoidal conditions are based on a limited number of current and voltage waveforms and do not exercise the dynamic range of the DUT. After reviewing a method recently developed at the National Physical Laboratory (NPL) to exercise the dynamic range of a DUT under sinusoidal and nonsinusoidal conditions for specified current and voltage waveforms, the paper reports on the performance of the DUT under nonsinusoidal conditions measured using the NPL method. Experimental results: 1) verify theoretical predictions that the active power fractional full-scale (FS) error depends on both the phase-angle group between the current and voltage waveforms and the phase angle between the harmonics and the fundamental of both the current and voltage waveforms and 2) show that the active power fractional FS error for sinewave excitation can be larger than that for nonsinusoidal conditions

The celebrated Liouville theorem in complex analysis which asserts that any bounded holomorphic function on the entire complex plane has to be constant, has been extended to various areas of analysis.

A general definition of ``cosine'' and ``sine'' operators, C and S, for harmonic oscillator phase is proposed and its consequences examined. An important feature of the spectral analysis is the ``chain sequence'' condition which ensures that C and S have unit norm. The (nonunitary) operator U = C + iS is shown to be an annihilation-type operator whose spectral properties bear a remarkable analogy to those of the standard annihilation operator, although its spectrum fills the unit circle rather than the entire complex plane. Statistical properties of the eigenstates of U are discussed briefly.

In this paper we describe some of the dynamical behavior of the complex exponential λ exp z. For various values of λ, this family exhibits chaotic behavior on the entire complex plane. For other values, the dynamics are relatively tame. We show how to analyze this behavior via symbolic dynamics and investigate the structural instability at various parameter values. Finally, we describe the relationship between the parameter space for the exponential family and the related families of polynomials given by [Formula: see text].

We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to a broad class of supersymmetric quadratic multiplication-differentiation operators acting on L^2 (\mathbb R^n) which includes the elliptic and weakly elliptic quadratic operators. We demonstrate a variety of sharp results on boundedness, decay, and return to equilibrium for these solution operators, connecting the short-time behaviorwith the range of the symbol and the long-time behavior with the eigenvalues of their generators. This is particularly striking when it allows for the definition of solution operators which are compact and regularizing for large times for certain operators whose spectrum is the entire complex plane.

In view of the central symmetry of the set of Riemann zeros, \(\rho \leftrightarrow 1 - \rho\) which crucially reflects the functional equation (3.26), there is no clear reason to pick either the ρ themselves (with \(\rho \equiv \frac{1}{2} \pm i\tau_{k}, {\rm Re} \tau_{k} > 0\)) or the \(\rho(1 - \rho) = \frac{1}{4} + \tau_{k}^{2}\) as the basic set upon which to build zeta functions over the Riemann zeros. This is a nonlinear remapping freedom as discussed in Sect. 1.1, which leads to generalized zeta functions of several kinds. This chapter gives an introductory overview of the various possibilities. In decreasing order of analytical tractability, and in our older notation to be soon discarded, we may define: Functions of first kind: \(\sum_{\rho}(x - \rho)^{-s}, \qquad {\rm Re} s > 1;\) Functions of second kind: \(\sum\limits_{k = 1}^{\infty}(\tau_{k}^{2} + v)^{-\sigma},\qquad \mathfrak{R}\sigma > \frac{1}{2};\) Functions of third kind: \(\sum\limits_{k = 1}^{\infty}(\tau_{k}^{2} + \tau)^{-s},\qquad {\rm Re} s > 1.\) In all three kinds the argument (in exponent) is the principal variable, the other one a shift parameter. Each parametric family starts as an analytic function of its argument in its indicated half-plane of convergence, due to (4.7) or (4.26), but it will extend to a meromorphic function in the entire complex plane (of its argument), with a computable singular part. The domain of each shift parameter is left as large as possible: simply, none of the quantities to be raised to a power should lie on the cut \(\mathbb{R}_{-}\); this will hardly matter with the fairly small parameter values that we will emphasize.KeywordsMeromorphic FunctionZeta FunctionCentral SymmetryShift ParameterRiemann HypothesisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A complex valued function defined and analytic in the entire complex plane is called an entire function or an integral function. In other words, in the extended complex plane, it can have a singularity only at infinity. If f is an entire function different from a polynomial and M(r, f) [or M(r) when there is no confusion] denotes the maximum of |f(z)| on the circle |z| = r, it follows from Liou-ville’s theorem that M(r, f) increases more rapidly than any power of r. Thus, to study the growth of the function we have to compare with exponentials.