System impedance

Z = positive sequence equivalent system impedance, Q/phase at the location of the fault = negative sequence equivalent system impedance, fj/phase at the location of the fault. 

Fouling produces dirty and inefficient steam-water systems, impeding the natural or forced circulation within a boiler, limiting the flow in... 

Fouling produces dirty and inefficient cooling systems, impeding the flow of cooling water. It involves the physical adherence to surfaces and mutual entanglement of insoluble salts, corrosion products, oils, fats, and other process contaminants, air-blown debris, and the like. Where... 

When large power factor correction capacitors are present in an electrical system, the flow of capacitive current through the power system impedance can actually... 

The physical meaning of the ambipolar conductivity relates to the correlated transport of several charge carriers, when an internal -> electrical field in the system impedes the migration of species with a higher - mobility, but enhances transfer of less mobile species. 

However, real electrochemical systems exhibit much more complex behaviours. They are not simply resistive. The electrochemical double layer adds a capacitive term. Other electrode processes, such as diffusion, are time and/or frequency dependent. Therefore, for an actual electrochemical system, impedance is used instead of resistance. The impedance of an electrochemical system (defined as Ziot)) is the AC response of the system being studied to the application of an AC signal (e.g., sinusoidal wave) imposed upon the system. The form of the current-voltage relationship of the impedance in an electrochemical system can also be expressed as... 

P. W. Appel, Electrochemical Systems Impedance of a Rotating Disk and Mass Transfer in Packed Beds, Ph.D. dissertation. University of California, Berkeley, Berkeley, California (1976). 

A parallel development has taken place for related transfer-fimction methods. For electrochemical systems, impedance spectroscopy, which relies on measurement of current and potential, provides the general system response. As described in Chapters 14 and 15, transfer-function methods allow the experimentalist to isolate the portion of the response associated with specific inputs or outputs. 

In both cases considered here, the system impedance consists of the sum of two terms, corresponding to two elements resistance and capacitance or inductance. 

Other problems of transient system response may be solved in a similar way. More complex examples are presented, for example, in Refs. 33-34. It should be added that an arbitrary signal may be applied to the system and if the Laplace transforms of the potential and current are determined, for example, by numerical transform calculations, the system impedance is determined. In the Laplace space the equations [e.g., Eqs. (9) and (11)] are much simpler than those in the time space [e.g. Eqs. (10) and (12)] and analysis in the frequency space 5 allows the determination of the system parameters. This analysis is especially important when an ideal potential step caimot be applied to the system because of the bandwidth limitations of the potentiostat. In this case it is sufficient to know i(t) and the real value of the potential applied to the electrodes by the potentiostat, E(t), which allows numerical Laplace transformations to be carried out and the system impedance obtained. 

In order to simplify the calculations of impedances, the result obtained for the periodic perturbation of an electrical circuit may be represented using complex notation. The system impedance, Z(jco), may be represented as... 

The dc transient response of electrochemical systems is usually measured using potentiostats. In the case of EIS, an additional perturbation is added to the dc signal to obtain the frequency response of the system. The system impedance may be measured using various techniques ... 

It was shown in Section I. l(i) that the system impedance is defined as the ratio of Laplace transforms [Eq. (6)], of potential and current. In general, the transformation parameter is complex, 5 = v -i- jto. The imaginary Laplace transform... 

Palladium-gold on alumina catalysts are examples of bifunctional catalysts (3,4), in which the alumina carrier itself possesses acidic sites that are involved in the reactions. This property of the system impedes a detailed understanding of the effect of the gold in suppressing the formation of C,-C6 alkanes. However, when alkanes or cycloalkanes are contacted with simpler metal catalysts, specifically, metals which are either unsupported or supported on a relatively nonacidic carrier such as silica, a similar marked suppression in the formation of products of lower carbon number than the reactants is observed when a Group IB metallic element is incorporated with a Group VIII metal. Examples are given in our 1971 patent (5), for which the... 

This relation was proved by Nyquist (10) to be a consequence of basic thermodynamics laws and, except for quantum corrections, was never really challenged. Studies performed with glass microelectrodes (II) and heterogeneous ionic systems (12) showed that for zero ionic gradients and zero applied currents, the measured levels of noise were in agreement with noise levels calculated from the impedance according to eq 1. Hence, a study of electrical noise of a system under equilibrium conditions can be initiated for only two reasons. First, if there is some a priori information that the system is in equilibrium, then measurements of the system impedance or temperature can be performed without external perturbations (quantum effects are not considered here). Second, if impedance and temperature are measured independently by some other techniques, noise measurements can verify that the system under study is in an equilibrium state. 

The three factors of inertia (mass), resistance and capacitance (the reciprocal of spring compliance) are collectively known as impedance as intuitively, the system impedes the motion in the system. 

Impedance measurements are performed by applying an AC excitation voltage to an unknown system while measuring the current. The ratio of the excitation voltage to the current gives the complex impedance of the system. Impedance measurements of cells provide data on the intrinsic dielectric properties of the cells. 

A characteristic of PWM converters is that they are a source of voltage harmonics in all modes of operation (motoring and regeneration). The current harmonics will be a result of the system impedance at the harmonic frequencies. In order to comply with the IEEE 519 guidelines, the TMEIC P30 is normally operated with system impedances of 12 to 20% (based on a 1 PU rating equal to the drive capacity). 

Knowledge of the Laplace and Fourier transforms allows us to determine the system impedance and to solve the equations (f) =/[ (f)] for an arbitrary perturbation. 

In the presence of a redox reaction without diffusion limitations, the system impedance is described by the electrical equivalent circuit / s(Cdi ct) displayed in Fig. 2.34. Replacing the double-layer capacitance with the CPE produces complex plane and Bode plots (Fig. 8.4) corresponding to the equation for the impedance of such a system ... 

First, the system impedance must be written in the form of Eq. (13.22) 1... 

For the special case where the output signal is the system voltage and the input (or excitation function) is the current, the transfer function is the system impedance... 

In the following section we present a number of standard methods of measuring a system impedance or a frequency domain transfer function. In applying any of the methods described, the perturbation must be of a sufficiently small magnitude that the response is linear. Although the condition of linearity may be decided from theoretical considerations (Bertocci [1979], McKubre [1981], McKubre [1983], McKubre and Syrett [1986]), the most practical method is to inaease the input signal to the maximum value at which the response is independent of the excitation function amplimde. 

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