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.net barcode printing Transient Overvoltages Transient Overvoltages 119 in Software
Transient Overvoltages Transient Overvoltages 119 PDF417 Creation In None Using Barcode printer for Software Control to generate, create PDF 417 image in Software applications. Recognize PDF417 2d Barcode In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Figure 47 Coupling of impulses through the interwinding capacitance of transformers
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ANSI/AIM Code 128 Maker In C#.NET Using Barcode maker for VS .NET Control to generate, create Code 128A image in .NET framework applications. EAN 13 Generator In Java Using Barcode creation for Android Control to generate, create GS1  13 image in Android applications. The term ferroresonance refers to a special kind of resonance that involves capacitance and ironcore inductance The most common condition in which it causes disturbances is when the magnetizing impedance of a transformer is placed in series with a system capacitor This happens when there is an openphase conductor Under controlled conditions, ferroresonance can be exploited for useful purpose such as in a constantvoltage transformer (see Chap 3) Ferroresonance is different than resonance in linear system elements In linear systems, resonance results in high sinusoidal voltages and currents of the resonant frequency Linearsystem resonance is the phenomenon behind the magnification of harmonics in power systems (see Chaps 5 and 6) Ferroresonance can also result in high voltages and currents, but the resulting waveforms are usually irregular and chaotic in shape The concept of ferroresonance can be explained in terms of linearsystem resonance as follows Consider a simple series RLC circuit as shown in Fig 49 Neglecting the resistance R for the moment, the current flowing in the circuit can be expressed as follows: I where E XL XC driving voltage reactance of L reactance of C E j (XL XC) When XL XC, a seriesresonant circuit is formed, and the equation yields an infinitely large current that in reality would be limited by R An alternate solution to the series RLC circuit can be obtained by writing two equations defining the voltage across the inductor, ie, Downloaded from Digital Engineering Library @ McGrawHill (wwwdigitalengineeringlibrarycom) Copyright 2004 The McGrawHill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Transient Overvoltages Transient Overvoltages 121
XL I E XC
Simple series RLC circuit
jXLI E jXCI
where v is a voltage variable Figure 410 shows the graphical solution of these two equations for two different reactances, XL and XL XL represents the seriesresonant condition The intersection point between the capacitive and inductive lines gives the voltage across inductor EL The voltage across capacitor EC is determined as shown in Fig 410 At resonance, the two lines will intersect at infinitely large voltage and current since the XC line is parallel to the XL line Now, let us assume that the inductive element in the circuit has a nonlinear reactance characteristic like that found in transformer magnetizing reactance Figure 411 illustrates the graphical solution of the equations following the methodology just presented for linear circuits While the analogy cannot be made perfectly, the diagram is useful to help understand ferroresonance phenomena It is obvious that there may be as many as three intersections between the capacitive reactance line and the inductive reactance curve Intersection 2 is an unstable solution, and this operating point gives rise to some of the chaotic behavior of ferroresonance Intersections 1 and 3 are stable and will exist in the steady state Intersection 3 results in high voltages and high currents Figures 412 and 413 show examples of ferroresonant voltages that can result from this simple series circuit The same inductive characteristic was assumed for each case The capacitance was varied to achieve a different operating point after an initial transient that pushes the system into resonance The unstable case yields voltages in excess of 40 pu, while the stable case settles in at voltages slightly over 20 pu Either condition can impose excessive duty on power system elements and load equipment For a small capacitance, the XC line is very steep, resulting in an intersection point on the third quadrant only This can yield a range of voltages from less than 10 pu to voltages like those shown in Fig 413 Downloaded from Digital Engineering Library @ McGrawHill (wwwdigitalengineeringlibrarycom) Copyright 2004 The McGrawHill Companies All rights reserved Any use is subject to the Terms of Use as given at the website

