A Mathematical Modeling of Double Exponential Voltage – Waveshape (Impulse Generator) For Power Substations Using Laplace-Transform
Journal Title: International Journal of Engineering and Science Invention - Year 2018, Vol 7, Issue 5
Abstract
This paper presented a framework of mathematical model of double exponential voltage waveshape for purpose of generation of impulse voltages and currents. An impulse voltage is a unidirectional voltage which, without appreciable oscillations, rises rapidly to a maximum value and falls more or less rapidly to zero. The maximum value is called the peak value of the impulse and the impulse voltage is specified by this value. Small oscillations are tolerated provided that their amplitude is less than 5% of the peak value of the impulse voltage. An impulse voltage develops without causing flash over or puncture, is called a full impulse voltage, but if flash over or puncture occur thus causing sudden collapse of the impulse voltage is called a chopped impulse voltage. A full impulse voltage is characterized by its peak value and its two time interval, the wave – front the wave-tail time intervals. The wave front time of an impulse wave is the time taken by the wave to reach to its maximum value starting from zero value. It is difficult to identify the start and peak points of the wave, hence the wave front time is specified as 1.25 times (t2 – t1), where t2 is the time for the wave to reach to its 90% of the peak value and t1 is the time to reach 10% of the peak value. Since (t2 – t1), represents about 80% of the wavefront time, it is multiplied by 1.25 to give total wave front time. Evidently, some basic concept of circuit analysis including Laplace transform principle were used to solve for the double exponential voltage waveshape, formulated from the circuit analysis. The solutions of the formulated problems represents the model for the exponential growing voltage/currents wave shape representatively. Some specific assumptions were made in analyzing this models. The results from the analysis shows an exponential increase in voltage values with respect to time which represents the growth of the voltage pattern. This result are were represented on graph using matrix-laboratory (Matlab). Most importantly, the protection of power substations against lighting over voltages is critical reliable operation of electrical network since a frequent initiation of lighting surges etc without adequate moderation of the developed overvoltage may serious damage equipment, facilities etc resulting in power supply interruptions. This means that this paper will analyse time the voltage profile with respect to time in is order to access at what point the voltage is critical not adequate for power system equipments.
Authors and Affiliations
s. L. Braide, e. J. Diema
Keywords
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