Contents
Introduction 3
Fourier Series, Continuous Transform and Discreet Transform 3
it should be noted that the coefficients in the equations above are given as follows. 3
Application of DFT in power system relaying 7
10
Conclusion 10
References 10
Introduction
The use of digital computers for power system relaying has been proposed long time ago in [1]. Discrete Fourier transform (DFT) was one of the first algorithms that have been proposed to be used in digital relaying. DFT has been the focus of many researched due to its simplicity and its relevant properties. Variations of the DFT have been proposed. This includes the short window, long window and the symmetrical component DFT [2]. DFT has many advantages compared to other types of transforms. In this short report the DFT will be reviewed. An emphasis will be given on the DFT as compared to the usual Fourier transform. The use of DFT in relaying will be outlined and explained. The frequency response of the DFT will be sketched out and stressed. The report ends with the advantages and the disadvantages of the DFT used in power system relaying.
Fourier Series, Continuous Transform and Discreet Transform
Fourier series has been proposed by Fourier in the late 18 century to deal with some mathematical heat problems [4]. Fourier insight was that any signal can be decomposed to periodic components in terms of trigonometric functions. Euler and Lagrange has shown before Fourier that periodic functions can be decomposed to such an expansion but Fourier’s contribution has been in proposing that any function can be decomposed in such a way although he wasn’t able to prove it [5]. It took almost one hundred years for mathematicians to prove that Fourier’s claim was ...
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...erve to represent an arbitrary function between two given limits". Journal f¨ur die reine und angewandte Mathematik, Vol. 4 (1829) p. 157–169.
[5] Ivor Grattan-Guinness; J. R. Ravetz,” Joseph Fourier, 1768-1830: A Survey of His Life and Work”
[6] Georgi P. Tolstov,” Fourier Series”, Dover Publications, 1976
[7] Francis J. Narcowich; Albert Boggess,” A First Course in Wavelets with Fourier Analysis”, Wiley; 2 edition, 2008
[8] Mann, B.J.; Morrison, I. F., "Digital Calculation of Impedance for Transmission Line Protection," Power Apparatus and Systems, IEEE Transactions on , vol.PAS-90, no.1, pp.270,279, Jan. 1971
[9] Phadke, A.G.; Hlibka, T.; Ibrahim, M.; Adamiak, M.G., "A Microcomputer Based Symmetrical Component Distance Relay," Power Industry Computer Applications Conference, 1979. PICA-79. IEEE Conference Proceedings , vol., no., pp.47,55, 15-18 May 1979
Zimmerman, Franklin B. Henry Purcell, 1659-1695: His Life and times. Philadelphia: University of Pennsylvania, 1983.
In section II of this paper, theoretical background relevant to this problem is presented. Section III is a brief summary of the numerical data from Giorgini, Boronat, and Casulleras.
My knowledge of engineering is reasonable and includes transformer substations, power plants, power distribution and transmission systems, industrial motor control and PLC programming, protective relay coordination, FACTS devices, grounding systems, Matlab programming and project management. In addition, I possess practical experience performing power flow, short-circuit and relay coordination analyses while using a power system modelling software such as ETAP, EDSA, DigSilent and CYME. Consequently, the aforementioned experience and solid engineering education along with your training will allow me to provide support to operating and new
He took his teaching duties very seriously, while he was preparing lectures for his charge on variety an of topics about science. The first scientific work dates were all from this period. It involves topics, which would continue to occupy him throughout his life. In 1571, he began publication of his track. It was intended to form a preliminary mathematical part of a major study on the Ptolemaic astronomical model. He continued to embrace the Ptolemaic (Parshall 1).
Newton’s inventive years with mathematics were from 1664 to 1696. Even though his companions also had likely various elements of the calculus, Newton summed everything up and included these ideas of his while developing new and more exact methods. The necessary elements of his thought were on hand in three tracts, De analysi (On Analysis), which went unpublished until 1711. In 1671, Newton developed a more absolute account of his course of infinitesimals, which appeared nine years after his death as “Methodus fluxionum et serierum infinitarum”.
According to the modern way of life the need for computer in every work place and home is high which decreases even more the power of the customers. However, the switching costs are low (2.2)
For the prevantion of the electricity blackout we need to build smart power grid. A modernized electrical grid that uses analog or digital information and communications technology to gather and act on information, such as information about the behaviours of suppliers and consumers is known as a smart grid. This is used to improve the efficiency, reliability, economics, and sustainability of the production and distribution of electricity in an automated fashion[12]. The important aspects of smart grid is to electronic power conditioning and control of the production and distribution of
Allen, James. "Greatest Mathematicians Born Between 1800 and 1850 A.D.." Fabpedigree. N.p.. Web. 8 Dec 2013. .
Born in France on March 31st, 1596, Rene Descartes grew to be known as ‘The Father of Modern Philosophy”. Not only was Rene a philosophical man but he contributed greatly to Mathematics and his ideas have influenced our daily lives in a productive way. DesCartes was raised in a very religious christian family, his father was a member of the parliament and strongly believed in education at a young age. DesCartes studied at the Jesuit college at the mere age of eight. As a child and throughout his adulthood physical incapabilities enabled DesCartes to function as swift or promptly as his peers. Growing up and until the day of his death, Descartes’s health was always a major precaution he was forced to remain aware of. The Jesuit college granted him the immunity of resting in mornings before class. It was this education that led him to contribute philosophical and mathematical theories and devices that still hold a great value to mathematicians and everyday people even today in the 21st century. From a very young age he had interests in mathematics and analytical geometry. Descartes’s contributions to modern day society were affected by his young adulthood, soon he created mathematical and scientific ideas, and lastly philosophical ideas.
Blaise Pascal lived during a time when religion and science were clashing and challenging previous discoveries and ideas. Pascal lived from 1623 to 1662 due to his untimely death at the age of thirty nine. The scientific community grew enormously and Pascal was a great contributor to this growth. The growth in the scientific community is known as the Scientific Revolution. He lived in a time where an absolute monarch came into power, King Louis the XIV. Louis XIV was a believer in “one king, one law, and one faith” (Spielvogel, 2012). Pascal saw the destruction of protestant practices in France and the growth and acceptance of scientific discoveries. He used the scientific method to refine previous experiments that were thought to be logical but Pascal proved otherwise and eventually led to Pascal’s Law. He spent his life devoted to two loves: God and science. Within his book, “Pensees,” Pascal argues and shares his thoughts about God, science, and philosophy.
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
already formulated calculus conclusions of his own. It is also worth mentioning that many of the concepts of calculus were invented as a result of their collaboration during their letter correspondents; important discoveries such as the power series.
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Have, R. "Fourier Analysis and Synthesis." Gsu. edu. C.R. Nave, 2012. Web. 28 Nov. 2013. .