By F. W. J. Olver
A vintage reference, meant for graduate scholars, mathematicians, physicists, and engineers, this ebook can be utilized either because the foundation for educational classes and as a reference software.
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Extra info for Asymptotics and special functions
Sequence network connection for a SLG fault. 3. 4. 58). 5, consists of a generator, transformer, transmission line, load transformer, and load. Consider a SLG fault at bus 20 kV LINE 2+ j4 ohm Fig. 5. 1. Analysis of Unsymmetrical Faults: Three-Component Method 39 C with a fault resistance of 4 ohms. The following data concerning the system is known. 05 pu, connected y-~ static (constant z) load of 10 + j5 MVA at 5 kV Solution Select Sa = 20 MVA, a load voltage of 5 kV, and compute all system impedances.
1. Sketch a circuit diagram of the fault point showing all phase connections to the fault. Label all currents, voltages, and impedances, carefully noting assumed positive directions and polarities. 1. It is assumed that a "normal" system consisting of only balanced impedances is connected to the left and right of the fault point and that the Thevenin equivalent looking in at this point is known. Note that phase voltages are defined as drops from line to ground at this point and that currents are defined as flowing from the system toward the fault.
N Van' V b n, • • • , V n n = the final or nth set of n balanced phasors with an angle n (2rr In) = 21T between components a, b, ... 8. 2) = the system dimension or number of phases. Then a 2 = ei 41r/ n rotates a phasor by 41T In radians a 3 = ei 6"/n rotates a phasor by 61T In radians an = ei 2" rotates a phasor by 21T radians. Negative powers of a are also easily defined and amount to negative (clockwise) rotation of phase angles. 1) by multiplying the equations by 1, a, a 2 , ••• , an with the result Va = Val aVb = aVb l + + ..
Asymptotics and special functions by F. W. J. Olver