Lightning Induced Voltages On Power Lines: Theory And Experiment
Lightning Induced Voltages On Power Lines: Theory And Experiment
Master, Maneck Jal
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Ev(t) ^V2 ^2 ^3" ^V2 /t) = t^ • t . U{t) + [- i^ + t, - tJ • ^^-^2) • U(t-t2) ^ ^" ta- t2 ^ t. - t3^ • (^-^3) • U(t-t3) ^ ^- t^- t3 " ts- tJ • (t-t'*^ • "(t-tO + [- ts- t^ • (^-^5) - Evs^ • "(t-ts) (3.5) where u(t) is the unit step function. It can be seen that each term in Equation (3.5) represents a ramp, except for the last term which is a step, due to the fact that the field waveform in Figure 3.4 terminates at a finite non-zero value. At this point, a digression is necessary in order to de...termine the ramp and step response of W(s) as given in Equation 3.4. For a ramp input, i.e. we have, 158 Eylt) = m t u(t) (3.6) E,{s) = 1 /rr+~ojsT s2 Eh^s) = ^ • -fTo ^ TTo (3.7) /r s3/2(s + a/e^e^)l/2 Using a table of Inverse Laplace Transforms (e.g. Abramovitz and Stegun, 1968), we have from Equation (3.4) E^(t) =-iL . t . e'P^ [iQ(pt) + I^(pt)] . u(t) (3.8) ^r where P = o/2e^e^ Iq,Ii - modified Bessel's Functions of the first kind of the zeroth and first order respectively.
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