Note on surges of voltage and current in transmission lines
The increase in extent and capacity of electrical transmission systems lends increasing importance to the subject matter of this note; for excessive survoltage, particularly when it occurs suddenly, is apt to damage equipment and endanger life, cause a large and virtually instantaneous rise of potential at the point struck; and it is important, in the study of its effects, to determine the resulting disturbance at a distant point of the line. A solution of the fundamental case of an infinite transmission line, at the end of which a change of potential suddenly occurs, was propounded by Heaviside, but this solution appears to be incorrect. It nevertheless seems to have been very generally accepted by engineers who have dealt with the problem. The subject has also been discussed by Jeffreys, but it is felt that the present treatment offers advantages, not only in that it leads to a clearer physical apprehension of the phenomena, but also as being more amenable to the purpose of practical calculation. The equations between voltage V and current i at any point x and time t are d V/ dx + L di / dt + R i = 0, (1) di / dx + K d V/ dt + SV = 0, (2) where R is the resistance, S the leakage conductance, L the self-induction, and K the capacity of the line-all reckoned per unit length. Whence, d 2 V/ dx 2 = LK d 2 V/ dt 2 + (RK + SL) d V/ dt +RSV. (3)