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Theory Section 16: Phase Control of Transmission Lines

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FieldValue
SourceTheoretical Elements of Electrical Engineering
Year1915
Section IDtheoretical-elements-electrical-engineering-section-16
Locationlines 6222-6813
Statuscandidate
Word Count1806
Equation Candidates In Section0
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16. PHASE CONTROL OF TRANSMISSION LINES 76. If in the receiving circuit of an inductive transmission line the phase relation can be changed, the drop of voltage in the line can be maintained constant at varying loads or even decreased with increasing load; that is, at constant generator voltage the transmission can be compounded for constant voltage at the receiving end, or even over-compounded for a voltage increasing with the load. 1. Compounding of Transmission Lines for Constant Voltage Let r = resistance, x = reactance of the transmission line, CQ = voltage impressed upon the beginning of the line, e = vol- tage received at the end of end line. PHASE CONTROL OF TRANSMISSION LINES 91 Let i = power current in the receiving circuit; that is, P — ei = transmitted power, and
... nerator voltage the transmission can be compounded for constant voltage at the receiving end, or even over-compounded for a voltage increasing with the load. 1. Compounding of Transmission Lines for Constant Voltage Let r = resistance, x = reactance of the transmission line, CQ = voltage impressed upon the beginning of the line, e = vol- tage received at the end of end line. PHASE CONTROL OF TRANSMISSION LINES 91 Let i = power current in the receiving circuit; that is, P — e ...
... the receiving circuit; that is, P — ei = transmitted power, and ii = reactive current produced in the system for controlling the voltage. i\ shall be considered positive as lagging, negative as leading current. Then the total current, in symbolic representation, is / = i - jii; the line impedance is Z = r + jx, and thus the e.m.f. consumed by the line impedance is Ei = ZI = (r + jx) (i - jii) = ri + jrii + jxi - J2xii; and substituting f — — 1, Ei = (ri + xii) ...
... (r2 + x2) + 2 iQre0. (13) This equation gives i'o as function of io, e0, r, x. If now the reactive current i\ varies as linear function of the power current i, as in case of compounding by rotary converter with shunt and series field, it is Substituting this value in the general equation (eo + n0)2 + *V = (e + ri + a»i)» + (rii - xz)2 gives e as function of i; that is, gives the voltage at the receiving end as function of the load, at constant voltage 60 a ...
... . Between i = 0 and i = io, e > eo, and the current is lagging. Above i = io, e < eQ, and the current is leading. By the reaction of the variation of e from eo upon the receiving apparatus producing reactive current z'i, and by magnetic satura- tion in the receiving apparatus, the deviation of e from eo is reduced, that is, the regulation improved. 2. Over-compounding of Transmission Lines 78. The impressed voltage at the generator end of the line was found in the preced ...
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