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Grainger and Steven write in Power Systems Analysis that "in a well-designed and properly operated power transmission system... the line susceptances Bij are many times larger than the line conductances Gij" (where the subscripts i and j refer to nodes of the power system).

Given that susceptances and conductances are reciprocals of reactances and resistances (respectively), it seems that an equivalent statement to the Grainger/Stevenson quote might be "the line reactances are many times smaller than the line resistances"

Web searches, on the other hand, indicate that line reactance >> line resistance. How is this possible?

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artist_and_not_EE_by_training
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  • Post an image of the book please. – Andy aka May 10 '23 at 13:12
  • At low frequency reactance of a wire goes to zero. At high frequency it goes to infinity. At some frequency it's going to cross over the resistance. Is this a 50/60 Hz system or the PDN of a GHz digital system? The latter will have tremendously more reactance than the former, at least to switching current. – user1850479 May 10 '23 at 13:17

2 Answers2

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Without reference to the book in question I can only draw on what I know about transmission lines (whether power AC or otherwise). Susceptance (in the parlance of transmission lines) doesn't refer to series components; it refers to the capacitive reactance between the two wires. You wrote this: -

where the subscripts i and j refer to nodes of the power system

And, I suspect, it means "across" the two wires of a power transmission system.

If the book were talking about resistance and reactance we would be talking about the series resistance and series inductive reactance of the conductors in a transmission line. But, we're not; we're talking about line capacitance and line galvanic leakage and, the only thing that loses power or decreases transmission efficiency is the galvanic leakage.

So, we want the galvanic leakage currents to be low compared to the capacitive reactance currents between the two wires. And this means that susceptance (the inverse of capacitive reactance), is expected to be much higher than conductance.

Andy aka
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    Andy thank you for the clarification that, in the parlance of transmission lines, susceptance refers to shunt susceptance. – artist_and_not_EE_by_training May 12 '23 at 13:35
  • The OP is correct that in the context of the book, i and j refer to nodes. The admittance matrix Y relates the node voltages to the injected currents at each node as I = Y V. This admittance model is the subject of Chapter 7 of the Grainger textbook. Y = G + jB where G and B are just the real and imaginary parts of the complex matrix Y. In other contexts, Y, G, and B might represent the shunt parameters of a branch, but in this particular chapter of this book that is not the case. – pdb5627 May 18 '23 at 16:15
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You are mistaken in your foundational assumption:

Given that susceptances and conductances are reciprocals of reactances and resistances (respectively)

This is not correct. You seem to be working from an intuition that \$Y = \frac{1}{Z} = \frac{1}{R + jX} \approx \frac{1}{R} - j\frac{1}{X}\$ whereas this is not correct. The correct relation is

$$ Y = \frac{1}{Z} = \frac{1}{R + jX} = \frac{R - jX}{R^2 + X^2} $$

So \$G = \frac{R}{R^2 + X^2}\$ and \$B = \frac{-X}{R^2 + X^2}\$ and the ratios \$\frac{X}{R} = -\frac{B}{G}\$.

pdb5627
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