Network link (branch)
[Transmission flow solver (network)]

The link object implements the general solution elements for branches using the Gauss-Seidel method. More...

Detailed Description

The link object implements the general solution elements for branches using the Gauss-Seidel method.

The following operations are performed on each branch during a bottom-up sync event.

The effective admittance Y is calculated by including half of the line charging capacitance B [Kundur 1993, p. 258]:

$\widetilde{Y}_{eff} = \widetilde{Y} + \jmath \frac{B}{2}$

The admittance coefficient is the inverse of the transformer turns ratio n, if any [Kundur 1993, p. 236]:

$c \leftarrow \frac{1}{n}$

The effective line self-admittance is the product of the admittance coefficient and component admittance

$\widetilde{Y}_c = \widetilde{Y}_{eff} c$

Add the self-admittance and the shunt admittances to the busses [Kundur 1993, p. 259]

$\Sigma \widetilde{Y}_{from} \leftarrow \Sigma \widetilde{Y}_{from} + \widetilde{Y}_c + \widetilde{Y}_c (c-1)$

$\Sigma \widetilde{Y}_{to} \leftarrow \Sigma \widetilde{Y}_{to} + \widetilde{Y}_c + \widetilde{Y}_{eff} (1-c)$

Compute the line current injections on the busses

$\widetilde{I}_{from} \leftarrow \widetilde{V}_{to} Y c$

$\widetilde{I}_{to} \leftarrow \widetilde{V}_{from} Y c$

Add the current injections to the busses

$\Sigma \widetilde{YV}_{from} \leftarrow \Sigma \widetilde{YV} - \widetilde{I}_{from}$

$\Sigma \widetilde{YV}_{to} \leftarrow \Sigma \widetilde{YV} - \widetilde{I}_{to}$

Compute the line current (from -> to)

$\widetilde{I} \leftarrow \widetilde{I}_{from} - \widetilde{I}_{to}$