2012  OriginalPaper  Chapter
Flexible Transmission in the Smart Grid: Optimal Transmission Switching
Authors: Kory W. Hedman, Shmuel S. Oren, Richard P. O’Neill
Publisher: Springer Berlin Heidelberg
2012  OriginalPaper  Chapter
Authors: Kory W. Hedman, Shmuel S. Oren, Richard P. O’Neill
Publisher: Springer Berlin Heidelberg
Notation


Indices and Sets


g

Generator

g(n)

Set of generators at bus
n

k

Transmission element (line or transformer)

k(n,.), k(.,n)

Set of transmission elements with bus
n as the to bus and the set with bus
n as the from bus respectively

m, n

Nodes

Parameters


B
_{ k }

Susceptance of transmission element
k

c
_{ g }

Production cost for generator
g

d
_{ n }

Real power load at node
n

G
_{ k }

Conductance of transmission element
k

M
_{ k }

Big M value for transmission element
k

P
_{ g }
^{ max }
, P
_{ g }
^{ min }

Max and min capacity of generator
g

P
_{ k }
^{ max }
, P
_{ k }
^{ min }

Max and min rating of transmission element
k; typically
P
_{k}
^{max} = 
P
_{k}
^{min}

θ
^{ max }
, θ
^{ min }

Max and min bus voltage angle difference; typically
θ
^{max} = 
θ
^{min}

θ
^{ rec }

Max voltage angle difference when reclosing breakers to bring a line back into service

Variables


P
_{ g }

Real power supply from generator
g at node
n

P
_{ k }

Real power flow from node
m to node
n for transmission element
k

Q
_{ k }

Reactive power flow from node
m to node
n for transmission element
k

V
_{ n }

Bus voltage at node
n

z
_{ k }

Binary switching variable for transmission element
k (0 open/not in service, 1 closed/in service)

γ
_{ k }

Bus voltage angle variable that is equal to transmission element
k’s
to bus angle value when the line is in service but equal to transmission element
k’s
from bus angle value when the line is out of service

θ
_{ n }

Bus voltage angle at node n

Online publication date: 17112011
Print ISBN: 9783642231926
Electronic ISBN: 9783642231933
Copyright Year: 2012
https://doi.org/10.1007/9783642231933
Version: 0.923.0