ECE 598GG Fall 2007
Prof. George Gross
Room 339 Everitt Lab
Homework 7
due Thursday, October 18, 2007
Problem 1. [40 points] Impacts of a double-line outage contingency
We consider the simultaneous outage of two lines
′
and
′ ′
. Let
Δf
denote the changes
in the active power line flow on line
due to the simultaneous outage of lines
′
and
′ ′
.
We express
Δf
as the linear combination of the pre-outage active power line flows on lines
′
and
′ ′
:
Δf=
χ
′
f′
+
χ
′ ′
f′ ′
where
χ
′
and
χ
′ ′
are called LODFs for two line outage contingencies. Use two different
schemes to determine
χ
′
and
χ
′ ′
:
i)simultaneous outages
ii)sequential outages
Show that the two schemes lead to identical results.
Problem 2. [40 points] UTC evaluation considering two – line outage contingency
In the evaluation of the UTC
um,n
, we have considered the active power line flow constraints
for the base case and single line outage contingency cases. Now, we want to take into
account also the constraints for contingencies in which two lines are outaged
simultaneously. Formulate the optimization problem using the appropriate distribution
factors to determine
um,n
considering the constraints for all the following conditions:
i)the base case
ii)the set of single line outage contingencies for the subset
L=
1,2,,
L
{ }
⊂
L
: each line in the subset
L
is outaged individually
