Hello;
An optimal power flow, when confronted with an incremental load change,
dictates a distributed
slack-taking rule that maintains optimality conditions.
"The proportion is fixed for an incremental load change in any bus" -
yes, if the costs are linear.
If the costs are adequately smooth, the proportion changes smoothly,
though. If the costs are piecewise linear,
the proportion can change abruptly, as it can also change if new
constraints become "active".
An (I think) interesting analysis of OPF sensitivity can be found in
the appendix of
http://e3rg.pserc.cornell.edu/node/50
carlos.
z qin wrote:
Dear Mr.Zimmerman:
Thank you very much. Yes, I am using the same slack when I say "works
for DC PF".
In DC OPF, there are generator capacity constraints and transmission
line constraints. Before any constraint being reached, the proportion
is fixed for an incremental load change in any bus. However, the
proportion keeps changing as one and more constraints are reached. In
this case, is it possible to predict the flow changes among all
branches for an incremental load change? Can we resort to the original
equations to get an analytic solution?
Thanks a lot.
Jerry
On Wed, Mar 2, 2011 at 8:18 PM, Ray
Zimmerman <[email protected]> wrote:
The
PTDF shows how the power flows change based on load changes, given a
specific slack distribution. When you say that it "works for DC PF", I
assume you mean that you can use it to predict the new flows you get
when you run a new DC PF. That's because you probably are using the
same slack bus for both. If you think about how a DC OPF redispatches
for an incremental load change, the "slack" is taken up by the units
that are on the margin. I'm not sure how to compute what the proportion
is, but if you knew that proportion you could use it to specify the
slack distribution for computing the appropriate PTDF.
--
Ray Zimmerman
Senior Research Associate
211 Warren Hall, Cornell University, Ithaca, NY 14853
phone: (607) 255-9645
On Mar 2, 2011, at 5:27 PM, z qin wrote:
> Hello,
>
> It seems that the linear shift factors (PTDF matrix) only works
for DC PF, but not for DC OPF. Is there a corresponding matrix for DC
OPF? I am wondering how the power flows on all the branches change if
one bus's power demand changes. Any suggestions? Thanks a lot.
>
> Jerry
--
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Zhengrui (Jerry) Qin
Computer Science
College of William and Mary
Williamsburg, VA 23185
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