And, Jerry, you are correct that the proportion changes as different constraints are reached. I don't think you are going to find an analytic solution for large changes in load which involve a different set of binding constraints.
-- Ray Zimmerman Senior Research Associate 211 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Mar 2, 2011, at 11:31 PM, Carlos E Murillo-Sanchez wrote: > > 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 >> >> >> >> >> >> >> -- >> ------------------------------------------------------------------------------------ >> >> Zhengrui (Jerry) Qin >> >> Computer Science >> College of William and Mary >> Williamsburg, VA 23185 >> >> ------------------------------------------------------------------------------------ >
