Ray and Carlos, thank you very much. Jerry.
On Thu, Mar 3, 2011 at 9:57 AM, Ray Zimmerman <[email protected]> wrote: > 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 > > > ------------------------------------------------------------------------------------ > > > > -- ------------------------------------------------------------------------------------ Zhengrui (Jerry) Qin Computer Science College of William and Mary Williamsburg, VA 23185 ------------------------------------------------------------------------------------
