Dear Alexandra, Since the network equations in MATPOWER's DC OPF assume no losses, it seems you would have to introduce the losses as dummy (dispatchable) loads at the downstream end of each branch. You would have to add an additional set of constraints for each of these dummy loads constraining the consumption lie above the piecewise linear constraints you propose. These constraints could be added using the mechanism for user-defined constraints described in section 5.3.2 and chapter 6 of the User's Manual.
Another approach to using MATPOWER to solve a "DC OPF with losses" is to simply run the DC OPF iteratively, each time adjusting the set of dummy loads used to represent losses based on flows in the previous iteration. I'm guessing it wouldn't require more than a few iterations to converge to a pretty good solution. This approach is a bit brute-force, but may be simpler to implement and allows you to use whatever function you like (e.g. a quadratic) to compute the losses. Just another idea. -- Ray Zimmerman Senior Research Associate 419A Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On May 27, 2013, at 3:16 PM, Alexandra Kapetanaki <[email protected]> wrote: > Dear Dr Ray, > > As the AC power flow requires high computation time for the losses to be > calculated, a DC opf can be used in conjuction with a linear model for > transmission losses. > My aim is to adjust the piece wise linear approach of Matpower in order to > accommodate the losses of a transmission line. > More particularly, the losses can be expressed through the following > equation: Ploss=rij(Pk)^2 [where rij the resistance of the line and Pk the > power flow in the transmission line]. > However, the above equation is a quadratic function but can be expressed with > a piecewise linear model. The figure below shows a linear model consists of N > line pieces > <piecewiselinear.png> > > > > the equation of the nth line piece is: > > <bbbbbbbbbbbbbbb.png> > > > > > > > -How can I modify the piece wise linear approach of Matpower with the view to > include the losses model? > > > Thank you in advance, > > Alexandra Kapetanaki > PhD Student > Electrical Energy & Power Systems Group, School of Electrical & Electronic > Engineering > Ferranti Building (B18), The University of Manchester, M13 9PL, United Kingdom > Tel: +44 (0) 161 306 2263; Mobile: +44 (0) 7857 598179
