- Solve a DC OPF with no losses. - Compute the loss for each branch, Ploss = rij(Pk)^2. - Add half of the loss to the load at the buses connected by the branch. - Re-solve the DC OPF. - Recompute the loss for each branch based on the new flow. - Adjust the loads at each end of the branch to reflect the change in losses. - Repeat, until the change from one iteration to the next is smaller than some threshold.
-- Ray Zimmerman Senior Research Associate 419A Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On May 28, 2013, at 12:25 PM, Alexandra Kapetanaki <[email protected]> wrote: > Dear Ray, > > Thank you for your help! > Can you please explain me more what do you mean with the "adjusting the set > of dummy loads used to represent losses based on flows in the previous > iteration". > For example, I want to represent the losses as dummy loads according to the > following figure: > > > <losses.png> > > > > > and express the losses by using the quadratic equation : Ploss=rij(Pk)^2 . > How can I practically implement that within "few iterations", as you > recommend? > > Thank you once again for your support, > > > 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 > From: [email protected] > [[email protected]] on behalf of Ray Zimmerman > [[email protected]] > Sent: 28 May 2013 16:55 > To: MATPOWER discussion forum > Subject: Re: transmission losses-piece wise linear approach > > 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 > >
