You might consider implementing a different formulation of the piecewise linear function with a different set of user-defined costs and variables in the OPF.
Maybe one of the formulations in [1] would be applicable to the concave case. Ray [1] R. Fourer, “A simplex algorithm for piecewise-linear programming iii: Computational analysis and applications<https://rdcu.be/b9E6j>,” Mathematical Programming, vol. 53, no. 1-3, pp. 213–235, 1992. doi: 10.1007/BF01585703<https://doi.org/10.1007/BF01585703> On Nov 3, 2020, at 5:56 AM, Juraj Kardos <[email protected]<mailto:[email protected]>> wrote: Dear all, I am dealing with concave piecewise linear costs. Matpower adopts constrained cost variable (CCV) approach for piecewise linear costs (section 6.4.1 in the manual), but the assumption there is that the function is convex. Do you have any suggestion how to deal with concave functions? My best idea is to use a linear regression to transform the concave piecewise linear cost function into a purely linear function, but obviously this would under/over-estimate the actual cost. Thank you for any ideas!
