Piecewise linear approximation of generators cost functions using max-affine functions

Nonlinear functions are often encountered in power system optimizations. In this paper, an effective piecewise linear (PWL) approximation technique is introduced which shows promising performance in linearizing the nonlinear functions. This method uses a series of linear functions, called max-affine functions, to linearize a multivariate function over a bounded domain. The important advantage of this method is its ability to decide on the size of the subspaces, which other methods are not capable of. It is also shown that using the PWL approximation, significant efficiency is achievable in computation burden of most power system optimizations, such as unit commitment.