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Long term electricity markets models tend to use simplified representations of both the demand and the generation units, to reduce the amount of input data and decision variables used, and also to decrease their execution times. On the one hand, hourly demand curves are usually simplified into a reduced set of non-chronological demand levels, each one representing hours with similar demand values. On the other hand, individual generation units are condensed into technologies grouping their costs curves by similarity in different appropriated technological cost mappings. This paper proposes several novel Mixed Integer Programming models to solve these two curve-fitting problems when the approximating function is a Piece-Wise Linear Function. By means of two real cases study it shows that the approximation approach has real applicability since it does not significantly compromise the traditional system representation.