The Dynamic Economic Dispatch (DED) problem consists in satisfying a certain demand for electric power among scheduled generating units over a certain interval of time while satisfying the operating constraints of these units. The consideration of the valve-point effect (VPE) makes the problem more practicalbutalsomorechallengingduetothenon-linearandnonsmooth constraints that are required for representing the model. We present a method, based on a sequence of piecewise linear approximations, which produces a feasible solution along with a lower bound on the global solution. In this way, this deterministic approach can trade off the speed which characterizes certain heuristics that are usually used to solve the DED-VPE for a better solution and insights about the problem. The method is applied to a widely used case study and provides a lower solution objective than the best known solution to date.