Title: Representing value functions in power systems using parametric network series. Abstract: We describe a novel architecture for modeling the cost-to-go function in approximate dynamic programming problems involving country-scale, real-life electrical power generation systems. Our particular scenario features a heterogeneous power grid including dozens of renewable energy plants as well as traditional ones; the corresponding state space is in the order of thousands of variables of different types and ranges. While Artificial Neural Networks are a natural choice for modeling such complex cost functions, their effective use hinges on exploiting the particular structure of the problem which, in this case, involves seasonal patterns at many different levels (day, week, year). Our proposed model consists of a series of neural networks whose parameters are themselves parametric functions of a time variable. The parameters of such functions are learned during training along with the network parameters themselves. The new method is shown to outperform the standard backward dynamic programming program currently in use, both in terms of the objective function (total cost of operation over a period) and computational cost. Last, but not least, the resulting model is readily interpretable  in terms of the parameters of the learned functions, which capture general  trends of the problem, providing useful insight for future improvements.