Decentralized energy production is meant to reduce generation and distribution inefficiencies, leading to major economic and environmental benefits. This new model is meant to be supported by smart grids, electricity networks that can intelligently integrate the actions of all users connected to them —generators, consumers, and prosumers (those that do both)— to efficiently deliver sustainable, economic and secure electricity supplies. A major research challenge is the design of markets for prosumers in smart grids that consider distribution grid constraints. Recently, a discrete market model has been presented that allows prosumers to trade electricity while satisfying the constraints of the grid. However, most of the times energy flow problems possess a continuous nature, and that discrete market model can only provide approximate solutions. In this paper we extend the market model to deal with continuous (piecewise linear) utility functions. We also provide a mapping that shows that the clearing of such a market can be done by means of integer linear programming.