This study proposes a distributed model predictive control (DMPC) scheme based on population games for a system formed by a set of sub-systems. In addition to considering independent operational constraints for each sub-system, the controller addresses a coupled constraint that involves the sum of all control inputs. This constraint models an upper bound on the total amount of energy supplied to the plant. The proposed approach does not need a centralised coordinator when having a coupled constraint involving all the decision variables. The proposed methodology, which takes advantage of evolutionary game theory concepts, provides an optimal solution for the described problem. Moreover, it is shown that the methodology has plug- and-play features, i.e. for each already designed local MPC controller nothing changes when more sub-systems are added/ removed to/from the global constrained control problem. Furthermore, the stability analysis of the proposed DMPC scheme is presented.