We consider the so-called periodically aggregated resource-constrained project scheduling problem. This problem, introduced by Morin et al. 2017, is a variant of the well-known resource-constrained project scheduling problem that allows for a more flexible usage of the resource constraints. While the start and completion times of the activities can be arbitrary moments in time, the limitations on the resource usage are considered on average over aggregated periods of parameterized length. This paper presents new theoretical and experimental results for this problem. First, we settle the complexity status of the problem by proving NP-hardness of a number of special cases of the problem. Second, we propose a new mixed-integer programming formulation of the problem by disaggregating the precedence constraints over the periods. A theoretical comparison shows that the new formulation dominates the previously proposed one in terms of relaxation strength. Finally, we carry out computational experiments on instances from the literature to compare the merits of the different formulations.