Energy efficiency has become a major concern for manufacturing systems, due to industry being the largest user of scarce, finite energy sources, and also to recent events which have pushed energy prices to alarming levels. In the present Industry 4.0 context, Reconfigurable Manufacturing Systems (RMS) are therefore one of the most promising manufacturing paradigm. In this paper, we investigate the suitability of one of the most common types of RMS, the Parallel-Serial manufacturing line with Crossover, to help minimise the peak of the electric power consumption. More specifically, the balancing of such a production line is studied, so as to integrate power peak minimisation from the design stage. Thus, we define the Parallel-Serial-with-Crossover Assembly Line Balancing Problem with Power Peak Minimization, a new combinatorial NP-hard problem. We also propose a suitable time-indexed Integer Linear Program that integrates balancing and scheduling decisions and a matheuristic algorithm designed to tackle large-size instances. Both approaches are tested on a wide set of instances. The computational results show that relevant power peak reductions can be achieved (33% on average), opening up promising perspectives from both algorithmic and managerial viewpoints.