The constantly-increasing concern on environment and sustainability and the recent events which have pushed energy prices to alarming levels have led manufacturing systems to try to achieve higher standards of energy efficiency. This is the reason behind the growing interest of the research community in the study of optimization problems in production systems that deal with energy-related constraints and/or criteria. Among them is the Simple Assembly Line Balancing Problem with Power Peak Minimization (SALB3PM). The problem attempts to assign the tasks of a production process to the workstations of a paced straight machining line, and to determine their starting times so as to minimize the peak of the overall power consumption profile. This work focuses on the SALB3PM and proposes a new Mixed-Integer Linear Programming formulation in which a set of binary three-index variables models the core assignment and trigger decisions. We show that the proposed model outperforms the reference 01LP model on a benchmark instance set. We then test the model on new instances in which tasks have non constant power profiles and we propose some valid inequalities and preprocessing. Numerical results are presented and discussed.