Synthesis of energy systems is a complex task typically depending on multiple large time series for demands, prices and resources. Problem complexity increases further by time-coupling constraints, e.g., due to storage systems. To still efficiently solve complex synthesis problems, we propose the rigorous synthesis method RiSES(3). RiSES(3) provides feasible solutions (upper bounds) with known quality (lower bounds). Lower bounds are obtained by two competitive approaches: linear-programming relaxation and relaxation based on time-series aggregation. To obtain a feasible design for the energy system, we use time-series aggregation and subsequently solve an operational problem yielding an upper bound. To tighten the bounds, we iteratively increase the resolution of the time-series aggregation and tighten the relaxation. RiSES(3) is applied to two industrial synthesis problems of energy systems with time-coupling constraints, storage systems and volatile prices. RiSES(3) shows fast convergence, outperforming a commercial state-of-the-art solver. (C) 2019 Elsevier Ltd. All rights reserved.