This contribution proposes a new design methodology in energy system design, which integrates the branch and bound algorithm with exergy analysis (BBEx). In a search tree representation of the design problem, it applies upper and lower bounds to discharge ineffective branches at an early stage. At intermediate nodes, instead of solving the relaxed NLP subproblem, the BBEx algorithm calculates the residual exergy, which is a valid lower bound to an energetic objective function. This approach provides a lower bound at lower computational cost than the traditional branch and bound (BB) method and satisfies the constraint of system wide thermal autonomy. The numerical performance of the proposed method is compared with the classical BB and the total enumeration on a design problem of a wood based fuel cell power plant The results suggest that the proposed algorithm is a promising and efficient method for solving process synthesis problems in energy system design.