This paper proposes a new problem formulation to simplify the mathematical representation for a hybrid ac/dc domestic energy system. Instead of building the formulation from a component level, the new formulation is built at the whole system level such that all power transfers between ac/dc or dc/ac are reflected in the ac power drawn from the main grid. This is achieved by assigning the ac power drawn from the grid as a piecewise function of local dc power, each slope in the function represents the conversion efficiency, making it flexible to consider a wide range of conversion efficiencies for different system components. The new formulation substantially reduces the number of variables/constraints, improves efficiency modelling accuracy and increases the search efficacy. The piecewise functions are directly solved by a mixed integer linear programming (MILP). The performance of the proposed formulation is illustrated by the hybrid ac/dc energy systems at a primary school in the U.K. The results show that the proposed problem formulation and the MILP solution method provide an effective optimal control strategy for a mixed ac/dc domestic energy system in the presence of variable tariffs and differing conversion efficiency, achieved a cost saving of 24% increase in energy bills compared with the traditional approach.