This article investigates the potential of economic model predictive control of complex residential energy systems with electric coupling to the public grid. The examined system includes a battery energy storage system, photovoltaic power generation, an air-to-water heat pump, thermal energy storage and a building model. The said power generation provides energy for electric loads as well as domestic hot water and space heating. Model predictive control algorithms manage the energy system by nonlinear global optimization. Within this optimization, a time-varying state space model, which is derived from the energy system simulation model, reflects the system dynamics. Owing to the resulting high complexity, two algorithms for distributed model predictive control are developed. In addition, the developed approaches are compared to a common reference control concept as well as centralized model predictive control. For the comparison of annual operational costs, current German energy prices and subsidies are implemented into the economic calculation. Results show an improved performance of the developed approaches with 11.6% cost reduction in comparison to the reference. This is achieved through an increase of the heat pump seasonal performance factor by 3.4%, reduced curtailment of electrical photovoltaic energy to 21.5% of the reference value and prevention of auxiliary heater operation. Furthermore, increased photovoltaic self-consumption by the heat pump results in a slight reduction of battery storage operation. In conjunction with monetary and energetic advantages, model predictive control increases the comfort in regards to the violation of minimum limits for the comfort criteria.