Future energy infrastructure requires efficient and flexible residential energy systems. Model predictive control (MPC) enables optimized behavior by considering energy predictions. This study focuses on minimizing cost and uncertainties using MPC in electric-thermal systems. In addition a hierarchical control approach is proposed and evaluated through simulation in a new software framework called OptFlex and a laboratory experiment. The control system combines electricity and heat components for flexible and efficient energy production and consumption. It enables cost-effective and CO2 minimal utilization and a simple solution of accounting for the differences between forecasted and measured values of the energy components. The MPC is validated in a laboratory test for a PV-CHP system. Results show reliable control with a deviation of approximately 12%. The study also investigates a variable combined control variant to save computation time but incurs higher operating costs. The developed hierarchical control system effectively flexibilities, addresses uncertainties and can be applied to different energy systems including heat pumps.