This paper focuses on research into and simulations of an energy storage system with high efficiency (or high durability), consisting of an electrochemical battery, which was connected to a ultracapacitor by voltage converters. An active connection between the battery and the ultracapacitor leads to good load distribution during charging and discharging. By adjusting the DC/DC converter system to a predefined exemplary load cycle, the ultracapacitor assumes high momentary current demand, while the remaining range of power demand is covered by the electrochemical battery. This way the ultracapacitor is used as an efficient energy source, reducing high current consumption from the battery, thus limiting energy losses in the battery and increasing its durability. This paper presents test bench research regarding the static and dynamic states of battery and ultracapacitor work. It contains a discussion on the theoretical and analytical relations underpinning and informing the development of the battery and ultracapacitor models. The paper shows the characteristics of voltage, current, and heat generation on the battery and ultracapacitor selected on the basis of the adopted cycle of power demand. The hybrid energy storage system proposed in this work is particularly suited for use in the zero-emissions building sector, associated with renewable energy sources and other distributed generation devices, and for their stable, durable and efficient operation.