Validation of a lithium-ion commercial battery pack model using experimental data for stationary energy management application.

Background: A cost-effective solution for the design of distributed energy storage systems implies the development of battery performance models yielding a suitable representation of its dynamic behaviour under realistic operation conditions. Methods: In this work, a lithium-ion battery (LIB) is tested to be further modelled and integrated into an existing energy management control system. This specific LIB (5.0 kW /9.8 kWh) is integrated with a commercial inverter and solar photovoltaic (PV) system (3.3 kWp) as part of a microgrid that is also encompassing other energy storage technologies at the University of Évora, Pole of INIESC - National Research Infrastructure for Solar Energy Concentration. A testing protocol fully characterizes the battery and the inverter efficiency to describe their performance better. Then, a battery model is built upon both the existent LIB description and experimental fitting regression. The model allows obtaining the voltage curve, the internal resistance (i.e., to describe instantaneous voltage drop/rise and transients), and the state of charge (SOC) and/or energy capacity based on the current input. The developed model is validated through the comparison with the experimental results. Results: The model approach presented a higher voltage RMSE (root mean square error) of 5.51 V and an MRE (maximum relative error) of 5.68 % in the discharge state. Regarding SOC, the MRE obtained was approximately 6.82 %. In the charge state, the highest RMSE voltage was 5.27 V, with an MRE of 6.74 %. Concerning SOC, the MRE obtained was approximately 6.53 %.  Conclusions: The developed model is validated through the comparison with experimental results. Based on computational effort, simplicity of use and the associated model error, the approach is validated to the regular conditions of the commercial battery pack to be incorporated in the next research step, following a bottom-up modelling approach for an increasingly more complex smart grid.

Ideal concentrators with gaps.

Ideal concentrators with large gaps are presented. These new devices use optical elements surrounding the receiver. When their number is large, they (may) constitute a microstructure (many components with small sizes). Smaller gaps can also be achieved by use of a fewer number of optics. Different ways to combine these optical elements are presented for the case of larger and smaller gaps. Designs that use mirrors and total internal reflection are also presented for the case of larger gaps. The mathematical methods used to calculate the shape of the optics are outlined. In spite of the fact that the number of optics may be large, given the symmetries inherent to these designs, the elements in these microstructures are all equal. This is a simplifying feature that is important for their design and eventual production in the future.