SUMMARYWe consider the problem of designing an acoustic horn in order to efficiently transmit the incoming wave energy and favorably distribute the energy in the far field. A finite element solution of the Helmholtz equation, in planar or cylindrical symmetry, models the wave propagation. The transmission efficiency is monitored by measuring the back reflections into the feeding waveguide, and the far-field directivity pattern is computed using an integral expression known from scattering theory. The design problem is formulated as a non-linear least-squares problem, which is solved using a gradient-based algorithm, where the gradients are provided by solutions of the associated adjoint equations. The results demonstrate that this approach can generate horns with almost perfect transmission in a wide frequency band. Due to the improved transmission properties at the lower-frequency region, the optimization with respect to efficiency also generates improved far-field directivity patterns, that is, patterns that vary less with frequency. It is possible to obtain even more uniform directivity patterns by explicitly including directivity requirements in the optimization. However, those improvements in directivity seem to be associated with a substantial loss of efficiency.

Power imbalances such as power shortfalls and photovoltaic (PV) curtailments have become a major problem in conventional power systems due to the introduction of renewable energy sources. There can be large power shortfalls and PV curtailments because of PV forecasting errors. These imbalances might increase when installed PV capacity increases. This study proposes a new scheduling method to reduce power shortfalls and PV curtailments in a PV integrated large power system with a battery energy storage system (BESS). The model of the Kanto area, which is about 30% of Japan’s power usage with 60 GW grid capacity, is used in simulations. The effect of large PV power integration of 50 GW and 100 GW together with large BESS capacity of 100 GWh and 200 GWh has been studied. Mixed integer linear programming technique is used to calculate generator unit commitment and BESS charging and discharging schedules. The simulation results are shown for two months with high and low solar irradiance, which include days with large PV over forecast and under forecast errors. The results reveal that the proposed method eliminates power shortfalls by 100% with the BESS and reduce the PV curtailments by 69.5% and 95.2% for the months with high and low solar irradiance, respectively, when 200 GWh BESS and 100 GW PV power generation are installed.