This paper assesses the contribution of a controllable load (a reverse osmosis [RO] seawater desalination plant), together with an energy storage system in Porto Santo's small islanded electric power system. The controllable load and storage system are used to (i) smooth the net-demand fluctuations and adapt it to the availability of renewable energy sources (RES), thus avoiding possible curtailments and contributing to a higher dissemination of RES, (ii) minimize the overall operational cost associated with the production of electricity and potable-water, and (iii) reduce the environmental pollutants associated with the electric power systems on the island. The nonlinear nature of the problem makes it difficult to quickly obtain a robust solution through conventional mathematical tools. Therefore, an evolutionary algorithm is developed to find feasible solutions for dispatching the resources for a one-week simulation period. The proposed algorithm determined the power output of the conventional thermal power plant, the RO desalination plant operating periods, and the storage charging and discharging periods and powers. In the proposed scenario, through a seven-day simulation, 50% of the demand is supplied by renewable sources. The numerical results illustrate a reduction in the average total electricity-peak demand of the island. The obtained diagrams are compared with the data gathered on Porto Santo's energy system. They display that the proposed solution is economically beneficial for the management of the electric power grid of the island of Porto Santo, while reducing the global warming potential (GWP) of the electric power system. Furthermore, it reveals that in a scenario with 50% penetration of renewable sources, through the proposed solution, a more efficient and predictable operation of the conventional electricity generators and the RO desalination plants can be achieved.
In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration problem is modelled by an evolutionary process such that the restored image at any time satisfies an initial-boundary-value problem of cross-diffusion with reaction type. The coupled evolution of the two components of the image is determined by a nondiagonal matrix that depends on those components. A critical question when designing a good-performing filter lies in the selection of the optimal coefficients and influence functions which define the cross-diffusion matrix. We propose the use of deep learning techniques in order to optimize the parameters of the model. In particular, we use a back propagation technique in order to minimize a cost function related to the quality of the denoising processe, while we ensure stability during the learning procedure. Consequently, we obtain improved image restoration models with solid mathematical foundations. The learning framework and resulting models are presented along with related numerical results and image comparisons.
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