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Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time, households hold an increasing amount of flexibility, which can be exploited by demand-side management to decrease customer cost and support grid operation. Compared to the collection of individual flexibilities, aggregation reduces optimization complexity, protects households’ privacy, and lowers the communication effort. In mathematical terms, each flexibility is modeled by a set of power profiles, and the aggregated flexibility is modeled by the Minkowski sum of individual flexibilities. As the exact Minkowski sum calculation is generally computationally prohibitive, various approximations can be found in the literature. The main contribution of this paper is a comparative evaluation of several approximation algorithms in terms of novel quality criteria, computational complexity, and communication effort using realistic data. Furthermore, we investigate the dependence of selected comparison criteria on the time horizon length and on the number of households. Our results indicate that none of the algorithms perform satisfactorily in all categories. Hence, we provide guidelines on the application-dependent algorithm choice. Moreover, we demonstrate a major drawback of some inner approximations, namely that they may lead to situations in which not using the flexibility is impossible, which may be suboptimal in certain situations.
We have investigated the ablation behaviour of single crystal SrTiO3 <100> with focus on the influence of the pulse duration at a wavelength of 248 nm. The experiments were performed with KrF-excimer lasers with pulse durations of 34 ns and 500 fs, respectively. Femtosecond-ablation turns out to be more efficient by one order of magnitude and to eliminate the known problem of cracking of SrTiO3 during laser machining with longer pulses. In addition, the cavities ablated with femtosecond pulses display a smoother surface with no indication of melting and well-defined, sharp edges. These effects can be explained by the reduced thermal shock effect on the material by using ultrashort pulses.