We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.
The ever-increasing electrification of society has been a cause of utility grid issues in many regions around the world. With the increased adoption of electric vehicles (EVs) in the Netherlands, many new charge points (CPs) are required. A common installation practice of CPs is to group multiple CPs together on a single grid connection, the so-called charging hub. To further ensure EVs are adequately charged, various control strategies can be employed, or a stationary battery can be connected to this network. A pilot project in Amsterdam was used as a case study to validate the Python model developed in this study using the measured data. This paper presents an optimisation of the battery energy storage capacity and the grid connection capacity for such a P&R-based charging hub with various load profiles and various battery system costs. A variety of battery control strategies were simulated using both the optimal system sizing and the case study sizing. A recommendation for a control strategy is proposed.
