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We build upon previous work out of UC Berkeley's energy, controls, and applications laboratory (eCal) that developed a model for price prediction of the energy day-ahead market (DAM) and a stochastic load scheduling for distributed energy resources (DER) with DAM based objective\cite{Travacca}. In similar fashion to the work of Travacca et al., in this project we take the standpoint of a DER aggregator pooling a large number of electricity consumers - each of which have an electric vehicle and solar PV panels - to bid their pooled energy resources into the electricity markets. The primary contribution of this project is the optimization of an aggregated load schedule for participation in the California Independent System Operator (CAISO) real time (15-minute) electricity market. The goal of the aggregator is to optimally manage its pool of resources, particularly the flexible resources, in order to minimize its cost in the real time market. We achieves this through the use of a model predictive control scheme. A critical difference between the prior work in \cite{Travacca} is that the structure of the optimization problem is drastically different. Based upon our review of the current and public literature, no similar approaches exist. The main objective of this project were building methods. Nevertheless, to illustrate a simulation with 100 prosumers was realized. The results should therefore be taken with a grain of salt. We find that the Real Time operation does not substantially decrease or increase the total cost the aggregator faces in the RT market, but this is probably due to parameters that need further tuning and data, that need better processing.

We study the dynamics of semiclassical electrons in (gapped) graphene in two complementary limits, i.e. in the Klein tunneling and valley Hall effect regimes, by scattering wave packets off armchair step potentials and by exposing wave packets to a uniform electric field, respectively. Our numerical wave packet simulation goes beyond semiclassical analytical approximations and standard Klein tunneling treatments and allows to study intra- and intervalley scattering processes. We find distinct Klein tunneling characteristics for low and tall steps, which include unusual Berry curvature induced side shifts of the scattered wave packet trajectories. In the presence of a uniform field, our simulations capture the semiclassical valley Hall effect which manifests in the form of laterally shifted Bloch oscillations. Such anomalous trajectory corrections can be relevant for Klein tunneling experiments and electron optics devices. We present detailed simulation results., Comment: 8+ pages, 6 figures

We have theoretically investigated the time-evolution of electron transport from a two-dimensional electron system (2DES) to a quantum dot (QD). We clearly showed that the coherent electron transport is remarkably modified depending on the initial electronic state in the 2DES. The electron transport from the 2DES to the QD is strongly enhanced when the initial state of electron in the 2DES is localized below the QD. We indicate that these features should be obtained in other nano-structure-electrode coupled systems, and the electron transport between the systems having completely different geometrical conditions is significantly affected by the initial spatial distribution of the electron density., Comment: 3figures