The impact of location and type on the performance of Low-Voltage network connected Battery Energy Storage Systems

This paper assesses the impact of the location and configuration of Battery Energy Storage Systems (BESS) on Low-Voltage (LV) feeders. BESS are now being deployed on LV networks by Distribution Network Operators (DNOs) as an alternative to conventional reinforcement (e.g. upgrading cables and transformers) in response to increased electricity demand from new technologies such as electric vehicles. By storing energy during periods of low demand and then releasing that energy at times of high demand, the peak demand of a given LV substation on the grid can be reduced therefore mitigating or at least delaying the need for replacement and upgrade. However, existing research into this application of BESS tends to evaluate the aggregated impact of such systems at the substation level and does not systematically consider the impact of the location and configuration of BESS on the voltage profiles, losses and utilisation within a given feeder. In this paper, four configurations of BESS are considered: single-phase, unlinked three-phase, linked three-phase without storage for phase-balancing only, and linked three-phase with storage. These four configurations are then assessed based on models of two real LV networks. In each case, the impact of the BESS is systematically evaluated at every node in the LV network using Matlab linked with OpenDSS. The location and configuration of a BESS is shown to be critical when seeking the best overall network impact or when considering specific impacts on voltage, losses, or utilisation separately. Furthermore, the paper also demonstrates that phase-balancing without energy storage can provide much of the gains on unbalanced networks compared to systems with energy storage.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.