Electric mobility is one of the ways of containing greenhouse gas and local pollutants emissions in urban areas. Nevertheless, the massive introduction of battery-powered electric vehicles (EVs) is introducing some concerns related to their energy demand. Modelling vehicle usage and charging behavior is essential for charge demand forecasting and energy consumption estimation. Therefore, it is crucial to understand how the charging decisions of EV owners are influenced by different factors, ranging from the charging infrastructure characteristics to the users’ profiles. This review examines the approaches used to investigate charging behavior and highlights the trends and differences between the results, remarking on any gaps worthy of further investigation.

We consider the current correlation function for a three-dimensional system of fermions embedded in a homogeneous background and mutually interacting via an attractive short-range potential, below the (superconducting) critical temperature. Diagrammatic contributions in the broken-symmetry phase are identified, which yield for the (wave-vector and frequency-dependent) current correlation function the fermionic BCS approximation in the weak-coupling limit and the bosonic Bogoliubov approximation in the strong-coupling limit (whereby composite bosons form as bound-fermion pairs). The temperature dependence of the superfluid density (from the BCS exponential behavior at weak coupling to a power-law behavior at strong coupling) and the form of the Pippard-like kernel at zero temperature are explicitly obtained from weak to strong coupling. Quite generally, it is shown that the Pippard-like kernel is the sum of a local (London-like) term and of a nonlocal component, the local term being dominant in the strong-coupling limit and the nonlocal component in the BCS (weak-coupling) limit. It is also shown that the range of the nonlocal component is determined by the coherence length measuring the spatial correlations of the amplitude of the order parameter, namely, the correlations among different Cooper pairs (or composite bosons), rather than between the fermionic partners of a given pair. In addition, a prescription is provided for mapping the fermionic onto the bosonic diagrammatic theories in the broken-symmetry phase, thus complementing what has been already done in the normal phase.

We consider the role of the Ward identity in dealing with the transport properties of an interacting system forming a $d$-wave modulated charge-density wave or staggered flux phase. In particular, we address this issue from the point of view of the restricted optical-conductivity sum rule. Our aim is to provide a controlled approximation for the current-current correlation function which allows us also to determine analytically the corresponding sum rule. By analyzing the role of the vertex functions in both the microscopic interacting model and in the effective mean-field Hamiltonian, we propose a nonstandard low-energy sum-rule for this system. We also discuss the possible applicability of these results for the description of cuprate superconductors in the pseudogap regime.

An increasing share of renewable energy sources in power systems requires ad-hoc tools to guarantee the closeness of the system’s frequency to its rated value. At present, the use of new technologies, such as battery energy storage systems, is widely debated for its participation in the service of frequency containment. Since battery installation costs are still high, the estimation of their lifetime appears crucial in both the planning and operations of power systems’ regulation service. As the frequency response of batteries is strongly dependent on the stochastic nature of the various contingencies which can occur on power systems, the estimation of the battery lifetime is a very complex issue. In the present paper, the stochastic process which better represents the power system frequency is analyzed first; then the battery lifetime is properly estimated on the basis of realistic dynamic modeling including the state of the charge control strategy. The dynamic evolution of the state of charge is then used in combination with the celebrated rain-flow procedure with the aim of evaluating the number of charging/discharging cycles whose knowledge allows estimating the battery damage. Numerical simulations are carried out in the last part of the paper, highlighting the resulting lifetime probabilistic expectation and the impact of the state of the charge control strategy on the battery lifetime. The main findings of the present work are the proposed autoregressive model, which allows creating accurate pseudo-samples of frequency patterns and the analysis of the incidence of the control law on the battery lifetime. The numerical applications clearly show the prominent importance of this last aspect since it has an opposing impact on the economic issue by influencing the battery lifetime and technical effects by modifying the availability of the frequency regulation service.