Living with ghosts in Horava-Lifshitz gravity

We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts' spatial momenta, can be raised up to $\Lambda \sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared ($10^{-42}\lesssim$) $c^2_s \lesssim 10^{-20}$, that could be a promising candidate for the Dark Matter. Despite these advantages, the unavoidable presence of the strong coupling obscures the implementation of the original Horava's proposal on quantum gravity. Apart from the Horava-Lifshitz model, conclusions of the present work hold also for the mimetic matter scenario, where the analogue of the projectability condition is achieved by a non-invertible conformal transformation of the metric.Comment: 33 pages, 1 figure. The proof of an equivalence between the IR limit of the projectable Horava-Lifshitz gravity and the mimetic matter scenario is given in Appendix A. Version accepted for publication in JHE

Spherically Symmetric Solutions in Ghost-Free Massive Gravity

Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz invariant and a Lorentz breaking asymptotically flat behaviour and also fall in two branches. In the first branch, all solutions can be found analitycally and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.Comment: 15 pages. Some change in the reference

Models for characterising the final electricity demand

Nowadays the consumption and generation profile estimation is of the greatest importance. New loads characterized by coincident peak of consumption (e.g., home charging of electric vehicles) or by high absorption peaks (heat pumps) are increasingly frequent. The presence of such loads must be carefully considered for network investments and for the optimization of asset management. Moreover, the massive diffusion of non-programmable renewable sources gives a leading role to the flexibility of demand, which is crucial for the success of the energy transition. The variety and difference of the electrical behaviour of LV customers, even nominally homogeneous, need stochastic methods for estimating the load profile on the LV/MV interfaces for the planning and the operation of distribution network, and for estimating the flexibility potential of demand. In this paper different techniques for modelling the demand composition are compared to evaluate the quality of the DSO models on real customers. In particular, the power peak of a given network section is calculated as key indicator for estimating the risk of overloading of lines and secondary substation transformers. Different methods of calculation have been applied on a dataset gathered with a recent measurement campaign in Italy by considering real LV distribution networks

Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity

We study the exact spherically symmetric solutions in a class of Lorentz-breaking massive gravity theories, using the effective-theory approach where the graviton mass is generated by the interaction with a suitable set of Stuckelberg fields. We find explicitly the exact black hole solutions which generalizes the familiar Schwarzschild one, which shows a non-analytic hair in the form of a power-like term r^\gamma. For realistic self-gravitating bodies, we find interesting features, linked to the effective violation of the Gauss law: i) the total gravitational mass appearing in the standard 1/r term gets a multiplicative renormalization proportional to the area of the body itself; ii) the magnitude of the power-like hairy correction is also linked to size of the body. The novel features can be ascribed to presence of the goldstones fluid turned on by matter inside the body; its equation of state approaching that of dark energy near the center. The goldstones fluid also changes the matter equilibrium pressure, leading to an upper limit for the graviton mass, m <~ 10^-28 - 10^29 eV, derived from the largest stable gravitational bound states in the Universe.Comment: 22 pages, 4 Figures. Final version to be published in PRD. Typos corrected, comments adde

Optimal Location of Energy Storage Systems with Robust Optimization

The integration of intermittent sources of energy and responsive loads in distribution system make the traditional deterministic optimization-based optimal power flow no longer suitable for finding the optimal control strategy for the power system operation. This paper presents a tool for energy storage planning in the distribution network based on AC OPF algorithm that uses a convex relaxation for the power flow equations to guarantee exact and optimal solutions with high algorithmic performances and exploits robust optimization approach to deal with the uncertainties related to renewables and demand. The proposed methodology is applied for storage planning on a distribution network that is representative of a class of networks

A hybrid approach for planning and operating active distribution grids

This paper investigates the planning and operational processes of modern distribution networks (DNs) hosting Distributed Energy Resources (DERs). While in the past the two aspects have been distinct, a methodology is proposed in this paper to co-optimize the two phases by considering the operational flexibility offered by DERs already in the planning phase. By employing AC Optimal Power Flow (OPF) to analyse the worst-case forecasts for the load and distributed generator (DG) injection, the optimal set-points for the DERs are determined such that the network's security is ensured. From these results, the optimized individual characteristic curves are then extracted for each DER which are used in the operational phase for the local control of the devices. The optimized controls use only local measurements to address system-wide issues and emulate the OPF solution without any communication. Finally, the proposed methodology is tested on the Cigre LV benchmark grid confirming that it is successful in mitigating with acceptable violations over- and under-voltage problems, as well as congestion issues. Its performance is compared against the OPF-based approach and currently employed local control schemes