## Section: New Results

### Green Networking and Smart Grids

Participants : Sara Alouf, Eitan Altman, Alain Jean-Marie, Giovanni Neglia, Dimitra Politaki.

#### Power Demand Control

Demand-Response (DR) programs, whereby users of an electricity network are encouraged by economic incentives to rearrange their consumption in order to reduce production costs, are envisioned to be a key feature of the smart grid paradigm. Several recent works proposed DR mechanisms and used analytical models to derive optimal incentives. Most of these works, however, rely on a macroscopic description of the population that does not model individual choices of users. In [34], [57] G. Neglia and A. Benegiamo (PhD student in Maestro at the submission time), in collaboration with P. Loiseau, conduct a detailed analysis of those models and argue that the macroscopic descriptions hide important assumptions that can jeopardize the mechanisms' implementation (such as the ability to make personalized offers and to perfectly estimate the demand that is moved from a timeslot to another). Then, they start from a microscopic description that explicitly models each user's decision. They introduce four DR mechanisms with various assumptions on the provider's capabilities. Contrarily to previous studies, they find that the optimization problems that result from these mechanisms are not convex. Local optimizers can be found numerically through a heuristic. The authors present numerical simulations that compare the different mechanisms and their sensitivity to forecast errors. At a high level, their results show that the performance of DR mechanisms under reasonable assumptions on the provider's capabilities are significantly lower than those suggested by previous studies, but that the gap reduces when the population's flexibility increases.

In [22] A. Jean-Marie and G. Neglia in collaboration with I. Tinnirello, L. Giarré, M. Ippolito (Univ. of Palermo, Italy) and G. Di Bella (Telecom Italia, Italy) investigate a realistic and low-cost deployment of large scale direct control of inelastic home appliances whose energy demand cannot be shaped, but simply deferred. The idea is to exploit 1) some simple actuators to be placed on the electric plugs for connecting or disconnecting appliances with heterogeneous control interfaces, including non-smart appliances, and 2) the Internet connections of customers for transporting the activation requests from the actuators to a centralized controller. The solution requires no interaction with home users: in particular, it does not require them to express their energy demand in advance. A queuing theory model is derived to quantify how many users should adopt this solution in order to control a significant aggregated power load without significantly impairing their quality of service.

#### Geographical Load Balancing across Green Datacenters

“Geographic Load Balancing” is a strategy for reducing the energy cost of data centers spreading across different terrestrial locations. In [20] G. Neglia, in collaboration with M. Sereno (Univ. of Torino, Italy) and G. Bianchi (Univ. of Roma “Tor Vergata”, Italy), focuses on load balancing among micro-datacenters powered by renewable energy sources. They model via a Markov Chain the problem of scheduling jobs by prioritizing datacenters where renewable energy is currently available. Not finding a convenient closed form solution for the resulting chain, they use mean field techniques to derive an asymptotic approximate model which instead is shown to have an extremely simple and intuitive steady state solution. After proving, using both theoretical and discrete event simulation results, that the system performance converges to the asymptotic model for an increasing number of datacenters, they exploit the simple closed form model's solution to investigate relationships and trade-offs among the various system parameters.

#### Stochastic models for solar energy

The recent popularization of renewable energy sources makes it urgent to have realistic and practical models for the renewable energy harvested by photovoltaic panels for instance. Solar radiation is intrinsically stochastic and exhibits fluctuations at several time scales. Due to the sun's position during the day with respect to a given point on Earth, there is a periodic day-night pattern that is observed on top of which short-time burstiness occurs due to fluctuating weather conditions. In [64], D. Politaki and S. Alouf propose a stochastic model for the global solar radiation. They introduce a multiplicative factor that is the ratio between the actual global solar radiation and the idealized clear sky global radiation. The latter is obtained using known astronomical models and captures the day-night pattern of the solar radiation at any given point on Earth. On the other hand, the multiplicative factor captures the short-time burstiness caused by cloudiness. A semi-Markov model is proposed for the latter such that most of the time correlation found in measured data can be reproduced in synthetic traces.