Mathematical Models for Improving Flexibility within the Smart Grid domain

One of the most important topics of the last decades has been finding energy sources who can replace fossil fuels. Renewable energy is a good candidate, being virtually inexhaustible and more environment-friendly. In order to allow for this transition, electric energy grids have evolved and have become new objects, called \emph{smart grids}. However, the complexity of this new type of grid brings new issues and challenges, which are currently object of study for many researchers. The purpose of this thesis is to showcase some of these problems, and to build mathematical models and algorithms in order to solve them, by leveraging a new property relative to energy loads: flexibility. Since smart devices are becoming more common and they can be remotely controlled, manipulation of energy profiles is possible, and this is a powerful tool for the management of smart grids. Going more into detail, a framework for managing demand response, peak shaving and energy trading has been designed by the means of a combinatorial approach, and it has been enhanced by exploitation of parallel computing. Moreover, an incentive mechanism for usage of renewable energy has been analyzed and improved, by changing some functions which define its behavior. This mechanism has also been examined from a game-theoretic point of view, and it has been further improved in order to always guarantee an agreement between users for flexibility usage. Finally, a decentralized, multi-agent system approach has been used to solve the problems of cost optimization and congestion management. Most of the content of this thesis derives from research works published in journals and conferences

Heat FlexOffers:a device-independent and scalable representation of electricity-heat flexibility

The increasing relevance of Renewable Energy Sources (RES) makes energy flexibility an extremely important aspect, not only regarding electricity, but also for other energy vectors such as heat. Because of this, there is the need for a flexibility model which can i) provide a common representation of flexibility for different device types, ii) perform aggregation, optimization and disaggregation while scaling for long time horizons and many devices, iii) capture most of the available flexibility, and iv) support energy conversion between different vectors. Properties i)-iii) are addressed by FlexOffer (FO), a device-independent model that describes energy constraints in an approximate yet accurate way. This paper proposes an extension of FOs, Heat FlexOffers (HFOs), capable of modeling flexibility for different energy vectors such as heat and handling energy conversion, and therefore addressing iv) as well as i)-iii). HFOs can model the optimal power curve for heat pumps, and can provide constraints for continuous optimization problems while complying to the Smart Grid-Ready (SG-Ready) interface, which operates on discrete states. We show that HFOs are very accurate, being able to retain up to of total flexibility before aggregation and of it after aggregation. HFOs aggregation is scalable, as 2 · 10^6 devices can be aggregated for a 24 hours time horizon, vastly outperforming exact models as they fail to aggregate more than 500 devices.</p

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR &lt; 60 mL/min/1.73 m2) or eGFR reduction &gt; 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR &lt; 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR &gt; 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening

Immersioni di superfici in 3-varieta' iperboliche chiuse

Nella tesi viene trattata la dimostrazione del Teorema della superficie di Kahn-Markovic. Nel primo capitolo vengono introdotti alcuni concetti fondamentali e si lavora sullo spazio iperbolico, arrivando a dimostrare un teorema importante. Nel secondo ci si concentra maggiormente su superfici immerse in 3-varietà iperboliche, arrivando a enunciare un teorema che, insieme a quello precedente, consente di dimostrare quello che è l'obiettivo della tesi. La sua dimostrazione viene ridotta a quella di un altro teorema, la quale verrà trattata nel terzo e ultimo capitolo

Peer-to-peer energy trading for smart energy communities

Local energy communities (LECs) comprise prosumers cooperating for the satisfaction of their energy needs. Prosumers are community members that can both produce and consume energy. LECs facilitate the integration of renewables and provide the potential for reducing energy costs. Peer-to-peer (P2P) energy trading allows direct energy exchange between members of a local energy community. The surplus of energy from renewables is traded to meet a local consumption demand so that costs and revenues stay within community avoiding transmission losses and stress on the grid. This study presents a design of the peer-to-peer market for local energy communities where prosumers are rational and self-interested agents acting selfishly in an attempt to optimize their trades. The market design aims to ensure self-consumption of locally produced energy and provides incentives for balancing supply and demand within community. The proposed design is investigated in comparison with existing ones using theoretical analysis and simulations. The obtained results are promising and reveal advantageous properties of the proposed P2P energy trading

Multiagent system for community energy management

Local energy communities (LECs) represent a shift in energy management from an individual approach towards a collective one. LECs can reduce energy costs for end-users and contribute to meeting climate objectives through the use of renewable energy. This paper presents the application of a multiagent system (MAS) approach to realize the concept of LEC in a real-world scenario involving a community of households. An appropriate agent-based model for the given community is presented. This model effectively distributes the tasks among the agents considering electrical and heat energy flows. The agent coordination mechanism is based on the Alternative Direction Method of Multipliers. The obtained results provide evidence of the validity of the developed MAS and show its potential to increase a total social welfare of the community

Incentive mechanisms for the secure integration of renewable energy in local communities: A game-theoretic approach

International audienceIn the context of local energy communities (LECs), prosumers are the main actors, as they can both produce and consume energy. Prosumers can interact with each other, and peer-to-peer (P2P) energy trading allows prosumers belonging to the same LEC to exchange energy with each other. This allows energy production to be consumed internally by the community, which has the benefits of reducing costs for energy consumption and reducing the amount of energy traveling from/to the external grid, which causes transmission losses and wears and tear to the grid itself. This paper proposes a design for the P2P market from a game-theoretical point of view, where prosumers are modeled as selfish agents whose goal is to maximize their own profits in energy trading. The purposes of this market design are to (i) discourage prosumers from curtailing their own energy production, (ii) avoid congestions as much as possible, (iii) encourage self-consumption from prosumers, and (iv) guarantee that the selfish behavior of prosumers allows for a common strategy. Furthermore, this work considers the possibility of prosumers making coalitions between themselves, and show how this still allows for the existence of a common strategy. Simulations of the proposed market design have been run on data from a grid in Cardiff, UK, and show how the proposed mechanism allows for cost reduction and encourages energy self-consumption. Experiments results show that the system discourages the formation of small coalitions, and encourages instead cooperation from all the prosumers in the community

A novel payment scheme for trading renewable energy in smart grid

With the increasing diffusion of renewable energy producers in electricity grids, new policies and tariff systems have been recently developed. This work revolves around a particular support system named NRG-X-Change, which makes use of a virtual currency called NRGcoin. The NRG-X-Change system is based on two NRGcoin payment functions: one to establish the price at which prosumers are rewarded for their energy production, and the other to establish the price at which consumers pay the energy they consume. The detailed analysis provided in this paper identifies some important issues in these payment functions limiting their applicability, namely: (i) not taking congestions into account; (ii) encouraging curtailment of renewable energy production; and (iii) not ensuring that the prosumers consume their own energy before selling it. This work addresses these limitations by proposing two novel payment functions whose advantageous properties are demonstrated by theoretical analysis and in simulation using real data coming from an existing grid

Poster: Uncertain FlexOffers, a scalable, uncertainty-Aware model for energy flexibility

As the usage of Renewable Energy Sources (RES) in electricity grids increases in popularity, energy flexibility has a crucial role. The most common weaknesses of current flexibility models are: i) being hard-coded for specific devices, ii) not scaling for long time horizons and many devices, iii) losing a lot of flexibility if the model is approximated, and iv) not considering the uncertainty affecting flexibility representations, which causes the model to capture too much excess flexibility when imbalance penalties are high. The FlexOffer (FO) model can perform approximations of flexibility with good accuracy across different devices, and scales well to long time horizons and many devices: this work extends FOs to uncertain FOs (UFOs), which keep the good properties while capturing uncertainty. We show that UFOs are very fast by performing optimization in under 5.27 seconds for a 24 hours time horizon, while exact models use more than 29.05 hours for even a 6 hours 15 minutes time horizon, making them totally infeasible in practice. UFOs can capture more flexibility than other uncertain models: UFOs considering energy dependencies can model flexibility without losses for a charging battery, and retain of the total flexibility for batteries and for EVs when imbalance penalties are high, compared to and respectively for other models. UFOs allow to aggregate up to 6000 loads for up to 96 time units while retaining of the total flexibility: exact models fail already for 330 loads or 21 time units.</p