Superconductivity and Electric Fields: A Relativistic Extension of BCS Superconductivity

The effects of static electric fields on the superconducting state are studied within a relativistic extension of the BCS theory of superconductivity.Comment: To appear in the Proceedings of the Fourth International Workshop on Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou (Republic of Benin) (World Scientific, Singapore, 2006), 1+17 pages, no figure

Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution

With the increasing share of renewable and distributed generation in electrical distribution systems, Active Network Management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies

Blockchain for peer-to-peer energy exchanges: design and recommendations

peer reviewedEnergy communities and peer-to-peer energy exchanges are expected to play an important role in the energy transition. In this context, the blockchain approach can be employed to foster this decentralized energy market. Our goal is to determine the design that should allow a Distribution System Operator (DSO) to accept peer-to-peer energy exchanges based on a distributed ledger supported by the blockchain technology. To this end, we will evaluate several designs based on criteria such as acceptance of the wholesale/retail market, the resilience of the consensus to approve a block, the accuracy, traceability, privacy and security of the proposed schemes

A SC/battery Hybrid Energy Storage System in the Microgrid

The major challenges in power systems are driven by the energy shortage and environmental concerns, namely facilitating the penetration of renewable energy and improving the efficiency of the renewable powers. Due to the variable nature of renewables, the generated power profile may not be able to match the load requirement. Accordingly, much attention has been focused on the development of energy storage technologies to guarantee renewable power penetrations. Recently, advances in the supercapacitor (SC) have made the SC and battery hybrid energy storage systems (HESS) technically attractive. Compared with other energy storage technologies the principal advantages of SC are: the high power density, high cycling life, and high peak current handling capacities. However, SC is also deficient in low energy density. The battery is characterised by large energy density but low in power capacity. In the microgrid systems, high-frequency power fluctuations will cause a significant degree of battery power cycling. This, in turn, has been shown to lead to a significant reduction in battery service life. Therefore, the concept of the SC and battery hybrid scheme is proposed. A case study of the HESS based on a microgrid is introduced in this paper. A simplified microgrid system is established to test the performance of the proposed design

Global capacity announcement of electrical distribution systems: A pragmatic approach

We propose a pragmatic procedure to facilitate the connection process of Distributed Generation (DG) with reference to the European regulatory framework where Distribution System Operators (DSOs) are, except in specific cases, not allowed to own their generation. The procedure is termed Global Capacity ANnouncement (GCAN) and is intended to compute the estimates of maximum generation connection amount at appropriate substations in a distribution system, to help generation connection decisions. The pragmatism of the proposed procedure stems from its reliance on the tools that are routinely used in distribution systems planning and operation, and their use such that the possibilities of network sterilization are avoided. The tools involved include: long-term load forecasting, long-term planning of network extension/reinforcement, network reconfiguration, and power flow. Network sterilizing substations are identified through repeated power flow computations. The proposed procedure is supported by results using an artificially created 5-bus test system, the IEEE 33-bus test system, and a part of real-life distribution system of ORES (a Belgian DSO serving a large portion of the Walloon region in Belgium).GREDO

Finite-scale singularity in the renormalization group flow of a reaction-diffusion system

International audienceWe study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a new (conjugated) universality class

The Curse of Unrolling: Rate of Differentiating Through Optimization

Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few. Unrolled differentiation is a popular heuristic that approximates the solution using an iterative solver and differentiates it through the computational path. This work provides a non-asymptotic convergence-rate analysis of this approach on quadratic objectives for gradient descent and the Chebyshev method. We show that to ensure convergence of the Jacobian, we can either 1) choose a large learning rate leading to a fast asymptotic convergence but accept that the algorithm may have an arbitrarily long burn-in phase or 2) choose a smaller learning rate leading to an immediate but slower convergence. We refer to this phenomenon as the curse of unrolling. Finally, we discuss open problems relative to this approach, such as deriving a practical update rule for the optimal unrolling strategy and making novel connections with the field of Sobolev orthogonal polynomials