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This paper presents a novel method based on midpoint-radius interval arithmetic to deal with uncertainties in the power flow problem. The proposed technique aims at finding a balance between accuracy and computational efficiency. It relies on an original decoupling of the interval power flow equations into midpoint and radius parts. This representation allows avoiding the factorisation of an interval Jacobian matrix. Moreover, the proposed formulation is combined with an optimisation problem in order to prevent overestimation of the interval solution while preserving uncertainty. The proposed technique proves to be more efficient than existing approaches based on interval and affine arithmetic and as accurate as the conventional Monte Carlo method. [ABSTRACT FROM AUTHOR]

The impact of air-side and methane-side dilution (CO 2 , N 2 and Ar) on the lifting process of attached non-premixed methane/air coaxial jet flames is studied over a wide range of aerodynamic conditions. The study of the competition between aerodynamics and dilution has allowed to discriminate and quantify the different phenomena involved in the lifting process. First, two effects, only dependent on the amount of the added diluent, contribute to promoting flame detachment (liftoff): a fluid mechanical effect that causes the bulk velocity of the reactants to increase; a mixing effect that changes the mixture fraction spatial distribution. They are significant for the methane-side dilution but negligible for the air-side dilution. Then, the main mechanism and the dimensionless numbers characterizing flame liftoff are identified. The attached-flame stability is analyzed on the basis of the lifting limits measured by the critical flow rate ratios, ( Q d / Q f ) lift and ( Q d / Q ox ) lift when the diluent is added either to the methane or the air stream. These limits follow self-similarity relationships based on the fuel and oxidant Peclet numbers of the diluted streams, satisfied whatever the diluents. Results using PIV and CH * measurements are interpreted through a flame-leading-edge approach, where CH 4 /air/diluent are mixed locally at the flame base. The flame propagation velocity S L which balances the incoming gas velocity, is shown to be described by self-similarity relationships based on the molar fraction at the leading-edge reduced by values at liftoff, X d / X l i f t d . To confirm the leading-edge propagation characteristics, the flame attachment height H a and radius R a are investigated at the attached-flame base. R a is representative of the mixing and mass effects induced by the pure dilution. Contrary to R a , H a is piloted by S L , and evolves according to a unique law dictated by X d / X l i f t d . X l i f t d is a self-similar parameter highlighting the propagation nature of the leading-edge. [ABSTRACT FROM AUTHOR]

The transition towards more sustainable energy systems poses new requirements on energy system models. New challenges include representing more uncertainties, including short-term detail in long-term planning models, allowing for more integration across energy sectors, and dealing with increased model complexities. SpineOpt is a flexible, open-source, energy system modelling framework for performing operational and planning studies, consisting of a wide spectrum of novel tools and functionalities. The most salient features of SpineOpt include a generic data structure, flexible temporal and spatial structures, a comprehensive representation of uncertainties, and model decomposition capabilities to reduce the computational complexity. These enable the implementation of highly diverse case studies. SpineOpt's features are presented through several publicly-available applications. An illustrative case study presents the impact of different temporal resolutions and stochastic structures in a co-optimised electricity and gas network. Using a lower temporal resolution in different parts of the model leads to a lower computational time (44%–98% reductions), while the total system cost varies only slightly (-1.22–1.39%). This implies that modellers experiencing computational issues should choose a high level of temporal accuracy only when needed. • Open-source energy system model with a rich set of features suitable for modelling operational and planning optimisation problems. • Novel composition of the temporal structure allowing for a trade-off between required modelling detail and complexity reduction. • New flexible stochastic structure for custom branching and recombining of scenarios. • Multitude of open-source published case studies for different energy sectors. [ABSTRACT FROM AUTHOR]