Dual Formulation of the Lie Algebra S-expansion Procedure

The expansion of a Lie algebra entails finding a new, bigger algebra G, through a series of well-defined steps, from an original Lie algebra g. One incarnation of the method, the so-called S-expansion, involves the use of a finite abelian semigroup S to accomplish this task. In this paper we put forward a dual formulation of the S-expansion method which is based on the dual picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra, which in turn is relevant for physical applications in, e.g., Supergravity. It also sheds new light on the puzzling relation between two Chern-Simons Lagrangians for gravity in 2+1 dimensions, namely the Einstein-Hilbert Lagrangian and the one for the so-called "exotic gravity".Comment: 12 pages, no figure

Evaluation of a Local Fault Detection Algorithm for HVDC Systems

A great increase in the amount of energy generated from clean and renewable sources integrated in the electric power system is expected worldwide in the coming years. High Voltage Direct Current (HVDC) systems are seen as a promising alternative to the traditional Alternating Current (AC) systems for the expansion of the electric power system. However, to achieve this vision, there are some remaining challenges regarding HVDC systems which need to be solved. One of the main challenges is related to fault detection and location in HVDC grids. This paper reviews the main protection algorithms available and presents the evaluation of a local fault detection algorithm for DC faults in a multi-terminal Voltage Source Conversion (VSC) based HVDC grid. The paper analyses the influence of the DC voltage sampling frequency and the cable length in the performance of the algorithm. © 2019, European Association for the Development of Renewable Energy, Environment and Power Quality (EA4EPQ).The authors thank the support from the Spanish Ministry of Economy, Industry and Competitiveness (project ENE2016-79145-R AEI/FEDER, UE) and GISEL research group IT1083-16), as well as from the University of the Basque Country UPV/EHU (research group funding PPG17/23)