Multiple roots of systems of equations by repulsion merit functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global min- imizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several ite- rations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.Fundação para a Ciência e a Tecnologia (FCT

Pool trading model within a local energy community considering flexible loads, photovoltaic generation and energy storage systems

This paper presents a pool trading model within a local energy community considering home energy management systems (HEMSs) and other consumers. A transparent mechanism for market clearing is proposed to incentivise active prosumers to trade their surplus energy within a rule-based pool market in the local energy community. A price-based demand response program (PBDRP) is considered to increase the consumers’ willingness to modify their consumption. The mathematical optimization problem is a standard mixed-integer linear programming (MILP) problem to allow for rapid assessment of the trading market for real energy communities which have a considerable number of consumers. This allows for novel energy trading strategies amongst different clients in the model and for the integration of a pool energy trading model at the level of the local energy community. The objective function of the energy community is to minimize the overall bills of all participants while fulfilling their demands. Two different scenarios have been evaluated, independent and integrated operation modes, to show the impacts of coordination amongst different end-users. Results show that through cooperation, end-users in the local energy community market can reduce the total electricity bill. This is shown in a 16.63% cost reduction in the independent operation and a 21.38% reduction in the integrated case. Revenues for active consumers under coordination increased compared to independent operation of the HEMS.© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).fi=vertaisarvioitu|en=peerReviewed