Assessing the robustness of solutions to a multi- objective model of an energy management system aggregator Andreia M. Carreiro PhD Program on Sustainable Energy Systems, University of Coimbra Coimbra, Portugal andreia.melo.carreiro@gmail.com Carlos Henggeler Antunes and Humberto Jorge Dept. of Electrical and Computer Engineering, University of Coimbra, and INESC Coimbra Coimbra, Portugal ch@deec.uc.pt Abstract—An approach for robustness analysis of non- dominated solutions to a multi-objective optimization model of an energy management system aggregator (EMSA) in face of uncertainty is presented. The EMSA is an intermediary entity between households and the System Operator (SO), capable of contributing to balance load and supply, and therefore coping with the intermittency of renewable energy sources (RES) and facilitating a load follows supply strategy in a Smart Grid environment. Household clusters provide load flexibility to satisfy system services requested by the SO, involving decreasing or increasing load in specific time slots. The EMSA multi- objective optimization model considers the maximization of profits and the minimization of the imbalance between the amounts of load flexibility provided by the end-user clusters to satisfy SO requests, taking into account revenues from the SO and payments to the clusters. A hybrid evolutionary approach combining Genetic Algorithms (GA) with Differential Evolution (DE) has been designed to deal with this model, and its behaviour subject to different scenarios of uncertainty is evaluated. The robustness analysis of non-dominated solutions produced by the hybrid evolutionary approach is based on the degree of robustness concept, taking into account the changes in the performance of the objective functions when small perturbations of the model nominal coefficients occur. Keywords— multi-objective optimization, evolutionary algorithms, energy management systems, aggregator, uncertainty, robustness; I. INTRODUCTION In a smart grid environment, in which the electricity delivery system is integrated with Information and Communication Technologies (ICT), it is expected that the end-user will become a prosumer (i.e., simultaneously producer and consumer of electricity) and dynamic (time- differentiated) electricity tariffs will be applicable. In order to engage end-users into Demand Response (DR) programs, i.e. adjusting consumption patterns by reacting to price signals, households need to have home energy management systems (HEMS) based on ICT and endowed with intelligence to optimize the usage of loads without compromising comfort requirements, also allowing the two-way communication with the System Operator (SO) [1]. In this context, DR programs can contribute to delivery ancillary services, i.e., services provided by the SO to ensure reliable system operations, by exploiting the load flexibility displayed by end-users [2]. This role can be performed by an energy management system aggregator (EMSA), which an intermediary entity operating between household clusters and the SO, enabling the optimization and coordination of a large- scale dissemination of HEMS. The EMSA uses the demand- side flexibility offered by end-user clusters to provide system services requests, involving decreasing or increasing the power required in each time slot of a planning horizon. The EMSA multi-objective optimization model considers the maximization of profits and the minimization of the imbalance between the amounts of load flexibility provided by the end-user clusters to satisfy SO requests, taking into account revenues from the SO and payments to the clusters. However, several sources of uncertainty are at stake that should be incorporated into the EMSA decision-making process to obtain robust non-dominated solutions to the multi-objective model, i.e., solutions that are in some way “immune” to some degree of data uncertainty, having in mind their practical implementation. The purpose of this paper is to present an approach that analyzes whether the non-dominated solutions computed by a hybrid genetic/differential evolution algorithm are robust based on a degree of robustness concept. The assessment of solution robustness is done considering perturbations in the nominal coefficients of the model within a prespecified range and evaluating the corresponding changes in the objective function space for a given solution structure. This paper is structured as follows. Section II describes the methodological framework for the assessment of solution robustness in multi-objective optimization also presenting a brief literature review. Section III presents the EMSA multi- objective model and the robustness analysis approach, as well as the case study. Section IV presents some illustrative results and the main conclusions are drawn in section V.