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The Pareto frontier is extensively adopted in multi-objective optimization, especially in multi-carrier energy system modeling. Despite the various methodologies available to derive the frontier, it represents different optimal solutions, making the final selection non-trivial. The modeler's expertise is crucial in determining the weight factors assigned to each objective for selecting the final solution from the Pareto frontier. This study proposes a novel approach to support such decision-making, introducing an additional key performance indicator, the state of health of the battery, evaluated through physical battery modeling. By comparing different scheduling schemes in multi-objective multi-carrier energy systems, each with its distinct battery operational strategy, this newly introduced indicator has deployed to automatically identify the ultimate solution from the Pareto frontier, without additional weighting coefficients. Such an approach, therefore, automates the decision process, which supports easy engineering, especially for the small scale multi-energy systems such as smart homes, like the case study presented in this work that has four distinct energy carriers, adopting the 12 V 128 Ah LFP chemistry Li-ion battery modules, demonstrates the effectiveness of this automated selection process. Furthermore, when compared to the maximum values across the entire frontier, the automatically chosen solution exhibits reductions of 27.96% in CO2 emissions and 3.67% reduction in overall costs. Over long-term operation, this approach has the potential to extend battery lifespan by up to 26.67%, directly impacting the economics of multi-carrier energy systems.
Jin et al. (Tue,) studied this question.