Flexible models for aggregated residential loads are needed to analyze the impact of demand response policies and programs on the minimum comfort setting required by end-users. This impact has to be directly deduced from the probability profiles of thermal and electrical performance variables. The purpose of this paper is to compare different aggregation techniques in order to estimate, as accurately and flexibly as possible, the probability distribution function of thermal and electrical variables of thermostatically controlled loads. Two different approaches are considered: on the one hand, intensive numerical simulations-Monte Carlo process-combined with either Euler-Maruyama discrete approximation method or smoothing techniques; and, on the other hand, a numerical resolution of the Fokker-Planck partial differential equations. In all cases, a stochastic differential equation system-based on perturbed physical models-is used to model the individual load behavior. This individual system was previously developed and validated by the authors.

Response Surface Methodology (RSM) is a widely used mathematical tool for process optimization, setting their main factorial variables. The current research analyzes and summarizes the current knowledge about the RSM in the extraction of carotenoids from fruit and vegetable by-products, following a systematic review protocol (Prisma 2020 Statement). After an identification of manuscripts in Web of Science (September 2023) using inclusion search terms (“carotenoids”, “extraction”, “response-surface methodology”, “ultrasound”, “microwave” and “enzyme”), they were screened by titles and abstracts. Finally, 29 manuscripts were selected according to the PRISMA methodology (an evidence-based minimum set of items for reporting in systematic reviews), then, 16 questions related to the quality criteria developed by authors were applied. All studies were classified as having an acceptable level of quality criteria (≤50% “yes answers”), with four of them reaching a moderate level (>50 to ≤70% “yes answers”). No studies were cataloged as complete (>70% “yes answers”). Most studies are mainly focused on ultrasound-assisted extraction, which has been widely developed compared to microwave or enzymatic-assisted extractions. Most evidence shows that it is important to provide information when RSM is applied, such as the rationale for selecting a particular design, the specification of input variables and their potential levels, a discussion on the statistical model’s validity, and an explanation of the optimization procedure. In addition, the principles of open science, specifically data availability, should be included in future scientific manuscripts related to RSM and revalorization.