Abstract--The operation of aggregators of distributed energy resources (DER) is highly complex, since it entails the optimal coordination of a diverse portfolio of DER under multiple sources of uncertainty. The large number of possible stochastic realizations that arise, can lead to complex operational models that become problematic in real-time market environments. Previous stochastic programming approaches resort to two-stage uncertainty models and scenario reduction techniques to preserve the tractability of the problem. However, two-stage models cannot fully capture the evolution of uncertain processes and the a priori scenario selection can lead to suboptimal decisions. In this context, this paper develops a novel stochastic dual dynamic programming (SDDP) approach which does not require discretization of either the state space or the uncertain variables and can be efficiently applied to a multi-stage uncertainty model. Temporal dependencies of the uncertain variables as well as dependencies among different uncertain variables can be captured through the integration of any linear multidimensional stochastic model, and it is showcased for a porder vector autoregressive (VAR) model. The proposed approach is compared against a traditional scenario-tree-based approach through a Monte-Carlo validation process, and is demonstrated to achieve a better trade-off between solution efficiency and computational effort.Index Terms--Aggregator, distributed energy resources, multidimensional uncertainty, stochastic dual dynamic programming, vector autoregressive modeling. I. NOMENCLATURE A. IndexesIndex of time periods, running from 1 to . Index of energy storage (ES) units, running from 1 to . Index of flexible loads (FL), running from 1 to . Index of wind turbines (WT), running from 1 to . Index of micro-generators, running from 1 to . B. ParametersEnergy market price at period . Operating cost of micro-generator . Cost of demand shedding. C. VariablesPower sold to (positive)/bought from (negative) the market at period . ,Power output of micro-generator at period . Demand shed at period ., Energy level of ES unit at period . ,Power input (positive) / output (negative) of ES unit at period . , ℎChange of demand of FL at period due to load shifting. ,Demand of FL at period after load shifting., Dispatched wind power output of WT at period . II. INTRODUCTIONA. Background FUNDAMENTAL feature of the emerging Smart Grid paradigm involves the integration of a large number of distributed energy resources (DER) storage units, in order to support the economic operation of the future low-carbon power system [1]- [2]. However, the large number, small individual size and inherent stochasticity characterizing these DER have complicated system scheduling and market coordination. Furthermore, driven by the wide integration of renewable generation in power systems, there is a general consensus to move energy trading as close as possible to real-time [3]- [4], which intensifies the complexity of DER coordination. These challenges have...

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Abstract-The operation of aggregators of distributed energy resources (DER) is a highly complex task that is affected by numerous factors of uncertainty such as renewables injections, load levels and market conditions. However, traditional stochastic programming approaches neglect information around temporal dependency of the uncertain variables due to computational tractability limitations. This paper proposes a novel stochastic dual dynamic programming (SDDP) approach for the optimal operation of a DER aggregator. The traditional SDDP framework is extended to capture temporal dependency of the uncertain wind power output, through the integration of an n-order autoregressive (AR) model. This method is demonstrated to achieve a better trade-off between solution efficiency and computational time requirements compared to traditional stochastic programming approaches based on the use of scenario trees.

HypothesisThe main hypothesis is that a digital, biodata-driven, and personalized program would exhibit high user retention and engagement, followed by more effective management of their depressive and anxiety symptoms.ObjectiveThis pilot study explores the feasibility, acceptability, engagement, and potential impact on depressive and anxiety and quality of life outcomes of the 16-week Feel Program. Additionally, it examines potential correlations between engagement and impact on mental health outcomes.MethodsThis single-arm study included 48 adult participants with mild or moderate depressive or anxiety symptoms who joined the 16-week Feel Program, a remote biodata-driven mental health support program created by Feel Therapeutics. The program uses a combination of evidence-based approaches and psychophysiological data. Candidates completed an online demographics and eligibility survey before enrolment. Depressive and anxiety symptoms were measured using the Patient Health Questionnaire and Generalized Anxiety Disorder Scale, respectively. The Satisfaction with Life Scale and the Life Satisfaction Questionnaire were used to assess quality of life. User feedback surveys were employed to evaluate user experience and acceptability.ResultsIn total, 31 participants completed the program with an overall retention rate of 65%. Completed participants spent 60 min in the app, completed 13 Mental Health Actions, including 5 Mental Health Exercises and 4.9 emotion logs on a weekly basis. On average, 96% of the completed participants were active and 76.8% of them were engaged with the sensor during the week. Sixty five percent of participants reported very or extremely high satisfaction, while 4 out of 5 were very likely to recommend the program to someone. Additionally, 93.5% of participants presented a decrease in at least one of the depressive or anxiety symptoms, with 51.6 and 45% of participants showing clinically significant improvement, respectively. Finally, our findings suggest increased symptom improvement for participants with higher engagement throughout the program.ConclusionsThe findings suggest that the Feel Program may be feasible, acceptable, and valuable for adults with mild or moderate depressive and/or anxiety symptoms. However, controlled trials with bigger sample size, inclusion of a control group, and more diverse participant profiles are required in order to provide further evidence of clinical efficacy.

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