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Carbon emission flow is an effective tool to obtain carbon emission distribution in power systems, which can guide the active carbon reductions of consumers through proper incentive schemes. With the increasing penetration of renewable energy, the existing single-valued carbon emission flow model based on deterministic forecasted power outputs cannot describe the impacts of renewable energy uncertainties on carbon flows. Therefore, this paper mainly focuses on the assessment of the probabilistic carbon emission flow through the power systems considering the impacts of load and renewable energy uncertainties. In this paper, the probabilistic carbon emission flow (PCEF) is innovatively proposed. With the PCEF, consumers can make better energy use plans considering their own risk appetites for carbon emission payment. Firstly, the impact factors of the PCEF are modeled, including load and renewable energy uncertainties and integrated carbon intensity of thermal plants. The uncertainties of load, wind power and photovoltaics are modeled based on a p-box method while the uncertainty of hydropower is modeled based on the multi-state model. Besides, the integrated carbon intensity model of thermal plants are proposed considering the carbon intensity variations during the operating, start-up, and shut-down stages. Furthermore, the probabilistic carbon emission evaluation framework is proposed to assess the probabilistic carbon distribution. In this framework, novel probabilistic carbon indices are defined to precisely characterize the carbon emission situation with probabilistic representations. A solution method based on an adaptive interval point estimation (AIPEM) algorithm is proposed to efficiently solve the developed evaluation problem. Tests on an IEEE-30 node system, and a real provincial power system in China validate the effectiveness and application of the proposed model. The results showed that the PCEF can be a useful tool for obtaining the probabilistic representation of carbon emission flow and guiding the consumers' active carbon reduction in power systems. • Probabilistic carbon emission flow is proposed considering multiple uncertainties. • Integrated carbon intensity model for thermal plants is developed. • A p-box model is used to describe the uncertainties of load and renewable energy. • PCEF can help consumers balance the cost and carbon risk when making decisions. [ABSTRACT FROM AUTHOR]

In this paper, a real time implementable load coordination strategy is developed for the optimization of electric demands in a smart home. The strategy minimizes the electricity cost to the home owner, while limiting the disruptions associated with the deferring of flexible power loads. A multi-objective nonlinear mixed integer programming is formulated as a sequential model predictive control, which is then solved using genetic algorithm. The load shifting benefits obtained by deploying an advanced coordination strategy are compared against a baseline controller for various home characteristics, such as location, size and equipment. The simulation study shows that the deployment of the smart home energy management strategy achieves approximately 5% reduction in grid cost compared to a baseline strategy. This is achieved by deferring approximately 50% of the flexible loads, which is possible due to the use of the stationary energy storage. • Real-time load coordination strategy for optimizing electrical loads in smart homes. • Inclusion of renewable energy sources and stationary batteries in the coordination. • Definition of generalizable metrics for the evaluation of load shifting strategy. • Improvements in improved energy efficiency and reduced electricity costs. • Comprehensive analysis that considers diverse home characteristics such as location. [ABSTRACT FROM AUTHOR]