The reliability of the transmission grid is challenged by the integration of intermittent renewable energy sources into the grid. For model-based reliability studies, it is important to have suitable models available of renewable energy sources like wind and solar power. In this study, we investigate to what extent the power output of wind farms can be modeled with discrete Hidden Markov Models (HMMs). The parameters of the HMMs are inferred from measurement data from multiple turbines in a wind farm. We use these models both for individual turbine output and for total aggregated power output of multiple turbines. When modeling individual turbine output, the hidden process in the HMM is instrumental in capturing the dependencies between the output of the different turbines. It is important to account for these dependencies in order to correctly capture the upper quantiles (90%, 95%, 99%) of the distribution of the wind farm aggregated power output. We show that despite their simple structure, HMMs are able to reproduce important features of the power output of wind farms. This opens up possibilities to model and analyze these features with methods and techniques stemming from the field of Markov models and stochastic processes. Index Terms-Wind farm power generation, data models, power system modeling, time series analysis, hidden Markov models.
We have performed ab initio density functional theory calculations, incorporating London dispersion corrections, to study the absorption of molecular hydrogen on zigzag graphene nanoribbons whose edges have been functionalized by OH, NH2, COOH, NO2, or H2PO3. We find that hydrogen molecules always preferentially bind at or near the functionalized edge, and display induced dipole moments. Binding is generally enhanced by the presence of polar functional groups. The largest gains are observed for groups with oxygen lone pairs that can facilitate local charge reorganization, with the biggest single enhancement in adsorption energy found for "strong functionalization" by H2PO3 (115 meV/H2 versus 52 meV/H2 on bare graphene). We show that for binding on the "outer edge" near the functional group, the presence of the group can introduce appreciable contributions from Debye interactions and higher-order multipole electrostatic terms, in addition to the dominant London dispersion interactions. For those functional groups that contain the OH moiety, the adsorption energy is linearly proportional to the number of lone pairs on oxygen atoms. Mixed functionalization with two different functional groups on a graphene edge can also have a synergistic effect, particularly when electron-donating and electron-withdrawing groups are combined. For binding on the "inner edge" somewhat farther from the functional group, most of the binding again arises from London interactions; however, there is also significant charge redistribution in the π manifold, which directly reflects the electron donating or withdrawing capacity of the functional group. Our results offer insight into the specific origins of weak binding of gas molecules on graphene, and suggest that edge functionalization could perhaps be used in combination with other strategies to increase the uptake of hydrogen in graphene. They also have relevance for the storage of hydrogen in porous carbon materials, such as activated carbons.
The intermittent nature of the renewable energy sources challenges the power network reliability. However these challenges can be alleviated by incorporating energy storage devices in the network. The aim of this study is to develop a computational technique which can find the optimal storage placement in the network with stochastic generations and demands such that the power network can be made more reliable. We use the probability of a line current violation as the reliability index of the network and find the optimal storage position so that this probability is minimal. We use the simulated annealing algorithm to minimize this probability under the variation of storage locations and capacities in the network, keeping the total storage capacity constant. In order to estimate the small probabilities of line current violations we use the splitting technique of rare-event simulation. We construct an appropriate importance function for splitting which enhances the efficiency of the probability estimator compared to the conventional Crude Monte Carlo estimator. As an illustration, we apply our method to the IEEE-14 bus network.
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