Wind speed prediction with spatio-temporal correlation is among the most challenging tasks in wind speed prediction. In this paper, the problem of predicting wind speed for multiple sites simultaneously is investigated by using spatio-temporal correlation. This paper proposes a model for wind speed prediction with spatio-temporal correlation, i.e., the predictive deep convolutional neural network (PDCNN). The model is a unified framework, integrating convolutional neural networks (CNNs) and a multi-layer perceptron (MLP). Firstly, the spatial features are extracted by CNNs located at the bottom of the model. Then, the temporal dependencies among these extracted spatial features are captured by the MLP. In this way, the spatial and temporal correlations are captured by PDCNN intrinsically. Finally, PDCNN generates the predicted wind speed by using the learnt spatio-temporal correlations. In addition, three error indices are defined to evaluate the prediction accuracy of the model on the wind turbine array. Experiment results on real-world data show that PDCNN can capture the spatio-temporal correlation effectively, and it outperforms the conventional machine learning models, including multi-layer perceptron, support vector regressor, decision tree, etc.Energies 2018, 11, 705 2 of 18 for exploitation. With the enrichment of spatio-temporal data of wind farms, wind prediction with both temporal correlation and spatial correlation, i.e., spatio-temporal correlation, has come to the research forefront.Existing work on wind speed prediction with spatio-temporal correlation can be roughly classified into three categories:(1) Physical methods, such as numerical weather prediction (NWP)-an accurate technique over longer horizons (from several hours to several days) [10]-formulate the problem of wind speed prediction as a set of high-dimensional, non-linear, differential algebraic equations, according to meteorology and computational fluid dynamics theories. Though physical methods have a good theory base, there are still many factors that limit their application [11], including the demand for considerable computational resources, relatively coarse spatial and temporal resolutions, high dependency for full and accurate information of the environment, etc.(2) Statistical methods find statistical regularities or patterns in massive historical data by establishing the mapping relationship between the predicted wind speed and explanatory variables [12]. These methods include the time-series analysis method [13], the Kriging interpolation method [14], the augmented Kriging interpolation method [15], clustering analysis [16], Von Mises distribution [17], etc. (3) Artificial intelligence (AI) methods, inspired by bionics and natural laws, intend to represent the complex nonlinear relationship between the inputs and the outputs. Various methods have been adopted for wind speed prediction, such as artificial neural networks (ANN) [18], support vector regressor (SVR), recurrent neural networks (RNN) [19], etc. However, the majority ...

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To optimize the performance of a heat engine in finite-time cycle, it is important to understand the finite-time effect of thermodynamic processes. Previously, we have shown that extra work is needed to complete a quantum adiabatic process in finite time, and proved that the extra work follows a C/τ 2 scaling for long control time τ . There the oscillating part of the extra work is neglected due to the complex energy-level structure of the particular quantum system. However, such oscillation of the extra work can not be neglected in some quantum systems with simple energy-level structure, e. g. the two-level system or the quantum harmonic oscillator. In this paper, we build the finite-time quantum Otto engine on these simple systems, and find that the oscillating extra work leads to a jagged edge in the constraint relation between the output power and the efficiency. By optimizing the control time of the quantum adiabatic processes, the oscillation in the extra work is utilized to enhance the maximum power and the efficiency. We further design special control schemes with the zero extra work at the specific control time. Compared to the linear control scheme, these special control schemes of the finite-time adiabatic process improve the maximum power and the efficiency of the finite-time Otto engine.

A probabilistic load flow method based on polynomial normal transformation (PNT) and Latin hypercube sampling (LHS) is proposed. The correlation between input random variables has been taken into consideration. The proposed method uses the statistical moments and correlation matrix of input random variables instead of their marginal distribution functions and joint distribution functions, which are very difficult to be obtained, to establish their probability distribution models by PNT and LHS. The statistical moments and probability distribution functions of node voltage and line flow are calculated by Monte Carlo simulation method. Performance of the proposed method is investigated using IEEE 14-bus and IEEE 118-bus test systems. The impacts of correlation factor on the statistical moments of power injections and system operation are analysed. Finally, conclusions are duly drawn.