We develop an integrative framework to predict the wind power output, considering many uncertainties. For probabilistic wind power forecasts, all the sources of uncertainties arising from both wind speed prediction and wind-to-power conversion process should be collectively addressed. To this end, we model the wind speed using the inhomogeneous geometric Brownian motion and convert the wind speed's prediction density into the wind power density in a closed-form. The resulting wind power density allows us to quantify prediction uncertainties through prediction intervals and to forecast the power that can minimize the expected prediction cost with unequal penalties on the overestimation and underestimation. We evaluate the predictive power of the proposed approach using data from commercial wind farms located in different sites. The results suggest that our approach outperforms alternative approaches in terms of multiple performance measures.
This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive Integrated Moving Average assumes a linear correlation structure in time series data. When a stochastic process is highly volatile, such an assumption can be easily violated, leading to inaccurate predictions. We develop a new prediction model that can flexibly characterize a time-varying volatile process without assuming linearity. We formulate the prediction problem as an optimization problem with unequal overestimation and underestimation costs. Based on real option theories developed in finance, we solve the optimization problem and obtain a predicted value, which can minimize the expected prediction cost. We evaluate the proposed approach using multiple datasets obtained from real-life applications including manufacturing, finance, and environment. The numerical results demonstrate that the proposed model shows competitive prediction capability, compared with alternative approaches.
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