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Uncertainty analysis in the form of probabilistic forecasting cansignificantly improve decision making processes in the smart power grid whenintegrating renewable energy sources such as wind. Whereas point forecastingprovides a single expected value, probabilistic forecasts provide moreinformation in the form of quantiles, prediction intervals, or full predictivedensities. Traditionally quantile regression is applied for such forecastingand recently quantile regression neural networks have become popular forweather and renewable energy forecasting. However, one major shortcoming ofcomposite quantile estimation in neural networks is the quantile crossoverproblem. This paper analyzes the effectiveness of a novel smoothed loss andpenalty function for neural network architectures to prevent the quantilecrossover problem. Its efficacy is examined on the wind power forecastingproblem. A numerical case study is conducted using publicly available wind datafrom the Global Energy Forecasting Competition 2014. Multiple quantiles areestimated to form 10\%, to 90\% prediction intervals which are evaluated usinga quantile score and reliability measures. Benchmark models such as thepersistence and climatology distributions, multiple quantile regression, andsupport vector quantile regression are used for comparison where resultsdemonstrate the proposed approach leads to improved performance whilepreventing the problem of overlapping quantile estimates.

A Novel Smoothed Loss and Penalty Function for Noncrossing Composite Quantile Estimation via Deep Neural Networks