Combining Probability Density Forecasts for Power Electrical Loads

Researchers have proposed various probabilistic load forecasting models in the form of quantiles, densities, or intervals to describe the uncertainties of future energy demand. Density forecasts can provide more uncertainty information than can be expressed by just the quantile and interval. However, the combining method for density forecasts is seldom investigated. This paper proposes a novel and easily implemented approach to combine density probabilistic load forecasts to further improve the performance of the final probabilistic forecasts. The combination problem is formulated as an optimization problem to minimize the continuous ranked probability score of the combined model by searching the weights of different individual methods. Under the Gaussian mixture distribution assumption of the density forecasts, the problem is cast to a linearly constrained quadratic programming problem and can be solved efficiently. Case studies on the electric load datasets of eight areas verify the effectiveness of the proposed method.

[1]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[2]  Rob J. Hyndman,et al.  Forecasting Uncertainty in Electricity Smart Meter Data by Boosting Additive Quantile Regression , 2016, IEEE Transactions on Smart Grid.

[3]  T. Gneiting,et al.  Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules , 2011 .

[4]  Bikash Pal,et al.  Statistical Representation of Distribution System Loads Using Gaussian Mixture Model , 2010, IEEE Transactions on Power Systems.

[5]  Ming Yang,et al.  A Multi-Model Combination Approach for Probabilistic Wind Power Forecasting , 2017, IEEE Transactions on Sustainable Energy.

[6]  Tao Hong,et al.  Probabilistic electric load forecasting: A tutorial review , 2016 .

[7]  Goran Strbac,et al.  Probabilistic Peak Load Estimation in Smart Cities Using Smart Meter Data , 2019, IEEE Transactions on Industrial Electronics.

[8]  Jie Zhang,et al.  A Data-Driven Methodology for Probabilistic Wind Power Ramp Forecasting , 2019, IEEE Transactions on Smart Grid.

[9]  Kit Po Wong,et al.  A Hybrid Approach for Probabilistic Forecasting of Electricity Price , 2014, IEEE Transactions on Smart Grid.

[10]  Tao Hong,et al.  GEFCom2014 probabilistic electric load forecasting: An integrated solution with forecast combination and residual simulation , 2016 .

[11]  Joakim Widén,et al.  Residential probabilistic load forecasting: A method using Gaussian process designed for electric load data , 2018 .

[12]  Tianqi Chen,et al.  XGBoost: A Scalable Tree Boosting System , 2016, KDD.

[13]  Zhao Xu,et al.  Conditional Density Forecast of Electricity Price Based on Ensemble ELM and Logistic EMOS , 2019, IEEE Transactions on Smart Grid.

[14]  Siddharth Arora,et al.  Forecasting electricity smart meter data using conditional kernel density estimation , 2014, 1409.2856.

[15]  Alexis Boukouvalas,et al.  GPflow: A Gaussian Process Library using TensorFlow , 2016, J. Mach. Learn. Res..

[16]  D. R. Limaye,et al.  Selected statistical methods for analysis of load research data. Final report , 1984 .

[17]  Duehee Lee,et al.  Short-Term Wind Power Ensemble Prediction Based on Gaussian Processes and Neural Networks , 2014, IEEE Transactions on Smart Grid.

[18]  Song Li,et al.  Wind Power Forecasting Using Neural Network Ensembles With Feature Selection , 2015, IEEE Transactions on Sustainable Energy.

[19]  Song Li,et al.  A Novel Wavelet-Based Ensemble Method for Short-Term Load Forecasting with Hybrid Neural Networks and Feature Selection , 2016, IEEE Transactions on Power Systems.

[20]  Yi Wang,et al.  Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges , 2018, IEEE Transactions on Smart Grid.

[21]  Jian Xiao,et al.  Short-Term Solar Power Forecasting Based on Weighted Gaussian Process Regression , 2018, IEEE Transactions on Industrial Electronics.

[22]  R. Horst,et al.  DC Programming: Overview , 1999 .

[23]  Chongqing Kang,et al.  An Ensemble Forecasting Method for the Aggregated Load With Subprofiles , 2018, IEEE Transactions on Smart Grid.

[24]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[25]  Tao Hong,et al.  Global energy forecasting competition 2017: Hierarchical probabilistic load forecasting , 2019, International Journal of Forecasting.

[26]  Rob J Hyndman,et al.  Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond , 2016 .

[27]  Yandong Yang,et al.  Power load probability density forecasting using Gaussian process quantile regression , 2017 .

[28]  Georgios Giasemidis,et al.  A hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting , 2016, 1610.05183.

[29]  Daniel Kirschen,et al.  Combining Probabilistic Load Forecasts , 2018, IEEE Transactions on Smart Grid.

[30]  R. Weron,et al.  Recent advances in electricity price forecasting: A review of probabilistic forecasting , 2016 .

[31]  Duehee Lee,et al.  Bivariate Probabilistic Wind Power and Real-Time Price Forecasting and Their Applications to Wind Power Bidding Strategy Development , 2018, IEEE Transactions on Power Systems.

[32]  L. Baringhaus,et al.  On a new multivariate two-sample test , 2004 .

[33]  Shanlin Yang,et al.  Short-term power load probability density forecasting based on quantile regression neural network and triangle kernel function , 2016 .