Quantile regression for the qualifying match of GEFCom2017 probabilistic load forecasting

We present a simple quantile regression-based forecasting method that was applied in the probabilistic load forecasting framework of the Global Energy Forecasting Competition 2017 (GEFCom2017). The hourly load data are log transformed and split into a long-term trend component and a remainder term. The key forecasting element is the quantile regression approach for the remainder term, which takes into account both weekly and annual seasonalities, such as their interactions. Temperature information is used only for stabilizing the forecast of the long-term trend component. Information on public holidays is ignored. However, the forecasting method still placed second in the open data track and fourth in the definite data track, which is remarkable given the simplicity of the model. The method also outperforms the Vanilla benchmark consistently.     

Neural networks for GEFCom2017 probabilistic load forecasting

This report describes the forecasting model which was developed by team “4C” for the global energy forecasting competition 2017 (GEFCom2017), with some modifications added afterwards to improve its accuracy. The model is based on neural networks. Temperature scenarios obtained from historical data are used as inputs to the neural networks in order to create load scenarios, and these load scenarios are then transformed into quantiles. By using a feature selection approach that is based on a stepwise regression technique, a neural network based model is developed for each zone. Furthermore, a dynamic choice of the temperature scenarios is suggested. The feature selection and dynamic choice of the temperature scenarios can improve the quantile scores considerably, resulting in very accurate forecasts among the top teams.     

Data visualization and forecast combination for probabilistic load forecasting in GEFCom2017 final match

This paper describes the methods used by Team Cassandra, a joint effort between IBM Research Australia and the University of Melbourne, in the GEFCom2017 load forecasting competition. An important first phase in the forecasting effort involved a deep exploration of the underlying dataset. Several data visualisation techniques were applied to help us better understand the nature and size of gaps, outliers, the relationships between different entities in the dataset, and the relevance of custom date ranges. Improved, cleaned data were then used to train multiple probabilistic forecasting models. These included a number of standard and well-known approaches, as well as a neural-network based quantile forecast model that was developed specifically for this dataset. Finally, model selection and forecast combination were used to choose a custom forecasting model for every entity in the dataset.     

An ensemble approach to GEFCom2017 probabilistic load forecasting

We present an ensembling approach to medium-term probabilistic load forecasting which ranked second out of 73 competitors in the defined data track of the GEFCom2017 qualifying match. In addition to being accurate, the ensemble method is highly scalable, due to the fact that it had to be applied to nine quantiles in ten zones and for six rounds. Candidate forecasts were generated using random settings for input data, covariates, and learning algorithms. The best candidate forecasts were averaged to create the final forecast, with the number of candidate forecasts being chosen based on their accuracy in similar validation periods.     

Machine learning methods for GEFCom2017 probabilistic load forecasting

This paper describes the preprocessing and forecasting methods used by team Orbuculum during the qualifying match of the Global Energy Forecasting Competition 2017 (GEFCom2017). Tree-based algorithms (gradient boosting and quantile random forest) and neural networks made up an ensemble. The ensemble prediction quantiles were obtained by a simple averaging of the ensemble members’ prediction quantiles. The result shows a robust performance according to the pinball loss metric, with the ensemble model achieving third place in the qualifying match of the competition.     

Probabilistic energy forecasting using the nearest neighbors quantile filter and quantile regression

Parametric quantile regression is a useful tool for obtaining probabilistic energy forecasts. Nonetheless, traditional quantile regressions may be complicated to obtain using complex data mining techniques (e.g., artificial neural networks), since they are trained using a non-differentiable cost function. This article presents a method that uses a new nearest neighbors quantile filter to obtain quantile regressions independently of the data mining technique utilized and without the non-differentiable cost function. This method is subsequently validated using the dataset from the 2014 Global Energy Forecasting Competition. The results show that the method presented here is able to solve the competition’s task with a similar accuracy to the competition’s winner and in a similar timeframe, but requiring a much less powerful computer. This property may be relevant in an online forecasting service for which the fast computation of probabilistic forecasts using less powerful machines is required.     

A robust support vector regression model for electric load forecasting

Electric load forecasting is a crucial part of business operations in the energy industry. Various load forecasting methods and techniques have been proposed and tested. With growing concerns about cybersecurity and malicious data manipulations, an emerging topic is to develop robust load forecasting models. In this paper, we propose a robust support vector regression (SVR) model to forecast the electricity demand under data integrity attacks. We first introduce a weight function to calculate the relative importance of each observation in the load history. We then construct a weighted quadratic surface SVR model. Some theoretical properties of the proposed model are derived. Extensive computational experiments are based on the publicly available data from Global Energy Forecasting Competition 2012 and ISO New England. To imitate data integrity attacks, we have deliberately increased or decreased the historical load data. Finally, the computational results demonstrate better accuracy of the proposed robust model over other recently proposed robust models in the load forecasting literature.     

Blending gradient boosted trees and neural networks for point and probabilistic forecasting of hierarchical time series

In this study, we addressed the problem of point and probabilistic forecasting by describing a blending methodology for machine learning models from the gradient boosted trees and neural networks families. These principles were successfully applied in the recent M5 Competition in both the Accuracy and Uncertainty tracks. The key points of our methodology are: (a) transforming the task into regression on sales for a single day; (b) information-rich feature engineering; (c) creating a diverse set of state-of-the-art machine learning models; and (d) carefully constructing validation sets for model tuning. We show that the diversity of the machine learning models and careful selection of validation examples are most important for the effectiveness of our approach. Forecasting data have an inherent hierarchical structure (12 levels) but none of our proposed solutions exploited the hierarchical scheme. Using the proposed methodology, we ranked within the gold medal range in the Accuracy track and within the prizes in the Uncertainty track. Inference code with pre-trained models are available on GitHub.¹     

Physics-informed Gaussian process regression for states estimation and forecasting in power grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method.We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power.For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.     

电力系统中长期负荷预测方法的研究与程序设计

文章探讨了电力系统负荷的组成、特点,在分析比较常用的预测方法优缺点的基础之上,采用了灰色．预测法与回归法相结合的方法建立了中长期负荷预测模型,把负荷预测工作分为2个部分：即用灰色预测法进行相关因素的预测和用回归法进行负荷预测。该模型充分利用了灰色预测法要求负荷数据少、不考虑分布规律、不考虑变化趋势、运算方便、易于检验等优点及回归法能够考虑到负荷所受的多种因素的特点,模型参数估许技术比较成熟,预测过程简单。     

Asymptotic results and tests for the choice of approximative models in nonlinear two-phases regression models, heteroscedatic case

This paper is devoted to the study of the least squares estimator of f for the classical, fixed design, nonlinear model X (t _i)=f(t _i)+ε(t _i), i=1,2,…,n, where the (ε(t _i))_i=1,…,n are independent second order r.v.. The estimation of f is based upon a given parametric form. In Brodeau (1993) this subject has been studied in the homoscedastic case. This time we assume that the ε(t _i) have non constant and unknown variances σ²(t _i). Our main goal is to develop two statistical tests, one for testing that f belongs to a given class of functions possibly discontinuous in their first derivative, and another for comparing two such classes. The fundamental tool is an approximation of the elements of these classes by more regular functions, which leads to asymptotic properties of estimators based on the least squares estimator of the unknown parameters. We point out that Neubauer and Zwanzig (1995) have obtained interesting results for connected subjects by using the same technique of approximation. Received: February 1996