Nonparametric probabilistic load forecasting based on quantile combination in electrical power systems

GEFCom2014 probabilistic electric load forecasting: An integrated solution with forecast combination and residual simulation

Load probability density forecasting by transforming and combining quantile forecasts

Probabilistic load forecasting for buildings considering weather forecasting uncertainty and uncertain peak load

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.

Long term load forecasting plays a vital role in power systems planning and utility financial planning. Traditional methods in long term load forecasting rely on monthly data, which offers limited observations to support the comprehensive models with sufficient explanatory variables to capture the salient features in the electricity demand series. The grid modernization efforts undertaken by many utilities over the past decade have made high-resolution data available for many analytical tasks including load forecasting. In this paper, we investigate the effectiveness of using high-resolution data in long term probabilistic load forecasting. The primary error measure we use for forecast evaluation is pinball loss function. Through a case study based on the data from a U.S. utility, we show that high-resolution data is beneficial to the improvement of probabilistic load forecasts.

A novel combined probabilistic load forecasting system integrating hybrid quantile regression and knee improved multi-objective optimization strategy

In the era of the smart grid, the electrical load on the demand side becomes more dynamic and less predictable than ever before. Differently from deterministic load forecasting, probabilistic load forecasting (PLF) estimates the uncertainty of future loads and has become increasingly important for power system planning and operations. We have previously proposed a deterministic load forecasting method by improving the Informer model in which the periodic property of load profiles is considered. In this paper, a PLF model is designed on the basis of the deterministic load forecasting method. The PLF model estimates the model and data uncertainties through running the deterministic load forecasting model several times with random initial parameters, and determines load intervals by combining the average value of multi runs of the deterministic load forecasting model, the estimated uncertainties and the critical value of the standard normal distribution. The experimental results on GEFCom2014 data set have demonstrated the superior forecasting performance than others.

To mitigate climate change, renewable energy sources are increasingly integrated into the energy system. Due to their volatility and uncertainty, smart grid applications are required to deal with this uncertainty and maintain grid stability. To operate effectively and in an automated manner, each of these applications requires a quantification of the uncertainty in future demand and generation, which probabilistic forecasts can provide. Furthermore, these applications often require specific probabilistic forecast properties, such as coverage rate and sharpness. However, existing probabilistic forecasts cannot be easily customised to exhibit these required properties. Therefore, we present a novel approach that creates loss-customised probabilistic forecasts using automated hyperparameter optimisation based on custom loss metrics. We combine a deterministic base forecaster and a conditional Invertible Neural Network to include specified uncertainty in a deterministic forecast. This uncertainty is defined by automated hyperparameter optimisation based on flexible and adaptable loss metrics, enabling the generation of loss-customised probabilistic forecasts with different properties without computationally expensive retraining. We evaluate our approach on four real-world data sets and compare the generated loss-customised forecasts with three state-of-the-art probabilistic forecasting benchmarks. We show that our approach generates probabilistic forecasts that can be customised to achieve state-of-the-art performance in either Continuous Ranked Probability Score, Pinball Loss, or Coverage Rate Error, depending on the selected customised loss metric.

Probabilistic load forecasts provide comprehensive information about future load uncertainties. In recent years, many methodologies and techniques have been proposed for probabilistic load forecasting. Forecast combination, a widely recognized best practice in point forecasting literature, has never been formally adopted to combine probabilistic load forecasts. This paper proposes a constrained quantile regression averaging (CQRA) method to create an improved ensemble from several individual probabilistic forecasts. We formulate the CQRA parameter estimation problem as a linear program with the objective of minimizing the pinball loss, with the constraints that the parameters are nonnegative and summing up to one. We demonstrate the effectiveness of the proposed method using two publicly available datasets, the ISO New England data and Irish smart meter data. Comparing with the best individual probabilistic forecast, the ensemble can reduce the pinball score by 4.39% on average. The proposed ensemble also demonstrates superior performance over nine other benchmark ensembles.

Probabilistic load forecasting (PLF) is able to present the uncertainty information of the future loads. It is the basis of stochastic power system planning and operation. Recent works on PLF mainly focus on how to develop and combine forecasting models, while the feature selection issue has not been thoroughly investigated for PLF. This paper fills the gap by proposing a feature selection method for PLF via sparse L_1-norm penalized quantile regression. It can be viewed as an extension from point forecasting-based feature selection to probabilistic forecasting-based feature selection. Since both the number of training samples and the number of features to be selected are very large, the feature selection process is casted as a large-scale convex optimization problem. The alternating direction method of multipliers is applied to solve the problem in an efficient manner. We conduct case studies on the open datasets of ten areas. Numerical results show that the proposed feature selection method can improve the performance of the probabilistic forecasting and outperforms traditional least absolute shrinkage and selection operator method.

A novel similar-day based probability density forecasting framework for residential loads

Abstract. Stream water temperatures influence water quality, with effects on aquatic biodiversity, drinking-water provision, electricity production, agriculture, and recreation. Therefore, stakeholders would benefit from an operational forecasting service that would support timely action. Deep-learning models are well-suited to providing probabilistic forecasts at individual stations of a monitoring network. Here, we train and evaluate several state-of-the-art models using 10 years of data from 54 stations across Switzerland. Static catchment features, time of the year, meteorological observations from the past 64 d, and their ensemble forecasts for the following 32 d are included as predictors in the models to estimate daily maximum water temperature over the next 32 d. Results show that the temporal fusion transformer (TFT) model performs best, with a continuous rank probability score (CRPS) of 0.70 °C averaged over all lead times, stations, and 90 forecasts distributed over 1 year. The TFT is followed by the recurrent neural network encoder–decoder, with a CRPS of 0.74 °C, and the neural hierarchical interpolation for time series, with a CRPS of 0.75 °C. These deep-learning models outperform other simpler models trained at each station: random forest (CRPS = 0.80 °C), multi-layer perceptron neural network (CRPS = 0.81 °C), and autoregressive linear model (CRPS = 0.96 °C). The average CRPS of the TFT degrades from 0.38 °C at lead a time of 1 d to 0.90 °C at a lead time of 32 d, largely driven by the uncertainty of the meteorological ensemble forecasts. In addition, TFT water temperature predictions at new and ungauged stations outperform those from the other models. When analyzing the importance of model inputs, we find a dominant role of observed water temperature and future air temperature, while including precipitation and time of the year further improves predictive skill. Operational probabilistic forecasts of daily maximum water temperature are generated twice per week with our TFT model and are publicly available at https://www.drought.ch/de/impakt-vorhersagen-malefix/wassertemperatur-prognosen/ (last access: 20 March 2025). Overall, this study provides insights into the extended-range predictability of stream water temperature and into the applicability of deep-learning models in hydrology.

In numerical weather prediction (NWP), the uncertainty about the future state of the atmosphere is described by a set of forecasts (called an ensemble). All ensembles have deficiencies that can be corrected via statistical post-processing methods. Several ensembles, based on different NWP models, exist and may be corrected using different statistical methods. These raw or post-processed ensembles can thus be combined. The theory of prediction with expert advice allows us to build combination algorithms with theoretical guarantees on the forecast performance. We adapt this theory to the case of probabilistic forecasts issued as stepwise cumulative distribution functions, computed from raw and post-processed ensembles. The theory is applied to combine wind speed ensemble forecasts. The second goal of this study is to explore the use of two forecast performance criteria: the continuous ranked probability score (CRPS) and the Jolliffe–Primo test. The usual way to build skilful probabilistic forecasts is to minimize the CRPS. Minimizing the CRPS may not produce reliable forecasts according to the Jolliffe–Primo test. The Jolliffe–Primo test generally selects reliable forecasts, but could lead to issuing suboptimal forecasts in terms of CRPS. We propose to use both criteria to achieve reliable and skilful probabilistic forecasts.

K-nearest neighbors and a kernel density estimator for GEFCom2014 probabilistic wind power forecasting

An improved convolutional neural network with load range discretization for probabilistic load forecasting