Load probability density forecasting by transforming and combining quantile forecasts

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

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

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.

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 for buildings considering weather forecasting uncertainty and uncertain peak load

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.

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.

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

Short term load forecasting and the effect of temperature at the low voltage level

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.

The extensive deployment of smart meters in millions of households provides a huge amount of individual electricity consumption data for demand side analysis at a fine granularity. Different from traditional aggregated system-level data, smart meter data is more irregular and unpredictable. As a result, probabilistic load forecasting (PLF), which can provide a better understanding of the uncertainty and volatility in future demand, is critical to constructing energy-efficient and reliable smart grids. In this article, a recently developed technique called Bayesian deep learning is employed to solve this challenging problem. In particular, a novel multitask PLF framework based on Bayesian deep learning is proposed to quantify the shared uncertainties across distinct customer groups while accounting for their differences. Further, a clustering-based pooling method is designed to increase the data diversity and volume for the framework. This not only addresses the problem of overfitting but also improves the predictive performance. Numerical results are presented which demonstrate that the proposed framework provides superior probabilistic forecasting accuracy over conventional methods.

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

The consumer-side load probabilistic forecasting is meaningful and useful in the smart grid area and becoming more and more possible with the explosion of electricity consumption data collected by smart meters. Compared to aggregated load, forecasting on the consumer-side load prefers to be stochastic and uncertain, which places higher demands on the forecast performance of models. In this paper, a novel probabilistic forecasting method, quantile Huber guided Temporal convolutional network (TCN), is proposed to quantify the variability and uncertainty of consumer-side load forecasting. Specifically, TCN is a new deep neural network implemented for capturing the dependencies information within the load sequences. The quantile Huber function formulated weighted average multiple losses (WAML) function is used to generate probabilistic prediction intervals (PIs). Conditional distribution of deterministic forecasting residual is also considered to calibrate the probabilistic forecasting. The performance of the proposed forecasting method is validated by numerical experiments using real load datasets of residential and industrial consumers. The comparative results show the superiority of the proposed method over traditional methods.

The integration of renewable energy in modern power systems has increased the stochasticity of load patterns. Probabilistic load forecasting (PLF) acts as a solution to capture the uncertainty of load data. Especially, neural network (NN)-based models can be flexibly adapted for PLF. However, the black-box characteristic of NN makes it difficult for us to understand where the uncertainty comes from, thereby reducing the reliability of the forecast. This paper provides a model-agnostic NN explanation framework for PLF, attributing the uncertainty quantification of the probabilistic forecast to the uncertainty of the input feature to evaluate where the uncertainty in the forecast comes from. Unlike traditional deep learning explanation techniques that examine how the information of the feature affects the result, our explanation focuses on exploring how the uncertainty of the feature affects the result. In this way, we can know the uncertainty and error sources of PLF and further understand its mechanism, which can help reduce the adverse effects of data uncertainty on forecasts. The codes can be found in <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hkuedl/Explanation-for-Probabilistic-Load-Forecasting</uri>.

Probability density forecast offers the whole distributions of forecasting targets, which brings greater flexibility and practicability than the other probabilistic forecast models such as prediction interval (PI) and quantile forecast. However, existing density forecast models have introduced various constraints on forecasted distributions, which has limited their ability to approximate real distributions and may result in suboptimality. In this paper, a distribution-free density forecast model based on deep learning is proposed, in which the real cumulative density functions (CDFs) of forecasting target are approximated by a large-capacity positive-weighted deep neural network (NN). Benefiting from the universal approximation ability of NNs, the range of forecasted distributions has been proven to contain all the distributions with continuous CDFs, which is superior to existing models' considering both width and accordance with reality. Three tests from different scenarios were implemented for evaluation, i.e., very-short-term wind power, wind speed, and day-ahead electricity price forecast, in which the proposed density forecast model has shown superior performance over the state of the art.