Probabilistic Load Forecasting Research Articles

Long Short-Term Memory-Based Twin Support Vector Regression for Probabilistic Load Forecasting.

A probabilistic load forecast that is accurate and reliable is crucial to not only the efficient operation of power systems but also to the efficient use of energy resources. In order to estimate the uncertainties in forecasting models and nonstationary electric load data, this study proposes a probabilistic load forecasting model, namely BFEEMD-LSTM-TWSVRSOA. This model consists of a data filtering method named fast ensemble empirical model decomposition (FEEMD) method, a twin support vector regression (TWSVR) whose features are extracted by deep learning-based long short-term memory (LSTM) networks, and parameters optimized by seeker optimization algorithms (SOAs). We compared the probabilistic forecasting performance of the BFEEMD-LSTM-TWSVRSOA and its point forecasting version with different machine learning and deep learning algorithms on Global Energy Forecasting Competition 2014 (GEFCom2014). The most representative month data of each season, totally four monthly data, collected from the one-year data in GEFCom2014, forming four datasets. Several bootstrap methods are compared in order to determine the best prediction intervals (PIs) for the proposed model. Various forecasting step sizes are also taken into consideration in order to obtain the best satisfactory point forecasting results. Experimental results on these four datasets indicate that the wild bootstrap method and 24-h step size are the best bootstrap method and forecasting step size for the proposed model. The proposed model achieves averaged 46%, 11%, 36%, and 44% better than suboptimal model on these four datasets with respect to point forecasting, and achieves averaged 53%, 48%, 46%, and 51% better than suboptimal model on these four datasets with respect to probabilistic forecasting.

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

In contemporary power systems, diverse energy integration and technological advancements have complicated load dynamics, revealing limitations in traditional deterministic forecasting techniques. Given the pivotal role of Probabilistic Load Forecasting (PLF) in mitigating risks in power system planning and operation, the pursuit of more accurate PLF techniques has evidently become a topic of paramount importance. Therefore, in this study, a novel hybrid Quantile Regression (QR) model integrating causal dilated convolution, residual connection, and Bidirectional Long Short-Term Memory (BiLSTM) is initially proposed for PLF, its core multi-scale feature extraction module can deeply mine the interactions between loads and their features. However, relying solely on a single-model often encounters inherent flaws in certain scenarios. Recognizing this, a Combined Probabilistic Load Forecasting System (CPLFS) is further proposed. This system incorporates the developed hybrid QR to establish a diversified candidate model pool, aiming to select the top-performing benchmarks in various scenarios and utilizes the Knee enhanced Pareto mechanism to adjust the combined weights of each benchmark, thereby bridging the gap created by the “No Free Lunch (NFL)” phenomenon. Taking the load uncertainty of Australia as an illustrative example, simulations indicate that the hybrid QR outperforms traditional models. Furthermore, CPLFS surpasses the best benchmarks and other combinations in both prediction accuracy and stability.

Short-Term Density Forecasting of Low-Voltage Load Using Bernstein-Polynomial Normalizing Flows

The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level to increase efficiency and ensure reliable control. However, high fluctuations and increasing electrification cause huge forecast variability, not reflected in traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus allow more informed decision-making for the planning and operation of low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein polynomial normalizing flows, where a neural network controls the parameters of the flow. In an empirical study with 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities. Also, they outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures.

Probabilistic forecast-based portfolio optimization of electricity demand at low aggregation levels

In the effort to achieve carbon neutrality through a decentralized electricity market, accurate short-term load forecasting at low aggregation levels has become increasingly crucial for various market participants' strategies. Accurate probabilistic forecasts at low aggregation levels can improve peer-to-peer energy sharing, demand response, and the operation of reliable distribution networks. However, these applications require not only probabilistic demand forecasts, which involve quantification of the forecast uncertainty, but also determining which consumers to include in the aggregation to meet electricity supply at the forecast lead time. While research papers have been proposed on the supply side, no similar research has been conducted on the demand side. This paper presents a method for creating a portfolio that optimally aggregates demand for a given energy demand, minimizing forecast inaccuracy of overall low-level aggregation. Using probabilistic load forecasts produced by either ARMA-GARCH models or kernel density estimation (KDE), we propose three approaches to creating a portfolio of residential households' demand: Forecast Validated, Seasonal Residual, and Seasonal Similarity. An evaluation of probabilistic load forecasts demonstrates that all three approaches enhance the accuracy of forecasts produced by random portfolios, with the Seasonal Residual approach for Korea and Ireland outperforming the others in terms of accuracy and computational efficiency.

MSGCN-ISTL: A multi-scaled self-attention-enhanced graph convolutional network with improved STL decomposition for probabilistic load forecasting

Probabilistic load forecasting has gained widespread attention for its effectiveness in providing scientific power dispatch plans in recent years. Most existing works adopted decomposition strategies to handle the temporal features of load data, but ignored the fact that decomposition components have different levels of importance, resulting in the incomplete extraction of temporal correlation information. Moreover, previous works have primarily concentrated on the geographical correlation among neighboring load zones and overlooked the semantic correlation among load zones, resulting in insufficient extraction of spatial correlation information. In this study, a novel multi-scaled self-attention-enhanced graph convolutional network with improved Seasonal-Trend decomposition based on Loess (STL) decomposition (MSGCN-ISTL) is proposed for probabilistic load forecasting. First, an improved STL decomposition is proposed, which adopts a convolutional neural network with dual convolutional channels to separately handle the different decomposition components, thus improving the extraction of temporal correlation information. Second, a new multi-scaled self-attention-enhanced graph convolutional network is proposed to extract the spatial correlation information from geographical and semantic aspects simultaneously, which enriches the receptive fields and extracts the multi-scaled enhanced spatial features. Experimental results conducted under various conditions demonstrate the superiority and robustness of the proposed model.

Study on Probabilistic Load Forecasting Model and Its Improvements

The current research on probabilistic load forecasting models mostly combines machine learning algorithms and quantile regression methods to construct quantile models. This paper first summarizes and combs the commonly used quantile regression forecast models. Combined with the actual data, we analyzed the main factors affecting the performance of probabilistic load forecasting and attempted to elaborate on the influencing mechanism. Then, a quantile regression probabilistic load forecasting strategy based on sample weight is designed. According to the analysis and experimental verification, we propose the future research direction for probabilistic load forecasting.

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

Probabilistic load forecasting can provide much richer information about uncertainties in residential loads than point load forecasting, and is gaining increasing attention in building efficient and economical demand response programs. However, obtaining satisfactory forecasting results for residential loads is challenging due to their intrinsic nonlinearity and volatility. Furthermore, existing probabilistic forecasting methods are limited in their ability to directly generate probability density forecasting in an efficient and accurate way. To address these issues, a new probability density forecasting framework for residential loads is proposed in this paper. Firstly, a similar-day choosing method is proposed by combining weighted external features and internal load curves to build a similar-day dataset. Then, point forecasting is achieved by training an exclusive predictor on the corresponding similar-day dataset for each forecasting target. Finally, probability density forecasting is realized by conducting kernel density estimation on the similar-day dataset and calibrating it according to the point forecasting result. Comparisons with other state-of-the-art methods carried out on the HUE dataset demonstrate the efficiency and superiority of the proposed framework in both point and probability density forecasting.

FedForecast: A federated learning framework for short-term probabilistic individual load forecasting in smart grid

Load forecasting plays a crucial role in the power system operation and planning. However, with people’s increased awareness of privacy, consumers may not be willing to share their data with the retailer. Thus, the conventional centralized training approach could not be adopted. To tackle these issues, we propose a distributed short-term individual load forecasting method based on the federated learning framework called FedForecast, which could protect the privacy of consumers and make full use of edge computing resources. In this framework, the forecasting models rather than load data are transmitted during the model training and in this way, the privacy of consumers is protected and computation capacity of edge device is fully utilized. The detailed theoretical mathematical proof is presented to verify the convergence of the proposed algorithm. Case studies on the PecanStreet dataset show that the proposed federated approach has comparable performance with the centralized method and robustness of the proposed framework is also verified. The results demonstrate that the proposed framework could achieve good accuracy and robustness in individual probabilistic load forecasting.

An improved encoder-decoder-based CNN model for probabilistic short-term load and PV forecasting

An improved encoder-decoder-based CNN model for probabilistic short-term load and PV forecasting

High-resolution probabilistic load forecasting: A learning ensemble approach

High-resolution probabilistic load forecasting can comprehensively characterize both the uncertainties and the dynamic trends of the future load. Such information is key to the reliable operation of the future power grid with a high penetration of renewables. To this end, various high-resolution probabilistic load forecasting models have been proposed in recent decades. Compared with a single model, it is widely acknowledged that combining different models can further enhance the prediction performance, which is called the model ensemble. However, existing model ensemble approaches for load forecasting are linear combination-based, like mean value ensemble, weighted average ensemble, and quantile regression, and linear combinations may not fully utilize the advantages of different models, seriously limiting the performance of the model ensemble. We propose a learning ensemble approach that adopts the machine learning model to directly learn the optimal nonlinear combination from data. We theoretically demonstrate that the proposed learning ensemble approach can outperform conventional ensemble approaches. Based on the proposed learning ensemble model, we also introduce a Shapley value-based method to evaluate the contributions of each model to the model ensemble. The numerical studies on field load data verify the remarkable performance of our proposed approach.

Probabilistic load forecasting for the low voltage network: Forecast fusion and daily peaks

Short-term forecasts of energy consumption are invaluable for the operation of energy systems, including low voltage electricity networks. However, network loads are challenging to predict when highly desegregated to small numbers of customers, which may be dominated by individual behaviours rather than the smooth profiles associated with aggregate consumption. Furthermore, distribution networks are challenged almost entirely by peak loads, and tasks such as scheduling storage and/or demand flexibility maybe be driven by predicted peak demand, a feature that is often poorly characterised by general-purpose forecasting methods. Here we propose an approach to predict the timing and level of daily peak demand, and a data fusion procedure for combining conventional and peak forecasts to produce a general-purpose probabilistic forecast with improved performance during peaks. The proposed approach is demonstrated using real smart meter data and a hypothetical low voltage network hierarchy comprising feeders, secondary and primary substations. Fusing state-of-the-art probabilistic load forecasts with peak forecasts is found to improve performance overall, particularly at smart-meter and feeder levels and during peak hours, where improvement in terms of CRPS exceeds 10%.

Probabilistic forecasting method for mid-term hourly load time series based on an improved temporal fusion transformer model

The growth of distributed renewable energy and demand-side responsiveness has increased the difficulty of mid-term hourly load time-series forecasting. This study presents a probabilistic forecasting method for hourly load time series based on an improved temporal fusion transformer (ITFT) model to achieve more accurate and thorough forecasting results. The raw univariate time series of the hourly load was reconstructed into multiple day-to-day load time series at different hour-points to reconcile the contradiction between learning the temporal dependence on a long prediction horizon and reducing model complexity. The corresponding hour point was used as a static covariable input to distinguish the differences. Based on the original temporal fusion transformer (TFT) model, the ITFT model replaces the long short-term memory (LSTM) with a gated recurrent unit (GRU) to learn long-term dependence more efficiently. Furthermore, quantile constraints and prediction interval (PI) penalty terms were incorporated into the original quantile loss function to prevent quantile crossover and construct more compact prediction intervals (PIs). The results of two actual examples show that the proposed method is explanatory and can significantly improve the reliability and compactness of probabilistic load forecasting (PLF) results compared with other popular methods.

A Novel Hybrid Method for Short-Term Probabilistic Load Forecasting in Distribution Networks

In recent decades, the evolution of loads and distributed energy resources has added great complexity and uncertainty to distribution networks. In such a context, a reliable characterization of the uncertainty associated with prediction is fundamental to the wide range of the newly emerging applications in the low-voltage level grid. In this regard, this paper proposes a novel method to solve the short-term probabilistic load forecasting (STPLF) problem in distribution networks in which the loads are usually too volatile to be forecasted accurately. The approach developed employs a Dirichlet process mixture model (DPMM) to handle the uncertainty of load patterns, which is inferred by a Markov chain Monte Carlo (MCMC)-based method. Thereafter, the DPMM representation of the load patterns is combined with a tree-based ensemble learning method to address the STPLF by solving a classification problem. The final result is averaged over all MCMC samples. The proposed technique is compared to selected benchmark methods at different aggregation levels using smart meter datasets collected from customers located in Ireland as well as the City of Saskatoon, SK, Canada. The results obtained demonstrate that the proposed approach outperforms the benchmark methods in STPLF at the given aggregation levels.

Probabilistic load forecasting using post-processed weather ensemble predictions

Probabilistic forecasting of electricity demand (load) facilitates the efficient management and operations of energy systems. Weather is a key determinant of load. However, modelling load using weather is challenging because the relationship cannot be assumed to be linear. Although numerous studies have focussed on load forecasting, the literature on using the uncertainty in weather while estimating the load probability distribution is scarce. In this study, we model load for Great Britain using weather ensemble predictions, for lead times from one to six days ahead. A weather ensemble comprises a range of plausible future scenarios for a weather variable. It has been shown that the ensembles from weather models tend to be biased and underdispersed, which requires that the ensembles are post-processed. Surprisingly, the post-processing of weather ensembles has not yet been employed for probabilistic load forecasting. We post-process ensembles based on: (1) ensemble model output statistics: to correct for bias and dispersion errors by calibrating the ensembles, and (2) ensemble copula coupling: to ensure that ensembles remain physically consistent scenarios after calibration. The proposed approach compares favourably to the case when no weather information, raw weather ensembles or post-processed ensembles without ensemble copula coupling are used during the load modelling.

A Novel Interval Energy-Forecasting Method for Sustainable Building Management Based on Deep Learning

Energy conservation in buildings has increasingly become a hot issue for the Chinese government. Compared to deterministic load prediction, probabilistic load forecasting is more suitable for long-term planning and management of building energy consumption. In this study, we propose a probabilistic load-forecasting method for daily and weekly indoor load. The methodology is based on the long short-term memory (LSTM) model and penalized quantile regression (PQR). A comprehensive analysis for a time period of a year is conducted using the proposed method, and back propagation neural networks (BPNN), support vector machine (SVM), and random forest are applied as reference models. Point prediction as well as interval prediction are adopted to roundly test the prediction performance of the proposed model. Results show that LSTM-PQR has superior performance over the other three models and has improvements ranging from 6.4% to 20.9% for PICP compared with other models. This work indicates that the proposed method fits well with probabilistic load forecasting, which could promise to guide the management of building sustainability in a future carbon neutral scenario.

An advanced deep neuroevolution model for probabilistic load forecasting

Probabilistic load forecasting (PLF) is necessary for power system operations and control as it assists in proper scheduling and dispatch. Moreover, PLF adequately captures the uncertainty whether that uncertainty is related to load data or the forecasting model. And there are not many PLF models, and those which exist are very complex or difficult to interpret. This paper proposes a novel neuroevolution algorithm for handling the uncertainty associated with load forecasting. In this paper, a new modified evolutionary algorithm is proposed which is used to find the optimal hyperparameters of 1D-Convolutional neural network (CNN). The probabilistic forecasts are produced by minimizing the mean scaled interval score loss function at 50%, 90% and 95% prediction intervals. The proposed neuroevolution algorithm is tested on a global energy forecasting competition (GEFCom-2014) load dataset, and two different experiments are conducted considering load only and one with load and temperature. Strong conclusions are drawn from these experiments. Also, the proposed model is compared with other benchmark models, and it has been shown that it outperforms the other models.

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

Probabilistic load forecasting (PLF) aims to predict the future uncertainties of loads to reduce the potential risks in power system planning and operation. In the increasingly complex power market environment, exploring advanced approaches to obtain more accurate PLF is still a significant topic. Optimizing individual forecasting method is no longer the only direction to improve the accuracy of load forecasting in recent years. Researchers started to focus on combination methods because of their better accuracy in most cases than a single model. There are existing combination methods designed for parametric environment, where some results are based on the certain assumption (e.g., Gaussian distribution assumption of single prediction). Combining probabilistic forecasts in nonparametric environment is rarely investigated, because modeling the combination problem without assuming distributions of parameters is hard. This paper proposes a novel combined model for probabilistic forecasting tailored to nonparametric environments, which combines multiple quantile-based models by minimizing the overall loss function composed of continuous ranked probability score (CRPS) under kernel density estimation (KDE). We define a multilayer Gaussian mixture distribution, which is an extended form of Gaussian mixture distribution that can simulate any distribution type in nonparametric environment. Based on the multilayer Gaussian mixture distribution, the combined model is further formulated into a quadratic programming problem with linear restrictions that can be solved efficiently. Case studies are performed using benchmark and competition datasets from the United States and China. The results show that our proposed method outperforms the best individual model and other existing combination methods. In summary, this paper constructs a complete theoretical framework of nonparametric probabilistic combination forecasting and proves its effectiveness in practical application.

Two-Stage Bootstrap Sampling for Probabilistic Load Forecasting

The integration of distributed renewable energy and the implementation of the demand response complicate the change patterns of load profiles and present great uncertainties. Probabilistic load forecasting, an effective method for capturing the future load uncertainty, has been a hot issue. This article proposes a two-stage bootstrap sampling method for probabilistic load forecasting. In the first stage, alpha-bootstrap, which is a modification of traditional bootstrap methods, is applied to characterize the uncertainties from multiple forecasting models; in the second stage, the residual bootstrap method is used to formulate the regression errors. Finally, the probabilistic load forecasts can be obtained by integrating the uncertainties in both stages. Various off-the-shelf point load forecasting methods such as random forest (RF) and gradient boosting regression tree (GBRT) can be integrated into the proposed framework. We illustrate the effectiveness of our proposed method and superiority over direct quantile regression methods such as quantile RF and quantile GBRT using the case studies on open load datasets of eight zones in ISO New-England.

Consumption Scenario-Based Probabilistic Load Forecasting of Single Household

Forecasting of a single household electricity consumption (load) would be very useful for home energy management systems. However, the load forecasting of a single household is challenging due to the unpredictability of the individual household consumption behaviour. In this paper, a consumption scenario-based probabilistic load forecasting (PLF) method is developed. An energy consumption scenario analysis is proposed to compute the probability of occurrence of each consumption scenario of an individual household at any future time horizon. Then, the analysed results are integrated with PLF algorithms to provide the load forecasting of an individual household. Case studies are conducted to compare the performance of three conventional PLF algorithms and the performance of these three algorithms integrating with consumption scenario analysis. Results show that the proposed method outperforms the conventional PLF methods.

Short-term load forecasting based on LSTM networks considering attention mechanism

Reliable and accurate zonal electricity load forecasting is essential for power system operation and planning. Probabilistic load forecasts can present more comprehensive information for decision-making processes by quantifying the uncertainties of the electric load. A suitable feature selection is a critical step in forecasting, especially for data-driven methods. Weather conditions are another major factor related to electricity demand and play an important role in load forecasting. In this paper, we propose a dual-stage attention based long short-term memory (LSTM) network for short-term zonal load probabilistic forecasting. In the first stage, a feature attention based encoder is built to calculate the correlation of input features with electricity load at each time step. The most relevant input features can be adaptively selected. In the second stage, a temporal attention based decoder is developed to mine the time dependencies. Then, an LSTM model integrates these attention results and the probabilistic forecasts can be obtained using a pinball loss function. We also discuss how the proposed method can be utilized for feature and weather station selection. The effectiveness of the proposed method for both point and probabilistic forecasting is adequately verified on an open dataset of GEFCom2014, showing higher accuracy and generalization ability over other state-of-the-art forecasting models.