Probabilistic Wind Power Forecasting Research Articles

Hybrid model based on similar power extraction and improved temporal convolutional network for probabilistic wind power forecasting

Accurate wind power generation forecasting is of great significance to improve the operation of power system. Probabilistic forecasting has a higher application value in power grid because it can provide more abundant forecasting information than deterministic forecasting. In addition, multi-step forecasting can provide forecasting results in a longer time range, so that decision makers can make longer-term planning and strategic arrangements. In this paper, we propose a novel multi-step improved temporal convolutional network based on quadratic spline quantile function (MITCN-QSQF) for probabilistic wind power forecasting. First, we combine maximum information coefficient, Gaussian similarity and adaptive resample to propose an effective similar power generation feature extraction method (MGR) for power generation. Then the temporal convolutional network is improved to construct the multi-step time series forecasting model MITCN. By combining the proposed model and the powerful probabilistic forecasting method quadratic spline quantile function (QSQF), high-quality probabilistic forecasting of wind power is achieved. Through comprehensive simulations on an open-source dataset, the superiority and efficiency of the proposed method are verified. Compared with some advanced benchmarks, the proposed model can obtain more accurate deterministic and probabilistic forecasting results.

Ultra-short-term wind power probabilistic forecasting based on an evolutionary non-crossing multi-output quantile regression deep neural network

Ultra-short-term wind power probabilistic forecasting is of significance for stable power grid operation; however, it is still challenging due to the inherent nonlinearity and uncertainty. Most state-of-the-art methods have focused on achieving quantile prediction using a combination of linear quantile regression and nonlinear complex deep neural networks. Yet, these methods struggle with several dilemmas. Quantile regression deep neural networks require a complete training once for each quantile. The multi-training mode and complex structure of quantile regression deep neural network can lead to extremely high computational complexity. Most of the training of quantile regression deep neural networks are guided by the loss of each quantile, and the weights are adjusted by gradient descent in which the gradient explosion and quantile crossover may be encountered. Therefore, this paper proposes a non-crossing multi-output quantile regression deep neural network optimized by chaotic particle swarm optimization. It designs a multi-output deep neural network to output all quantile estimations simultaneously through one training, effectively solving the structural complexity problem of traditional quantile regression deep neural networks. Since quantile regression produces a non-differentiable loss function which significantly hinders model training, the proposed neural network is trained by chaotic particle swarm optimization. It not only achieves the effect of optimizing all quantile losses simultaneously, but also can significantly alleviate the dilemma of training in traditional neural network weight optimization. In addition, several non-crossing constraints are designed for avoiding quantile crossover. The proposed model is trained and tested on two real-world wind power case studies. The experiment results show that the proposed model shows superiority in performance criteria, training speed, and avoiding quantile crossover.

Bayesian averaging-enabled transfer learning method for probabilistic wind power forecasting of newly built wind farms

This paper proposes a technique for the probabilistic wind power forecasting (WPF) of a newly built wind farm (NWF) using a limited amount of historical data. First, the state-of-the-art Transformer network is employed to capture the power generation pattern of different wind farms (WFs) based on abundant historical training samples. Then, the Bayesian averaging regression method is applied to transfer the learned power generation pattern to the NWF by assigning proper weights to the WPF results of different WFs. This enables the proposed method to yield accurate NWF power predictions utilizing a limited amount of historical data. The Bayesian characteristics further enable the quantification of multiple uncertainties in forecasting results that may be essential for the NWF operator when the input is uncertain. Comprehensive tests were also performed by employing other deterministic and probabilistic WPF methods using field data. By comparing the results, the proposed method is demonstrated to produce accurate forecasting results with sparse historical data. Moreover, the uncertainties of outcomes are quantified, and acceptable performance is achieved.

Data-Driven Nonparametric Probabilistic Optimal Power Flow: An Integrated Probabilistic Forecasting and Analysis Methodology

With large-scale integration of renewable energy such as wind power, probabilistic analysis of optimal power flow becomes crucial for the decision-making of power systems. This paper proposes a novel data-driven integrated probabilistic forecasting and analysis (IPFA) methodology for the nonparametric probabilistic optimal power flow (N-POPF), which internalizes the probabilistic forecasting and nonparametric distributional description forms into uncertainty analysis. The proposed IPFA methodology fully utilizes the uncertainty analysis method to guide the model-free nonparametric probabilistic forecasting of wind power, and then conducts the N-POPF analysis effectively based on the uncertainty information contained in historical data. A comprehensive uncertainty evaluation criterion based on point estimate method and differential entropy is proposed to assess both the inherent uncertainty and uncertainty influence of input random variables. Then a model-free multivariate probabilistic forecasting method is established to directly support the solving of N-POPF problems with similar historical measurements. Finally, with deterministic optimal power flow problems corresponding to the selected historical samples, a weighted combination approach for the power flow results is developed to derive the quantiles of the output random variables. Comprehensive experiments on IEEE 24-bus and 118-bus test systems validate the superiority of the proposed IPFA methodology in estimation accuracy and computational efficiency.

Transferable wind power probabilistic forecasting based on multi-domain adversarial networks

Due to the limited availability of historical data, forecasting the wind power of newly-built wind farms poses a significant challenge. Transfer learning methods offer a potential solution by transferring knowledge from the source domain to the target domain, thereby reducing the data requirements for wind power forecasting. However, the difference in dataset distribution between the source and target domains causes domain shift. To address this issue, we propose a multi-domain adversarial network (MDAN). MDAN uses multi-domain datasets for adversarial learning, which maps numerical weather prediction (NWP) data to an adaptive latent space, thereby reducing domain shift. Additionally, we propose a data fusion-based incremental learning method to mitigate catastrophic forgetting. Through comprehensive case studies, MDAN provides accurate short-term wind power probabilistic forecasts in zero-shot learning. The incremental learning method enhances forecast accuracy in few-shot learning. Moreover, visualization analysis using t-stochastic neighbor embedding (t-SNE) shows that MDAN successfully reduces the domain shift between the source and target domains.

Deterministic and Probabilistic Wind Power Forecasts by Considering Various Atmospheric Models and Feature Engineering Approaches

This study proposed a model for deterministic and probabilistic wind power generation forecasting and its corresponding procedures. The main contents include numerical weather prediction (NWP) systems, data preprocessing techniques, and forecasting models that use artificial intelligence methods. NWP wind speeds generated by the Central Weather Bureau (CWB) of Taiwan based on three atmospheric models, namely deterministic weather research and forecasting (WRFD), radar weather research and forecasting (RWRF), and WRF-based ensemble prediction system (WEPS), were used as model inputs. In terms of data preprocessing, the NWP wind speeds were corrected based on the height of the wind turbines, and principal components analysis (PCA) and empirical mode decomposition (EMD) were also evaluated for their feature extraction performance. Artificial neural network (ANN), long short-term memory (LSTM), gated recurrent unit (GRU), and eXtreme gradient boosting (XGBoost) were the forecast models used to predict wind power generation. The forecast results demonstrated that the use of the XGBoost model in conjunction with both PCA and EMD data preprocessing achieved the most accurate forecasting. The average forecasting errors (i.e., normalized root mean square error (NRMSE) and mean absolute percentage error (MAPE)) were 5.43% and 3.30% for one-hour-ahead and 9.78% and 6.83% for one-day-ahead, respectively. The empirical data collected at a wind farm in Taiwan verified the accuracy of the proposed method. Thus, the importance of model selection, NWP, and data preprocessing is ultimately self-evident.

A New Co-Optimized Hybrid Model Based on Multi-Objective Optimization for Probabilistic Wind Power Forecasting in a Spatio–Temporal Framework

A New Co-Optimized Hybrid Model Based on Multi-Objective Optimization for Probabilistic Wind Power Forecasting in a Spatio–Temporal Framework

Fluctuation pattern recognition based ultra-short-term wind power probabilistic forecasting method

-Probabilistic wind power forecasting includes more detailed information than deterministic forecasting, which can provide reliable guidance for the optimal decisions of power system scheduling operation. However, there are certain laws in the magnitude and direction of the forecasting errors corresponding to different power series fluctuations, which leads to different predictability and forecasting accuracy of different power fluctuation patterns. As most studies still focused on the model algorithm improvement and pay less attention to the law of power data itself, this paper proposes a novel probabilistic forecasting method based on the swinging door algorithm (SDA), fuzzy c means (FCM) clustering method, long short-term memory (LSTM) neural network, and nonparametric kernel density estimation (KDE), considering the correlation between wind power fluctuation patterns and forecasting errors. SDA and FCM are used to assign appropriate pattern labels to the power fluctuations, and then LSTM and KDE are used to introduce pattern recognition results in probabilistic forecasting models, excavating the inherent law of the data for classification modeling. Simulation shows that the proposed model can adapt to different error distribution patterns, and the models introduced fluctuation pattern recognition can improve the skill score of probabilistic forecasting by 36.50% on average than those without pattern recognition.

Mixture Density Network Based on Truncated Distribution and Genetic Algorithm For Wind Power Forecasting

Due to the excellent wind power probabilistic prediction performance, Mixture Density Network (MDN) is used in short-term wind power forecasting, but the density leakage problem the Not a Number (NaN) loss problem and the choice of hyperparameters in the MDN seriously affect the model performance. GA-TDMDN is proposed in this paper for wind power probabilistic forecasting. GA-TDMDN uses truncated distribution as kernel function to solve density leakage. For the NaN loss problem that occurs during model training, different output layer activation methods and improved loss function are used for different mixture component parameters, so that the shape of the truncated normal distribution can be better controlled. Genetic Algorithms (GA) is used to optimize key hyperparameters in the MDN structure. The experimental results show that it is feasible to use truncated distribution to solve the density leakage problem, and using the GA algorithm to optimize the model structure can improve the model performance

Ensemble probabilistic wind power forecasting with multi-scale features

The uncertainty of wind power forecasting has a significant impact on the decision-making process of power system operators. Herein, to comprehensively characterize this uncertainty, a novel ensemble probabilistic forecasting model is developed in this study. First, the best model inputs were selected to forecast future wind power based on the value of maximum information coefficient, which measures both linear and nonlinear relationships between two random variables. Second, to extract sufficient and useful features from historical wind power data, a multi-scale feature extraction module based on average pooling, convolutional neural network, bidirectional long short-term memory, and attention mechanism was proposed. Third, five multi-scale deep density neural networks with different distribution-based loss functions and the proposed multi-scale feature extraction module were designed as base probabilistic forecasters to characterize the uncertainty from various aspects. Finally, an ensemble framework that combines five multi-scale deep density neural networks was built to determine the optimal ensemble weights for all base forecasters by simultaneously minimizing the pinball loss and continuous ranked probability score. The proposed ensemble model was implemented on four real-world wind power datasets. The results demonstrated the effectiveness of the proposed ensemble strategy and the designed multi-scale feature extraction module for probabilistic wind power forecasting.

Nonparametric Probabilistic Forecasting for Wind Power Generation Using Quadratic Spline Quantile Function and Autoregressive Recurrent Neural Network

Compared with commonly-used point forecasting, probabilistic forecasting provides quantitative information on the uncertainty associated with wind power output. However, most studies focus on modelling only a fixed set of quantiles or intervals, which cannot provide the entire information of wind power distribution. In this paper, we propose a non-parametric and flexible method for probabilistic wind power forecasting. First, the distribution of wind power output is specified by spline quantile function, which avoids assuming a parametric form and also provides flexible shape for wind power density. Then, autoregressive recurrent neural network is used to build the non-linear mapping from input features to the parameters of quadratic spline quantile function. A novel loss function based on continuous ranked probability score (CRPS) is designed to train the forecasting model. We also derive the closed-form solution of the integral required in computing the CRPS-based loss function in order to improve the computational efficiency in training. The effectiveness of our proposed method has been validated with public real-world data from Global Energy Forecasting Competition 2014. Compared with some advanced benchmarks, our proposed approach outperforms them at least six percent in terms of CRPS, indicating that it can provide probabilistic wind power forecasting with high quality.

Continuous and Distribution-Free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach

We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities, hence avoiding quantile crossing. It relies on a base distribution and a set of bijective mappings. Both the shape parameters of the base distribution and the bijective mappings are approximated with neural networks. Spline-based conditional normalizing flow is considered owing to its non-affine characteristics. Over the training phase, the model sequentially maps input examples onto samples of base distribution, given the conditional contexts, where parameters are estimated through maximum likelihood. To issue probabilistic forecasts, one eventually maps samples of the base distribution into samples of a desired distribution. Case studies based on open datasets validate the effectiveness of the proposed model, and allows us to discuss its advantages and caveats with respect to the state of the art.

Wind power probabilistic forecasting based on combined decomposition and deep learning quantile regression

With the expansion of scale of the grid-connected wind power, wind power forecasting plays an increasing important role in ensuring the security and steady operation and instructing the dispatch of power systems. In consideration of the randomness and intermittency of wind power, the probabilistic forecasting is required in quantifying the uncertainty of wind power. This study proposes a probabilistic wind power prediction method that combines variational modal decomposition (VMD), singular spectrum analysis (SSA), quantile regression (QR), convolutional neural network (CNN) and bidirectional gated neural network (BGRU). Firstly, a combination decomposition method VMDS combining VMD and SSA is proposed to decompose wind power sequence to reduce the complexity of the sequence. Next, a feature extractor based on CNN and BGRU (CBG) is used to extract complex dynamic features of NWP data and high-frequency components. Then, the QR is performed by the BGRU based on the high-order features to obtain the predicted values for different quantiles. Finally, the kernel density estimation (KDE) is employed to estimate the probability density curve of wind power. The proposed model can achieve reliable probabilistic prediction while achieving accurate deterministic prediction. According to comparisons with related prediction models, the effectiveness of the proposed method is verified with the example test using datasets from the wind farm in China.

Short-term wind power probabilistic forecasting using a new neural computing approach: GMC-DeepNN-PF

With the increasing penetration of renewable energy in power generation, the increasing uncertainty of renewable energy has significant influence on the stability of energy system. In order to handle the system uncertainty as well as satisfying the energy demand and supply, a short-term wind power probabilistic forecasting under uncertainty using the Gaussian mixed clustering-Deep neural network probabilistic forecasting (GMC-DeepNN-PF) is proposed. To illustrate the applicability of the proposed method, a case study of a wind power data set from Kaggle is presented and comparisons among four different data situations and four different forecasting models are shown in this paper. The raw wind power data is firstly pre-processed based on Gaussian Mixture Model reducing data defects. After that, the cleaned data is extended for more information which can improve the output accuracy and time as a property is added to forecasting model. According to DeepNN-PF, deep conventional neural network concatenated with T distribution is then utilized for forecasting using extended data. The simulations and comparisons demonstrate the advancement of the proposed method.

Evaluating ensemble post‐processing for wind power forecasts

AbstractCapturing the uncertainty in probabilistic wind power forecasts is challenging, especially when uncertain input variables, such as the weather, play a role. Since ensemble weather predictions aim to capture the uncertainty in the weather system, they can be used to propagate this uncertainty through to subsequent wind power forecasting models. However, as weather ensemble systems are known to be biassed and underdispersed, meteorologists post‐process the ensembles. This post‐processing can successfully correct the biasses in the weather variables but has not been evaluated thoroughly in the context of subsequent forecasts, such as wind power generation forecasts. The present paper evaluates multiple strategies for applying ensemble post‐processing to probabilistic wind power forecasts. We use Ensemble Model Output Statistics (EMOS) as the post‐processing method and evaluate four possible strategies: only using the raw ensembles without post‐processing, a one‐step strategy where only the weather ensembles are post‐processed, a one‐step strategy where we only post‐process the power ensembles and a two‐step strategy where we post‐process both the weather and power ensembles. Results show that post‐processing the final wind power ensemble improves forecast performance regarding both calibration and sharpness whilst only post‐processing the weather ensembles does not necessarily lead to increased forecast performance.

A multi-quantile regression time series model with interquantile lipschitz regularization for wind power probabilistic forecasting

Modern decision-making processes require uncertainty-aware models, especially those relying on non-symmetric costs and risk-averse profiles. The objective of this work is to propose a dynamic model for the conditional non-parametric distribution function (CDF) to generate probabilistic forecasts for a renewable generation time series. To do that, we propose an adaptive non-parametric time-series model driven by a regularized multiple-quantile-regression (MQR) framework. In our approach, all regression models are jointly estimated through a single linear optimization problem that finds the global-optimal parameters in polynomial time. An innovative feature of our work is the consideration of a Lipschitz regularization of the first derivative of coefficients in the quantile space, which imposes coefficient smoothness. The proposed regularization induces a coupling effect among quantiles creating a single non-parametric CDF model with improved out-of-sample performance. A case study with realistic wind-power generation data from the Brazilian system shows: 1) the regularization model is capable to improve the performance of MQR probabilistic forecasts, and 2) our MQR model outperforms five relevant benchmarks: two based on the MQR framework, and three based on parametric models, namely, SARIMA, and GAS with Beta and Weibull CDF.

Online Ensemble Approach for Probabilistic Wind Power Forecasting

Probabilistic wind power forecasting is an important input in the decision-making process in future electric power grids with large penetrations of renewable generation. Traditional probabilistic wind power forecasting models are trained offline and are then used to make predictions online. However, this strategy cannot make full use of the most recent information during the prediction process. In addition, ensemble learning is recognized as an effective approach for further improving forecasting performance by combining multiple forecasting models. This paper studies an online ensemble approach for probabilistic wind power forecasting by taking full advantage of the most recent information and leveraging the strengths of multiple forecasting models. The online ensemble approach is first formulated as an online convex optimization problem. On this basis, a quantile passive-aggressive regression model is proposed to solve the online convex optimization problem. Case studies and comparisons with other online learning methods are conducted on an open wind power data set from Belgium. Results show that the proposed method outperforms competing methods in terms of pinball loss and Winkler score with high reliability.

Sparse Variational Gaussian Process Based Day-Ahead Probabilistic Wind Power Forecasting

In this paper, we present a probabilistic wind power forecasting (PWPF) model via quantification of epistemic uncertainty and aleatory uncertainty. Concretely, the epistemic uncertainty is described by the statistical characteristics of function space constituted by all wind power forecasting (WPF) mappings through Gaussian process (GP) frameworks. In particular, we adopt the sparse variational Gaussian process to address inference complexity and hyperparameters determination issues, which impede the performance of existing GP-based PWPF models. It introduces inducing variables and variational inference to minimize the difference between the approximated sparse GP model and the original GP, whereby a variational distribution is introduced to explicitly represent the inducing variables. All parameters are optimized via gradient descent optimization based on likelihood maximization. Experiments based on an open dataset demonstrate that the proposed model is comparable to state-of-the-art in terms of continuous ranked probability score, and robust to overfitting.

Incorporating Spatial and Temporal Correlations to Improve Aggregation of Decentralized Day-Ahead Wind Power Forecasts

In some electricity markets, individual wind farms are obliged to provide point forecasts to the power purchaser or system operator. These decentralized forecasts are usually based on on-site meteorological forecasts and measurements, and thus optimized for local conditions. Simply adding decentralized forecasts may not capture some of the spatial and temporal correlations of wind power, thereby lowering the potential accuracy of the aggregated forecast. This paper proposes the explanatory variables that are used to train the kernel density estimator and conditional kernel density estimator models to derive day-ahead aggregated point and probabilistic wind power forecasts from decentralized point forecasts of geographically distributed wind farms. The proposed explanatory variables include (a) decentralized point forecasts clustered using the clustering large applications algorithm to reduce the high-dimensional matrices, (b) hour of day and month of year to account for diurnal and seasonal cycles, respectively, and (c) atmospheric states derived from self-organizing maps to represent large-scale synoptic circulation climatology for a study area. The proposed methodology is tested using the day-ahead point forecast data obtained from 29 wind farms in South Africa. The results from the proposed methodology show a significant improvement as compared to simply adding the decentralized point forecasts. The derived predictive densities are shown to be non-Gaussian and time-varying, as expected given the time-varying nature of wind uncertainty. The proposed methodology provides system operators with a method of not only producing more accurate aggregated forecasts from decentralized forecasts, but also improving operational decisions such as dynamic operating reserve allocation and stochastic unit commitment.

Ensemble Deep Learning-Based Non-Crossing Quantile Regression for Nonparametric Probabilistic Forecasting of Wind Power Generation

Probabilistic forecasting that quantifies the prediction uncertainties is crucial for decision-making in power systems. As a prevalent nonparametric probabilistic forecasting approach, traditional machine learning-based quantile regression encounters the quantile crossing problem. This paper proposes a novel ensemble deep learning based non-crossing quantile regression (EDNQR) model for probabilistic wind power forecasting, which does not need any distribution assumption and demonstrates high generalization ability. A unique non-crossing quantile regression strategy is proposed to generate monotonous quantiles with deep learning models. The exponential stacking mapping method is proposed to guarantee the monotonicity of quantiles, and Huber norm pinball loss is introduced for deep learning quantile regression model training. To improve the generalization capability, a two-stage ensemble framework is proposed to integrate homogeneous and heterogeneous deep learning models. The newly-trained base model considers the training performance of the last base model, which benefits the performance boosting of the ensemble model. To overcome the complexity of conventional weight optimization-based model integration, an overall quantile loss index is proposed to serve as an indicator to directly integrate both the homogeneous and heterogeneous deep learning base models. Comprehensive numerical studies based on actual wind farm data validate the superior performance of the proposed EDNQR model in terms of reliability, overall skill and generalization ability.