Wind Power Probability Density Prediction Based on Quantile Regression Model of Dilated Causal Convolutional Neural Network

With the increasing penetration of wind power, the uncertainty associated with it brings more challenges to the operation of the integrated energy system (IES), especially the power subsystem. However, the typical strategies to deal with wind power uncertainty have poor performance in balancing economy and robustness. Therefore, this paper proposes a distributionally robust joint chance-constrained dispatch (DR-JCCD) model to coordinate the economy and robustness of the IES with uncertain wind power. The optimization dispatch model is formulated as a two-stage problem to minimize both the day-ahead and the real-time operation costs. Moreover, the ambiguity set is generated using Wasserstein distance, and the joint chance constraints are used to ensure that the safety constraints (e.g., ramping limit and transmission limit) can be satisfied jointly under the worst-case probability distribution of wind power. The model is remodeled as a mixed-integer tractable programming issue, which can be solved efficiently by ready-made solvers using linear decision rules and linearization methods. Case studies on an electricity–gas–heat regional integrated system, which includes a modified IEEE 24-bus system, 20 natural gas-nodes, and 6 heat-node system, are investigated for verification. Numerical simulation results demonstrate that the proposed DR-JCCD approach effectively coordinates the economy and robustness of IES and can offer operators a reasonable energy management scheme with an acceptable risk level.

With the increasing penetration of renewable generation such as wind power in modern power systems, there are many new challenges arising in power system operation with respect to reliability and economy. In this work, we study a two-stage data-driven distributionally robust (DR) energy and reserve dispatch problem with uncertain wind power. Different from the general moment-based ambiguity set, we design a new distance-based ambiguity set to describe the uncertain probability distribution of wind power, which can be constructed in a data-driven manner from historical data. Base on this new ambiguity set, the second-stage worst-case expectation of the problem is reformulated to a combination of conditional value-at-risk (CVaR) and an expected cost with respect to a reference distribution. Thus, the proposed two-stage DR model becomes a two-stage stochastic optimization problem which can be readily solved. Case studies are carried out to verify the effectiveness of the proposed method based on the IEEE 6-bus test system and modified IEEE 118-bus test system. Simulation results show the value of data in controlling the conservatism of the problem, and the DR problem converges to the stochastic problem with fixed distribution as the data size goes to infinity.

Probability density forecasting of wind power based on multi-core parallel quantile regression neural network

This paper focuses on economic dispatch (ED) in power systems with intermittent wind power, which is a very critical issue in future power systems. A stochastic ED problem is formed based on the recently proposed versatile probability distribution of wind power. The problem is then analyzed and proved to be strictly convex. Although such convex optimization is tractable in many cases, it may take a long time to solve due to its large scale. This paper proposes a dual decomposition method to decompose the large problem. Then, two methods are employed to solve the decomposed problem, namely, the subgradient method and a faster method, limited-memory BFGS with box constraints (L-BFGS-B, a quasi-Newton method). Case studies were conducted to verify the efficiency of the dual decomposition and L-BFGS-B method for solving the stochastic ED problem.

Wind power forecasting methods generally provide estimates of future wind power as point forecasts, but most of the decision making processes in electrical power systems management require more information than a single value. For this purpose, additional methods - complex or based on strong assumptions - have been developed for estimating so-called interval forecasts associated to point forecasts. The method proposed by the authors is based on the use of discrete time Markov chain models of a proper order, developed starting from wind power time series analysis. It allows to directly obtain in an easy way an estimate of the wind power distributions on a very short-term horizon, without requiring restrictive assumptions on wind power probability distribution. With reference to an application, results obtained via a First and Second Order Markov Chain Model, respectively, are compared to those of Persistent Model evaluating the related prediction errors.

This paper investigates the influence of geographical allocation of wind power generation in Northern Europe, assuming large scale integration of wind power. The work applies a linear cost optimization model of the heat and power sector with a 1-hour time resolution. The model minimizes the sum of running costs to meet the heat and power demand and the wind power and transmission investment costs. Wind data are taken from modelled wind speed data from the Swedish Meteorological and Hydrological Institute. The Nordic countries and Germany were divided into regions and the 200 sites with the highest yearly output were chosen to represent the region. The model gives the most favourable distribution of wind power between the regions. In addition, the paper provides an assessment of the effect of geographical distribution of wind power with respect to influence on the aggregated wind power production (only considering the wind power generation itself). The modelling results show that the largest investments in wind power are made in the windy region of Southern Norway. However, depending on the cost of transmission allocating wind power near large load centers in Germany may also be favourable. As for the assessment of distribution of wind power, the wind data gives that if the 400 best sites in Europe were used, this would result in a capacity factor of 38.5% and a lowest output of 2.5 % of rated power (applying 2009 wind data).

An improved versatile distribution for wind power is proposed, with higher representation accuracy and more suitable applications in economic dispatch (ED) compared with Versatile distribution. Further, versatile mixture distribution (VMD) is proposed to represent all possible wind power distribution with customized arbitrary errors. Compared with Gaussian Mixture distribution (GMD), it has more flexible forms and can represent wind power more accurately. Its cumulative distribution function has analytical forms with higher computational efficiency. Then, real-time dynamic ED model and algorithm based on VMD with multiple wind farms (WFs) is proposed. Based on the VMD model, the probability distributions of wind power of each WF and the summation of all WFs are modeled. The ED model and algorithm solve the problem of the correlation of multiple renewable energy random variables with high computation efficiency for real-time ED. The results show that compared with GMD or unimodal distributions, VMD can represent wind power more accurately and can greatly simplify and speed up the ED model and algorithm. Compared with other methods for multiple renewable energy random variables, the proposed model and algorithm can improve economy significantly.

The wind model based on Markov process was proposed to determine the best installed capacity of wind farm. Firstly, piecewise probability distribution model based on Markov process was proposed to establish the scheduling multiple state probability distribution of wind power. Secondly, the probability production simulation method using the sequential convolution and non-sequential convolution was proposed to calculate the evaluation index which includes annual utilization hours of wind farm, wind curtailment, cost of traditional units and benefit of wind farm. Then the best installed capacity of wind farm could be calculated according to the above evaluation index with the aim to minimize the cost of the system. A case study was employed to illustrate the effectiveness of the proposed approach.

This paper presents two probabilistic approaches based on bootstrap method and quantile regression (QR) method to estimate the uncertainty associated with solar photovoltaic (PV) power point forecasts. Solar PV output power forecasts are obtained using a hybrid intelligent model, which is composed of a data filtering technique based on wavelet transform (WT) and a soft computing model (SCM) based on radial basis function neural network (RBFNN) that is optimized by particle swarm optimization (PSO) algorithm. The point forecast capability of the proposed hybrid WT + RBFNN + PSO intelligent model is examined and compared with other hybrid models as well as individual SCM. The performance of the proposed bootstrap method in the form of probabilistic forecasts is compared with the QR method by generating different prediction intervals (PIs). Numerical tests using real data demonstrate that the point forecasts obtained from the proposed hybrid intelligent model can be effectively used to quantify PV power uncertainty. The performance of these two uncertainty quantification methods is assessed through reliability.

The MENA-CORDEX (the Middle East and North Africa-COordinated Regional Downscaling Experiment) wind speed data at the height of 10 m is converted to the turbine hub-height for estimating the mean wind power in the Gulf of Oman. The results show high spatial variability of the historical and future mean wind power projection. Furthermore, the impact of climate change on the mean wind power (under the representative concentration pathway 8.5, RCP8.5, scenario) is found to be less than 5%, which indicates the sustainability of wind renewable energy. Based on the wind power distribution, bathymetry, and distance from the coast, five sites are selected in the Gulf of Oman as tentative energy hotspots to provide a detailed assessment of the directional variability of wind power for the historical and future periods. Significant variability of the directional distribution of wind power is found in the five study sites, which make it imperative to optimally design wind turbines and farms to achieve the best efficiency. The findings also indicate that the main direction and magnitude of wind power in the five sites under the RCP8.5 climate change scenario will remain almost the same as those of the historical period. Overall, the sustainability of power production under climate change impacts is promising to plan for wind energy extraction in the Gulf of Oman.

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.

Varying coefficient model (VCM) is extensively used in various scientific fields due to its capability of capturing the changing structure of predictors. Classical mean regression analysis is often complicated in the existence of skewed, heterogeneous and heavy-tailed data. For this purpose, this work employs the idea of model averaging and introduces a novel comprehensive approach by incorporating quantile-adaptive weights across different quantile levels to further improve both least square (LS) and quantile regression (QR) methods. The proposed procedure that adaptively takes advantage of the heterogeneous and sparse nature of input data can gain more efficiency and be well adapted to extreme event case and high-dimensional setting. Motivated by its nice properties, we develop several robust methods to reveal the dynamic close-to-truth structure for VCM and consistently uncover the zero and nonzero patterns in high-dimensional scientific discoveries. We provide a new iterative algorithm that is proven to be asymptotic consistent and can attain the optimal nonparametric convergence rate given regular conditions. These introduced procedures are highlighted with extensive simulation examples and several real data analyses to further show their stronger predictive power compared with LS, composite quantile regression (CQR) and QR methods.

Improvement of wind power utilization through flexible operation of data center in wind parks

This paper focuses on the Least Square (LS) regression using the mean and Quantile (M) regression analysis using median which is based on “well-Known” parametric estimation methodologies. Data from Oregon and California highway bridges were used for the comparison of the two methods. Relationships were developed to predict the unit cost of FRP repair work and FRP cost was found to have a high degree of correlation with FRP area for both Oregon and California. It was observed that the Cost Estimating Relationships (CERs) obtained by Quantile (M) regression method had the smaller Mean Absolute Deviation (MAD) values and lower Mean Absolute Percentage Error (MAPE) values than Least Square (LS) regression. The stuudy showed that Quantile Regression is much less sensitive to outliers than Least Squares Regression.

Voltage over-limit risk assessment of wind power and photovoltaic access distribution system based on day-night segmentation and Gaussian mixture model