Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Short-Term Wind Power Forecasting Using Gaussian Processes Niya Chen, Zheng Qian, Xiaofeng Meng Ian T. Nabney Beihang University Aston University China United Kingdom {pekiny, qianzheng, mengxf}@aspe.buaa.edu.cn [email protected] Abstract data to build statistical models, such as autoregressive inte- grated moving average (ARIMA) [Liu et al., 2011], Kalman Since wind has an intrinsically complex and filters [Louka et al., 2008], artificial neural networks [Li stochastic nature, accurate wind power forecasts and Shi, 2010; Hong et al., 2010] and support vector ma- are necessary for the safety and economics of wind chines [Salcedo-Sanz et al., 2011]. Since wind varies rapidly energy utilization. In this paper, we investigate a with time, the statistical models are effective only for very combination of numeric and probabilistic models: short-term forecasts (about 1–4 hours ahead). On the other one-day-ahead wind power forecasts were made hand, physical models have advantages over longer horizons with Gaussian Processes (GPs) applied to the out- (from several hours to dozens of hours), because they include puts of a Numerical Weather Prediction (NWP) (3D) spatial and temporal factors in a full fluid-dynamics model. Firstly the wind speed data from NWP model. However, this type of model has limitations, such was corrected by a GP. Then, as there is always as the limited observation set for calibration, the relatively a defined limit on power generated in a wind tur- limited spatial resolution possible over such a wide area, and bine due the turbine controlling strategy, a Cen- the difficulty of accounting for local topography [Soman et sored GP was used to model the relationship be- al., 2010]. To overcome these limitations, some authors have tween the corrected wind speed and power output. combined statistical and physical models, by using NWP To validate the proposed approach, two real world (Numerical Weather Prediction) data from a physical model datasets were used for model construction and test- as inputs to a statistical model [Salcedo-Sanz et al., 2009; ing. The simulation results were compared with the Al-Yahyai et al., 2010]. persistence method and Artificial Neural Networks (ANNs); the proposed model achieves about 11% A forecast model combined with NWP data was proposed [ ] improvement in forecasting accuracy (Mean Ab- by Vaccaro Vaccaro et al., 2011 , in which one-day-ahead solute Error) compared to the ANN model on one wind power forecasting is realized based on information dataset, and nearly 5% improvement on another. amalgamated from a local atmospheric model and measured data. Giorgi [Giorgi et al., 2011] developed a series of fore- cast systems by combining an Elman network and an MLP 1 Introduction network, and predicted power production of a wind farm with As wind is an effective renewable energy resource, the uti- three wind turbines at 5 time horizons: 1, 3, 6, 12 and 24 lization of wind energy has been growing rapidly around hours. The normalized absolute average error of the systems the world. With approximately 68 GW capacity of wind varied from 5.67% to 15.50% depending on forecast time and farms, China has the largest wind energy generation in the different combining ways of networks. world, and has continued with a high growth rate of 9% Recently, Gaussian Processes (GP) have been applied in the first half of 2012 [GWEC, 2012]. However, the in- broadly in many domains, including wind energy prediction. trinsically variable and uncontrollable characteristics of wind Jiang and Dong focused on very short term (< 30min) wind- pose several operational challenges. Thus wind power pre- speed prediction using GPs [Jiang et al., 2010]. They evalu- diction is an essential process for the maintenance of wind ated their model on real-world datasets, and found that the GP power units and energy reserve scheduling [Costa et al., 2008; performs better than ARMA (a simpler variant of ARIMA) Lei et al., 2009]. and Mycielski algorithms [Hocaoglu et al., 2009]. Short-term wind power forecasts with a prediction horizon In this paper, wind-farm datasets including Numerical from one hour to several days are critical to optimize wind Weather Prediction (NWP) results and measured data from farm maintenance and plan electricity reserves which im- a SCADA (Supervisory Control And Data Acquisition) sys- pact grid reliability and market-based ancillary service costs. tem are analyzed and used to develop wind power forecasting Broadly speaking, there are two approaches to short-term models over a horizon of up to one day, with a Gaussian Pro- wind power forecasting: statistical models and physical mod- cess (GP) method. The main innovations in this paper are els. The former uses only historical wind speed and power listed below: 2790 1. The predicted wind speed from an NWP model is cor- casting with the horizon from 1 to 24 hours for wind power, rected using a GP. This process helps to improve per- based on hourly sampled NWP data. formance compared with earlier methods for combining statistical and physical models. 3 Gaussian Process Methods 2. Automatic Relevance Determination was used for fea- ture selection in order to improve generalization perfor- Gaussian processes have been successfully applied to many mance. machine learning tasks. A systematic and detailed expla- nation of Gaussian process regression and Automatic Rev- 3. A censored Gaussian Process (CGP) method is applied elance Determination (ARD) can be found in Rasmussen’s to build the relationship between corrected wind speed book [C. Rasmussen, 2006]. The extension to censored data and wind power. The method accounts for the proba- was developed in [Groot, 2012]: here we will only provide a bilistic character of the values that are not known pre- brief description. cisely because of censoring. 4. A subset of high-wind speed data is treated separately, 3.1 Gaussian Processes because of its different characteristics based on analysis Consider a Gaussian process f(x) for a classic regression of the initial models. problem. Assuming we have a training set D of n obser- 5. Historical wind speed data from the SCADA system is vations, D = {(xi,yi)|i =1,...,n}, where x denotes an used as an additional input to the forecasting model for input vector and y denotes a scalar output, the task is to build 1–4 hours-ahead prediction, since we have proved this a function that satisfies to be effective in this range of time horizons. yi = f(xi)+i. (1) Section 2 describes the NWP data used to provide daily forecasts of meteorological variables. Section 3 defines the The additive noise is assumed to have a Gaussian distri- 2 standard and censored Gaussian Process and Automatic Rel- bution: ∼N(0,σn). Note that y is a linear combi- evance Determination (ARD) methods applied to build all the nation of Gaussian variables and hence is itself Gaussian. 2 regression models. Section 4 describes the whole detailed Therefore, we have p(y|X, k)=N (0,K + σnI), where modeling process from NWP data to forecast wind power re- Kij = k(xi,xj), and the joint distribution for a new input sults. Simulation results are presented and analyzed in Sec- x∗ can be written as tion 5. Finally, Section 6 includes the final conclusions. y K(X, X)+σ2 Ik(X, x ) ∼ 0, n ∗ , (2) f∗ k(x ,X) k(x ,x ) 2 NWP model and power forecasting ∗ ∗ ∗ T Numerical weather prediction uses hydrodynamic and ther- where k(X, x∗)=k(x∗,X) =[k(x1,x∗),...,k(xn,x∗)], modynamic models of the atmosphere to predict weather which we will write more briefly as k∗. Then according to based on certain initial-value and boundary conditions. In our the properties of joint Gaussian distributions, the prediction research, we use the WRF (Weather Research and Forecast- distribution of the target is given by a Gaussian distribution ing) NWP model. WRF was created through a partnership f¯ = kT (K + σ2 I)−1y that includes NCAR (National Center for Atmospheric Re- ∗ ∗ n T 2 −1 (3) search), NOAA (National Oceanic and Atmospheric Admin- V [f∗]=k(x∗,x∗) − k∗ (K + σnI) k∗. istration), and more than 150 other organizations and univer- sities in the United States and internationally, and is released As a result of the wind turbine control strategy, there is as a free model for public use [Hosansky, 2006]. always a defined upper limit C and lower limit of 0 for In general, short-term wind power forecasting needs pre- the power generation of each turbine. Therefore, in statis- dictions from a NWP model with high spatial resolution. The tical terminology, the true values (unrestricted power out- data from WRF isn’t suitable directly for this application, and put) are ‘censored’ in that they are not observed but are re- hence need to be interpolated both horizontally and vertically. placed by the threshold value. Assuming that the latent val- The NWP data used in this paper is produced and interpolated ues y∗ = f(x) can be realized by a Gaussian process, then to from the location in the WRF model, in our case from 5km- predict the actual output y, the influence of censoring should resolution, to the accurate geographical point and hub height be considered inside the model. To implement this considera- of each wind turbine. This prediction data is produced once tion, a censored GP model was developed in [Groot, 2012],in each day, and is usually available at 00:00 GMT. The data in- which the posterior distribution of y was formed by integrat- cluding wind speed and direction, temperature, humidity and ing out the censored distribution of latent variables and ap- pressure, is provided at an interval of 10 minutes for the fol- proximated using Expectation Propagation (EP).