Comparison of two new ARIMA-ANN and ARIMA-Kalman hybrid methods for wind speed prediction
Highlights
► A new hybrid ARIMA-ANN model is proposed to forecast wind speed. ► A new hybrid ARIMA-Kalman model is proposed to predict wind speed. ► A detailed comparison of multi-step forecasting performance is provided. ► The two new hybrid models can obtain high-precision multi-step results. ► The two presented models are suitable for non-stationary wind speed.
Introduction
Wind energy as an ideal alternative energy source is developing fast in the world [1]. Just in China, the current total capacity of wind farms is 25805.3 MW, with a growth rate of 114% in 2009 [2], [3], [4]. With the increasing applications of wind energy, it is important for power utilities to plan the integration of wind power and other traditional powers. So an accurate wind speed prediction is desired [5], [6], [7].
Due to the chaotic fluctuations of wind speed, to make an accurate prediction is difficult [8]. In recent decades, many studies on wind speed prediction have been reported, which can be divided into four categories [9]: (a) physical models; (b) statistical models; (c) spatial correlation models; and (d) artificial intelligence models. Every category has its advantages and disadvantages. Physical models need more parameters, such as geographic and geomorphic conditions, temperature and pressure, to build multi-variable forecasting models. So it is good at long-term calculation and is applied in weather prediction [10], [11]. Statistical models employ mathematic equations to make wind speed prediction based on a number of historical data [5]. In statistical models, the time series models are popular in practice because their computation is simple [12], [13], [14], [15]. As for spatial correlation methods, they use multi dimensional data from different measurement stations to forecast the future wind speed [16]. Besides intelligent methods have been mushrooming, namely Artificial Neural Networks [8], [17], [18], [19], Fuzzy Logic Methods [20], Support Vector Machine [4], etc. At the same time hybrid methods mixing several algorithms are proposed to obtain better performance [13], [14], [20], [21].
In intelligent models, the Artificial Neural Network (ANN) [17], [18], [19] and the Kalman Filter [22], [23] are popular due to their good nonlinear performance. In this study they are chosen to do multi-step prediction for two sections of non-stationary wind speed series from a wind farm in China. This paper is organized as follows: Section 2 states the hybrid modeling framework; Section 3 displays the measurement of wind speed; Section 4 presents the computational steps of a proposed ARIMA-ANN model; Section 5 demonstrates the calculation steps of a presented ARIMA-Kalman model; Section 6 Comparison of prediction results, 7 Conclusions demonstrates two real cases; and Section 7 concludes the results of this work.
Section snippets
Frameworks of hybrid models
The framework of the proposed hybrid models [ARIMA-ANN and ARIMA-Kalman] is demonstrated in Fig. 1. Its details are given as follows:
- (1)
Build an ANN forecasting model for a section of wind speed sample. During ANN modeling process, a time series ARIMA is used to decide its best structure.
- (2)
Establish a Kalman forecasting model for the same section of wind speed data. To obtain the best initial parameters of the Kalman model, a time series ARIMA is employed.
- (3)
Do a comparison of the ARIMA-ANN model and
Measurement of wind speed
To sample wind speed data, several wireless movable wind stations are installed in the wind farm. Every station is comprised of a programmable logic controller (PLC), two redundant anemometers, three solar power plates, two batteries and a set of braces. The installed positions of these stations are determined by both considering the local wind resource and the requirements from power departments. Fig. 2 shows an hourly actual wind speed series (including 500 samplings) from a station. The
ARIMA part modeling
The Box–Jenkins methodology in time series theory is adopted to establish an ARIMA model in this study. Its calculation steps can be found in Ref. [12]. In the Box–Jenkins methodology, a differencing approach will be used to stable the original data, and an autocorrelation function (ACF) and a partial autocorrelation function (PACF) will be both utilized to decide which (if any) autoregressive or moving average component should be included in the ARIMA model. The ACF and PACF values for the
Kalman part modeling
Kalman Filter is a signal tracking method named after Scientist Rudolf E. Kálmán. Due to its good performance, it has been utilized in many applications [22], [23], [24], [25]. The key of utilizing Kalman Filter method is to initialize the State Equation (SE) and the Measurement Equation (ME) rightly.
- (1)
State Equation:
Comparison of prediction results
Fig. 10, Fig. 11, Fig. 12 show the multi-step ahead prediction results by an ARIMA-ANN model, an ARIMA-Kalman model and a pure ARIMA model, respectively. Their estimated results are given in Table 3.
Fig. 10, Fig. 11, Fig. 12 and Table 3 indicate that:
- (1)
The bigger the number of forecasting steps, the lower the accuracy;
- (2)
The performance of the two hybrid models is better than that of the pure ARIMA model, and the performance of the ARIMA-Kalman model is better than that of the ARIMA-ANN model;
- (3)
When
Conclusions
Two hybrid models including the ARIMA-ANN and the ARIMA-Kalman are proposed for multi-step ahead prediction of two sections of actual wind speed series. The results show that: (1) Both of them have good forecasting accuracy; and (2) they are suitable for the jumping wind samplings, which can be applied to real-time wind power systems.
Acknowledgment
This study is supported by the Fundamental Research Funds for the Central Universities of China (Project No. 2012QNZT029).
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