Prediction of hourly solar radiation with multi-model framework
Introduction
Solar radiation is one of the major energy sources for many engineering applications such as photovoltaic, passive solar design and solar-thermal systems. An accurate prediction of its energy level will largely improve the efficiency of these related applications [1]. Many researchers have tried to predict solar radiation series with meteorology model such as numeric weather prediction (NWP) which is based on solar zenith angle and clear sky index [2], [3], [4], [5]. However, the solar radiation series can also be regarded as a time series produced by a stochastic process. Hence, many time series analysis algorithms can also be used to conduct the prediction [6], [7], [8].
A well-known classical statistical model for time series prediction is autoregressive integrate moving average model which is also known as ARIMA [9]. The popularity of the ARIMA model is due to its ability to extract useful statistical properties and the adoption of the well-known Box–Jenkins methodology [10]. The ARIMA model is quite flexible since it can represent different types of time series with appropriate order. However, this model requires the time series to be stationary. Thus sometimes preprocessing may be necessary to convert the original non-stationary time series into a stationary time series.
Recently, research into using artificial neural network (ANN) in time series analysis is gaining popularity [11]. One type of ANN which is specific for time series prediction is time delay neural network (TDNN). It is used to uncover the non-linear relationship between past and future values of a time series [12], [13], [14], [15]. Support vector machine is another data mining algorithm which is applied in time series prediction. It has been applied to predict monthly average solar radiation but not used in daily solar radiation prediction yet [16].
Other studies show that using hybrid schema, which combines different models together, could present encouraging prediction performance [17]. The hybrid model of ARIMA and ANN is such an example which is capable of predicting various types of time series [18]. Hybrid models based on TDNN and ARMA was also used [19]. It performs better than individual TDNN and ARMA model.
In this paper, a novel framework is presented to conduct short term prediction of solar radiation time series. Solar radiation data is the only input parameter needed. The solar radiation is regarded as a stochastic time series. We assume that there exists several intrinsic patterns embedded in it. The expected value at a certain time of the time series relates not only to that time, but also to the pattern it belongs to. It is first segmented into subsequence. The subsequence is grouped into separate clusters according to the patterns. Training and building prediction models are performed with the data of each cluster. Hence, when predicting the future trend of time series, for cluster that the current time series belongs to is first determined and then the corresponding model is applied for the prediction.
Daily solar radiation data of Singapore was used in the experiment. The data was collected by an observation station located in Nanyang Technological University, Singapore and can be obtained online. To ensure the accuracy and adaptability of the framework, 24-month period data were used in the whole process. The data of 2009 is used to train and tune the framework. Then the trained framework is used to predict solar radiation data of year 2010.
The rest of the paper is organized as follows: Section 2 elaborates the building of the MMF (multi-model framework) and related algorithms. Section 3 discusses and analyzes the results of experiments and Section 4 compares the proposed work with other algorithms. Section 5 concludes with some comment on future works.
Section snippets
The proposed methodology
The proposed multi-model prediction framework contains two different phases: the clustering phase and the prediction phase.
In the clustering phase, the solar radiation series over a period (which is 1 year in this paper) is segmented into subsequence with fixed length. K-means clustering algorithm is used to cluster the subsequences with dynamic time warping (DTW) as the distance measurement. The data set of each group is applied to train TDNN separately to generate a specific TDNN for each
Simulation
To assess the performance of the methodology discussed above, the data of solar radiation obtained in 2009 and 2010 in Singapore is used in the simulation. The data is recorded by the observation station located in Nanyang Technological University (NTU) and can be obtained from the website: http://nwsp.ntu.edu.sg. CMP 3 pyranometer is used to record the solar radiation. Its elevation is 80 m above the sea level and its coordinate is E103°40′45.2712″, N1°20′36.8952″. The original sample rate is
Comparative analysis
As presented in [23], [34], ARMA and TDNN have been proved to be satisfactory in predicting the solar radiation of Singapore. We therefore compare the prediction result of MMF to ARMA and TDNN to assess its performance.
Hybrid model which combines ARMA and TDNN can provide better performance than the individual model [19]. Thus it is also incorporated in the comparison experiment.
The mean of SMAPE of prediction of the different months’ data was presented in Table 4. And the variance was
Conclusion
In this paper, a novel multi-model prediction framework for solar radiation time series is proposed. As described above, the framework starts with the assumption that there are several patterns in the stochastic component of solar radiation series. To extract the pattern embedded in it, the series is segmented into fixed length subsequences. The subsequences are then grouped into different clusters using K-means algorithm. To determine the optimal number of clusters and optimal length of
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