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Online Short-Term Solar Power Forecasting Downloaded from orbit.dtu.dk on: Oct 05, 2021 Online short-term solar power forecasting Bacher, Peder; Madsen, Henrik; Nielsen, Henrik Aalborg Published in: Solar Energy Link to article, DOI: 10.1016/j.solener.2009.05.016 Publication date: 2009 Document Version Peer reviewed version Link back to DTU Orbit Citation (APA): Bacher, P., Madsen, H., & Nielsen, H. A. (2009). Online short-term solar power forecasting. Solar Energy, 83(10), 1772-1783. https://doi.org/10.1016/j.solener.2009.05.016 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Online Short-term Solar Power Forecasting Peder Bacher Henrik Madsen Informatics and Mathematical Modelling, Richard Pedersens Plads, Technical University of Denmark Building 321, DK-2800 Lyngby, Denmark Henrik Aalborg Nielsen ENFOR A/S, Lyngsø All´e3, DK-2970 Hørsholm, Denmark Abstract This paper describes a new approach to online forecasting of power production from PV systems. The method is suited to online forecasting in many applications and in this paper it is used to predict hourly values of solar power for horizons of up to 36 hours. The data used is fifteen-minute observations of solar power from 21 PV systems located on rooftops in a small village in Denmark. The suggested method is a two-stage method where first a statistical normalization of the solar power is obtained using a clear sky model. The clear sky model is found using statistical smoothing techniques. Then forecasts of the normalized solar power are calculated using adaptive linear time series models. Both autoregressive (AR) and AR with exogenous input (ARX) models are evaluated, where the latter takes numerical weather predictions (NWPs) as input. The results indicate that for forecasts up to two hours ahead the most important input is the available observations of solar power, while for longer horizons NWPs are the most important input. A root mean square error improvement of around 35 % is achieved by the ARX model compared to a proposed reference model. Key words: Solar power, prediction, forecasting, time series, photovoltaic, numerical weather predictions, clear sky model, quantile regression, recursive least squares 1. Introduction tems on rooftops. The peak power of the installed PV systems is in the range of 1 to Efforts to increase the capacity of solar 4 kWp, which means that the larger sys- power production in Denmark are concen- tems will approximately cover the electric- trating on installing grid connected PV sys- ity consumption (except heating) of a typi- cal family household in Denmark. The PV Email addresses: [email protected] (Peder Bacher) URL: henrikmadsen.org (Henrik Madsen), systems are connected to the main electric- www.enfor.eu (Henrik Aalborg Nielsen) ity grid and thus the output from other p Solar power W pcs Clear sky solar power W τ Normalized solar power - t Time index - k Forecast horizon index - i; j Miscellaneous indexes - pt Observation of average solar power W p^t+kjt k-step prediction of solar power W cs p^t Estimated clear sky solar power W 2 g^i;k i'th update of NWP of global irradiance W=m 00 2 g^k;t NWP of global irradiance updated at 00:00 W=m 12 2 g^k;t NWP of global irradiance updated at 12:00 W=m 00 00 pk;t Observation of solar power corresponding tog ^k;t W 12 12 pk;t Observation of solar power corresponding tog ^k;t W τt Normalized solar power - τ^t+kjt k-step prediction of normalized solar power - nwp τ^t NWPs transformed into normalized solar power - xt Day of year - yt Time of day - et+k k-step prediction error - q Quantile level - h Bandwidth of smoothing kernel - λ Forgetting factor - power production units has to be adjusted Denmark is balanced by the energy mar- in order to balance the total power pro- ket Nord Pool, where electricity power is duction. The cost of these adjustments in- traded on two markets: the main market creases as the horizon of the adjustments Elspot and a regulation market Elbas. On decreases and thus improved forecasting of Nord Pool the producers release their bids solar power will result in an optimized total at 12:00 for production each hour the fol- power production, and in future power pro- lowing day, thus the relevant solar power duction systems where energy storage is im- forecasts are updated before 12:00 and con- plemented, power forecasting is an impor- sist of hourly values at horizons of 12 to tant factor in optimizing utilization of stor- 36 hours. The models in this paper focus age facilities (Koeppel and Korpas, 2006). on such forecasts, but with the 1-to-11-hour horizons also included. The total electricity power production in 2 Interest in forecasting solar power has in- hourly values of global irradiance. Differ- creased and several recent studies deal with ent types of meteorological observations are the problem. Many of these consider fore- used as input to the models; among others casts of the global irradiance which is essen- the daily mean global irradiance and daily tially the same problem as forecasting solar mean cloud cover of the day to be fore- power. Two approaches are dominant: casted. This paper describes a new two-stage • a two-stage approach in which the solar method where first the clear sky model ap- power (or global irradiance) is normal- proach is used to normalize the solar power ized with a clear sky model in order to and then adaptive linear time series mod- form a more stationary time series and els are applied for prediction. Such models such that the classical linear time series are linear functions between values with a methods for forecasting can be used. constant time difference, where the model • another approach in which neural net- coefficients are estimated by minimizing a works (NNs) with different types of in- weighted residual sum of squares. The co- put are used to predict the solar power efficients are updated regularly, and newer (or global irradiance) directly. values are weighted higher than old values, hence the models adapt over time to chang- In a study Chowdhury and Rahman (1987) ing conditions. make sub-hourly forecasts by normalizing Normalization of the solar power is ob- with a clear sky model. The solar power is tained by using a clear sky model which divided into a clear sky component, which gives an estimate of the solar power in clear is modelled with a physical parametriza- (non-overcast) sky at any given point in tion of the atmosphere, and a stochastic time. The clear sky model is based on sta- cloud cover component which is predicted tistical smoothing techniques and quantile using ARIMA models. Sfetsos and Coonick regression, and the observed solar power is (2000) use NNs to make one-step predic- the only input. The adaptive linear predic- tions of hourly values of global irradiance tion is obtained using recursive least squares and compare these with linear time series (RLS) with forgetting. It is found that the models that work by predicting clearness adaptivity is necessary, since the character- indexes. Heinemann et al. (2006) use satel- istics of a PV-system are subject to changes lite images for horizons below 6 hours, and due to snow cover, leaves on trees, dirt on in (Lorenz et al., 2007) numerical weather the panel, etc., and this has to be taken into predictions (NWPs) for longer horizons, as account by an online forecasting system. input to NNs to predict global irradiance. The data used in the modelling is de- This is transformed into solar power by a scribed in Section 2. The clear sky model simulation model of the PV system. Ho- used for normalizing the solar power is de- caoglu et al. (2008) investigate feed-forward fined in Section 3 followed by Section 4 NNs for one-step predictions of hourly val- where the adaptive time series models used ues of global irradiance and compare these for prediction are identified. In Section 5 an with seasonal AR models applied on solar approach to modelling of the uncertainty in power directly. Cao and Lin (2008) use NNs the forecasts is outlined. The evaluation of combined with wavelets to predict next day the models and a discussion of the results 3 are found in Section 6 and finally the con- which then covers the forecast horizons up clusions of the study are drawn in Section to 36 hours ahead, and is given in (W=m2). 7. Time series are resampled to lower sample frequencies by mean values and when the 2. Data resampled values are used this is noted in the text. In order to synchronize data with The data used in this study is observa- different sample frequencies, the time point tions of solar power from 21 PV systems for a given mean value is assigned to the located in a small village in Jutland, Den- middle of the period that it covers, e.g.
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