Optimization of an artificial neural network dedicated to the multivariate forecasting of daily global radiation

Abstract

This paper presents an application of Artificial Neural Networks (ANNs) to predict daily solar radiation. We look at the Multi-Layer Perceptron (MLP) network which is the most used of ANNs architectures. In previous studies, we have developed an ad-hoc time series preprocessing and optimized a MLP with endogenous inputs in order to forecast the solar radiation on a horizontal surface. We propose in this paper to study the contribution of exogenous meteorological data (multivariate method) as time series to our optimized MLP and compare with different forecasting methods: a naïve forecaster (persistence), ARIMA reference predictor, an ANN with preprocessing using only endogenous inputs (univariate method) and an ANN with preprocessing using endogenous and exogenous inputs. The use of exogenous data generates a nRMSE decrease between 0.5% and 1% for two stations during 2007 (Corsica Island, France). The prediction results are also relevant for the concrete case of a tilted PV wall (1.175 kWp). The addition of endogenous and exogenous data allows a 1% decrease of the nRMSE over a 6 months-cloudy period for the power production. While the use of exogenous data shows an interest in winter, endogenous data as inputs on a preprocessed ANN seem sufficient in summer. 2 Time series nomenclature Meteorological parameters x t , x d,y Radiation time series model at time t and at day d and year y P Pressure average [Pa] x t , x d,y Radiation time series data at time t and at day d and year y DGP Daily gradient pressure [Pa] y t Exogenous time series data at time t N Nebulosity, cloudy height class [Octa] t S , y d S , Stationary time series (clear sky index) for the day d and the year y or for the time t T Ambient temperature maximum (TM), minimum (Tm), average (Ta) and night (Tn) at 3:00 AM [°C] Clear sky model Ws Wind speed, Average at 10 meters [m.s -1 ] d clearsky gh H , Clear sky global horizontal irradiance [MJ/m²] integrate on the day d PKW Peak wind speed, Maximum speed of 10 meters [m.s -1 ] 0 H Extraterrestrial solar radiation coefficient [MJ/m²] Wd Wind direction measured at 10 meters [deg]  global total atmospheric optical depth Su Sunshine duration, direct irradiance from the Sun of at least 120 watts per square meter [h] H Solar elevation angle RH Relative humidity, Water vapor in the air [%] B Fitting parameter of Solis clear sky model RP Rain precipitations measured in standard rain gauge [mm] Correlation analysis Frontage PV parameters r k Autocorrelation factor estimation for time lag k E pv,ac/dc Photovoltaic wall power (MJ) kk  Estimation of partial autocorrelations for time lag k η PV Plant efficiency (%) R Cross-correlation estimation I β Daily global radiation (tilt of ) [MJ/m²] Levenberg-Marquard algorithm S Surface of PV wall [m²] x  Parameter to optimize PR Performance ratio of the PV plant J Jacobian matrix I Identity matrix e(x) Error term  specific algorithm parameter Nomenclature.

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