A Guide to Solar Power Forecasting using ARMA Models

In this short article, we summarize a step-by-step methodology to forecast power output from a photovoltaic solar generator using hourly auto-regressive moving average (ARMA) models. We illustrate how to build an ARMA model, to use statistical tests to validate it, and construct hourly samples. The resulting model inherits nice properties for embedding it into more sophisticated operation and planning models, while at the same time showing relatively good accuracy. Additionally, it represents a good forecasting tool for sample generation for stochastic energy optimization models.

[1]  J. Kleissl,et al.  Chapter 8 – Overview of Solar-Forecasting Methods and a Metric for Accuracy Evaluation , 2013 .

[2]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[3]  Wencong Su,et al.  Stochastic Energy Scheduling in Microgrids With Intermittent Renewable Energy Resources , 2014, IEEE Transactions on Smart Grid.

[4]  Consolación Gil,et al.  Optimization methods applied to renewable and sustainable energy: A review , 2011 .

[5]  Mario J. Durán,et al.  Short-Term Wind Power Forecast Based on ARX Models , 2007 .

[6]  J. Contreras,et al.  ARIMA Models to Predict Next-Day Electricity Prices , 2002, IEEE Power Engineering Review.

[7]  Mathieu David,et al.  Solar Forecasting in a Challenging Insular Context , 2016 .

[8]  P. Pinson,et al.  Generation and evaluation of space–time trajectories of photovoltaic power , 2016, 1603.06649.

[9]  P. Phillips.  Testing for a Unit Root in Time Series Regression , 1988 .

[10]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[11]  Xiaoyan Xu,et al.  Comparative study of power forecasting methods for PV stations , 2010, 2010 International Conference on Power System Technology.

[12]  Thomas Reindl,et al.  A novel hybrid approach based on self-organizing maps, support vector regression and particle swarm optimization to forecast solar irradiance , 2015 .

[13]  Mehdi Etezadi-Amoli,et al.  Stochastic Performance Assessment and Sizing for a Hybrid Power System of Solar/Wind/Energy Storage , 2014, IEEE Transactions on Sustainable Energy.

[14]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[15]  Henrik Madsen,et al.  Virtual Power Plants , 2014 .

[16]  Magnus Korpås,et al.  Variability Characteristics of European Wind and Solar Power Resources—A Review , 2016 .

[17]  Carlos F.M. Coimbra,et al.  History and trends in solar irradiance and PV power forecasting: A preliminary assessment and review using text mining , 2018, Solar Energy.

[18]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[19]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[20]  L. Mora-López,et al.  Multiplicative ARMA models to generate hourly series of global irradiation , 1998 .

[21]  Xu Andy Sun,et al.  Adaptive Robust Optimization With Dynamic Uncertainty Sets for Multi-Period Economic Dispatch Under Significant Wind , 2015 .