### Stochastic Model for Generating Synthetic Hourly Global Horizontal Solar Radiation Data Sets Based on Auto Regression Characterization

#### Abstract

*A large number of non-repetitive multi-year hourly solar radiation time-series dataset are desired when applying Monte Carlo techniques for planning and design of solar energy systems. Solar radiation models which utilize the clearness index and average value decomposition methods are commonly used to generate synthetic set of solar irradiances for this purpose. In this paper, a novel stochastic solar radiation model based on probability distributions of the first-order differences of hourly global solar horizontal radiation is proposed. The first-order differences are modeled using a trend component and a stochastic component represented using the cumulative distribution functions, both extracted from historical data taken over a window of 31 days around the considered day of the year. Measured solar radiation data from four different locations with varying climate characteristics were used to evaluate the proposed model in comparison to two previously reported models. The proposed method performed consistently better in terms of the similarity of probability distributions and autocorrelation functions, for all four locations and datasets.*

#### Keywords

#### Full Text:

PDF#### References

Abdelsamad S.F., Morsi W.G., and Sidhu T.S., 2015. Probabilistic impact of transportation electrification on the loss-of-life of distribution transformers in the presence of rooftop solar photovoltaic. IEEE Transactions on Sustainable Energy 6: 1565–73.

Hopkins M. and A. Pahwa. 2008. Monte-Carlo simulation of energy production by a small wind generator. In Proceedings of th 40th North American Power Symposium, USA, pp.1–6.

Sharma H., Bora B., Sharma S., Kumar R. and Jain R., 2017. Reliability study of solar pv power production in terms of weather parameters using Monte Carlo simulation. International Journal of Engineering Research and Applications 07: 37–45.

Liu B.Y.H. and R.C. Jordan. 1960. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4: 1–19.

Morf H., 2013. A stochastic solar irradiance model adjusted on the Ångström-Prescott regression. Solar Energy 87: 1–21.

De Alfragide E., 1992. Tag : a time-dependent, autoregressive, Gaussian model for generating synthetic hourly radiation. Solar Energy 49: 167–74.

Brecl K. and M. TopiI. 2014. Development of a stochastic hourly solar irradiation model. International Journal of Photoenergy 28(1): 33-40.

Aguiar R.J., Collares-Pereira M. and Conde J.P., 1988. Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices. Solar Energy 40: 269–79.

Graham V.A. and K.G.T. Hollands. 1990. A method to generate synthetic hourly solar radiation globally Solar Energy 44: 333–41.

Suehrcke H. and P.G. McCormick. 1988. The frequency distribution of instantaneous insolation values. Solar Energy 40: 413–22.

Besharat F., Dehghan A.A. and Faghih A.R., 2013. Empirical models for estimating global solar radiation: A review and case study. Renewable and Sustainable Energy Reviews 21: 798–821.

Grantham A.P., Pudney P.J. and Boland J.W., 2018. Generating synthetic sequences of global horizontal irradiation. Solar Energy 162: 500–9.

Ngoko B.O., Sugihara H., and Funaki T., 2014. Synthetic generation of high temporal resolution solar radiation data using Markov models. Solar Energy 103: 160–70.

Bright J.M., Smith C.J., Taylor P.G., and Crook R., 2015. Stochastic generation of synthetic minutely irradiance time series derived from mean hourly weather observation data. Solar Energy 115: 229–42.

Duffie J.A and W.A Beckman. 2013. Solar engineering of thermal processes (Wiley).

Polo J., Zarzalejo L.F., Marchante R., and Navarro A.A., 2011. A simple approach to the synthetic generation of solar irradiance time series with high temporal resolution. Solar Energy 85: 1164–70.

Grantham A.P., Pudney P.J., Ward L.A., Belusko M., and Boland J.W., 2017. Generating synthetic five-minute solar irradiance values from hourly observations Solar Energy 147: 209–21.

Bright J.M., Babacan O., Kleissl J., Taylor P.G. and Crook R., 2017. A synthetic, spatially decorrelating solar irradiance generator and application to a LV grid model with high PV penetration. Solar Energy 147: 83–98.

Azzouz M.A., Shaaban M.F., and El-Saadany E.F., 2015. Real-time optimal voltage regulation for distribution networks incorporating high penetration of PEVs. IEEE Transactions on Power Systems 30: 3234-3247.

Gordon J.M. and T.A. Reddy. 1988. Time series analysis of daily horizontal solar radiation. Solar Energy 41: 215–26.

Government of Canada 2015. Engineering Climate Datasets - Canadian Weather Energy and Engineering Datasets (CWEEDS) Retrieved on May 20, 2020 from the World Wide Web: https://climate.weather.gc.ca/prods_servs/engineering_e.html.

Solar Anywhere 2019. Solar Anywhere Datasets Retrieved on May 20, 2020 from World Wide Web: https://www.solaranywhere.com/solutions/solaranywhere-data/.

Perez R., Seals R., Ineichen P., Stewart R. and Menicucci D., 1987. A new simplified version of the perez diffuse irradiance model for tilted surfaces. Solar Energy 39: 221–31.

Peel M.C., Finlayson B.L. and McMahon T.A., 2007. Updated world map of the Köppen-Geiger climate classification Hydrology and Earth System . Sciences 11: 1633–44.

Peruchena C.F., Larrañeta M., Blanco M., and Bernardos A., 2018. High frequency generation of coupled GHI and DNI based on clustered dynamic paths. Solar Energy 159: 453–7.

Larrañeta M., Moreno-Tejera S., Silva-Pérez M.A., and Lillo-Bravo I., 2015. An improved model for the synthetic generation of high temporal resolution direct normal irradiation time series. Solar Energy 122: 517–28.

Munkhammar J., 2020. Polynomial Probability Distribution Estimation MATLAB Central File Exchange. Retrieved on May 20, 2020 from the World Wide Web: https://www.mathworks.com/matlabcentral/fileexchange/62520-polynomial-probability-distribution-estimation.

R2017a - MATLAB & Simulink. MathWorks Retrieved on May 20, 2020 from World Wide Web: https://www.mathworks.com/products/matlab.html.

Chamola V. and B. Sikdar. 2010. Synthetic generation of hourly solar irradiance using a multi-state Markov model. In Proceedings of the IEEE Conference Publications 1 1–3.