[논문]On the Use of Maximum Likelihood and Input Data Similarity to Obtain Prediction Intervals for Forecasts of Photovoltaic Power Generation

Fonseca Junior, Joao Gari da Silva; Oozeki, Takashi; Ohtake, Hideaki; Takashima, Takumi; Kazuhiko, Ogimoto

doi:10.5370/jeet.2015.10.3.1342

[국내논문] On the Use of Maximum Likelihood and Input Data Similarity to Obtain Prediction Intervals for Forecasts of Photovoltaic Power Generation 원문보기

Journal of electrical engineering & technology, v.10 no.3, 2015년, pp.1342 - 1348

Fonseca Junior, Joao Gari da Silva (Institute of Industrial Science, University of Tokyo) , Oozeki, Takashi (System and Applications Team, Research Center for Photovoltaic Technologies, National Institute of Advanced Industrial Science and Technology) , Ohtake, Hideaki (System and Applications Team, Research Center for Photovoltaic Technologies, National Institute of Advanced Industrial Science and Technology) , Takashima, Takumi (System and Applications Team, Research Center for Photovoltaic Technologies, National Institute of Advanced Industrial Science and Technology) , Kazuhiko, Ogimoto (Institute of Industrial Science, University of Tokyo)

Abstract ▼ AI-Helper

The objective of this study is to propose a method to calculate prediction intervals for one-day-ahead hourly forecasts of photovoltaic power generation and to evaluate its performance. One year of data of two systems, representing contrasting examples of forecast’ accuracy, were used. The method is based on the maximum likelihood estimation, the similarity between the input data of future and past forecasts of photovoltaic power, and on an assumption about the distribution of the error of the forecasts. Two assumptions for the forecast error distribution were evaluated, a Laplacian and a Gaussian distribution assumption. The results show that the proposed method models well the photovoltaic power forecast error when the Laplacian distribution is used. For both systems and intervals calculated with 4 confidence levels, the intervals contained the true photovoltaic power generation in the amount near to the expected one.

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문제 정의

Thus, the objective of this study is to present a simple method to calculate prediction intervals for one-day- ahead forecasts of power generation of single PV systems. The method is based on the use of the maximum likelihood estimation method, and on the concept of similarity between PV power forecasts for different hours and different days.
Moreover, two naive reference methods to calculate the intervals are presented. Their objective is to provide a basis of comparison to analyze the performance of the proposed method.
The objective of this study was to present a simple method to calculate prediction intervals for forecasts of power generation of PV systems. The method is based on the use of the maximum likelihood estimation, and on the concept of similarity between the input data used in the forecasts.

가설 설정

In Eq. 3 L_lim and U_lim are the lower and upper limits of the prediction interval.

제안 방법

systems. The method is based on the use of the maximum likelihood estimation method, and on the concept of similarity between PV power forecasts for different hours and different days.
To validate the method, it was applied to calculate prediction intervals, with different theoretical confidence levels, for 1 year of hourly forecasts of power generation of two PV systems installed in different locations in Japan. The forecasts of PV power were done using a method previously proposed [6], which was based on numerical weather prediction data and a support vector regression algorithm.
The forecasts of PV power were done using a method previously proposed [6], which was based on numerical weather prediction data and a support vector regression algorithm. The performance of the prediction intervals calculation method was verified analyzing the corres- pondence of pre-specified confidence levels used in the intervals calculations and the achieved annual forecast error coverage they provided. Moreover, comparisons with 2 naive reference approaches were done to evaluate the sizes of the prediction intervals according to their forecast error coverage.
The performance of the prediction intervals calculation method was verified analyzing the corres- pondence of pre-specified confidence levels used in the intervals calculations and the achieved annual forecast error coverage they provided. Moreover, comparisons with 2 naive reference approaches were done to evaluate the sizes of the prediction intervals according to their forecast error coverage.
They estimated the forecast error of the method based on the errors of a cross-validation procedure on the training data used to construct the forecast model. Furthermore, they assumed that the distribution of the forecast errors followed a symmetric Gaussian distribution, as shown in Eq.
In this study we propose to use past forecast errors instead of using the ones of a cross-validation procedure applied on training data. Furthermore, a criterion based on input data similarity is used to obtain suitable prediction intervals according to the forecast hour and input data of the forecasts.
They depend only of the past input data used and the output data the forecast method yielded. In this study they were applied to provide intervals to forecasts done with a method based on the use of support vector regression, hourly extraterrestrial insolation and numerical weather prediction data. These data are provided on the day preceding the forecast day.
is in Table 1. The method provides hourly forecasts based on the hourly input data and for each day of forecasts the model is trained with hourly input data and measured PV power of the previous 60 days. Details about the setup of the algorithm and its application are in previous studies [6, 12].
Comparing both PV systems, PV system 2, which generally had high forecast errors, caused the proposed method to yield prediction intervals naturally larger than the ones obtained for PV system 1. The overall result was higher forecast error coverage for PV system 2 than for PV system 1.
generation of PV systems. The method is based on the use of the maximum likelihood estimation, and on the concept of similarity between the input data used in the forecasts.

이론/모형

Japan. The forecasts of PV power were done using a method previously proposed [6], which was based on numerical weather prediction data and a support vector regression algorithm. The performance of the prediction intervals calculation method was verified analyzing the corres- pondence of pre-specified confidence levels used in the intervals calculations and the achieved annual forecast error coverage they provided.
The forecast horizon is therefore of one day ahead of time. The numerical weather prediction is provided by grid-point value forecasts with a meso-scale model, GPV-MSM, of the Japan Meteorological Agency.
5 are examples of prediction intervals calculated with the proposed method for a given day. The calculations were done for PV system 1 using the Laplacian distribution assumption. In Fig.

성능/효과

The results showed that the proposed method used with the Laplacian distribution assumption is more suitable to PV systems with low forecast errors. For PV systems with high forecast errors the Gaussian distribution assumption was more suitable.
Based on the results, it can be concluded that the proposed method to calculate the prediction intervals in the problem PV power generation forecast is valid. The forecast error coverage obtained with it approximated well the confidence levels of the intervals, and it used significantly less reserve power than the reference method 2.

후속연구

In further studies a comprehensive analysis containing a wide range of PV systems installed in Japan will be done to better characterize the validity of the method and of the forecast error distribution assumptions.

참고문헌 (12)

A. Mellit and A. M. Pavan, “A 24-h forecast of solar irradiance using artificial neural network: Application for performance prediction of a grid-connected PV plant at Trieste, Italy,” Solar Energy, vol. 84, no. 5, pp. 807-821, 2010.

상세보기
E. Lorenz, D. Heinemann, H. Wickramarathne, H. G. Beyer, and S. Bofinger, "Forecast of Ensemble Power Production by Grid-Connected PV Systems," in Proceedings of the 20th European PV Conference, Italy, pp. 3.9-7.9, 2007.
A. Yona, T. Senjyu, A. Y. Saber, T. Funabashi, H. Sekine, and C. H. Kim, “Application of Neural Network to One-Day-Ahead 24 hours Generating Power Forecasting for Photovoltaic System,” in Proceedings of International Conference on Intelli-gent Systems Applications to Power Systems 2007, pp. 1-6, 2008.
M. Paulescu, E. Paulescu, P. Gravila, and V. Badescu, Weather Modeling and Forecasting of PV Systems Operation, Springer, 2012.
B. Espinar, J.-L. Aznarte, R. Girard, A. M. Moussa, and G. Kariniotakis, "Photovoltaic Forecasting: A state of the art," in Proceedings 5th European PV-Hybrid and Mini-Grid Conference, Spain, pp. 250-255, 2010.
J. G. da S. Fonseca, T. Oozeki, T. Takashima, G. Koshimizu, Y. Uchida, and K. Ogimoto, “Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan,” Progress in Photovoltaics Research and Applications, vol. 20, no. 7, pp. 874-882, 2012.

상세보기
S. Geisser, Predictive Inference, CRC Press, 1993.
C. J. Lin and R. C. Weng, “Simple probabilistic predictions for support vector regression,” Natl. Taiwan Univ. Taipei, 2004.
J. Platt, “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods,” Advances in Large Margin Classifiers, vol. 10, no. 3, pp. 61-74, 1999.
J.G.S. Fonseca Jr., T. Oozeki, H. Ohtake, K. Shimose, T. Takashima, and K. Ogimoto, "Uncertainty Information in Forecasts of Photovoltaic Power Generation with Support Vector Regression: A Preliminary Study," in Proceedings of the 17th International Con-ference on intelligent System Applications to Power Systems, Japan, 2013.
J. G. da S. Fonseca Jr., T. Oozeki, H. Ohtake, T. Takashima, and K. Ogimoto, “On the Use of Maximum Likelihood Estimation and Data Similarity to Obtain Prediction Intervals for Forecasts of Photovoltaic Power Generation,” in Proceedings of the International Conference on Electrical Engineering 2014, Jeju, 2014, pp. 1181-1188.
J. G. da S. Fonseca Jr., T. Oozeki, H. Ohtake, K. Shimose, T. Takashima, and K. Ogimoto, "A Comprehensive Study of Photovoltaic Power Generation Forecasts in Multiple Locations in Japan," in Proceedings of the 28th European Photovoltaic Solar Energy Conference and Exhibition, France, pp. 3601-3606, 2013.

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