Abstract
The energy yield estimation of a photovoltaic (PV) system operating under partially shaded conditions is a challenging task and a very active area of research. In this paper, we attack this problem with the aid of machine learning techniques. Using data simulated by the equivalent circuit of a PV string operating under partial shading, we train and evaluate three different gradient boosted regression tree models to predict the global maximum power point (MPP). Our results show that all three approaches improve upon the state-of-the-art closed-form estimates, in terms of both average and worst-case performance. Moreover, we show that even a small number of training examples is sufficient to achieve improved global MPP estimation. The methods proposed are fast to train and deploy and allow for further improvements in performance should more computational resources be available.
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Notes
- 1.
Standard Test Conditions: 1000 W/m\(^2\) irradiance, 25 \(^{\circ }\)C temperature & 1.5 air mass.
- 2.
Initial attempts at exploiting interactions between \(P_{max}\) & \(V_{P_{max}}\) by first predicting the value of one and then using it to predict the other, yielded worse results than assuming independence. Their further investigation is left for future work.
- 3.
As we will see in this section, \(\hat{X}\) can be an estimate of \(P_{max}\) or \(V_{P_{max}}\), or of any of the ‘intermediate outputs’ –\(P_1\), \(V_1\), \(P_2\), \(V_2\)– depending on the method.
- 4.
Denoting MPP1 & MPP2 with ‘1’ & ‘\(-1\)’, respectively, the classifier’s prediction is of the form \(\hat{H} = sign\big [\sum _{m=1}^M {a_m h_m(G, T, s, n_{sh})}\big ]\in \{-1,1\}\), where \(h_m(G, T, s, n_{sh})\in \{-1,1\}\) is the prediction of the base learner added on the m-th round and \(a_m\) its voting weight, both the learner and \(a_m\) being the learned parameters of the model.
- 5.
- 6.
More precisely, \(95\%\) of the times, \(99.99\%\) of the estimates of \(P_{max}\) under the Stagewise model will have a NAE smaller than some value that lies between \(5.03\%\) and \(5.93\%\). In the discussion, we sacrifice this level of mathematical rigour for simplicity.
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Acknowledgements
This project was partially supported by the EPSRC Centre for Doctoral Training [EP/I028099/1] & the EPSRC LAMBDA [EP/N035127/1] & Anyscale Apps [EP/L000725/1] project grants. N. Nikolaou acknowledges the support of the EPSRC Doctoral Prize Fellowship. E. Batzelis carried out this research at NTUA, Athens, Greece under the support of the ‘IKY Fellowships of Excellence for Postgraduate Studies in Greece-Siemens Program’.
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Nikolaou, N., Batzelis, E., Brown, G. (2017). Gradient Boosting Models for Photovoltaic Power Estimation Under Partial Shading Conditions. In: Woon, W., Aung, Z., Kramer, O., Madnick, S. (eds) Data Analytics for Renewable Energy Integration: Informing the Generation and Distribution of Renewable Energy. DARE 2017. Lecture Notes in Computer Science(), vol 10691. Springer, Cham. https://doi.org/10.1007/978-3-319-71643-5_2
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