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Energy (2017) 000–000 133–138 EnergyProcedia Procedia122 00 (2017) www.elsevier.com/locate/procedia CISBAT 2017 International Conference – Future Buildings & Districts – Energy Efficiency from Nano to Urban Scale, CISBAT 2017 6-8 September 2017, Lausanne, Switzerland CISBAT 2017 International Conference – Future Buildings & Districts – Energy Efficiency from Nano to Urban Scale, CISBAT 2017 6-8 September 2017, Lausanne, Switzerland

SVR based PV models for MPC based energy flow management ThePV 15thmodels International Symposium on District and Cooling SVR based forBoegli MPC based energy flow management a a Heating M. *, Y. Stauffer

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I. Andrić *, A. Pina , P.production Ferrãocan , J.beFournier B.operational Lacarrière Le Corre The ever increasing penetration of renewable used to lower.,the costs,ofO. households and districts. Abstract However, given its intermittent nature predicting their production in order to use it efficiently is mandatory. This article will discuss a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal how photovoltaic can production be addressed. based on support regression (SVR) The ever increasingproduction penetration of renewable can Prediction be used to algorithms lower the operational costs of vector households and districts. b prediction Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France technique given are cdeveloped and compared to a classical persistence model benchmark. Prediction errors between 7 to 12% for SVR However, its intermittent nature predicting their production in order to use it efficiently is mandatory. This article will discuss Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France algorithms with different forecast solar irradiance obtained,algorithms which is twice better to a classical persistence how photovoltaic production prediction can be accuracies addressed.are Prediction based on compared support vector regression (SVR) model (PM) models were integratedpersistence in a modelmodel predictive based battery management system 7intothe12% scope the technique arebenchmark. developed These and compared to a classical benchmark. Prediction errors between forofSVR European project AMBASSADOR. algorithms with different forecast solar irradiance accuracies are obtained, which is twice better compared to a classical persistence model (PM) benchmark. These models were integrated in a model predictive based battery management system in the scope of the Abstract European project AMBASSADOR. ©District 2017 The Authors. Published by Elsevier addressed Ltd. heating networks are commonly in the literature as one of the most effective solutions for decreasing the © 2017 The Authors. Published by Elsevier Ltd. Peer-review responsibility scientific committee the scientific of the CISBAT International greenhouseunder gas emissions from of thethe building sector. These of systems require committee high investments which are2017 returned through the heat Peer-review under responsibility of the scientific committee of the CISBAT 2017 International Conference – Future Buildings & Conference – Future Buildings & Districts – Energy Efficiency from Nano to Urban Scale. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, © 2017 The Authors. Published by Elsevier Ltd. Districts – Energy Efficiency from Nano to Urban Scale prolonging under the investment returnofperiod. Peer-review responsibility the scientific committee of the scientific committee of the CISBAT 2017 International Keywords: photovoltaic, batteries, storage,the vector regression The mainMPC, scope of this paper is&toDistricts assess feasibility of using the Nano heat demand – outdoor Conference – Future Buildings –support Energy Efficiency from to Urban Scale. temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Keywords: storage,period supportand vector regression buildingsMPC, that photovoltaic, vary in bothbatteries, construction typology. Three weather scenarios (low, medium, high) and three district 1.renovation Introduction scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. results showed that when weatherofchange is considered, the margin of such error could be acceptable for is some applications 1.The Introduction Accurately predicting the only production intermittent renewable sources as photovoltaic (PV) critical given (the ever errorhigher in annual demand was 20% for all weather However, after their penetration [1].lower Such than prediction models can bescenarios coupledconsidered). to battery controllers [2] tointroducing enable newrenovation energy scenarios, theschemes. error value increased 59.5% (depending on the weather andwas renovation scenarios combination Accurately predicting theaim production of intermittent sources such photovoltaic (PV) is critical given management The of up thetoEuropean projectrenewable AMBASSADOR toasaddress this challenge by considered). providing The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the their ever higher penetration [1]. Such prediction models can be coupled to battery controllers [2] to enable new energy decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and management schemes. The aim of the European project AMBASSADOR was to address this challenge by providing renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and * Corresponding author. Tel.: +41-32-720-5194; fax: +41-32-720-5740. improve the accuracy of heat demand estimations. E-mail address: [email protected]

* Corresponding author. Tel.: +41-32-720-5194; fax: +41-32-720-5740. © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. E-mail address: [email protected] Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Peer-review under responsibility of the scientific committee of the CISBAT 2017 International Conference – Future Buildings & Districts – Cooling. Energy Efficiency Nano to Urban Scale. 1876-6102 © 2017from The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the CISBAT 2017 International Conference – Future Buildings & Districts – Keywords: Heat demand; Forecast; Climate change Energy Efficiency from Nano to Urban Scale.

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the CISBAT 2017 International Conference – Future Buildings & Districts – Energy Efficiency from Nano to Urban Scale 10.1016/j.egypro.2017.07.317

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a control strategy for dispatchable loads at district level. In that context, self tuning PV models were developed and included in a model predictive controller (MPC). The latter was developed to control the charging strategy of batteries so as to minimize the exploitation costs at district level [1]. The quality of such a control strategy greatly depends on the ability of the control models to accurately predict their behavior. The objective of this article is to present the work carried out for the photovoltaic control model development and validation. It is to be pointed out that the developed models represent the PV system behaviour and do rely on weather forecasts. The latter can be provided by various services such as [3] or [4]. The quality of the forecast has a direct impact on the overall prediction quality. When benchmarked to the review of [5], the developed models falls within Support Vector Regression (SVR) machines day-ahead forecasting. The SVR model is compared to the commonly used Persistence Model (PM) [5]. Even though smarter PM benchmark models taking into account the clear sky index exist, this study only considers the standard PM (Chapter 3.2). This article is composed of the following main chapters. Chapter two presents the AMBASSADOR project with emphasizes on the optimization at district level and in particular the PV production forecast. Chapter three describes in detail the work carried out for the development and validation of self-training PV models. Finally, chapter four summarizes the work and provides the outlook. 2. Optimization at district level The objective is to minimize the exploitation costs at district level by optimally using the available batteries. In order to do so an objective function that takes into account all elements represented in Figure 1 is implemented. Moreover, various constraints are imposed by the battery limitations and energy balance [6]. This latter point incorporates the expected production, from various renewable sources and consumption. In the present article, emphasizes is given on photovoltaic (PV) production prediction models (Chapter 3). The MPC considers a 24h prediction horizon to catch a complete day/night cycle. The prediction horizon is sampled and updated every 15 min. to offer enough granularity while keeping reasonable computation load. This algorithm was validated in simulation on various scenarios (i.e. sites, electricity tariffs, ...). It was shown that when compared to a standard battery controller (i.e. that stores overproduction and uses it at a later stage) savings up to 80% could be achieved in very favorable cases. This value however can drop to zero if the boundary conditions do not allow for any meaningful optimization to take place. Nevertheless on average savings between 20-30% are obtained [3].

Figure 1 – Terms taken into account in the objective function and optimization constraints.

3. PV model Efficient use of renewable energy and optimal storage rely on accurate prediction of PV power production for the next 24 hours. This section presents the model structure used for PV prediction and further compare its performance with a commonly used benchmark model.



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3.1. Model structure The PV model structure for prediction is based on nonparametric support vector regression (SVR) techniques [7] [8] [9]. SVR is build upon support vector machine (SVM) commonly used for classification. In an optimization problem, it roughly means that the inequality constraint, for classification, is replaced by an equality constraint, for regression, in addition to solve a regularized least square problem. In this sense, SVR is also known as least squares support vector machine (LS-SVM). SVR methods use non-linear mapping of kernel function to project data into a higher dimensional space where solving the regression task is easier than in the original space [7] [8]. Here, a Gaussian 2 kernel function 𝐾𝐾𝐾𝐾�𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖 , 𝑥𝑥𝑥𝑥𝑗𝑗𝑗𝑗 � = exp �−�𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖 − 𝑥𝑥𝑥𝑥𝑗𝑗𝑗𝑗 � ⁄2ℎ2 � is used. Two SVR tuning parameters are needed: the kernel bandwidth ℎ, which defines the regression smoothness or granularity, and the regularization parameter 𝜆𝜆𝜆𝜆, which defines the regression robustness. The tuning procedure can either be done manually or by an auto-tuning procedure such as a global optimizer based on a coupled simulated annealing procedure followed by a fine-tuning derivative-free search algorithm [7]. In our study, a systematic manual approach has been used by following tuning guidelines in Table 1. The following parameter values are selected : ℎ = 1 and 𝜆𝜆𝜆𝜆 = 0.01. Table 1 – SVR tuning parameters.

Bandwidth ℎ Regularization 𝜆𝜆𝜆𝜆

Increased value 

Decreased value 

Wide kernel bandwidth. Filtering / smoothing effect.

Narrow kernel bandwidth. Sharp and spiky effects.

Better robustness to unpredictable dynamics. Less fitting accuracy. Avoiding overfitting.

Better fit on the training data set. May lack robustness towards unpredictable dynamics. Risk of overfitting.

The SVR algorithm is implemented using a moving horizon approach, in which the training is done over the last 7 days and the prediction is carried out for the next 24 hours. For the training phase, the input signals needed are the measured global solar irradiance and a daily cycle time reference to map the measured PV power production. This training phase provides a set of SVR kernel coefficients that are used in the prediction phase to project the forecast solar irradiance and the daily cycle time frame into an expected predicted PV power production. Input/Output signals for training and prediction phases are summarized in Table 2. All signals are normalized to ensure well behaved numerical conditioning and SVR tuning consistency. Table 2 – SVR training and prediction with input and output signals.

Training (7 days)

Prediction (24 h)

Input

Measured global solar irradiance Daily cycle time reference Measured PV power production

Forecast global solar irradiance Daily cycle time frame SVR kernel coefficients

Output

SVR kernel coefficients

Predicted PV power production

To validate the prediction algorithms, experimental data from Mt-Soleil PV installation in Northwest Switzerland for the period of June 2014 are used. Figure 2 shows a snapshot as per June 21st 2014 with the signals for the 7 days training phase (left) and the 24 hours prediction phase (right).

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3.2. Gold standard The most common reference model used in solar forecast field is the Persistence Model (PM) [5][10]. The PM is a trivial model that assumes that the weather conditions of one day ahead (forecast day) are identical to the current day. The simple PM assumes the persistence of the solar irradiance for the forecast day ahead and is used as benchmark for our SVR model for PV power prediction. Training

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3.3. Benchmarking results The forecast error 𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖 = 𝑥𝑥𝑥𝑥 for − 𝑥𝑥𝑥𝑥 obs is defined as the difference between the PV power forecast 𝑥𝑥𝑥𝑥 for and the PV power observed 𝑥𝑥𝑥𝑥 obs (measured). The error metrics used to evaluate the models accuracy are the root mean square error (RMSE), the standard deviation (STD), the mean bias error (MBE) and the mean absolute error (MAE). The relation RMSE2 = STD2 + MBE2 holds. Forecast models include the PM benchmark and the SVR algorithm with six different solar irradiance forecast: an optimal one without noise nor bias, and five others with added white noise and bias. In this benchmark, a 24h delayed off-line scheme was used with solar irradiance forecast replaced by the measured solar irradiance, called optimal irradiance forecast. The added noise and bias to the optimal forecast tend to mimic more realistic irradiance forecasts. Error metrics for the different cases are shown in Table 3. Table 3 – Error metrics : RMSE, STD, MBE and MAE for the PM benchmark and the SVR algorithms with different irradiance forecast.

Forecast error: 𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖 = 𝑥𝑥𝑥𝑥 for − 𝑥𝑥𝑥𝑥 obs

Forecast models (𝑥𝑥𝑥𝑥 for ):

Persistence Model (PM) SVR +40% noise (no bias)

RMSE (%) �

∑𝑛𝑛𝑛𝑛𝑖𝑖𝑖𝑖=1 𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖2 𝑛𝑛𝑛𝑛

18.7 11.8

STD (%) �

MBE (%)

2 ∑𝑛𝑛𝑛𝑛 𝑒𝑒𝑒𝑒 ∑𝑛𝑛𝑛𝑛𝑖𝑖𝑖𝑖=1(𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖 − 𝑒𝑒𝑒𝑒�) 𝑖𝑖𝑖𝑖=1 𝑖𝑖𝑖𝑖 𝚤𝚤𝚤𝚤 𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛

16.8 11.7

8.17 1.65

MAE (%) ∑𝑛𝑛𝑛𝑛𝑖𝑖𝑖𝑖=1|𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖 | 𝑛𝑛𝑛𝑛 10.5 6.2



M. Boegli et al. / Energy Procedia 122 (2017) 133–138 M. Boegli and Y. Stauffer / Energy Procedia 00 (2017) 000–000

SVR +20% noise & +25 % bias SVR +20% noise & -20% bias SVR +20% noise (no bias) SVR without noise nor bias

10.5 8.72 7.24 5.42

9.70 7.90 7.18 5.38

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4.08 3.68 0.94 0.72

5.56 5.07 3.87 2.79

The PM benchmark shows a RMSE of 18.7, while with the SVR algorithm with an optimal irradiance forecast the RMSE drops to 5.42 %. In case of less accurate irradiance forecast, the error metric spans in between these two values. Note that the forecast error based on the irradiance with extra bias is reflected in its higher MBE metric (3.6 to 4%). In addition, Taylor diagram [8] offers a way of visually summarizing how closely a pattern matches observation. The similarity between two patterns (i.e. forecast and observation) is quantified in term of their correlation coefficient 𝜌𝜌𝜌𝜌, their centered root mean square deviation (𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅) and their standard deviation 𝜎𝜎𝜎𝜎for and 𝜎𝜎𝜎𝜎obs . These metrics are defined as: for 2 2 𝑁𝑁𝑁𝑁 − ����� 𝑥𝑥𝑥𝑥𝚤𝚤𝚤𝚤for ��𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖obs − ������ 𝑥𝑥𝑥𝑥𝚤𝚤𝚤𝚤obs � + 𝜎𝜎𝜎𝜎obs − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅2 𝑁𝑁𝑁𝑁1 ∑𝑁𝑁𝑁𝑁 𝜎𝜎𝜎𝜎for 2 𝑖𝑖𝑖𝑖=1�𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖 1 = 𝜎𝜎𝜎𝜎for = �𝑁𝑁𝑁𝑁 � �𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖for − ����� 𝑥𝑥𝑥𝑥𝚤𝚤𝚤𝚤for � 𝜌𝜌𝜌𝜌 = 2𝜎𝜎𝜎𝜎for 𝜎𝜎𝜎𝜎obs 𝜎𝜎𝜎𝜎for 𝜎𝜎𝜎𝜎obs 𝑖𝑖𝑖𝑖=1 𝑁𝑁𝑁𝑁

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2 �𝑥𝑥𝑥𝑥𝑖𝑖𝑖𝑖obs − ������ 𝑥𝑥𝑥𝑥𝚤𝚤𝚤𝚤obs �

All these metrics are further normalized by 𝜎𝜎𝜎𝜎obs so that the normalized observed power (reference) has the following values : 𝜎𝜎𝜎𝜎obs = 1, 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 0, 𝜌𝜌𝜌𝜌 = 1, to lie on the red point A in the Taylor diagram of Figure 3. Then, the forecast models, including the PM benchmark (point B), the SVR prediction with optimal irradiance forecast (point C) and the SVR prediction with different corrupted irradiance forecasts (points D to G) are spatially represented in this Taylor diagram.

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Figure 3 – Taylor diagram for different PV power estimations (red dots): PM benchmark and SVR with corrupted or optimal irradiance forecast. The blue dashed-dotted lines indicate the correlation coefficient, the dashed green circles cantered around the reference point A represent the cantered root mean square deviation (RMSD) and the dotted grey circles show the normalized standard deviation.

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M. Boegli et al. / Energy Procedia 122 (2017) 133–138 M. Boegli and Y. Stauffer / Energy Procedia 00 (2017) 000–000

We can clearly see that the PM benchmark (B) has the highest RMSD and also the lowest correlation coefficient towards the real observed PV power (A). On the other hand, the SVR algorithm with optimal irradiance forecast (C) is closest to the reference (A). All others (D to G) lie in between. All PV power predictions have a normalized standard deviation around unity, excepted the two predictions with biased irradiance forecast (F and G). 4. Conclusion Renewable production when coupled to electrical energy storage allows to not only reduce the operational costs of households and districts but can also provide additional services to the grid. In order to achieve these goals at an affordable cost, smart control is an enabler. In that context, a MPC based controller that aims at optimally controlling batteries at district level was developed. In order to function properly, the ability of forecasting the various electrical loads and production is mandatory. This latter point was addressed in this article for PV power production and it was shown that support vector regression (SVR) algorithms are well suited for the prediction of PV power. Expected RMSE between 7 to 12% for SVR algorithm with different forecast solar irradiance accuracies are obtained, which is almost twice better compared to the classical persistence model (PM) benchmark. Acknowledgements The work presented here is carried out in the European collaboration project AMBASSADOR (FP7EeB.NMP.2012-1). References [1] T. Mai, R. Wiser, D. Sandor, G. Brinkman, G. Heath, P. Denholm, D. Hostick, N. Darghouth, A. Schlosser et K. Strzepek, «Exploration of High-Penetration Renewable Electricity Futures,» NREL/TP-6A20-52409-1, Golden, CO, 2012. [2] A. Hirtenstein, «Batteries Storing Power Seen as Big as Rooftop Solar in 12 Years,» 13 June 2016. [En ligne]. Available: https://www.bloomberg.com/news/articles/2016-06-13/batteries-storing-power-seen-as-big-as-rooftop-solar-in-12-years. [Accès le April 2017]. [3] «www.meteosuisse.admin.ch,» 2017. [En ligne]. [4] «www.solarwebservices.ch,» 2017. [En ligne]. [5] J. Antonanzas, N. Osorio, R. Escobar, R. Urraca, F.J. Martinez-de-Pison, F. Antonanzas-Torres, «Review of photovoltaic power forecasting,» Solar Energy, vol. 136, pp. 78-111, 2016. [6] S. Arberet, Y. Stauffer, M. Boegli et E. Onillon, «Centralized energy optimization at district level,» chez EnergyCon 2016, Leuven, 2016. [7] K. De Brabanter, J. A. K. Suykens et B. De Moor, «Nonparametric Regression via StatLSSVM,» Journal of Statistical Software, vol. 55(2), pp. 1-21, 2013. [8] A. J. Smola et B. Schoelkopf, «A tutorial on Support Vector Regression,» Statistics and Computing, vol. 14, pp. 199-222, 2004. [9] M. Espinoza, J. A. K. Suykens, R. Belmans et B. De Moor, «Electric Load Forecasting using Kernel-based Modeling for Nonlinear System Identification,» IEEE Control Systems, vol. 27(5), pp. 43-57, 2007. [10] M. Pierro, F. Bucci, M. De Felice, E. Maggioni, D. Moser, A. Perotto, F. Spada et C. Cornaro, «Multi-Model Ensemble for day ahead prediction of photovoltaic power generation,» Solar Energy, vol. 134, pp. 132-146, 2016. [11] K. E. Taylor, «Summarizing multiple aspects of model performance in a single diagram,» Journal of Geophysical Research, vol. 106, pp. 7183-7192, 2001.