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To mitigate the effects of the intermittent generation of renewable energy sources, reliable and efficient energy storage is critical. Since nearly 80% of households energy consumption is destined to water and space heating, thermal energy storage is particularly important. In this context, we propose and validate a new model for one of the most efficient heat storage systems: stratified thermal storage tanks. The novelty of the model is twofold: first, unlike the non-smooth models from the literature, it identifies the mixing and buoyancy dynamics using a smooth and continuous function. This smoothness property is critical to efficiently integrate thermal storage vessels in optimization and control problems. Second, unlike models from literature, it considers two types of buoyancy: slow, linked to naturally occurring buoyancy, and fast, associated with charging/discharging effects. As we show, this distinction is paramount to identify accurate models. To show the relevance of the model, we consider a real tank that can satisfy heat demands up to 100 kW. Using real data from this vessel, we validate the proposed model and show that the estimated parameters correctly identify the physical properties of the vessel. Then, we employ the model in a control problem where the vessel is operated to minimize the cost of providing a given heat demand and we compare the model performance against that of a non-smooth model from literature. We show that: (1)the smooth model obtains the best optimal solutions; (2)its computation costs are 100 times cheaper; (3)it is the best alternative for use in real-time model- based control strategies, e.g. model predictive control., Team DeSchutter, Delft Center for Systems and Control

To mitigate the effects of the intermittent generation of renewable energy sources, reliable and efficient energy storage is critical. Since nearly 80% of households energy consumption is destined to water and space heating, thermal energy storage is particularly important. In this context, we propose and validate a new model for one of the most efficient heat storage systems: stratified thermal storage tanks. The novelty of the model is twofold: first, unlike the non-smooth models from the literature, it identifies the mixing and buoyancy dynamics using a smooth and continuous function. This smoothness property is critical to efficiently integrate thermal storage vessels in optimization and control problems. Second, unlike models from literature, it considers two types of buoyancy: slow, linked to naturally occurring buoyancy, and fast, associated with charging/discharging effects. As we show, this distinction is paramount to identify accurate models. To show the relevance of the model, we consider a real tank that can satisfy heat demands up to 100 kW. Using real data from this vessel, we validate the proposed model and show that the estimated parameters correctly identify the physical properties of the vessel. Then, we employ the model in a control problem where the vessel is operated to minimize the cost of providing a given heat demand and we compare the model performance against that of a non-smooth model from literature. We show that: (1)the smooth model obtains the best optimal solutions; (2)its computation costs are 100 times cheaper; (3)it is the best alternative for use in real-time model- based control strategies, e.g. model predictive control., Team Bart De Schutter, Delft Center for Systems and Control

Due to the increasing integration of solar power into the electrical grid, forecasting short-term solar irradiance has become key for many applications, e.g.~operational planning, power purchases, reserve activation, etc. In this context, as solar generators are geographically dispersed and ground measurements are not always easy to obtain, it is very important to have general models that can predict solar irradiance without the need of local data. In this paper, a model that can perform short-term forecasting of solar irradiance in any general location without the need of ground measurements is proposed. To do so, the model considers satellite-based measurements and weather-based forecasts, and employs a deep neural network structure that is able to generalize across locations; particularly, the network is trained only using a small subset of sites where ground data is available, and the model is able to generalize to a much larger number of locations where ground data does not exist. As a case study, 25 locations in The Netherlands are considered and the proposed model is compared against four local models that are individually trained for each location using ground measurements. Despite the general nature of the model, it is shown show that the proposed model is equal or better than the local models: when comparing the average performance across all the locations and prediction horizons, the proposed model obtains a 31.31% rRMSE (relative root mean square error) while the best local model achieves a 32.01% rRMSE.

In recent years, as the share of solar power in the electrical grid has been increasing, accurate methods for forecasting solar irradiance have become necessary to manage the electrical grid. More specifically, as solar generators are geographically dispersed, it is very important to have general models that can predict solar irradiance without the need of ground data. In this paper, we propose a novel technique that can accomplish that: using satellite images, the proposed model is able to forecast solar irradiance without the need of ground measurements. To illustrate the performance of the proposed model, we consider 15 locations in The Netherlands, and we show that the proposed model is as accurate as local models that are individually trained with ground data., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team DeSchutter, Delft Center for Systems and Control

Due to the increasing integration of solar power into the electrical grid, forecasting short-term solar irradiance has become key for many applications, e.g. operational planning, power purchases, reserve activation, etc. In this context, as solar generators are geographically dispersed and ground measurements are not always easy to obtain, it is very important to have general models that can predict solar irradiance without the need of local data. In this paper, a model that can perform short-term forecasting of solar irradiance in any general location without the need of ground measurements is proposed. To do so, the model considers satellite-based measurements and weather-based forecasts, and employs a deep neural network structure that is able to generalize across locations; particularly, the network is trained only using a small subset of sites where ground data is available, and the model is able to generalize to a much larger number of locations where ground data does not exist. As a case study, 25 locations in The Netherlands are considered and the proposed model is compared against four local models that are individually trained for each location using ground measurements. Despite the general nature of the model, it is shown show that the proposed model is equal or better than the local models: when comparing the average performance across all the locations and prediction horizons, the proposed model obtains a 31.31% rRMSE (relative root mean square error) while the best local model achieves a 32.01% rRMSE., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team DeSchutter

In this paper, a novel modeling framework for forecasting electricity prices is proposed. While many predictive models have been already proposed to perform this task, the area of deep learning algorithms remains yet unexplored. To fill this scientific gap, we propose four different deep learning models for predicting electricity prices and we show how they lead to improvements in predictive accuracy. In addition, we also consider that, despite the large number of proposed methods for predicting electricity prices, an extensive benchmark is still missing. To tackle that, we compare and analyze the accuracy of 27 common approaches for electricity price forecasting. Based on the benchmark results, we show how the proposed deep learning models outperform the state-of-the-art methods and obtain results that are statistically significant. Finally, using the same results, we also show that: (i) machine learning methods yield, in general, a better accuracy than statistical models; (ii) moving average terms do not improve the predictive accuracy; (iii) hybrid models do not outperform their simpler counterparts., Erratum: https://doi.org/10.1016/j.apenergy.2018.06.131, Team DeSchutter

Motivated by the increasing integration among electricity markets, in this paper we propose two different methods to incorporate market integration in electricity price forecasting and to improve the predictive performance. First, we propose a deep neural network that considers features from connected markets to improve the predictive accuracy in a local market. To measure the importance of these features, we propose a novel feature selection algorithm that, by using Bayesian optimization and functional analysis of variance, evaluates the effect of the features on the algorithm performance. In addition, using market integration, we propose a second model that, by simultaneously predicting prices from two markets, improves the forecasting accuracy even further. As a case study, we consider the electricity market in Belgium and the improvements in forecasting accuracy when using various French electricity features. We show that the two proposed models lead to improvements that are statistically significant. Particularly, due to market integration, the predictive accuracy is improved from 15.7% to 12.5% sMAPE (symmetric mean absolute percentage error). In addition, we show that the proposed feature selection algorithm is able to perform a correct assessment, i.e. to discard the irrelevant features., Accepted Author Manuscript, Team DeSchutter

In recent years, as the share of solar power in the electrical grid has been increasing, accurate methods for forecasting solar irradiance have become necessary to manage the electrical grid. More specifically, as solar generators are geographically dispersed, it is very important to have general models that can predict solar irradiance without the need of ground data. In this paper, we propose a novel technique that can accomplish that: using satellite images, the proposed model is able to forecast solar irradiance without the need of ground measurements. To illustrate the performance of the proposed model, we consider 15 locations in The Netherlands, and we show that the proposed model is as accurate as local models that are individually trained with ground data., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Bart De Schutter, Delft Center for Systems and Control

In this paper, a novel modeling framework for forecasting electricity prices is proposed. While many predictive models have been already proposed to perform this task, the area of deep learning algorithms remains yet unexplored. To fill this scientific gap, we propose four different deep learning models for predicting electricity prices and we show how they lead to improvements in predictive accuracy. In addition, we also consider that, despite the large number of proposed methods for predicting electricity prices, an extensive benchmark is still missing. To tackle that, we compare and analyze the accuracy of 27 common approaches for electricity price forecasting. Based on the benchmark results, we show how the proposed deep learning models outperform the state-of-the-art methods and obtain results that are statistically significant. Finally, using the same results, we also show that: (i) machine learning methods yield, in general, a better accuracy than statistical models; (ii) moving average terms do not improve the predictive accuracy; (iii) hybrid models do not outperform their simpler counterparts., Erratum: https://doi.org/10.1016/j.apenergy.2018.06.131, Team Bart De Schutter

Due to the increasing integration of solar power into the electrical grid, forecasting short-term solar irradiance has become key for many applications, e.g. operational planning, power purchases, reserve activation, etc. In this context, as solar generators are geographically dispersed and ground measurements are not always easy to obtain, it is very important to have general models that can predict solar irradiance without the need of local data. In this paper, a model that can perform short-term forecasting of solar irradiance in any general location without the need of ground measurements is proposed. To do so, the model considers satellite-based measurements and weather-based forecasts, and employs a deep neural network structure that is able to generalize across locations; particularly, the network is trained only using a small subset of sites where ground data is available, and the model is able to generalize to a much larger number of locations where ground data does not exist. As a case study, 25 locations in The Netherlands are considered and the proposed model is compared against four local models that are individually trained for each location using ground measurements. Despite the general nature of the model, it is shown show that the proposed model is equal or better than the local models: when comparing the average performance across all the locations and prediction horizons, the proposed model obtains a 31.31% rRMSE (relative root mean square error) while the best local model achieves a 32.01% rRMSE., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Bart De Schutter

Motivated by the increasing integration among electricity markets, in this paper we propose two different methods to incorporate market integration in electricity price forecasting and to improve the predictive performance. First, we propose a deep neural network that considers features from connected markets to improve the predictive accuracy in a local market. To measure the importance of these features, we propose a novel feature selection algorithm that, by using Bayesian optimization and functional analysis of variance, evaluates the effect of the features on the algorithm performance. In addition, using market integration, we propose a second model that, by simultaneously predicting prices from two markets, improves the forecasting accuracy even further. As a case study, we consider the electricity market in Belgium and the improvements in forecasting accuracy when using various French electricity features. We show that the two proposed models lead to improvements that are statistically significant. Particularly, due to market integration, the predictive accuracy is improved from 15.7% to 12.5% sMAPE (symmetric mean absolute percentage error). In addition, we show that the proposed feature selection algorithm is able to perform a correct assessment, i.e. to discard the irrelevant features., Accepted Author Manuscript, Team Bart De Schutter

Motivated by the increasing integration among electricity markets, in this paper we propose two different methods to incorporate market integration in electricity price forecasting and to improve the predictive performance. First, we propose a deep neural network that considers features from connected markets to improve the predictive accuracy in a local market. To measure the importance of these features, we propose a novel feature selection algorithm that, by using Bayesian optimization and functional analysis of variance, evaluates the effect of the features on the algorithm performance. In addition, using market integration, we propose a second model that, by simultaneously predicting prices from two markets, improves the forecasting accuracy even further. As a case study, we consider the electricity market in Belgium and the improvements in forecasting accuracy when using various French electricity features. We show that the two proposed models lead to improvements that are statistically significant. Particularly, due to market integration, the predictive accuracy is improved from 15.7% to 12.5% sMAPE (symmetric mean absolute percentage error). In addition, we show that the proposed feature selection algorithm is able to perform a correct assessment, i.e. to discard the irrelevant features.

This report evidences factors controlling soil organic carbon at the national scale by modelling data of 2,158 soil samples from France. The global soil carbon amount, of about 1,500 Gt C, is approximately twice the amount of atmosphere C. Therefore, soil has major impact on atmospheric CO2, and, in turn, climate change. Soil organic carbon further controls many soil properties such as fertility, water retention and aggregate stability. Nonetheless, precise mechanisms ruling interactions between soil organic carbon and environmental factors are not well known at the large scale. Indeed, most soil investigations have been conducted at the plot scale using a limited number of factors. Therefore, a national soil survey of 2,158 soil samples from France was carried out to measure soil properties such as texture, organic carbon, nitrogen and heavy metal content. Here, we studied factors controlling soil organic carbon at the national scale using a model based on stepwise linear regression. Factors analysed were land use, soil texture, rock fragment content, climate and land management. We used several criteria for model selection, such as the Akaike information criterion (AIC), the corrected AIC rule and the Bayesian information criterion. Results show that organic carbon concentrations in fine earth increase with increasing rock fragment content, depending on land use and texture. Spreading farmyard manure and slurry induces higher carbon concentrations mostly in wet and stony grasslands. Nonetheless, a negative correlation has been found between carbon and direct C input from animal excrements on grasslands. Our findings will therefore help to define better land management practices to sequester soil carbon. © INRA and Springer-Verlag, France 2012.

For any quantitative data interpretation it is crucial to have information about the noise variances. Unfortunately, this information is often unavailable a priori. We propose a procedure to estimate the noise variances starting from the residuals. The method takes two difficulties into account. (i) The noise can be heteroscedastic (not constant over the measurement domain). This implies that one number is not enough anymore to characterise the total noise variance structure. (ii) The initial model used to generate the residuals may be imperfect. As a consequence, the residuals contain more than only stochastic information. The outcome of our procedure is an estimate of the noise variances which depends on the sample number, but is independent of the postulated model. A by-product of the procedure is information about the distribution of the degrees of freedom over the measurement domain. Indeed, as a consequence of the heteroscedastic noise, the model parameters will be fitted more to those data with low uncertainty and most of the degrees of freedom are lost at these locations.

The time base reconstruction method proposed by Wilkinson and Ivany [Paleoclimatic inference from stable isotope profiles of accretionary biogenic hardparts - a quantitative approach to the evaluation of incomplete data. Palaeogeogr. Palaeocl. Palaeoecol. 185 (2002), 95-114] can be further refined. They have shown that variations in accretion rate can be reconstructed from variations in the period of the measured signal. Here, it is shown that such variations influence not only the period, but also the phase of the signal. So, a refined estimator for the time base is constructed, which takes both period and phase variations into account.

An empirical method to reconstruct distributions of mixing water masses is developed and applied to two Southern Ocean ( Australian sector) data sets. The method is a parametric extension of the well-known Optimum Multiparameter (OMP) analysis, therefore called POMP ( parametric OMP). The main development consists of parameterizing the mixing fractions as a function of position ( e. g. latitude and depth) and estimating the parameters of the resulting function, instead of estimating the mixing fractions for every sampling point individually. Because this enables to reduce the total number of unknowns to be estimated, the proposed adjustments result in more robust estimates of the mixing fractions, as illustrated on the Southern Ocean CLIVAR-SR3 data set ( early spring 2001). An additional consequence of the new working scheme is that the mixing distributions are smoothed. It is emphasized that the degree of smoothing should be chosen with care in order not to neglect any significant features. Statistical rules to do this are applied. Application of the POMP method to the second Southern Ocean data set (SAZ' 98, summer 1998) revealed the importance of a careful selection of the mixing source water types. This study was limited to the subantarctic region and upper 1000 m, where variations in water mass characteristics and distributions are most important. Indeed, it seems necessary to redefine the source water characteristics for each data set. The direction of these changes suggests that interannual variability or long term changes of water masses overwhelm the seasonal variability.

The problem of estimating parameters and their uncertainty from experimental measurements in marine ecosystems is a common task and often necessitates solving nonlinear equations. If the measurements are subject to individually varying errors (i.e., heteroscedastic data), the parameters are often estimated using a Weighted Least Squares (WLS) method. For estimating the parameter uncertainties, a linearized expression for the covariance matrix exists. Yet, both methods assume that the errors on the independent variable, also called "input", is negligible, which is often not true. For instance, in order to determine uptake and regeneration rates of silicic acid by phytoplankton, concentration and isotopic abundance measurements are performed at the beginning (input) and at the end (output) of an incubation experiment. Here, the so-called input and output are measurements of the same quantities, i.e., determined in exactly the same way, only differing by the time at which the measurements were performed. Clearly, there is no reason to assume that the input measurements are subject to less error than the output measurements. We propose a refinement of the two abovementioned estimation methods which enlarges their applicability to cases where input noise is not negligible. The refined methods are evaluated on the uptake and regeneration processes of silicic acid and compared to the original procedures using Monte-Carlo simulations. The results reveal a smaller bias for the refined WLS estimator compared with the original one. An additional advantage of using the refined WLS cost function is that its residual value can be interpreted as a sample from a chi(2) distribution. This property is especially useful because it enables an internal quality control of the results. In addition, the parameter uncertainty estimation is significantly improved. By neglecting the effect of the input noise, a (potentially) important origin of the parameter variation is simply ignored. There