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Optimal Control Strategies for Seasonal Thermal Energy Storage Systems With Market Interaction

Journal Paper
Jesus Lago, Gowri Suryanarayana, Ecem Sogancioglu, Bart De Schutter
IEEE Transactions on Control Systems Technology, Early Access, September 2020

Seasonal thermal energy storage systems (STESSs) can shift the delivery of renewable energy sources and mitigate their uncertainty problems. However, to maximize the operational profit of STESSs and ensure their long-term profitability, control strategies that allow them to trade on wholesale electricity markets are required. While control strategies for STESSs have been proposed before, none of them addressed electricity market interaction and trading. In particular, due to the seasonal nature of STESSs, accounting for the long-term uncertainty in electricity prices has been very challenging. In this article, we develop the first control algorithms to control STESSs when interacting with different wholesale electricity markets. As different control solutions have different merits, we propose solutions based on model predictive control and solutions based on reinforcement learning. We show that this is critical since different markets require different control strategies: MPC strategies are better for day-ahead markets due to the flexibility of MPC, whereas reinforcement learning (RL) strategies are better for real-time markets because of fast computation times and better risk modeling. To study the proposed algorithms in a real-life setup, we consider a real STESS interacting with the day-ahead and imbalance markets in The Netherlands and Belgium. Based on the obtained results, we show that: 1) the developed controllers successfully maximize the profits of STESSs due to market trading and 2) the developed control strategies make STESSs important players in the energy transition: by optimally controlling STESSs and reacting to imbalances, STESSs help to reduce grid imbalances.

Incentivizing renewables and reducing grid imbalances through market interaction

PhD Thesis
Jesus Lago

Building day-ahead bidding functions for seasonal storage systems: A reinforcement learning approach

Conference paper
Jesus Lago, Ecem Sogancioglu, Gowri Suryanarayana, Fjo De Ridder, Bart De Schutter
Proceedings of the 2019 IFAC Worshop on Control of Smart Grids and Renewable Energy Systems (CSGRES)

Due to the increasing integration of renewable sources in the electrical grid, electricity generation is expected to become more uncertain. In this context, seasonal thermal energy storage systems (STESSs) are key to shift the delivery of renewable energy sources and tackle their uncertainty problems. In this paper, we propose an optimal controller for STESSs that, using reinforcement learning, builds bidding functions for the day-ahead market. In detail, considering that there is an uncertain energy demand that the STESS has to satisfy, the controller buys energy in the day-ahead market so that the uncertain demand is satisfied while the profits are maximized. Since prices are low during periods of large renewable energy generation (and vice versa), maximizing the profit of a STESS indirectly shifts the delivery of renewable energy to periods of high energy demand while reducing their uncertainty problems. To evaluate the proposed algorithm, we consider a real STESS providing different yearly-demand levels; then, we compare the performance of the controller to the theoretical upper bound, i.e. the optimal cost of buying energy given perfect knowledge of the demand and prices. The results indicate that the proposed controller performs reasonably well: despite the large uncertainty in prices and demand, the proposed controller obtains 70%-50% of the maximum gains given by the theoretical bound.

Effect of market design on strategic bidding behavior: Model-based analysis of European electricity balancing markets

Journal Paper
Ksenia Poplavskaya, Jesus Lago, Laurens De Vries
Applied Energy, Volume 270, Pages 115130, July 2020

Market-based procurement of balancing services in Europe is prone to strategic bidding due to the relatively small market size and a limited number of providers. In the European Union, balancing markets are undergoing substantial regulatory changes driven the efforts to harmonize the market design and better align it with the goals of the energy transition. It is proposed to decouple the balancing energy (real-time) market from the (forward) balancing capacity market and the price of balancing energy will be based on the marginal bid. In this paper, the potential effects of these changes on market participants’ strategies are analyzed using an agent-based model. This model compares the effects of a standalone balancing energy market with different pricing rules on economic efficiency with agents that apply naïve, rule-based and reinforcement-learning strategies. The results indicate that the introduction of a standalone balancing energy market reduces the cost of balancing, even in a concentrated market with strategic bidders. Marginal pricing consistently leads to lower weighted average prices than pay-as-bid pricing, regardless of the level of competition. Nevertheless, in an oligopoly with actors bidding strategically, prices can deviate from the competitive benchmark by a factor of 4–5. This implies that the introduction of a standalone balancing energy market does not entirely solve the issue of strategic bidding, but helps dampen the prices, as compared to the balancing market prior to the design change.

A generalizable and sensor-independent deep learning method for fault detection and location in low-voltage distribution grids

Journal Paper
Nikolaos Sapountzoglou, Jesus Lago, Bart De Schutter, Bertrand Raison
Applied Energy, Volume 276, Pages 115299, October 2020

Power outages in electrical grids can have very negative economic and societal impacts rendering fault diagnosis paramount to their secure and reliable operation. In this paper, deep neural networks are proposed for fault detection and location in low-voltage smart distribution grids. Due to its key properties, the proposed method solves some of the drawbacks of the existing literature methods, namely a method that: 1) is not limited by the grid topology; 2) is branch-independent; 3) can localize faults even with limited data; 4) is the first to accurately detect and localize high-impedance faults in the low-voltage distribution grid. The generalizability of the method derives from the non-grid specific nature of the inputs that it requires, inputs that can be obtained from any grid. To evaluate the proposed method, a real low-voltage distribution grid in Portugal is considered and the robustness of the method is tested against several disturbances including large fault resistance values (up to 1000 ). Based on the case study, it is shown that the proposed methodology outperforms conventional fault diagnosis methods: it detects faults with 100% accuracy, identifies faulty branches with 83.5% accuracy, and estimates the exact fault location with an average error of less than 11.8%. Finally, it is also shown that: 1) even when reducing the available measurements to the bare minimum, the accuracy of the proposed method is only decreased by 4.5%; 2) while deep neural networks usually require large amounts of data, the proposed model is accurate even for small dataset sizes.

A 1-dimensional continuous and smooth model for thermally stratified storage tanks including mixing and buoyancy

Journal Paper
Jesus Lago, Fjo De Ridder, Wiet Mazairac, Bart De Schutter
Applied Energy, Volume 248, Pages 640-655, August 2019.

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.

Fault diagnosis in low voltage smart distribution grids using gradient boosting trees

Journal Paper
Nikolaos Sapountzoglou, Jesus Lago, Bertrand Raison
Electric Power Systems Research, Volume 182, Pages 106254, May 2020

In this paper, a gradient boosting tree model is proposed to detect, identify and localize single-phase-to-ground and three-phase faults in low voltage (LV) smart distribution grids. The proposed method is based on gradient boosting trees and considers branch-independent input features to be generalizable and applicable to different grid topologies. Particularly, as it is shown, the method can be estimated in a specific grid topology and be employed in a different one. To test the algorithm, the method is evaluated in a simulated real LV distribution grid of Portugal. In this case study, different fault resistances, fault locations and hours of the day are considered. In detail, the algorithm is evaluated at eighteen fault resistance values between 0.1 and 1000 ; similarly, nine fault locations are considered within each one of the 32 sectors of the grid and the faults are simulated across different hours of a day. The developed algorithm showed promising results in both out-of-sample branch and fault resistance data especially for fault detection, demonstrating a maximum fault detection error of 0.72%.

Short-term forecasting of solar irradiance without local telemetry: A generalized model using satellite data

Journal Paper
Jesus Lago, Karel De Brabandere, Fjo De Ridder, Bart De Schutter
Solar Energy, Volume 173, Pages 566-577, October 2018.

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.

Warping model predictive control for application in control of a real airborne wind energy system

Journal Paper
Jesus Lago, Michael Erhard, Moritz Diehl
Control Engineering Practice, Volume 78, Pages 65-78, September 2018

Fast online generation of feasible and optimal reference trajectories is crucial in tracking model predictive control, especially for stability and optimality in presence of a time varying parameter. In this paper, in order to circumvent the operational efforts of handling a discrete set of precomputed trajectories and switching between them, time warping of a single trajectory is proposed as an alternative concept. In particular, the conceptual ideas of warping theory are presented and illustrated based on the example of a tethered kite system for airborne wind energy. In detail, for warpable systems, feasibility and optimality of trajectories are discussed. Subsequently, the full algorithm of a nonlinear model predictive control implementation based on warping a single precomputed reference is presented. Finally, the warping algorithm is applied to the airborne wind energy system. Simulation results in presence of real world perturbations are evaluated and compared.

Scenario-based Model Predictive Control Approach for Heating Systems in an Office Building

Conference paper
Tomas Pippia, Jesus Lago, Roel De Coninck, Joris Sijs, Bart De Schutter
Proceedings of the 2019 IEEE 15th International Conference on Automation Science and Engineering (CASE)

In the context of building heating systems control in office buildings, the current state-of-the-art applies either a deterministic Model Predictive Control (MPC) controller together with a nonlinear model, or a linearized model with a stochastic MPC controller. Deterministic MPC considers only one realization of the external disturbances, which can lead to a low performance solution if the forecasts of the disturbances are not accurate. Similarly, linear models are simplified representations of the building dynamics and might fail to capture some relevant behavior. In this paper, we improve upon the current literature by combining these two approaches, i.e. we adopt a nonlinear model together with a stochastic MPC controller. We consider a scenario-based MPC (SBMPC), where many realizations of the disturbances are considered, so as to include more possible future trajectories for the external disturbances. The adopted scenario generation method provides statistically significant scenarios, whereas so far in the current literature only approximate methods have been applied. Moreover, we use Modelica to obtain the model description, which allows to have a more accurate and nonlinear model. Lastly, we perform simulations comparing standard MPC vs SBMPC vs an optimal control approach with measurements of the external disturbances, and we show how our proposed scenario-based MPC controller can achieve a better performance compared to standard deterministic MPC.

Forecasting spot electricity prices: Deep learning approaches and empirical comparison of traditional algorithms

Journal Paper
Jesus Lago, Fjo De Ridder, Bart De Schutter
Applied Energy, Volume 221, Pages 386–405, July 2018.

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.

Forecasting day-ahead electricity prices in Europe: the importance of considering market integration

Journal Paper
Jesus Lago, Fjo De Ridder, Peter Vrancx, Bart De Schutter
Applied Energy, Volume 211, Pages 890-903, February 2018.

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.

A probabilistic approach to allocate building parameters within district energy simulations

Conference paper
Ina De Jaeger, Jesus Lago, Dirk Saelens
Proceedings of the 2018 Urban Energy Simulation (uSIM) Conference

Urban building energy models (UBEMs) are expected to play a key role in the integrated assessment of sustainability measures on both district and city level. However, due to limited availability of data sources, those models are often created through an archetype approach, which is a deterministic method to allocate building envelope characteristics to building groups. Unfortunately, this deterministic approach may underestimate the variability of the existing building stock, which is important when designing district energy systems to optimise the location of production and storage units within the system. In contrast to the deterministic approach, this work presents a new probabilistic approach to allocate building envelope characteristics within UBEMs that in combination with stochastic occupants enables to include the variability of existing districts. A thorough comparison of the deterministic and the probabilistic method is established for 820 buildings of the Boxbergheide district in Genk by performing dynamic energy simulations in the IDEAS Modelica library. For the studied district, a probabilistic building envelope characterisation with standard occupants increases the coefficient of variation (CV) on the energy demand for space heating, compared to a deterministic approach with standard occupants, from 17.8% to 46.4%. Including a probabilistic building envelope characterisation increases the variability on the energy demand for space heating to a larger extent than including stochastic occupants, which increases the CV to only 29.6%.

Thermal load forecasting in district heating networks using deep learning and advanced feature selection methods

Journal Paper
Gowri Suryanarayana, Jesus Lago, Davy Geysen, Piotr Aleksiejuke, Christian Johansson
Energy, Volume 157, Pages 141-149, August 2018

Recent research has seen several forecasting methods being applied for heat load forecasting of district heating networks. This paper presents two methods that gain significant improvements compared to the previous works. First, an automated way of handling non-linear dependencies in linear models is presented. In this context, the paper implements a new method for feature selection based on [1], resulting in computationally efficient models with higher accuracies. The three main models used here are linear, ridge, and lasso regression. In the second approach, a deep learning method is presented. Although computationally more intensive, the deep learning model provides higher accuracy than the linear models with automated feature selection. Finally, we compare and contrast the proposed methods with earlier work for day-ahead forecasting of heat load in two different district heating networks.

Warping NMPC for Online Generation and Tracking of Optimal Trajectories

Conference paper
Jesus Lago, Michael Erhard, Moritz Diehl
Proceedings of the 2017 World Congress of the International Federation of Automatic Control

Generation of feasible and optimal reference trajectories is crucial in tracking Nonlinear Model Predictive Control. Especially, for stability and optimality in presence of a time varying parameter, adaptation of the tracking trajectory has to be implemented. General approaches are real-time generation of trajectories or switching between a discrete set of precomputed trajectories. In order to circumvent the operational efforts of these methods for a special type of dynamical systems, we propose time warping as an alternative approach. This algorithm implements online generation of tracking trajectories by warping a single precomputed reference. In detail, warpable systems, feasibility and optimality of trajectories and the controller implementation are discussed. Finally, as an application example, simulation results of a tethered kite system for airborne wind energy generation are presented.

From Consumption to Prosumption - Operational Cost Optimization for Refrigeration System With Heat Waste Recovery.

Conference paper
Tomasz Minko, Jesus Lago, Jan Dimon Bendtsen, Rafael Wisniewski, Roozbeh Izadi-Zamanabadi
Proceedings of the 2017 World Congress of the International Federation of Automatic Control

Carbon dioxide based refrigeration systems are considered to have a particularly high potential for becoming efficient heat energy producers. In this paper, a carbon dioxide system that operates in the subcritical region is examined. The modelling approach is presented, and used for operation optimisation by way of non-linear model predictive control techniques. Assuming that the heat is sold, it turns out that the system has negative operational cost. Depending on the choice of objective function, daily revenue can vary from about 7.9 [eur] to 11.9 [eur].

A quadratically convergent primal decomposition algorithm with soft coupling for nonlinear parameter estimation

Conference paper
Dimitris Kouzoupis, Rien Quirynen, Jesus Lago, Michael Erhard, Moritz Diehl
Proceedings of the 2016 IEEE Conference on Decision and Control (CDC)
Distributed algorithms for sparse, large-scale optimization problems are preferable over centralized solvers whenthe computational units are physically far apart from each other or the problem size is too large for the available memory. However, most distributed methods sacrifice convergence speed for simpler computations. In this paper, we propose a novel algorithm for a certain class of nonconvex, separable optimization problems that combines both distributed computations and locally quadratic convergence. It is based on the principle of primal decomposition with exact Hessian information but uses soft coupling between the agents to avoid global calculations and adapt faster to online data changes. An important application field of the presented method is nonlinear parameter estimation, where increasing the number of experiments may lead to problem dimensions that are prohibitive for conventional solvers. We assess the performance of our method on the identification of an Airborne Wind Energy (AWE) system using real-world experimental data.

Periodic Optimal Control and Model Predictive Control Of a Tethered Kite for Airbone Wind Energy

Master's thesis
Jesus Lago Garcia
Master Thesis, University of Freiburg, June 2016

Classical wind turbines suffer from a significant problem: while their power output scales with the square of the height, the mass does so cubically; as a result, material costs are high and the technology becomes non-competitive. Considering that the bulk of the power is generated by the outer parts of the rotor blades, AWE tries to extract wind power by means of tethered kite or airplanes (“wings”) while avoiding these high material costs. The conceptual idea is to fly these “wings” in a crosswind motion with the help of a strong cable and extract power by means of pumping cycles or small generators on board.

In this context and in collaboration with the company Skysails, this Masters thesis focuses on two research areas: computation of optimal trajectories for energy maximization by means of an OCP and design and implementation of NMPC on a real AWE system.

Using as a basis a previous research on periodic optimal trajectories, this thesis contributes to the field of optimal control and airborne wind energy with a set of four ideas: new safety conditions to augment the extracted power; the study of dynamic invariants within the periodic OCP; a proposed tethered kite model in natural coordinates and a performance comparison between the introduced model, a quaternion parameterization, and a model based on Euler angles; and the generation of different flight topologies to enhance the power efficiency.

Furthermore, in its second research domain, this thesis strengthens the field of airborne wind energy and control theory with the following three contributions: the design of a NMPC scheme on a real AWE system to track generated optimal trajectories; NMPC stability and robustness against real life perturbations such as wind gusts, delays in control inputs, parameter mismatches and realistic estimation errors; and development of the theory of warping systems, a manifold of dynamical systems for which an algorithm to perform online generation of optimal trajectories is proposed.