The energy consumption in buildings become the largest part of energy consumption worldwide, accounting for 40% of total global energy consumption and one third of the green house emission (Ahmed et al., Dec 2021). The optimization of building HVAC system require in many cases a thermodynamic model and mathematical solver which consumes a lot of hardware and time. However the data driven methods that presents 48% are often focusing on one type of HVAC systems (Grassi et al., May 2022). The real engineering problem is that the data driven methods are limited to specific systems and investigated for specific configurations. To overcome this problem, many machine learning solutions for optimized control data for HVAC are proposed. Those solutions are tested for real buildings in Germany. This new controller approach considers the effect of sequential inputs such as weather conditions, internal energy and time, and it consider a historical HVAC optimized data output. The investigation is done for CNN, LSTM, RNN-GRU, RNN-attention, and for each method we try to idealize the hyper-parameters and configurations. The goal of the study is to investigate the accuracy of machine learning routine on building optimization controlling and the ability to learn controlled and optimized data for different systems, to compare difference between generation of single output and multiple outputs, to decide the best inputs prepossessing, and to evaluate the extreme weather effects. This investigation proves that data control solution have limitation especially with extreme weather conditions but it can be improved by working on the pre-processing and different configurations.

For the simulation and optimization of the optical efficiency in a central receiver system, an accurate and fast ray tracer is needed. Within this work, an accurate integration of the bivariate Gaussian distribution for a convolution ray tracer is developed. This new analytical ray tracer can include the effect of multiple solar rays without the need of simulating each ray. To further align our convolution of sun, slope, and tracking error, a new equation is derived that perfectly matches the results obtained by a separate accounting for these errors. Additionally, new approximation methods for sun shapes are developed which are accurately approximated with a Gaussian.The newly integrated convolution ray tracer is developed on the same platform as a bidirectional Monte Carlo ray tracer, and a convolution method. Beside a large cross-validation of the results, this allows for a reasonable direct run-time comparison. With extensive case studies, the quality of the solution, the run time, and various other aspects are investigated. Furthermore, all ray tracers are also implemented on the GPU improving the run time compared to the CPU version by a factor of 50, which leads to simulation times of a few seconds for a whole year.

. Aiming strategies are used to distribute the heat flux on the receiver surface with the aim to maximize the mass flow of the heat transfer fluid in the receiver tubes while avoiding thermal overloading. The optimization problem is modeled as an integer program (IP) to provide deterministic solutions. To improve the runtime, several accelerations are investigated as the grouping of heliostats to reduce the size of the optimization problem. In a case study we show that an optimal solution can be found within seconds while maintaining high accuracy.

An accurate and computationally fast ray-tracer is the key part for the simulation and optimization of the optical irradiation of a heliostat field layout in a solar central receiver system. Within this work we present an analytical ray-tracer which is fast in runtime while obtaining highly accurate results. The runtime improvement is achieved by a faster integration method that does not require a discretization of the receiver. This allows for discretizing the heliostat surface into smaller cells each having a representative flux function to better account for a variety of optical errors. Our new ray-tracer is implemented on the same C++ platform as other existing ray-tracers, such that reasonable cross validation with direct run-time comparisons are possible. Within a case study we demonstrate that the new convolution method decreases the run-time by a factor of 20 compared to HELCal, and a factor of three compared a bidirectional Monte-Carlo ray-tracer, while achieving a stable accuracy of 99.98 %.

Aiming strategies in central receiver systems search for an optimal assignment between heliostats and aim point on the receiver surface. In this work, we develop an accelerated aiming strategy which can be used for dynamic scenarios such as short-term environmental influences. The strategy bases on the linear formulation of the problem. To achieve a performance close to real-time, we present several accelerations based on carefully chosen methods to reduce the problem size. The performance of different solvers is evaluated and the problem reduction is adjusted according to accuracy, prediction time and computational run-time. The accelerated aiming strategy is applied to central receiver systems with up to 8600 heliostats in a dynamic test scenario with cloud shadows passing over the heliostat field. The accelerated aiming strategy is effective enough to be used as a real-time control strategy.

For the optimization of the energy consumption in buildings, a calibrated model is of paramount importance. To calibrate the model, initial value ranges for unknown parameters must be defined which is often done through manual tuning and engineering methods. These values are often inaccurate or not available, thus set arbitrarily. Therefore, in this paper, we examine the possibility of defining thermodynamic value ranges by clustering geometrical building patterns. Two issues are analyzed by the method, building pattern clustering via machine learning and the predictive ability of geometrical clusters. The method involves testing multiple clustering algorithms on features extracted from calibrated commercial buildings. The algorithms are either executed on an untransformed or Box-Cox transformed feature space and then evaluated by their geometrical patterns and U-value ranges. For the assesment of U-value ranges, two new evaluation indices are introduced. The shared nearest neighbor algorithm turns out to be the most promising one for clustering geometrical data, reducing initial U-value ranges by 50% on average. In some applications, it might be undesirable to use the shared nearest neighbor algorithm, as data points are assigned as noise. For these cases a Box-Cox transformation of the data is necessary. Without a transformation, other algorithms were not able to determine any geometrical patterns. The method shows the possibility of determining unique U-value ranges by using geometrical data only. The application of such machine learning approaches enables saving time in determining initial value ranges and further the possibility of accelerating calibrations, as smaller value ranges are used.

A hybrid solar power plant effectively combines the two main advantages of solar power plants: concentrated solar power (CSP) with a cheap thermal storage system and photovoltaic (PV) with cheap electricity production. In a hybrid plant, both systems are coupled with the thermal storage, where an immersion heater can transfer the PV energy into thermal energy. A real-time storage strategy is developed using model predictive control considering the future energy tariff and future weather conditions. The efficiency of the power block is considered as quadratic function in dependency of the bulb temperature. As strategy the optimization problem is formulated as linear program. The methods are tested in a realistic scenario for a hybrid CSP-PV power plant with real weather data and different tariffs. Furthermore, on the basis of the best strategy, the optimal design for CSP, PV and storage size is investigated. In comparison to the state of the art (heuristic) optimization we gain 14 % by using a predictive control strategy in combination with an optimal power plant configuration. We show that the storage strategy not only impacts the achievable plant output but also very strongly the subsystem sizing. It can be seen that the plant configuration is massively influenced by the storage control scheme.

The power produced by an offshore wind farm is subject to multiple uncertainties, such as volatile wind, turbine performance wear, and availability losses. Knowledge about the propagation of these uncertainties and their effect on the produced power is crucial in the design stage of a wind farm. Due to the multitude of uncertainties, an analysis requires high-dimensional numerical integration to determine these parameter sensitivities. Such an analysis has not been done in the current literature for the full set of parameters. In this work, a thorough analysis of all uncertainties is provided, modeled from several years of collected data from the existing wind farms Horns Rev 1, DanTysk, and Sandbank. The analysis reveals four major parameters, allowing the other parameters to be neglected in future measurement data acquisitions and sensitivity analysis processes. Furthermore, the accuracy of several Uncertainty Quantification techniques is analyzed and a recommendation for future analysis is given.

Heliostat field layout optimization bases on simulations of the annual energy production. To reduce the computation time of the optimization process, one can try to reduce the number of simulation points of the annual domain, while keeping similar accuracy. For the temporal domain, there exist already different approaches as aggregation of days. To further reduce the number of needed simulation points, in this paper we decouple the power computation from the irradiation, such that we just regard the computation of the power plant efficiency. This time-dependent parameter is transformed into a celestial coordinate system where the solar angle-dependent efficiency will be approximated using suitable multi-dimensional interpolation methods. We distinguish between an accurate approximation of the received annual optical energy and the electrical energy of each moment of a year. These methods are demonstrated for the existing heliostat field layouts PS10 and Gemasolar in Seville, while using realistic weather conditions. With this new approach just around 40 simulation points suffice to reach an accuracy of 99.9% for the received power for smaller power plants as PSIO, and for larger plants as Gemasolar. Compared to a state-of-the-art method, this investigation helps to accelerate the simulation by factor three.

A central receiver system is a power plant that consists of a receiver mounted atop of a central tower and a field of adjustable mirrors called heliostats. The heliostats concentrate solar radiation onto the receiver where a fluid is heated to produce electricity in a conventional thermodynamic cycle.Aiming strategies are used to assign each heliostat to an individual aim point on the receiver such that a given flux distribution on the receiver surface is reached. As uncertainties in the tracking of the heliostats exist, aiming strategies are applied that use large safety margins to avoid dangerously high flux concentrations on the receiver. This approach leads to an inefficient use of the power plant and thus economical losses. In this paper, we consider advanced methods to include these uncertainties into the design of efficient aiming strategies. To this end, we present a mixed-integer linear programming (MILP) formulation for the optimization of aiming strategies based on Γ-robustness.In a case study, we show that the Γ-robust optimization approach yields solutions with strong objective values and thus economical benefits while maintaining a high degree of safety. Compared to non-robust solutions, the Γ-robust solutions achieve better objective values while guaranteeing the same safety.

A concentrated solar tower power plant consists of a receiver mounted atop of a central tower and a field of movable mirrors called heliostats. The heliostats concentrate solar radiation onto the receiver where a fluid is heated to produce electricity in a conventional thermodynamic cycle. Aiming strategies are used to assign each heliostat to an individual aim point on the receiver such that a given flux distribution on the receiver surface is reached. As uncertainties in the tracking of the heliostats exist, aiming strategies are applied that use large safety margins to avoid dangerously high flux concentrations on the receiver. This approach leads to an inefficient use of the power plant and thus economical losses. In this paper, we consider advanced methods to include these uncertainties into the design of efficient aiming strategies. To this end, we present a mixed-integer linear programming (MILP) formulation for the optimization of aiming strategies based on Γ-robustness. In a case study, we show that the Γ-robust optimization approach yields solutions with strong objective values and thus high economical benefits while maintaining a high degree of safety. Compared to non-robust solutions, the Γ-robust solutions achieve better objective values while guaranteeing the same ∗Corresponding author Preprint submitted to Journal of Renewable Energy September 16, 2019 degree of safety.

To ensure economic and safe operation of parabolic trough collectors a precise control of the output temperature of the troughs is necessary. Here, promising control algorithms as the recently proposed bilinear Lyapunov controller have been formulated. Drawbacks of this controller design are a row of simplifying assumptions along with a rough system description, which results in strict limits of the controller gain, as the control loop tends to high frequent oscillation otherwise. Those problems are treated in this work by use of model reduction involving proper orthogonal decomposition and alternative formulations of the control problem, which relax some of the assumptions. In consequence, an improved version of the bilinear Lyapunov control - with robust performance and zero tracking error proven - and potentially higher controller gains is proposed. Realistic simulations confirm the theoretical results while showing shorter rise times without the risk of high frequent oscillations.

In solar tower power plants aiming strategies are used to distribute the heat flux on the receiver surface. An optimal strategy maximizes the mass flow while avoiding thermal overloading to prevent the risk of damage to receiver components. This problem has been modeled as an integer program (IP) to provide deterministic solutions. To consider disturbances caused by the tracking error, the aiming strategy is extended to ensure a robust solution.

New approaches for the computation of the sampling points for an annual simulation of a solar tower power plant are presented. The annual sun-path in azimuth and elevation and in ecliptic longitude and the hour angle are considered. Real measured weather data is considered in the computation of these sampling points.

GPS ist ein globales Satellitennavigationssystem zur Positionsbestimmung, bei dem vielfältige mathematischen Methoden angewandt werden. Genutzt wird es fast alltäglich: Sei es beim Pokémon Go‐Spielen, im Straßenverkehr oder um die nächste Haltestelle samt Busverbindung zu finden. Die Fragestellung, wie die GPS‐Positionsbestimmung funktioniert, dürfte also für Schülerinnen und Schüler aufgrund dieses starken Lebensweltbezugs relevant sein. Weiter handelt es sich um eine realistische Problemstellung, die die Anwendung von Mathematik erfordert und somit authentisch ist. Ihre Behandlung bemüht von Pythagoras über Gleichungssysteme bis hin zu Winkelfunktionen einiges an Schulmathematik. Im vorliegenden Artikel werden die mathematischen Hintergründe der Positionsbestimmung mittels GPS und eine konkrete didaktisch‐methodische Umsetzung im Rahmen eines computergestützten Workshops für Schülerinnen und Schüler der Oberstufe vorgestellt. Die Schülerinnen und Schüler arbeiten mit echten vor Ort aufgenommenen Satellitendaten und erleben sehr anschaulich, wie sich ein Modell immer weiter verbessert. Die Modellverbesserung wird sichtbar, indem sich die ermittelte Position auf einer Karte immer weiter der tatsächlichen Position der Datenaufnahme annähert. Zur Beschreibung dieses Modellbildungsprozesses wird das Bild einer computergestützten Modellierungsspirale verwendet, was die Annäherung an eine optimale Lösung durch Wiederholung der Modellierungsschritte betont. Die Workshop‐Materialien (Arbeitsblätter, MATLAB‐Skripte) sind zum Download verfügbar.

SunFlower is a new model for the simulation of Solar Tower Power Systems. The model has been cross-validated with the NREL tool SolTrace and is currently compared to other tools. This tool is freely accessible via a user-friendly web interface. The idea behind this Web App is to provide a high accurate tool with strong support for comparable programs, such that the exchange of simulation results is made easier.

We introduce a model to compute the annual performance of a heliostat field. We take into account topography, tracking errors, and the position and intensity of the sun. An approach is introduced, which improves on the otherwise expensive pairwise comparison to calculate shading and blocking. Because the computational time is reduced significantly, the presented implementation is sufficiently fast to allow for heliostat field layout optimization within a couple of hours. The optimization is executed via a genetic algorithm, which optimizes the heliostat positioning parameters as well as other design parameters, e.g. receiver tilt angle. A novel approach is used to reduce the search domain. Because the search domain delivers several local optima with comparable values of the objective function, the objective function is augmented. We use smoothing functionals to disperse the local optima. A field layout is optimized on a hilly ground in South Africa, with additional constraints on the heliostat positions.

In this paper the optimization of a heliostat field with triangular heliostat pods is addressed. The use of structures which allow the combination of several heliostats into a common pod system aims to reduce the high costs associated with the heliostat field and therefore reduces the Levelized Cost of Electricity value. A pattern-based algorithm and two pattern-free algorithms are adapted to handle the field layout problem with triangular heliostat pods. Under the Helio100 project in South Africa, a new small-scale Solar Power Tower plant has been recently constructed. The Helio100 plant has 20 triangular pods (each with 6 heliostats) whose positions follow a linear pattern. The obtained field layouts after optimization are compared against the reference field Helio100.

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant. We propose a solution to this global, non-convex optimization problem by using an evolutionary algorithm. We show that the convergence rate of a conventional evolutionary algorithm is too slow, such that modifications of the recombination and mutation need to be tailored to the problem. This is achieved with a new genotype representation of the individuals. Experimental results show the applicability of our approach.