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Alleviating the curse of dimensionality in minkowski sum approximations of storage flexibility
(2023)
Many real-world applications require the joint optimization of a large number of flexible devices over some time horizon. The flexibility of multiple batteries, thermostatically controlled loads, or electric vehicles, e.g., can be used to support grid operations and to reduce operation costs. Using piecewise constant power values, the flexibility of each device over d time periods can be described as a polytopic subset in power space. The aggregated flexibility is given by the Minkowski sum of these polytopes. As the computation of Minkowski sums is in general demanding, several approximations have been proposed in the literature. Yet, their application potential is often objective-dependent and limited by the curse of dimensionality. In this paper, we show that up to 2d vertices of each polytope can be computed efficiently and that the convex hull of their sums provides a computationally efficient inner approximation of the Minkowski sum. Via an extensive simulation study, we illustrate that our approach outperforms ten state-of-the-art inner approximations in terms of computational complexity and accuracy for different objectives. Moreover, we propose an efficient disaggregation method applicable to any vertex-based approximation. The proposed methods provide an efficient means to aggregate and to disaggregate typical battery storages in quarter-hourly periods over an entire day with reasonable accuracy for aggregated cost and for peak power optimization.
Vast amounts of oily wastewater are byproducts of the petrochemical and the shipping industry and to this day frequently discharged into water bodies either without or after insufficient treatment. To alleviate the resulting pollution, water treatment processes are in great demand. Bubble column humidifiers (BCHs) as part of humidification–dehumidification systems are predestined for such a task, since they are insensitive to different feed liquids, simple in design and have low maintenance requirements. While humidification in a bubble column has been investigated plentiful for desalination, a systematic investigation of oily wastewater treatment is missing in literature. We filled this gap by analyzing the treatment of an oil–water emulsion experimentally to derive recommendations for future design and operation of BCHs. Our humidity measurements indicate that the air stream is always saturated after humidification for a liquid height of only 10 cm. A residual water mass fraction of 3.5 wt% is measured after a batch run of six hours. Furthermore, continuous measurements show that an increase in oil mass fraction leads to a decrease in system productivity especially for high oil mass fractions. This decrease is caused by the heterogeneity of the liquid temperature profile. A lower liquid height mitigates this heterogeneity, therefore decreasing the heat demand and improving the overall efficiency. The oil content of the produced condensate is below 15 ppm, allowing discharge into various water bodies. The results of our systematic investigation prove suitability and indicate a strong future potential for the use of BCHs in oily wastewater treatment.
Activation of heat pump flexibilities is a viable solution to support balancing the grid via Demand Side Management measures and fulfill the need for flexibility options. Aggregators as interface between prosumers, distribution system operators and balance responsible parties face the challenge due to data privacy and technical restrictions to transform prosumer information into aggregated available flexibility to enable trading thereof. Thereby, literature lacks a generic, applicable and widely accepted flexibility estimation method for heat pumps,which incorporates reduced sensor and system information, system- and demand-dependent behaviour. In this paper, we adapt and extend a method from literature, by incorporating domain knowledge to overcome reduced sensor and system information. We apply data of five real-world heat pump systems, distinguish operation modes, estimate power and energy flexibility of each single heat pump system, proof transferability of the method, and aggregate the flexibilities available to showcase a small HP pool as a proof of concept.
Power plant operators increasingly rely on predictive models to diagnose and monitor their systems. Data-driven prediction models are generally simple and can have high precision, making them superior to physics-based or knowledge-based models, especially for complex systems like thermal power plants. However, the accuracy of data-driven predictions depends on (1) the quality of the dataset, (2) a suitable selection of sensor signals, and (3) an appropriate selection of the training period. In some instances, redundancies and irrelevant sensors may even reduce the prediction quality.
We investigate ideal configurations for predicting the live steam production of a solid fuel-burning thermal power plant in the pulp and paper industry for different modes of operation. To this end, we benchmark four machine learning algorithms on two feature sets and two training sets to predict steam production. Our results indicate that with the best possible configuration, a coefficient of determination of R^2 = 0.95 and a mean absolute error of MAE=1.2 t/h with an average steam production of 35.1 t/h is reached. On average, using a dynamic dataset for training lowers MAE by 32% compared to a static dataset for training. A feature set based on expert knowledge lowers MAE by an additional 32 %, compared to a simple feature set representing the fuel inputs. We can conclude that based on the static training set and the basic feature set, machine learning algorithms can identify long-term changes. When using a dynamic dataset the performance parameters of thermal power plants are predicted with high accuracy and allow for detecting short-term problems.
Grey Box models provide an important approach for control analysis in the Heating, Ventilation and Air Conditioning (HVAC) sector. Grey Box models consist of physical models where parameters are estimated from data. Due to the vast amount of component models that can be found in literature, the question arises, which component models perform best on a given system or dataset? This question is investigated systematically using a test case system with real operational data. The test case system consists of a HVAC system containing an energy recovery unit (ER), a heating coil (HC) and a cooling coil (CC). For each component, several suitable model variants from the literature are adapted appropriately and implemented. Four model variants are implemented for the ER and five model variants each for the HC and CC. Further, three global optimization algorithms and four local optimization algorithms to solve the nonlinear least squares system identification are implemented, leading to a total of 700 combinations. The comparison of all variants shows that the global optimization algorithms do not provide significantly better solutions. Their runtimes are significantly higher. Analysis of the models shows a dependency of the model accuracy on the number of total parameters.