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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.
Flexibility estimation is the first step necessary to incorporate building energy systems into demand side management programs. We extend a known method for temporal flexibility estimation from literature to a real-world residential heat pump system, solely based on historical cloud data. The method proposed relies on robust simplifications and estimates employing process knowledge, energy balances and manufacturer's information. Resulting forced and delayed temporal flexibility, covering both domestic hot water and space heating demands as constraints, allows to derive a flexibility range for the heat pump system. The resulting temporal flexibility lay within the range of 24 minutes and 6 hours for forced and delayed flexibility, respectively. This range provides new insights into the system's behaviour and is the basis for estimating power and energy flexibility - the first step necessary to incorporate building energy systems into demand side management programs.
Grid-scale electrical energy storage (EES) is a key component in cost-effective transition scenarios to renewable energy sources. The requirement of scalability favors EES approaches such as pumped-storage hydroelectricity (PSH) or compressed-air energy storage (CAES), which utilize the cheap and abundant storage materials water and air, respectively. To overcome the site restriction and low volumetric energy densities attributed to PSH and CAES, liquid-air energy storage (LAES) has been devised; however, it suffers from a rather small round-trip efficiency (RTE) and challenging storage conditions. Aiming to overcome these drawbacks, a novel system for EES is developed using solidified air (i.e., clathrate hydrate of air) as the storable phase of air. A reference plant for solidified-air energy storage (SAES) is conceptualized and modeled thermodynamically using the software CoolProp for water and air as well as empirical data and first-order approximations for the solidified air (SA). The reference plant exhibits a RTE of 52% and a volumetric storage density of 47 kWh per m3 of SA. While this energy density relates to only one half of that in LAES plants, the modeled RTE of SAES is comparable already. Since improved thermal management and the use of thermodynamic promoters can further increase the RTEs in SAES, the technical potential of SAES is in place already. Yet, for a successful implementation of the concept - in addition to economic aspects - questions regarding the stability of SA must be first clarified and challenges related to the processing of SA resolved.
Bubble columns are recently used for the humidification of air in water treatment systems and fuel cells. They are well applicable due to their excellent heat and mass transfer and their low technical complexity. To design and operate such devices with high efficiency, the humidification process and the impact of the operating parameters need to be understood to a sufficient degree. To extend this knowledge, we use a refined and novel method to determine the volumetric air–liquid heat and mass transfer coefficients and the humidifier efficiency for various parametric settings. The volumetric transfer coefficients increase with both of the superficial air velocity and the liquid temperature. It is further shown that the decrease of vapor pressure with an increase of the salinity results in a corresponding decrease in the outlet humidity ratio. In contrast to previous studies, liquid heights smaller than 0.1 m are investigated and significant changes in the humidifier efficiency are seen in this range. We present the expected humidifier efficiency with respect to the superficial air velocity and the liquid height in an efficiency chart, such that optimal operating conditions can be determined. Based on this efficiency chart, recommendations for industrial applications as well as future scientific challenges are drawn.
Violation-mitigation-based method for PV hosting capacity quantification in low voltage grids
(2022)
Hosting capacity knowledge is of great importance for distribution utilities to assess the amount of PV capacity possible to accommodate without troubling the operation of the grid. In this paper, a novel method to quantify the hosting capacity of low voltage grids is presented. The method starts considering a state of fully exploited building rooftop solar potential. A downward process is proposed - from the starting state with expected violations on the grid operation to a state with no violations. In this process, the installed PV capacity is progressively reduced. The reductions are made sequentially and selectively aiming to mitigate specific violations: nodes overvoltage, lines overcurrent and transformer overloading. Evaluated on real data of fourteen low voltage grids from Austria, the method proposed exhibits benefits in terms of higher hosting capacities and lower computational costs compared to stochastic methods. Furthermore, it also quantifies hosting capacity expansions achievable by overcoming the effect of the violations. The usage of a potential different from solar rooftops is also presented, demonstrating that a user-defined potential allows to quantify the hosting capacity in a more general setting with the method proposed.
Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time, households hold an increasing amount of flexibility, which can be exploited by demand-side management to decrease customer cost and support grid operation. Compared to the collection of individual flexibilities, aggregation reduces optimization complexity, protects households’ privacy, and lowers the communication effort. In mathematical terms, each flexibility is modeled by a set of power profiles, and the aggregated flexibility is modeled by the Minkowski sum of individual flexibilities. As the exact Minkowski sum calculation is generally computationally prohibitive, various approximations can be found in the literature. The main contribution of this paper is a comparative evaluation of several approximation algorithms in terms of novel quality criteria, computational complexity, and communication effort using realistic data. Furthermore, we investigate the dependence of selected comparison criteria on the time horizon length and on the number of households. Our results indicate that none of the algorithms perform satisfactorily in all categories. Hence, we provide guidelines on the application-dependent algorithm choice. Moreover, we demonstrate a major drawback of some inner approximations, namely that they may lead to situations in which not using the flexibility is impossible, which may be suboptimal in certain situations.