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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.
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.
Industrial demand side management has shown significant potential to increase the efficiency of industrial energy systems via flexibility management by model-driven optimization methods. We propose a grey-box model of an industrial food processing plant. The model relies on physical and process knowledge and mass and energy balances. The model parameters are estimated using a predictive error method. Optimization methods are applied to separately reduce the total energy consumption, total energy costs and the peak electricity demand of the plant. A viable potential for demand side management in the plant is identified by increasing the energy efficiency, shifting cooling power to low price periods or by peak load reduction.
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.
In contrast to fossil energy sources, the supply by renewable energy sources likewind and photovoltaics can not be controlled. Therefore, flexibilities on the demandside of the electric power grid, like electro-chemical energy storage systems, are usedincreasingly to match electric supply and demand at all times. To control those flex-ibilities, we consider two algorithms that both lead to linear programming problems.These are solved autonomously on the demand side, i.e., by household computers.In the classic approach, an energy price signal is sent by the electric utility to thehouseholds, which, in turn, optimize the cost of consumption within their constraints.Instead of an energy price signal, we claim that an appropriate power signal that istracked in L1-norm as close as possible by the household has favorable character-istics. We argue that an interior point of the household’s feasibility region is neveran optimal price-based point but can result in a L1-norm optimal point. Thus, pricesignals can not parametrize the complete feasibility region which may not lead to anoptimal allocation of consumption.We compare the price and power tracking algorithms over a year on the base ofone-day optimizations regarding different information settings and using a large dataset of daily household load profiles. The computational task constitutes an embarrassingly parallel problem. To this end, the performance of the two parallel computation frameworks DEF [1] and Ray [2] are investigated. The Ray framework is used to run the Python applications locally on several cores. With the DEF frameworkwe execute our Python routines parallelly in a cloud. All in all, the results providean understanding of when which computation framework and autonomous algorithmwill outperform the other.
In the regime of incentive-based autonomous demand response, time dependent prices are typically used to serve as signals from a system operator to consumers. However, this approach has been shown to be problematic from various perspectives. We clarify these shortcomings in a geometric way and thereby motivate the use of power signals instead of price signals. The main contribution of this paper consists of demonstrating in a standard setting that power tracking signals can control flexibilities more efficiently than real-time price signals. For comparison by simulation, German renewable energy production and German standard load profiles are used for daily production and demand profiles, respectively. As for flexibility, an energy storage system with realistic efficiencies is considered. Most critically, the new approach is able to induce consumptions on the demand side that real-time pricing is unable to induce. Moreover, the pricing approach is outperformed with regards to imbalance energy, peak consumption, storage variation, and storage losses without the need for additional communication or computation efforts. It is further shown that the advantages of the optimal power tracking approach compared to the pricing approach increase with the extent of the flexibility. The results indicate that autonomous flexibility control by optimal power tracking is able to integrate renewable energy production efficiently, has additional benefits, and the potential for enhancements. The latter include data uncertainties, systems of flexibilities, and economic implementation.
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.