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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.
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.