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Grey-box modelling combines physical and data-driven models to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling, as differential equations given by physical laws and neural networks can be combined in a single modelling framework. This simplifies the simulation and optimization and allows to consider irregularly-sampled data during training and evaluation of the model. We demonstrate this approach using two levels of model complexity; first, a simple parallel resistor-capacitor circuit; and second, an equivalent circuit model of a lithium-ion battery cell, where the change of the voltage drop over the resistor-capacitor circuit including its dependence on current and State-of-Charge is implemented as NODE. After training, both models show good agreement with analytical solutions respectively with experimental data.
Lithium-ion batteries show strongly nonlinear behaviour regarding the battery current and state of charge. Therefore, the modelling of lithium-ion batteries is complex. Combining physical and data-driven models in a grey-box model can simplify the modelling. Our focus is on using neural networks, especially neural ordinary differential equations, for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis for the grey-box model. Unknown parameters and dependencies are then replaced by learnable parameters and neural networks. We use experimental full-cycle data and data from pulse tests of a lithium iron phosphate cell to train the model. Finally, we test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.
In this paper we report on further success of our work to develop a multi-method energy optimization which works with a digital twin concept. The twin concept serves to replicate production processes of different kinds of production companies, including complex energy systems and test market interactions to then use them for model predictive optimizing. The presented work finally reports about the performed flexibility assessment leading to a flexibility audit with a list of measures and the impact of energy optimizations made related to interactions with the local power grid i.e., the exchange node of the low voltage distribution grid. The analysis and continuous exploration of flexibilities as well as the exchange with energy markets require a “guide” leading to continuous optimization with a further tool like the Flexibility Survey and Control Panel helping decision-making processes on the day-ahead horizon for real production plants or the investment planning to improve machinery, staff schedules and production
infrastructure.
The twin concept is increasingly used for optimization tasks in the context of Industry 4.0 and digitization. The twin concept can also help small and medium-sized enterprises (SME) to exploit their energy flexibility potential and to achieve added value by appropriate energy marketing. At the same time, this use of flexibility helps to realize a climate-neutral energy supply with high shares of renewable energies. The digital twin reflects real production, power flows and market influences as a computer model, which makes it possible to simulate and optimize on-site interventions and interactions with the energy market without disturbing the real production processes. This paper describes the development of a generic model library that maps flexibility-relevant components and processes of SME, thus simplifying the creation of a digital twin. The paper also includes the development of an experimental twin consisting of SME hardware components and a PLC-based SCADA system. The experimental twin provides a laboratory environment in which the digital twin can be tested, further developed and demonstrated on a laboratory scale. Concrete implementations of such a digital twin and experimental twin are described as examples.