Proton exchange membrane electrolyzers (PEMEL) are considered a promising technology for intermittent generation of green hydrogen if connected to fluctuating energy sources and in volatile electricity markets. For an economic operation, a coupling of PEMEL with a battery energy storage system (BESS) is advantageous. In this work, optimized operating strategies of a grid connected PEMEL supported by a BESS are developed based on dynamic programming. Furthermore, a generic aging model is implemented to ensure that performance degradation is taken into account. The optimization is carried out for different hydrogen production targets per week based on day-ahead market electricity prices, system configurations with and without combined operation of electrolyzer and battery as well as aging effects. The results show that an optimized operating strategy can decrease the effective operating costs, i.e. electricity procurement costs and costs related to system degradation, of the considered use case by up to 7 %.

The open circuit voltage hysteresis of lithium-ion batteries is a phenomenon that, despite intensive research, is still not fully understood. However, it must be taken into account for accurate state-of-charge estimation in battery management systems. Mechanistic models of the open circuit voltage hysteresis previously published are not suitable for deployment in a battery management system. Phenomenological models on the other hand can only superficially represent the processes taking place. To address this limitation, we propose a probability distributed equivalent circuit model motivated by the physical insights into hysteresis. The model incorporates hysteresis effects that are often disregarded for state estimation, while keeping the computational cost low. Although the parameterization is more demanding, the model has the advantage of providing insight into the internal state of the battery and intrinsically incorporating the effect of path-dependent rate capability.

The recently introduced impedance-based detection method for the retrospective identification of lithium deposition is used in a long-term ageing study. Six lithium-ion cells are fast charged for 250 cycles with two different strategies, (i) constant-current constant-voltage and (ii) detection-based, adaptive charging control in which the current of the following step is controlled by the detection result of the previous step. The adaptive charging control leads intentionally to critical charging currents with minor lithium deposition effects for the majority of cases. Nevertheless, only marginal capacity fade can be observed after the whole long-term experiment, proving that the detection method reacts sensitively and reliably on minor lithium deposition. On the other hand, the adaptive charge control leads to significantly higher currents, thus reduced charging durations. Hence, the method qualifies for both adaptive fast charging control and for the identification of charging rate limits. A differential voltage analysis is performed before and after the long-term study, identifying the loss of lithium inventory, as well as the loss of anode active material as dominant degradation modes. Additionally, a sensitivity analysis with varying detection time and measurement accuracy is carried out to identify minimum measurement requirements and to increase the method’s time- and cost-efficiency.

For the estimation of the state of charge of lithium‐ion batteries Kalman filters are the state of the art. To ensure precise and reliable estimations these filters use covariance matrices, which need to be tuned correctly by the developer. This process is time‐consuming and depends largely on the experience and skill of the developer. Hence, filter tuning is not reproducible and not optimal with regard to goals as accuracy and convergence speed. Herein a multiobjective optimization framework called hyperspace exploration is used for the first time to automate the filter tuning procedure for an extended Kalman filter and two versions of adaptive extended Kalman filters. Four key performance indicators, including the maximum error in the estimation of the state of charge and the according root mean square error, are used to describe, validate, and compare the filter performance. This automated process enables optimal usage of the degrees of freedom in filter tuning and no longer requires manual tuning while the whole hyperspace, including different use cases and validation scenarios, is considered in the optimization. Furthermore, the proposed approach yields a novel method for the evaluation of filter parameters and their influence on the estimation behavior.

The operation of electrical networks, microgrids, or heterogeneous battery systems, especially the dispatch of single units within the system, requires sophisticated power flow control strategies. If objectives such as efficiency are demanded for the operation of the energy system, typical control strategies lack the ability to verify the optimality of the operation. Dynamic programming is a widely used method for determining the global optima of trajectory problems. In the context of energy systems and power flow optimization, it is restricted to applications with a low number of states and decisions. The reason for this is the rapid growth of computational effort with increasing dimensionality of the state and decision space. The approach of iterative dynamic programming (iDP) makes dynamic programming applicable to the planning and benchmarking of complex power flow optimization problems. To illustrate this, a heterogeneous battery energy storage system is introduced for which the iDP optimizes the power split at the point of common coupling to minimize the total cumulative loss of energy. The method can be adopted for a broad range of energy systems such as microgrids, utility grids, or electric vehicles. The applicability is limited only by the computation time, which depends on the model complexity and the length of the time series. To verify the functionality of the iterative dynamic programming, its results are directly compared to those of the standard dynamic programming. The total computation time can be reduced by 98% in the tested scenario. As relevant use cases, static and dynamic methods of power sharing are validated and benchmarked. The iDP offers a novel and computationally efficient method for the design and validation of power flow control strategies.

Transmission line-or mixed conducting network models are a widely used model category for the characterization of porous electrodes in the frequency domain. Their benefits in time domain modeling and simulation are strongly underestimated as the transfer function of the model's impedance cannot be transformed into the time domain analytically. Instead, spatial discretization is required, which leads to a differential-algebraic equation system. This allows for a spatial resolution of the porous electrode and for the investigation of local phenomena. Therefore, the introduced model is considered a discrete electrochemical model. In this study, we efficiently solve the differential-algebraic equation system using a linear-implicit method. The time-domain model of a graphitic anode is parametrized based on frequency domain impedance measurement data. The validity of the parameter transformation is shown in low- and high-dynamic test profiles, for a wide range of the degree of lithiation of the negative electrode. Finally, the parametrized model is used for the prediction of lithium deposition during charging at various C-rates. The comparison with a standard-equivalent circuit model reveals that the discrete electrochemical model is capable of detecting local Li plating due to the spatial resolution and is significantly more sensitive. Hence, real-time capable transmission line models are applicable for sophisticated fast charging controls.

Besides the limited driving range of battery electric vehicles, the insufficient fast charging capability of lithium-ion batteries is the major drawback hindering electric vehicles to be fully competitive to combustion vehicles. However, fast charging is kinetically and thermodynamically limited: When the surface potential of the anode particles drops below 0 V vs. Li/Li+, Li-ions will deposit on the particles’ surface instead of intercalating into the active material. Thermodynamically, this lithium plating side reaction starts, when the anode material is fully lithiated and no more lattice sites for ions are available. Kinetically, the sum of charge transfer and diffusive overpotential may be higher than the open circuit voltage (OCV), which also leads to a negative surface potential vs. Li/Li+. The latter is supported by high charging rates and low temperature. This behavior is unavoidable. The limits in which safe operation is possible, can be widened by cell and electrode design. Identifying and especially approaching these limits without damaging the cell is not trivial. Up to date, 0D equivalent circuit (EC) models are used to predict and control the overpotential to avoid plating in real-time battery management systems (BMS). As these models lack spatial information, e.g. local degree of lithiation within the electrode or the current distribution, these models are inaccurate and cannot provide additional information. To conserve the lifetime of the battery a large safety margin has to be applied, in many cases charge currents might get limited more than actually needed. In contrast, electrochemical models offer 1D to 3D information about degree of lithiation, concentrations, potentials and currents. Furthermore, due to the large number of parameters and variables, these models cannot be parametrized unambiguously and are only valid in a very limited operational range. As a result, discrete electrochemical models based on a transmission line (TLM) or mixed conducting network structure have become of interest. These models provide spatial information by a distribution of interfacial processes, i.e. charge transfer, solid electrolyte interphase (SEI) and solid-state lithium transport, alongside the current collector’s normal. As displayed in the Figure, these distributed elements are segregated by ionic resistances, while the conductivity of the electrode itself is assumed to be very large. The lithium transport within the particle is described by a TLM as well, consisting of charge dependent voltage sources representing the OCV and diffusion resistances. The model, discretized into n electrode and m particle elements, results in a 2n (m +1)-1-dimensional differential-algebraic equation (DAE) system, which is solved using a linear implicit method. For sufficiently large n and m, the model has been proven to be real-time capable at a sample time of 10 ms. Moreover, with eight parameters, which is the same as in an EC model containing an ohmic resistance, two RC and a Warburg element, it can easily be parametrized in time and frequency domain by pulse and impedance spectroscopy measurement. Hence, this is a large benefit compared to the electrochemical models which also allows the application of the model for a large number of applications. In this study, we introduce a non-equally distributed discretization, allowing for a high resolution at the separator-electrode-interface, where lithium plating is proven to begin. Simulating the lithiation of a graphite electrode at various charging currents, the sensitivity of the discrete electrochemical model with and without unequally spaced discretization, which could enable an increased precision, is compared to a standard EC model. The time until plating starts and the degree of lithiation is investigated. The influence of the discretization is shown. The non-equally distributed resolution is beneficial as expected as with a constant dimension of the equation system, the precision increases and with constant precision, the equation system may be chosen smaller. The latter is of high interest regarding the application in BMS as a smaller DAE system strongly decreases the computational effort and hence computational time. Compared to the EC, the TLM is significantly more sensitive in detecting local lithium plating, especially at intermediate currents between 1C and 3C which are most relevant for fast charging applications. This is caused by the spatially distributed degree of lithiation, which increases at the separator interface more rapidly than at the current collector interface. Hence, this inhomogeneity leads to different SOCs and OCVs across the electrode and consequently the plating criterion is reached significantly earlier. In future, this model could not only be used for simulation and analysis, but also for battery management: for state estimation and for charge control optimizing the charge time while aging due to lithium plating is avoided. Figure 1