The reduction and prevention of degradation effects of proton exchange membrane fuel cells calls for precise on-line monitoring and control tools such as coupled virtual observers. To present ...significant progress in the area of computationally fast electrochemical models used in observer applications, this paper provides the derivation of a zero-dimensional thermodynamically consistent electrochemical model for proton exchange membrane fuel cells performance modelling and control. The model is further extended to accommodate the transport of gaseous species along the channel and through gas diffusion layer, yielding a quasi-one-dimensional electrochemical model. In addition, the presented work features the determination of an optimal set of calibration parameters proposed and based on mathematical and physical rationale, which is further supported with parameter sensitivity analysis. Multiple validation steps against polarisation curves at different operational points confirm the capability of the newly developed model to replicate experimental data. Furthermore, investigation in models generalisation capabilities shows that the model exhibits very good extrapolation capabilities for operation points outside the calibrated variation space of parameters. Additionally, the newly developed model can be successfully parametrised with little effort on a small calibration data set. These features position the proposed modelling framework as a beyond state-of-the-art model for virtual observers.
•Advanced 0D thermodynamically consistent electrochemical model of PEMFC is derived.•Identifiability of calibration parameters was proven by sensitivity analysis.•Ease of parametrisation on the small calibration data is achieved.•Model exhibit good extrapolation capabilities beyond calibrated operational area.•Newly derived model is applicable in on-line monitoring and control applications.
Determination of the optimal design of experiments that enables efficient parametrisation of fuel cell (FC) model with a minimum parametrisation data-set is one of the key prerequisites for ...minimizing costs and effort of the parametrisation procedure. To efficiently tackle this challenge, the paper present an innovative methodology based on the electrochemical FC model, parameter sensitivity analysis and application of D-optimal design plan. Relying on this consistent methodological basis the paper answers fundamental questions: a) on a minimum required data-set to optimally parametrise the FC model and b) on the impact of reduced space of operational points on identifiability of individual calibration parameters. Results reveal that application of D-optimal DoE enables enhancement of calibration parameters information resulting in up to order of magnitude lower relative standard errors on smaller data-sets. In addition, it was shown that increased information and thus identifiability, inherently leads to improved robustness of the FC electrochemical model.
•Analysis is based on a thermodynamically consistent electrochemical fuel cell model.•Optimal set of fuel cell model parameters is determined by sensitivity analysis.•D-optimal criterion is used to determine the optimal design of experiments.•Enhanced parameter information results in up to few orders of magnitude lower RSE.•It is shown that variation of inlet pressure significantly increases information.
We consider the nonadiabatic dynamics of internal conversions (ICs) in systems rigid enough to allow a description of the coupled potential energy surfaces (PES) within the harmonic approximation. ...Through a hierarchical representation of the Hamiltonian, we define a set of sequentially coupled effective modes and obtain reduced-dimensionality models by truncating the sequence of modes. We systematically investigate the predictions on the electronic populations of these models and of a recently proposed mean-field mixed quantum-classical (MQC) approach, where the most important effective modes are treated at the quantum level and the motion of the remaining ones is approximated with a swarm of classical trajectories. As a test case, we consider a linear vibronic coupling (LVC) model for the
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IC in thymine. LVC PES are computed both in gas phase and in water to explore the different performance of the investigated methods for different relative stabilities of the coupled PES. Reference full quantum dynamical (QD) results are obtained with the MultiLayer Multiconfigurational Time Dependent Hartree method. We show that reduced-dimensionality models work very well in the ultrafast time scale (< 100 fs). At longer times, they tend to predict smaller differences between
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populations than those computed with full QD simulations because they cannot fully account for trapping mechanisms which are found to involve most of the molecular modes. The proposed MQC model always improves the agreement with reference full QD simulations, even when only few modes are included in the quantum partition. It correctly reproduces the quenching of oscillations in electronic populations and partially recovers the error of reduced-dimensionality models on the long-time populations.
The displacement of a sprint kayak can be described by a one-dimensional mathematical model, which, in its simplest case, is analogous to the free-fall problem with quadratic drag and constant ...propulsion. To describe realistic cases, it is necessary to introduce a propulsion capable of reproducing the characteristics of the kayak stroke, including periodicity, average force and effects of stroke frequency, among others. Addressing the problem in terms of a Fourier series allows us to separate the equation into two parts, one of which is equivalent to the constant propulsion case and results in an asymptotic expression, while the second accounts for the periodic contributions. This approach allows us to solve several cases of interest: to propose a quadrature rule for the asymptotic part that allows fast estimations; to compare results with the literature; and finally to propose a general mathematical method for this problem which could help to understand some key strategies in the kayak race.
Achieving efficient solid oxide fuel cell operation and simultaneous prevention of degradation effects calls for the development of precise on-line monitoring and control tools based on predictive, ...computationally fast models. The originality of the proposed modelling approach originates from the hypothesis that the innovative derivation procedure enables the development of a thermodynamically consistent multi-species electrochemical model that considers the electrochemical co-oxidation of carbon monoxide and hydrogen in a closed-form. The latter is achieved by coupling the equations for anodic reaction rates with the equation for anodic potential. Furthermore, the newly derived model is capable of accommodating the diffusive transport of gaseous species through the gas diffusion layer, yielding a computationally efficient quasi-one-dimensional model. This resolves a persistent knowledge gap, as the proposed modelling approach enables the modelling of multi-species fuels in a closed form, resulting in very high computational efficiency, and thus enable the model’s real-time capability. Multiple validation steps against polarisation curves with different fuel mixtures confirm the capability of the newly developed model to replicate experimental data. Furthermore, the presented results confirm the capability of the model to accurately simulate outside the calibrated variation space under different operating conditions and reformate mixtures. These functionalities position the proposed model as a beyond state-of-the-art tool for model supported development and control applications.
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