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With rising market deployment the condition monitoring of solid oxide fuel cell systems is gaining particular importance. The conventional approaches mainly use electrochemical impedance spectroscopy based on the repeated sinusoidal perturbation over a range of frequencies. One of the notable weaknesses of the approach is excessively long perturbation time needed to properly evaluate the impedance curve. In this paper, we propose a time-efficient approach in which, a short, persistently exciting and small-amplitude perturbation is used to excite all the relevant system eigenmodes. A model structure from a class of linear fractional order models is selected to describe the perturbed dynamics and to account for anomalous diffusion processes in the cells. Then, the model parameters are estimated directly from measured input and output records. The paper presents a computationally efficient parameter estimation procedure in which the numerical issues of differentiation of noisy signals are alleviated by using modulating functions. In practice, that means a combination of filtering and application of conventional least squares. The approach is applied on a case of health assessment of solid oxide fuel cells.

Maintaining a high fuel-to-electricity conversion efficiency over a long period of time is important for successful market deployment of SOFC power systems. The conventional control solutions usually do not suffice to reach this goal. In order to properly handle variable load conditions and to mitigate degradation processes, on-line optimization is needed to adjust the process variables and to run the process as close as possible to the operational optimum. In this paper, a supervisory controller is proposed to optimize the operation of the SOFC power system. The outputs of the supervisory controller are references for the low-level controllers. The optimization is solved by means of the extremum-seeking approach where optimum is sought directly on the process. The main advantage is that the model of the process is not needed. The supervisory controller is assessed on a detailed physical model of a 2.5 kW SOFC power system at different load conditions. Simulation results show that the supervisory controller is capable to improve electrical efficiency and keep the system temperatures within the safe ranges. Consequently, degradation processes associated with the thermal stress of the stack are reduced. Due to the slow dynamics of the stack thermal processes, the convergence rate of the supervisory controller is rather slow. The proposed supervisory controller is thus appropriate for SOFC power systems that operate at constant load conditions over long periods of time.

Higher exploitation of fuel cell technologies can be achieved employing effective maintenance and condition monitoring tools. Electrochemical impedance spectroscopy (EIS) is a common way for state-of-health characterisation of fuel cells. However, parameters of an equivalent circuit model (ECM) used to describe the EIS seem to be more convenient and informative. Usually, an ECM structure is selected a priori, and an optimisation problem is formulated to fit the parameters of the model and gain their corresponding point estimates. However, for more precise reasoning, better information about the parameters is desirable. This can be achieved through Bayesian inference. In this paper, Bayesian inference is employed to estimate model parameters and so to obtain the posterior marginal density functions of the model’s parameters. It is shown how point estimates may be misleading. The approach is demonstrated on solid oxide fuel cell (SOFC) short stack.

One of the main challenges for wide-spread utilization of the solid oxide fuel cell (SOFC) power systems is how to achieve high electrical efficiency without increasing the degradation rate of the fuel cells. To run the SOFC power system at high efficiency over a long period of time, properly designed controllers are indispensable. Although a number of various approaches to control SOFC have been proposed so far, it seems that the design of control system, along with simple tuning procedure, has not been treated in a consistent manner. This issue is addressed in the present paper resulting in a feedforward-feedback control structure. The feedforward part is based on the stoichiometry of electro-oxidation, reforming and combustion reactions, which allow immediate response to variable current demand. The feedback part performs additional fine adjustment of fuel and air supply in order to minimize the undesired system temperatures variations. The selection of pairings of manipulated and controlled variables for control is based on physical knowledge of the system. Input/output pairing for single-loop feedback control is assessed by the relative gain analysis. An efficient procedure for tuning the parameters of the feedback controllers is suggested, relying on simple open-loop step responses of the system. The proposed low-level control is assessed on a detailed physical model of a 2.5 kW SOFC power system by simulating two nonstationary load regimes. Simulations show that the control provides a robust operation under large load variations while meeting the operating constraints. Due to its simplicity, the control is feasible for implementation on a real SOFC system.

Having concurrent information regarding the state of health (SoH) of an operating solid oxide fuel cell (SOFC) stack can actively improve its overall management. Firstly, operating the SOFC by taking into account current health conditions, and its anticipated trend, can be beneficial to the total life span of the stack. Furthermore, such information can be of great importance to the maintenance staff, e.g. unplanned shutdowns can be avoided. Relatively little work has been done in the field of remaining useful life (RUL) prediction of SOFCs. The majority of work employs stack/cell voltage as a direct link for RUL predictions. This paper proposes an integrated approach for SoH estimation based on stack’s Ohmic area specific resistance (ASR). Subsequently, a drift model that describes the ASR increase over time enables accurate RUL prediction. The approach consists of three steps. Firstly, an Unscented Kalman filter, based on a lumped stack model, estimates the current ASR value. Secondly, a drift model for describing the temporal evolution in ASR is recursively identified employing the linear Kalman filter. Finally, employing the identified drift model, Monte Carlo simulation is performed to predict future time evolution in ASR and so to obtain RUL. The developed approach is validated with experimental data from a 10 kW SOFC power system. The results confirm that ASR is a viable SoH indicator for the SOFC stack.

Degradation and poisoning of solid oxide fuel cell (SOFC) stacks are continuously shortening the lifespan of SOFC systems. Poisoning mechanisms, such as carbon deposition, form a coating layer, hence rapidly decreasing the efficiency of the fuel cells. Gas composition of inlet gases is known to have great impact on the rate of coke formation. Therefore, monitoring of these variables can be of great benefit for overall management of SOFCs. Although measuring the gas composition of the gas stream is feasible, it is too costly for commercial applications. This paper proposes three distinct approaches for the design of gas composition estimators of an SOFC system in anode off-gas recycle configuration which are (i.) accurate, and (ii.) easy to implement on a programmable logic controller. Firstly, a classical approach is briefly revisited and problems related to implementation complexity are discussed. Secondly, the model is simplified and adapted for easy implementation. Further, an alternative data-driven approach for gas composition estimation is developed. Finally, a hybrid estimator employing experimental data and 1st-principles is proposed. Despite the structural simplicity of the estimators, the experimental validation shows a high precision for all of the approaches. Experimental validation is performed on a 10 kW SOFC system.

The solid oxide fuel cells (SOFCs) represent a promising technology for sustainable power generation from hydrogen rich fuels with high efficiency of energy conversion. However, only a limited number of papers address the problem of on-line maximisation of the efficiency of SOFC operation. Optimal operating conditions are normally chosen either based on experience or by using elaborated models, which are not easy to obtain. Moreover, the process changes over time due to degradation, hence the model-based performance optimisation requires on-line model update. To avoid these problems, a model-free approach is proposed. It is realised in the form of a two-tier control structure where the low-level controllers take over control of the auxiliary units around the fuel cells, while the supervisory controller (SC) controller optimises the operation point of the system. The low-level controllers are conventional feed-forward feed-back controllers, while optimisation on the higher level is solved by using the extremum seeking approach. The proposed control system is demonstrated on a simulated 10 kW SOFC system showing reliable convergence, relative rise of efficiency up to 2% and easy design and maintenance.

Thermal stress is one of the main factors affecting the degradation rate of solid oxide fuel cell (SOFC) stacks. In order to mitigate the possibility of fatal thermal stress, stack temperatures and the corresponding thermal gradients need to be continuously controlled during operation. Due to the fact that in future commercial applications the use of temperature sensors embedded within the stack is impractical, the use of estimators appears to be a viable option. In this paper we present an efficient and consistent approach to data-driven design of the estimator for maximum and minimum stack temperatures intended (i) to be of high precision, (ii) to be simple to implement on conventional platforms like programmable logic controllers, and (iii) to maintain reliability in spite of degradation processes. By careful application of subspace identification, supported by physical arguments, we derive a simple estimator structure capable of producing estimates with 3% error irrespective of the evolving stack degradation. The degradation drift is handled without any explicit modelling. The approach is experimentally validated on a 10 kW SOFC system.

The lifespan of a solid oxide fuel cell (SOFC) stack depends on several factors, such as the internal stack temperature and temperature gradients as well as the fuel gas oxygen-to-carbon (O/C) ratio within the stack. An excessively high stack operating temperature generally accelerates degradation processes while large temperature gradients over the stack increase the thermal stress within the stack which may lead to the delamination of repeating unit components. A too low O/C ratio inflicts carbon deposition which quickly leads to stack breakage. Therefore, monitoring these variables is of vital importance. Although measuring temperatures within the stack and measuring the fuel gas composition at the stack inlet is feasible, this raises the overall equipment cost. In this paper a data-driven design of soft sensors for stack minimum and maximum temperatures as well as the O/C ratio at the anode and pre-reformer inlet is presented. For temperature estimation both dynamic and static models are derived and their performance is compared. The dynamic model is identified using subspace identification, which results in a causal state-space model. The non-causal static model assumes that a combination of process variables at the stack inlet and outlet describe its internal condition. The estimation of gas composition at the inlets, which is required for O/C ratio estimation, is based solely on static relationships. The soft sensors are designed in such a way that adding extra inputs yields no further increase in estimate accuracy. The empirical data required for modelling were obtained from a complete SOFC power generation unit. The results show that estimates of all the relevant variables can be accomplished by simple linear regression models. Keywords: SOFC, soft sensor, O/C estimation, temperature estimation Figure 1

Improvement in efficiency and reliability are essential for more intensive deployment and exploitation of solid oxide fuel cell (SOFC) systems in modern society. Having the information about current health, degradation rate, and estimated remaining useful life (RUL) of the stack, at all times during operation, can greatly benefit the control system performance. Such information can be beneficial also for the service providers and end-users as the maintenance needs, including stack replacements, can be planned in advance. The control system can be able to optimize performance through a trade-off between maximal life span and best efficiency of power conversion. The knowledge on health status and its anticipated evolution assures easy and cost-effective maintainability. However, works that address issue of RUL prediction for SOFC are scant. On top of that, most of authors define voltage as health index and predict RUL accordingly. Such a selection of health index becomes inappropriate when SOFC is working under varying load conditions. In such a case stack voltage becomes affected by the changes in operating conditions and it is difficult to correlate drop in voltage with degradation rate. In this paper, we propose a novel hybrid approach to RUL prediction of SOFC systems, which overcomes the limitations of the known approaches and allows for reliable RUL prediction in non-stationary operating conditions. The approach consists of three main modules: (i.) estimation of area specific resistance (ASR) of the stack, (ii.) prediction of its future progress based on collected data, and (iii.) prediction of RUL. The methodology is evaluated on a 6 kW SOFC system. Figure 1