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Gas composition modeling in a reformed Methanol Fuel Cell system using adaptive Neuro-Fuzzy Inference Systems
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 0 5 7 7 e1 0 5 8 4
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Gas composition modeling in a reformed Methanol Fuel Cell system using adaptive Neuro-Fuzzy Inference Systems Kristian Kjær Justesen*, Søren Juhl Andreasen, Hamid Reza Shaker, Mikkel Præstholm Ehmsen, John Andersen Department of Energy Technology, Aalborg University, Pontoppidanstræde 101, DK-9220 Aalborg East, Denmark
article info
abstract
Article history:
This work presents a method for modeling the gas composition in a Reformed Methanol
Received 21 December 2012
Fuel Cell system. The method is based on Adaptive Neuro-Fuzzy-Inference-Systems which
Received in revised form
are trained on experimental data. The developed models are of the H2, CO2, CO and CH3OH
15 May 2013
mass flows of the reformed gas. The ANFIS models are able to predict the mass flows with
Accepted 1 June 2013
mean absolute errors for the H2 and CO2 models of less than 1% and 6.37% for the CO model
Available online 8 July 2013
and 4.56% for the CH3OH model.
Keywords:
observation and control, advanced control algorithms, or fuel cell diagnostics systems.
HTPEM fuel cell
Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
The models have a wide range of applications such as dynamic modeling, stoichiometry
reserved.
Methanol Reformed Methanol Fuel Cell Gas composition modeling ANFIS Fuzzy-logic and neural networks
1.
Introduction
Hydrogen fuel cells are being considered as a cleaner alternative in many mobile applications. Hydrogen is, however, difficult to store on gas form because of its low energy content per volume unit. This means that it either has to be compressed in a pressure vessel or cooled to below 252.87 C to be on liquid form. Both of these processes are energy consuming, require heavy equipment which take up space. In addition they require the construction of a new transport and storage infrastructure. An alternative where the hydrogen is stored in a liquid fuel where the existing transport and storage infrastructure can be used is preferable.
A process where hydrogen is bonded to CO2 from the air to form methanol, CH3OH, has been suggested [1]. Methanol is liquid at room temperature and has a relatively high energy content per volumetric unit. It is therefore easy to store and transport. If methanol is mixed with water, it can be reformed into hydrogen and CO2 according to the following steam reforming reaction [2]: CH3 OH þ H2 O43H2 þ CO2
(1)
The reaction requires a suitable catalyst and a temperature between 240 and 300 C. This reaction is endothermic and needs a supply of heat energy to take place. In addition to the
* Corresponding author. Tel.: þ45 99403810. E-mail address: [email protected] (K.K. Justesen). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.06.013
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List of parameters Oi2,i mAi(x1) ai, bi, ci wi
Output of the ith note of the i2th layer in the ANFIS models The degree of membership of the input x1 to the linguistic variable Ai Adaptive premise parameters which determine the shape of a membership function Firing level of the ith fuzzy rule
above reaction, a decomposition of methanol can also take place according to: CH3 OH42H2 þ CO
(2)
This reaction leaves a certain amount of CO in the reformed gas, which is undesirable for fuel cell applications. The reason for this will be described later. In addition a water gas shift reaction can take place according to: CO þ H2 O4H2 þ CO2
(3)
The rate at which these reactions occur depend on the temperature of the reformer, the fuel flow into the reformer, the ratio of water to methanol, called the steam to carbon ratio, and the amount of catalyst present and its state of degradation [3,4]. A system where a fuel cell is fed with hydrogen from a reformer where the above reactions take place, is called a Reformed Methanol Fuel Cell system (RMFC). When a fuel cell is operated on a mixed gas, a certain over stoichiometry has to be present. If this is not the case the fuel cell is “starved”, which results in fuel cell degradation. The anode exhaust can be fed to a catalytic burner which supplies heat to the reformation process. A blower can be used to supply the process air for the burner and control its temperature by superimposing a cooling flow on the process air. The waste heat from the fuel cell is in some fuel cells removed using the blower which supplies cathode air to the fuel cell. This hot air can be used to preheat and evaporate the fuel before it goes into the reformer. Fig. 1 shows a diagram of a Serenus H3-350 system from Serenergy which uses these principles. The system uses a high temperature polymer electrolyte membrane fuel cell (HT-PEM), which has a high degree of tolerance to the CO created by the reaction in Equation (2) [5e7]. The system therefore does not include any gas cleanup stages as other similar systems [8,9] which use low temperature PEM fuel cells. Fig. 2 shows a picture of a Serenus H3-350 module which functions as an off-grid battery charger.
Fig. 1 e Diagram of a Reformed Methanol Fuel Cell system.
n pi, qi, ri y MAE lFC ANFIS lFC
Number of fuzzy rules Adaptive consequent parameters Calculated model output Mean Absolute Error Fuel cell stoichiometry calculated using ANFIS models Standard Fuel cell stoichiometry calculated using standard method
As mentioned earlier the composition of the reformed gas is dependent on, among other things, the temperature of the reformer bed and the fuel flow. In many integrated systems, as for example the H3-350 module from Serenergy, the temperature of the reformer is only measured in the bulk material next to the bed. This means that the temperature which is available for gas composition calculation is different to the reformer bed temperature. The deviation also depend on the fuel flow which has a cooling effect on the reformer bed, which changes the temperature gradient between the burner and the reformer bed. This concept is illustrated in Fig. 3. Calculating the reformer bed temperature on the basis of the measured temperature can be laborious and this paper therefore introduces an alternative method. This method is based on Adaptive Neuro-Fuzzy Inference System models, ANFIS models for short, trained on experimental data. ANFIS is, as the name suggests, a modeling approach based on a combination of Fuzzy logic and Neural Networks. It was developed by Jyh-Sing Roger Jang [10] and can be trained to behave like a nonlinear physical system. The modeling section of this paper will describe the theory behind the ANFIS modeling scheme. ANFIS modeling and similar approaches have previously been used for modeling the voltage of a PEM-fuel cell [11,12] with success. It has also been used to model solid oxide fuel cells [13,14] as well as for direct Methanol Fuel Cell systems [15]. There are, however, no examples in the literature of
Fig. 2 e The H3-350 system from Serenergy.
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Fig. 3 e Concept drawing of a reformer and burner with sensor placement.
ANFIS models being used to predict the composition of the output gas of a reformer or in RMFC systems. Based on the reactions in Equations (1)e(3), models of the H2, CO2, CO and CH3OH content in the reformed gas will be developed. The mass flow of water in the fuel can be calculated by summing the water present due to the steam to carbon ratio and the extra water present due to the CH3OH which passes through the reformer. The developed models can be used in a wide range of applications. For example in a dynamic model of the H3-350 module, for fuel cell stoichiometry observation and control, advanced control systems, or fuel cell diagnostics systems.
2.
Reforming process modeling
This section describes the ANFIS modeling structure employed in this work and the training based on identification experiments as developed by Jyh-Sing Roger Jang [10]. It also includes an evaluation of the model performance.
2.1.
Adaptive Neuro-Fuzzy Inference Systems
As mentioned in the previous section, ANFIS modeling has been used to model various complex nonlinear phenomena. This is possible because ANFIS uses a human-like reasoning scheme which learns to imitate a physical system based on experimental data. This is achieved by combining the virtues of Fuzzy Inference Systems (FIS) and Neural Networks (NN). These virtues are the ability to make decisions based on expert knowledge for the FIS and the ability to make adaptations based on data for the NN. Fig. 4 shows an ANFIS system with two inputs and one output. In this work the inputs will be the measured reformer temperature and the fuel flow into the reformer. The output is the mass flow of the gas in question. The ANFIS model structure consists of five layers. The first layer is the fuzzification layer. Here the crisp input signals are converted into fuzzy variables. These are numbers between 0 and 1 and can be interpreted as the degree to which the input has a certain property. In Fig. 4 where a system with two membership functions per input is depicted, the properties will be interpreted as high and low. In this work bell-shaped membership functions are used. Bell-shaped means that the edges of the membership functions are smooth, which ensures a smooth transition between membership functions. Fig. 5 shows three bell-shaped membership functions.
Fig. 4 e ANFIS model structure used in this work.
Equation (4) shows a bell shaped membership function. O1;i ¼ mAi ðx1 Þ ¼
1 x1 ci 2bi 1 þ ai
(4)
O1,i denotes the output of the ith note of the 1st layer. mAi(x1) is the degree of membership of the input x1 to the linguistic variable Ai. ai, bi and ci are the adaptive premise parameters which determine the shape of the membership function. The nodes in layer 2,which are non-adaptive, determine the firing levels of the individual rules. They are marked T because fuzzy T-norms are used, here the fuzzy AND is employed. There are many versions of this, but here the product method is used as shown in Equation (5). O2;i ¼ wi ¼ mAi ðx1 Þ$mBi ðx2 Þ
(5)
Where wi is the firing level of the ith rule. This can be interpreted as the degree to which x1 is Ai AND x2 is Bi. If another AND method is chosen, the adaptive parameters will be different but it will not necessarily effect the accuracy of the model. Layer 3 is the normalization layer where each firing level is normalized according to Equation (6). wi O3;i ¼ wi ¼ Pn
(6)
i2 ¼1 wi2
Where wi is the normalized firing levels of the individual rules and n is the number of rules. This layer is also non-adaptive. In layer 4 the contribution of each individual rule to the output of the model is calculated according to: O4;i ¼ wi $fi ¼ wi $ pi $x1 þ qi $x2 þ ri
(7)
Here x1 and x2 are the inputs for the model and pi, qi and ri are the adaptive consequent parameters. The output of this layer can be interpreted as, for example, the consequence of
1 A1
A2
A3 x
Fig. 5 e Bell-shaped membership functions.
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low temperature and high fuel flow on the output. In layer 5 all of the contributions of the individual rules are summed up to give the output of the ANFIS model. O5 ¼ y ¼
n X
wi $fi
(8)
i¼1
Here y is the output of the model as in Fig. 4. The training of the ANFIS models is an iterative process which takes place over a series of epochs. Each epoch contains a forward and a backwards pass. In the forward pass, the node outputs are calculated up to layer 4. The consequent parameters in layer 5 are then calculated using a leastsquares regression method. In the following backwards pass, the premise parameters in the membership functions are updated by gradient descent methods. After a number of epochs no performance improvements are achieved by further optimization. In this work 5 epochs are used because experience shows this number to be sufficient. The relatively simple nature of the mathematical operations performed in each layer means that the ANFIS models can be implemented in systems which have relatively small computing power. This could for example be in a DSP as part of a control system. It is also advantageous in a larger dynamic model where the output has to be calculated in every in model iteration.
2.2.
Identification experiments
A test setup where the fuel cell is replaced by a gas analyzer is used for the identification experiments. The hydrogen for the burner which provides process heat for the reformer is supplied by a mass flow controller as is the process air for the burner. The cathode air from the fuel cell which is used to heat the evaporator is supplied by a mass flow controller which has a built in temperature controller. Fig. 6 shows a diagram of the test setup. The gas analyzer takes a sample of the reformer’s output gas and splits it between a Total Organic Carbon, or TOC, analyzer and a dry gas analyzer. The TOC analyzer is a Siemens Fidamat 6 which is used to measure the CH3OH content of the gas. The dry gas analyzer is a Siemens Ultramat which measures CO2 and CO content connected in series with a Siemens Calomat 6 which measures the hydrogen content. For the ANFIS models to be useful they must be trained on data which covers the entire operating range of the reformer.
This applies to both the operating temperature and the fuel flow. The maximum operating temperature of the catalyst is 300 C and the minimum is 240 C. Therefore the identification experiment is performed in 10 C intervals from 240 to 300 C. 10 C intervals were chosen, because initial experiments showed, that this was sufficient to model the gas composition precisely. The maximum rated fuel flow of the H3-350 module is 440 [mL/h], which is chosen as the maximum flow in the experiment. Experiments show that the gas analyzer used in the experiments needs a minimum fuel flow of 125 [mL/h] to perform its measurements. The minimum current of the H3-350 module, however, corresponds to a fuel flow of about 200 [mL/h], which is therefore chosen as the minimum flow in the experiment. At each temperature the fuel flow starts at 200 [mL/h] and is then stepped through 250, 300, 350, 400 and 450 [mL/h]. It is then brought back to 200 [mL/h] through the same steps. This is done to see if the past operating point effects the performance in the new operating point. It is chosen to keep the temperature constant while the fuel flow is stepped through the chosen operating points. Each operating point is evaluated over a period of 20 [min] to ensure that the reformer has entered steady state operation. Plot a in Fig. 7 shows the measured reformer temperature and plot b shows the fuel flow set point during the experiment. Plot c in Fig. 7 shows the measured hydrogen flow during the experiment and the value calculated assuming full reformation. The plot shows that the degree to which the fuel is reformed is dependent on the reformer temperature as expected. Higher temperature means a hydrogen flow which is closer to full reformation and therefore a more complete reformation of the fuel. The figure also shows that higher flows cause a larger discrepancy between full reformation and the measured flow. These observations demonstrate the need for accurate gas flow models. Plot d shows the measured CO2 mass flow in the reformed gas and the mass flow calculated using full reformation. Plot e shows the fuel flow in the top plot and the CO flow in the reformed gas in the bottom plot. In general higher temperature means a more CO in the reformed gas. This is also observed in the experiments. Intuitively one would assume that higher mass flow of fuel would mean more CO, but this is not always the case in the experiment. When the fuel flow is stepped up, the mass flow of CO increases until the fuel flow reaches 350 [mL/h] and then starts to decrease. This can be an indication that the actual reformer bed temperature is dropping as the fuel flow is increased as suggested in the introduction. Plot f shows the CH3OH flow in the reformed gas. As expected the measured CH3OH mass flow is lowest at high temperatures. There is in addition a correlation between fuel flow and the CH3OH mass flow in the reformed gas. These tendencies mirror those observed in the H2 measurements.
2.3. Fig. 6 e Test setup used to evaluate the reformed gas flow from the reformer.
Model construction and evaluation
The data from the experiment described in the previous section is used to train ANFIS models of the mass flow of H2, CO2,
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Fig. 7 e Temperature and fuel flow during the experiment as well as the mass flows measured in the reformed gas.
CO and CH3OH in the reformed gas. The input for these models is the measured reformer temperature and the fuel flow set point. The ANFIS function in MATLAB is used for the model construction. Bell-shaped membership functions and 5 training epochs are used in all models. As mentioned earlier the number of membership functions determines the model’s ability to model nonlinearities. However, more membership functions does mean more computationally heavy models. This is because the number of rules
in the models increases with the number of membership functions squared. Models with different numbers of membership functions are therefore constructed. The final choice of model is a compromise between performance or low error, and a subjective preference for the simplest model which shows good performance. The Mean Absolute Error, or MAE, is used to evaluate the performance of the models with different numbers of membership functions. Equation (9) shows how the MAE is calculated.
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Table 1 e MAE of the ANFIS models using different numbers of membership functions. # Membership functions H2 MAE % CO2 MAE % CO MAE % CH3OH MAE %
MAE ¼ mean
n X jei j i¼1
3
4
5
6
0.7 0.71 6.86 5.31
0.60 0.67 6.37 4.56
0.59 0.6 6.4 4.5
0.56 0.55 6.42 4.3
n
! (9)
Table 1 shows the MAE of H2, CO2, CO and CH3OH models with 3, 4, 5, and 6 membership functions. Because all of the H2 models have similar MAE, the simplest model, the one with 3 membership functions, is chosen. The same is the case for the CO2 models. The noisy nature of the training data for the ANFIS models means that the MAE of the CO models is higher than those of
Fig. 8 e Mass flow of the different components of the reformed gas measured during the experiments and the output of the ANFIS models when they are subjected to the same reformer temperature and fuel flow.
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Fig. 9 e Calculated stoichiometry using full reformation lFC Standard and the developed ANFIS models lFC ANFIS during a series of changes in fuel cell current.
the H2 and CO2 models. The tendencies of the measured data are, however, reflected in the models and it the use of 4 membership functions is chosen because it gives the lowest MAE. Again the noisy training data means that the MAEs of the CH3OH models are larger than those of the H2 and CO2 models. 4 membership functions are chosen because increasing to five or six only improves the performance slightly. Fig. 8 shows the mass flows measured in the experiment and those calculated using the developed models. After a period of operation the experiment is repeated to further evaluate the performance of the models. It is observed in the experiment that the catalyst in the reformer has degraded resulting in a less complete reformation. The MAE of the H2 model is now 4.32%, the CO2 model is 4.32%, the CO model is 39.46% and the CH3OH model is 46.48%. This indicates a need to include catalyst degradation in the models in the future. To illustrate the usefulness of the models, the stoichiometry of the H3-350 module is analyzed during a series of load changes. The CAN-bus data readout of the module is used to obtain the module’s stoichiometry set point which is set assuming full conversion. This is plotted in Fig. 9 together with the stoichiometry calculated using the developed ANFIS models. The specified minimum stoichiometry of the system is 1.15. The standard stoichiometry predictor is approximately 1.5 throughout the experiment, which is the standard set point. The stoichiometry predicted by the ANFIS model, however, is constantly lower than this and changes with the operating point. It does not drop below the lower stoichiometry limit, but the example does highlight the lack of control over the module’s stoichiometry when full reformation is assumed. The ANFIS model can be implemented in the H3-350 module’s control system to remedy this problem. The usefulness of these models is not limited to stoichiometry prediction. They can also be used in a dynamic system model where the CO models are very useful in determining the fuel cell efficiency. By deducting the CH3OH in the exhaust before calculating the energy consumed by the reformation process, this can be calculated with greater accuracy. The
CH3OH in the exhaust gas will also be present in the anode exhaust and is therefore fed to the catalytic burner which supplies heat energy to the reformer. This can also be modeled using the ANFIS models.
3.
Conclusion
In this work the problem of predicting the mass flow of the different constituents of the reformed gas from a methanol steam reformer is described. An accurate prediction is important for modeling and stoichiometry observation on Reformed Methanol Fuel Cell systems. A solution to the problem based on Adaptive Neuro-Fuzzy Inference Systems, or ANFIS for short, is proposed. The ANFIS models are of the mass flow of H2, CO2, CO and CH3OH in the reformed gas and they are trained on experimental data. The models of the H2 and CO2 are accurate to within 1% when compared to the training data when using Mean Absolute Error, or MAE for comparison. They are both determined to have the optimal performance for the smallest model complexity when 3 membership functions are used. The CO model has an MAE of 6.37% and the CH3OH model has an MAE of 4.56%. This higher deviation is primarily due to the noisy nature of the training data used to construct these models. They do, however, display the same tendencies as the experimental data and are therefore deemed valid for modeling purposes. When the experiment is repeated after a period of operation, an increase in MAE is observed for all models. This is because of degradation of the reformer catalyst. It was demonstrated how the H2 model can be used to calculate the stoichiometry of the fuel cell online.
4.
Future work
A high degree of catalyst degradation was observed during the experiments. This effect is interesting to include in the
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models, because it would make it possible to analyze the performance of a RMFC module throughout its lifetime. This could be done by including the total amount of methanol, which has passed through the reformer in its lifetime as an input. The models developed in this work can be used in a dynamic model of the system. This model can be used to evaluate the stability of the H3-350 module’s control systems while taking varying gas compositions into account. If the model contains an accurate fuel cell model, it can also be used to find the optimal operating temperatures for the module at different current set points. This will be a balancing act between high CO content, which harms the fuel cell efficiency, and a low CH3OH slip at high reformer temperature and low CO content and large CH3OH slip at low temperatures. The models can also be included in an online optimization scheme which optimizes the system efficiency at different operating points. As mentioned before, the H2 model can be used to observe the stoichiometry of the fuel cell online and can be the basis of an online stoichiometry controller. It is, however, also possible to reverse the model to predict the fuel flow which is necessary to uphold a certain stoichiometry and thereby use the model as an open loop fuel controller. The models can also be included in a fuel cell diagnostics system.
Acknowledgments We gratefully acknowledge the cooperation of Serenergy A/S and the financial support from the EUDP Program and the Danish Energy Agency.
references
[1] Graves CG, Ebbesen SD, Mogensen M, Lackner KS. Sustainable hydrocarbon fuels by recycling CO2 and H2O with renewable or nuclear energy. Renewable and Sustainable Energy Reviews 2011;15:1e23. [2] Amphlett JC, Creber KAM, Davis JM, Mann RF, Peppley BA, Stokes DM. Hydrogen production by steam reforming of methanol for polymer electrolyte fuel cells. International Journal of Hydrogen Energy 1994;19(2):131e7.
[3] Juhl Andreasen Søren, Knudsen Kær Søren, Pagh Nielsen Mads. Experimental evaluation of a pt-based heat exchanger methanol reformer for a HTPEM fuel cell stack. ECS Transactions 2008;12:571e8. [4] Chul Yoon Hyung, Otero Jonathan, Erickson Paul A. Reactor design limitations for the steam reforming of methanol. Applied Catalysis B: Environmental 2007;75:264e71. [5] Andreasen Søren Juhl, Rabjerg Vang Jakob, Knudsen Kær Søren. High temperature PEM fuel cell performance characterisation with CO and CO2 using electrochemical impedance spectroscopy. International Journal of Hydrogen Energy 2011;36:9815e30. [6] Li Qingfeng, Oluf Jensen Jens, Savinell Robert F, Bjerrum Niels J. High temperature proton exchange membranes based on polybenzimidazoles for fuel cells. Progress in Polymer Science 2009;34:449e77. [7] Zhang Jianlu, Xie Zhong, Zhang Jiujun, Tang Yanghua, Songa Chaojie, Navessin Titichai, et al. High temperature PEM fuel cells. Journal of Power Sources 2006;160:872e91. [8] Chrenko Daniela, Gao Fei, Blunier Benjamin, Bouquain David, Miraoui Abdellatif. Methanol fuel processor and PEM fuel cell modeling for mobile application. International Journal of Hydrogen Energy 2010;35:6863e71. [9] Chang Hsuan, Cheng Shueh-Hen, Chiang Hao-Chang, Chen Yih-Hang, Chang Yin-Yu. Simulation study of an integrated methanol micro fuel processor and fuel cell system. Chemical Engineering Science 2012;74:27e37. [10] Roger Jang Jyh-Sing. ANFIS: adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics 1993;23:665e85. [11] Vural Yasemin, Ingham Derek B, Pourkashanian Mohamed. Performance prediction of a proton exchange membrane fuel cell using the ANFIS model. International Journal of Hydrogen Energy 2009;34:9181e7. [12] Kishor Nand, Mohanty Soumya R. Fuzzy modeling of fuel cell based on mutual information between variables. International Journal of Hydrogen Energy 2010;35:3620e31. [13] Entchev Evgueniy, Yang Libing. Application of adaptive neuro-fuzzy inference system techniques and artificial neural networks to predict solid oxide fuel cell performance in residential microgeneration installation. Journal of Power Sources 2007;170:122e9. [14] Wu Xiao-Juan, Zhu Xin-Jian, Cao Guang-Yi, Tu Heng-Yong. Nonlinear modeling of a sofc stack based on ANFIS identification. Simulation Modelling Practice and Theory 2008;16:399e409. [15] Wang Rongrong, Qi Liang, Xie Xiaofeng, Ding Qingqing, Li Chunwen, Mad ChenChi M. Modeling of a 5-cell direct methanol fuel cell using adaptive-network-based fuzzy inference systems. Journal of Power Sources 2008;185:1201e8.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Gas composition modeling in a reformed Methanol Fuel Cell system using adaptive Neuro-Fuzzy Inference Systems Kristian Kjær Justesen*, Søren Juhl Andreasen, Hamid Reza Shaker, Mikkel Præstholm Ehmsen, John Andersen Department of Energy Technology, Aalborg University, Pontoppidanstræde 101, DK-9220 Aalborg East, Denmark
article info
abstract
Article history:
This work presents a method for modeling the gas composition in a Reformed Methanol
Received 21 December 2012
Fuel Cell system. The method is based on Adaptive Neuro-Fuzzy-Inference-Systems which
Received in revised form
are trained on experimental data. The developed models are of the H2, CO2, CO and CH3OH
15 May 2013
mass flows of the reformed gas. The ANFIS models are able to predict the mass flows with
Accepted 1 June 2013
mean absolute errors for the H2 and CO2 models of less than 1% and 6.37% for the CO model
Available online 8 July 2013
and 4.56% for the CH3OH model.
Keywords:
observation and control, advanced control algorithms, or fuel cell diagnostics systems.
HTPEM fuel cell
Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
The models have a wide range of applications such as dynamic modeling, stoichiometry
reserved.
Methanol Reformed Methanol Fuel Cell Gas composition modeling ANFIS Fuzzy-logic and neural networks
1.
Introduction
Hydrogen fuel cells are being considered as a cleaner alternative in many mobile applications. Hydrogen is, however, difficult to store on gas form because of its low energy content per volume unit. This means that it either has to be compressed in a pressure vessel or cooled to below 252.87 C to be on liquid form. Both of these processes are energy consuming, require heavy equipment which take up space. In addition they require the construction of a new transport and storage infrastructure. An alternative where the hydrogen is stored in a liquid fuel where the existing transport and storage infrastructure can be used is preferable.
A process where hydrogen is bonded to CO2 from the air to form methanol, CH3OH, has been suggested [1]. Methanol is liquid at room temperature and has a relatively high energy content per volumetric unit. It is therefore easy to store and transport. If methanol is mixed with water, it can be reformed into hydrogen and CO2 according to the following steam reforming reaction [2]: CH3 OH þ H2 O43H2 þ CO2
(1)
The reaction requires a suitable catalyst and a temperature between 240 and 300 C. This reaction is endothermic and needs a supply of heat energy to take place. In addition to the
* Corresponding author. Tel.: þ45 99403810. E-mail address: [email protected] (K.K. Justesen). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.06.013
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 0 5 7 7 e1 0 5 8 4
List of parameters Oi2,i mAi(x1) ai, bi, ci wi
Output of the ith note of the i2th layer in the ANFIS models The degree of membership of the input x1 to the linguistic variable Ai Adaptive premise parameters which determine the shape of a membership function Firing level of the ith fuzzy rule
above reaction, a decomposition of methanol can also take place according to: CH3 OH42H2 þ CO
(2)
This reaction leaves a certain amount of CO in the reformed gas, which is undesirable for fuel cell applications. The reason for this will be described later. In addition a water gas shift reaction can take place according to: CO þ H2 O4H2 þ CO2
(3)
The rate at which these reactions occur depend on the temperature of the reformer, the fuel flow into the reformer, the ratio of water to methanol, called the steam to carbon ratio, and the amount of catalyst present and its state of degradation [3,4]. A system where a fuel cell is fed with hydrogen from a reformer where the above reactions take place, is called a Reformed Methanol Fuel Cell system (RMFC). When a fuel cell is operated on a mixed gas, a certain over stoichiometry has to be present. If this is not the case the fuel cell is “starved”, which results in fuel cell degradation. The anode exhaust can be fed to a catalytic burner which supplies heat to the reformation process. A blower can be used to supply the process air for the burner and control its temperature by superimposing a cooling flow on the process air. The waste heat from the fuel cell is in some fuel cells removed using the blower which supplies cathode air to the fuel cell. This hot air can be used to preheat and evaporate the fuel before it goes into the reformer. Fig. 1 shows a diagram of a Serenus H3-350 system from Serenergy which uses these principles. The system uses a high temperature polymer electrolyte membrane fuel cell (HT-PEM), which has a high degree of tolerance to the CO created by the reaction in Equation (2) [5e7]. The system therefore does not include any gas cleanup stages as other similar systems [8,9] which use low temperature PEM fuel cells. Fig. 2 shows a picture of a Serenus H3-350 module which functions as an off-grid battery charger.
Fig. 1 e Diagram of a Reformed Methanol Fuel Cell system.
n pi, qi, ri y MAE lFC ANFIS lFC
Number of fuzzy rules Adaptive consequent parameters Calculated model output Mean Absolute Error Fuel cell stoichiometry calculated using ANFIS models Standard Fuel cell stoichiometry calculated using standard method
As mentioned earlier the composition of the reformed gas is dependent on, among other things, the temperature of the reformer bed and the fuel flow. In many integrated systems, as for example the H3-350 module from Serenergy, the temperature of the reformer is only measured in the bulk material next to the bed. This means that the temperature which is available for gas composition calculation is different to the reformer bed temperature. The deviation also depend on the fuel flow which has a cooling effect on the reformer bed, which changes the temperature gradient between the burner and the reformer bed. This concept is illustrated in Fig. 3. Calculating the reformer bed temperature on the basis of the measured temperature can be laborious and this paper therefore introduces an alternative method. This method is based on Adaptive Neuro-Fuzzy Inference System models, ANFIS models for short, trained on experimental data. ANFIS is, as the name suggests, a modeling approach based on a combination of Fuzzy logic and Neural Networks. It was developed by Jyh-Sing Roger Jang [10] and can be trained to behave like a nonlinear physical system. The modeling section of this paper will describe the theory behind the ANFIS modeling scheme. ANFIS modeling and similar approaches have previously been used for modeling the voltage of a PEM-fuel cell [11,12] with success. It has also been used to model solid oxide fuel cells [13,14] as well as for direct Methanol Fuel Cell systems [15]. There are, however, no examples in the literature of
Fig. 2 e The H3-350 system from Serenergy.
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Fig. 3 e Concept drawing of a reformer and burner with sensor placement.
ANFIS models being used to predict the composition of the output gas of a reformer or in RMFC systems. Based on the reactions in Equations (1)e(3), models of the H2, CO2, CO and CH3OH content in the reformed gas will be developed. The mass flow of water in the fuel can be calculated by summing the water present due to the steam to carbon ratio and the extra water present due to the CH3OH which passes through the reformer. The developed models can be used in a wide range of applications. For example in a dynamic model of the H3-350 module, for fuel cell stoichiometry observation and control, advanced control systems, or fuel cell diagnostics systems.
2.
Reforming process modeling
This section describes the ANFIS modeling structure employed in this work and the training based on identification experiments as developed by Jyh-Sing Roger Jang [10]. It also includes an evaluation of the model performance.
2.1.
Adaptive Neuro-Fuzzy Inference Systems
As mentioned in the previous section, ANFIS modeling has been used to model various complex nonlinear phenomena. This is possible because ANFIS uses a human-like reasoning scheme which learns to imitate a physical system based on experimental data. This is achieved by combining the virtues of Fuzzy Inference Systems (FIS) and Neural Networks (NN). These virtues are the ability to make decisions based on expert knowledge for the FIS and the ability to make adaptations based on data for the NN. Fig. 4 shows an ANFIS system with two inputs and one output. In this work the inputs will be the measured reformer temperature and the fuel flow into the reformer. The output is the mass flow of the gas in question. The ANFIS model structure consists of five layers. The first layer is the fuzzification layer. Here the crisp input signals are converted into fuzzy variables. These are numbers between 0 and 1 and can be interpreted as the degree to which the input has a certain property. In Fig. 4 where a system with two membership functions per input is depicted, the properties will be interpreted as high and low. In this work bell-shaped membership functions are used. Bell-shaped means that the edges of the membership functions are smooth, which ensures a smooth transition between membership functions. Fig. 5 shows three bell-shaped membership functions.
Fig. 4 e ANFIS model structure used in this work.
Equation (4) shows a bell shaped membership function. O1;i ¼ mAi ðx1 Þ ¼
1 x1 ci 2bi 1 þ ai
(4)
O1,i denotes the output of the ith note of the 1st layer. mAi(x1) is the degree of membership of the input x1 to the linguistic variable Ai. ai, bi and ci are the adaptive premise parameters which determine the shape of the membership function. The nodes in layer 2,which are non-adaptive, determine the firing levels of the individual rules. They are marked T because fuzzy T-norms are used, here the fuzzy AND is employed. There are many versions of this, but here the product method is used as shown in Equation (5). O2;i ¼ wi ¼ mAi ðx1 Þ$mBi ðx2 Þ
(5)
Where wi is the firing level of the ith rule. This can be interpreted as the degree to which x1 is Ai AND x2 is Bi. If another AND method is chosen, the adaptive parameters will be different but it will not necessarily effect the accuracy of the model. Layer 3 is the normalization layer where each firing level is normalized according to Equation (6). wi O3;i ¼ wi ¼ Pn
(6)
i2 ¼1 wi2
Where wi is the normalized firing levels of the individual rules and n is the number of rules. This layer is also non-adaptive. In layer 4 the contribution of each individual rule to the output of the model is calculated according to: O4;i ¼ wi $fi ¼ wi $ pi $x1 þ qi $x2 þ ri
(7)
Here x1 and x2 are the inputs for the model and pi, qi and ri are the adaptive consequent parameters. The output of this layer can be interpreted as, for example, the consequence of
1 A1
A2
A3 x
Fig. 5 e Bell-shaped membership functions.
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low temperature and high fuel flow on the output. In layer 5 all of the contributions of the individual rules are summed up to give the output of the ANFIS model. O5 ¼ y ¼
n X
wi $fi
(8)
i¼1
Here y is the output of the model as in Fig. 4. The training of the ANFIS models is an iterative process which takes place over a series of epochs. Each epoch contains a forward and a backwards pass. In the forward pass, the node outputs are calculated up to layer 4. The consequent parameters in layer 5 are then calculated using a leastsquares regression method. In the following backwards pass, the premise parameters in the membership functions are updated by gradient descent methods. After a number of epochs no performance improvements are achieved by further optimization. In this work 5 epochs are used because experience shows this number to be sufficient. The relatively simple nature of the mathematical operations performed in each layer means that the ANFIS models can be implemented in systems which have relatively small computing power. This could for example be in a DSP as part of a control system. It is also advantageous in a larger dynamic model where the output has to be calculated in every in model iteration.
2.2.
Identification experiments
A test setup where the fuel cell is replaced by a gas analyzer is used for the identification experiments. The hydrogen for the burner which provides process heat for the reformer is supplied by a mass flow controller as is the process air for the burner. The cathode air from the fuel cell which is used to heat the evaporator is supplied by a mass flow controller which has a built in temperature controller. Fig. 6 shows a diagram of the test setup. The gas analyzer takes a sample of the reformer’s output gas and splits it between a Total Organic Carbon, or TOC, analyzer and a dry gas analyzer. The TOC analyzer is a Siemens Fidamat 6 which is used to measure the CH3OH content of the gas. The dry gas analyzer is a Siemens Ultramat which measures CO2 and CO content connected in series with a Siemens Calomat 6 which measures the hydrogen content. For the ANFIS models to be useful they must be trained on data which covers the entire operating range of the reformer.
This applies to both the operating temperature and the fuel flow. The maximum operating temperature of the catalyst is 300 C and the minimum is 240 C. Therefore the identification experiment is performed in 10 C intervals from 240 to 300 C. 10 C intervals were chosen, because initial experiments showed, that this was sufficient to model the gas composition precisely. The maximum rated fuel flow of the H3-350 module is 440 [mL/h], which is chosen as the maximum flow in the experiment. Experiments show that the gas analyzer used in the experiments needs a minimum fuel flow of 125 [mL/h] to perform its measurements. The minimum current of the H3-350 module, however, corresponds to a fuel flow of about 200 [mL/h], which is therefore chosen as the minimum flow in the experiment. At each temperature the fuel flow starts at 200 [mL/h] and is then stepped through 250, 300, 350, 400 and 450 [mL/h]. It is then brought back to 200 [mL/h] through the same steps. This is done to see if the past operating point effects the performance in the new operating point. It is chosen to keep the temperature constant while the fuel flow is stepped through the chosen operating points. Each operating point is evaluated over a period of 20 [min] to ensure that the reformer has entered steady state operation. Plot a in Fig. 7 shows the measured reformer temperature and plot b shows the fuel flow set point during the experiment. Plot c in Fig. 7 shows the measured hydrogen flow during the experiment and the value calculated assuming full reformation. The plot shows that the degree to which the fuel is reformed is dependent on the reformer temperature as expected. Higher temperature means a hydrogen flow which is closer to full reformation and therefore a more complete reformation of the fuel. The figure also shows that higher flows cause a larger discrepancy between full reformation and the measured flow. These observations demonstrate the need for accurate gas flow models. Plot d shows the measured CO2 mass flow in the reformed gas and the mass flow calculated using full reformation. Plot e shows the fuel flow in the top plot and the CO flow in the reformed gas in the bottom plot. In general higher temperature means a more CO in the reformed gas. This is also observed in the experiments. Intuitively one would assume that higher mass flow of fuel would mean more CO, but this is not always the case in the experiment. When the fuel flow is stepped up, the mass flow of CO increases until the fuel flow reaches 350 [mL/h] and then starts to decrease. This can be an indication that the actual reformer bed temperature is dropping as the fuel flow is increased as suggested in the introduction. Plot f shows the CH3OH flow in the reformed gas. As expected the measured CH3OH mass flow is lowest at high temperatures. There is in addition a correlation between fuel flow and the CH3OH mass flow in the reformed gas. These tendencies mirror those observed in the H2 measurements.
2.3. Fig. 6 e Test setup used to evaluate the reformed gas flow from the reformer.
Model construction and evaluation
The data from the experiment described in the previous section is used to train ANFIS models of the mass flow of H2, CO2,
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Fig. 7 e Temperature and fuel flow during the experiment as well as the mass flows measured in the reformed gas.
CO and CH3OH in the reformed gas. The input for these models is the measured reformer temperature and the fuel flow set point. The ANFIS function in MATLAB is used for the model construction. Bell-shaped membership functions and 5 training epochs are used in all models. As mentioned earlier the number of membership functions determines the model’s ability to model nonlinearities. However, more membership functions does mean more computationally heavy models. This is because the number of rules
in the models increases with the number of membership functions squared. Models with different numbers of membership functions are therefore constructed. The final choice of model is a compromise between performance or low error, and a subjective preference for the simplest model which shows good performance. The Mean Absolute Error, or MAE, is used to evaluate the performance of the models with different numbers of membership functions. Equation (9) shows how the MAE is calculated.
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Table 1 e MAE of the ANFIS models using different numbers of membership functions. # Membership functions H2 MAE % CO2 MAE % CO MAE % CH3OH MAE %
MAE ¼ mean
n X jei j i¼1
3
4
5
6
0.7 0.71 6.86 5.31
0.60 0.67 6.37 4.56
0.59 0.6 6.4 4.5
0.56 0.55 6.42 4.3
n
! (9)
Table 1 shows the MAE of H2, CO2, CO and CH3OH models with 3, 4, 5, and 6 membership functions. Because all of the H2 models have similar MAE, the simplest model, the one with 3 membership functions, is chosen. The same is the case for the CO2 models. The noisy nature of the training data for the ANFIS models means that the MAE of the CO models is higher than those of
Fig. 8 e Mass flow of the different components of the reformed gas measured during the experiments and the output of the ANFIS models when they are subjected to the same reformer temperature and fuel flow.
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Fig. 9 e Calculated stoichiometry using full reformation lFC Standard and the developed ANFIS models lFC ANFIS during a series of changes in fuel cell current.
the H2 and CO2 models. The tendencies of the measured data are, however, reflected in the models and it the use of 4 membership functions is chosen because it gives the lowest MAE. Again the noisy training data means that the MAEs of the CH3OH models are larger than those of the H2 and CO2 models. 4 membership functions are chosen because increasing to five or six only improves the performance slightly. Fig. 8 shows the mass flows measured in the experiment and those calculated using the developed models. After a period of operation the experiment is repeated to further evaluate the performance of the models. It is observed in the experiment that the catalyst in the reformer has degraded resulting in a less complete reformation. The MAE of the H2 model is now 4.32%, the CO2 model is 4.32%, the CO model is 39.46% and the CH3OH model is 46.48%. This indicates a need to include catalyst degradation in the models in the future. To illustrate the usefulness of the models, the stoichiometry of the H3-350 module is analyzed during a series of load changes. The CAN-bus data readout of the module is used to obtain the module’s stoichiometry set point which is set assuming full conversion. This is plotted in Fig. 9 together with the stoichiometry calculated using the developed ANFIS models. The specified minimum stoichiometry of the system is 1.15. The standard stoichiometry predictor is approximately 1.5 throughout the experiment, which is the standard set point. The stoichiometry predicted by the ANFIS model, however, is constantly lower than this and changes with the operating point. It does not drop below the lower stoichiometry limit, but the example does highlight the lack of control over the module’s stoichiometry when full reformation is assumed. The ANFIS model can be implemented in the H3-350 module’s control system to remedy this problem. The usefulness of these models is not limited to stoichiometry prediction. They can also be used in a dynamic system model where the CO models are very useful in determining the fuel cell efficiency. By deducting the CH3OH in the exhaust before calculating the energy consumed by the reformation process, this can be calculated with greater accuracy. The
CH3OH in the exhaust gas will also be present in the anode exhaust and is therefore fed to the catalytic burner which supplies heat energy to the reformer. This can also be modeled using the ANFIS models.
3.
Conclusion
In this work the problem of predicting the mass flow of the different constituents of the reformed gas from a methanol steam reformer is described. An accurate prediction is important for modeling and stoichiometry observation on Reformed Methanol Fuel Cell systems. A solution to the problem based on Adaptive Neuro-Fuzzy Inference Systems, or ANFIS for short, is proposed. The ANFIS models are of the mass flow of H2, CO2, CO and CH3OH in the reformed gas and they are trained on experimental data. The models of the H2 and CO2 are accurate to within 1% when compared to the training data when using Mean Absolute Error, or MAE for comparison. They are both determined to have the optimal performance for the smallest model complexity when 3 membership functions are used. The CO model has an MAE of 6.37% and the CH3OH model has an MAE of 4.56%. This higher deviation is primarily due to the noisy nature of the training data used to construct these models. They do, however, display the same tendencies as the experimental data and are therefore deemed valid for modeling purposes. When the experiment is repeated after a period of operation, an increase in MAE is observed for all models. This is because of degradation of the reformer catalyst. It was demonstrated how the H2 model can be used to calculate the stoichiometry of the fuel cell online.
4.
Future work
A high degree of catalyst degradation was observed during the experiments. This effect is interesting to include in the
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models, because it would make it possible to analyze the performance of a RMFC module throughout its lifetime. This could be done by including the total amount of methanol, which has passed through the reformer in its lifetime as an input. The models developed in this work can be used in a dynamic model of the system. This model can be used to evaluate the stability of the H3-350 module’s control systems while taking varying gas compositions into account. If the model contains an accurate fuel cell model, it can also be used to find the optimal operating temperatures for the module at different current set points. This will be a balancing act between high CO content, which harms the fuel cell efficiency, and a low CH3OH slip at high reformer temperature and low CO content and large CH3OH slip at low temperatures. The models can also be included in an online optimization scheme which optimizes the system efficiency at different operating points. As mentioned before, the H2 model can be used to observe the stoichiometry of the fuel cell online and can be the basis of an online stoichiometry controller. It is, however, also possible to reverse the model to predict the fuel flow which is necessary to uphold a certain stoichiometry and thereby use the model as an open loop fuel controller. The models can also be included in a fuel cell diagnostics system.
Acknowledgments We gratefully acknowledge the cooperation of Serenergy A/S and the financial support from the EUDP Program and the Danish Energy Agency.
references
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