Modeling and Control Strategies of Proton Exchange Membrane Fuel Cells

Modeling and Control Strategies of Proton Exchange Membrane Fuel Cells

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Energy Procedia Procedia 00 159(2017) (2019)000–000 54–59 Energy www.elsevier.com/locate/procedia

Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018, 29–30 September 2018, Rhodes, Greece International Symposium District Heating and Cooling ModelingThe and15th Control Strategies ofonProton Exchange Membrane Cellsthe heat demand-outdoor Assessing the feasibilityFuel of using aa bb a, a,* Yuanxin Qiaa, Marcus Thern , Mayken Espinoza-Andaluz , Martin Andersson temperature function for a long-term district heat demand forecast a aLund

Lund University, University, P.O.Box P.O.Box 118, 118, Lund Lund 22100, 22100, Sweden Sweden

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc bb Escuela

a

P.O.Box 09-01-5683, 09-01-5683, Guayaquil 90112, Ecuador Escuela Superior Superior Politécnica Politécnica del del Litoral, Litoral, P.O.Box Guayaquil 90112, Ecuador IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France

Abstract Abstract

In for polymer polymer electrolyte (PEFCs) with with three three different different controllers controllers (PID, (PID, In this this work, work, comprehensive comprehensive mathematical mathematical models models for electrolyte fuel fuel cells cells (PEFCs) Abstract FOPID and fuzzy fuzzy + + PID) PID) are are developed. developed. The are designed designed to to control control the the PEMFCs’ PEMFCs’ output output voltage voltage at at aa determined determined value value by by FOPID and The models models are indirectly regulating the input hydrogen mass flow rate. The simulation results show that the developed model is well suitable for indirectly regulating the input hydrogen mass flow rate. The simulation results show that the developed model is well suitable for District heating networks areaa commonly in the literature as one in the most the effective decreasing the characterizing the performance performance PEFC. The The addressed developed controllers controllers are effective effective inofstabilizing stabilizing the voltage,solutions the fuzzy fuzzyfor + PID PID controller characterizing the PEFC. developed are voltage, the + controller greenhouse gas performance emissions from building sector. These systems require high investments which are returned through the heat exhibits superior performance withthesmaller smaller overshoot and faster faster response. exhibits superior with overshoot and response. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, ©prolonging 2019 The Published byperiod. Elsevier Ltd. Copyright © 2018 Elsevier Ltd. All rights Copyright © Authors. 2018 Elsevier Ltd. All rights reserved. reserved. the investment return This is an open access article under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of committee the Energy Symposium and Selection peer-review underis responsibility of the the scientific scientific committee of the Applied Applied Energy Symposium and Forum, Forum, The mainand scope of this paper to assess the feasibility of using the heat of demand – outdoor temperature function for heat demand Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with REM 2018. Renewable Energy Integration with Mini/Microgrids, Mini/Microgrids, REM 2018. was used as a case study. The district is consisted of 665 forecast. The district of Alvalade, located in Lisbon (Portugal), Renewable Energy Integration with Mini/Microgrids, REM 2018. buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: PEFCs, modeling, PID controller, (shallow, FOPID controller, controller, fuzzy + + deep). PID controller; controller; Keywords: PEFCs, modeling, PID controller, FOPID fuzzy PID renovation scenarios were developed intermediate, To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value ofelectrolyte slope coefficient increased on have average within the as range of 3.8% up to 8% per for decade, that corresponds the Polymer electrolyte fuel cells cells (PEFCs) have been proved as the most most prime candidate for portable, automotivetoand and Polymer fuel (PEFCs) been proved the prime candidate portable, automotive decrease in the number due of heating 22-139h duringlow the operating heating season (depending the durability combination of weather and stationary applications due to their theirhours highofpower density, low operating temperature andonhigh high durability [1-4]. stationary applications to high power density, temperature and [1-4]. renovation the otherof function increased for 7.8-12.7% perand decade (depending on the Modelingscenarios researchconsidered). and control controlOn strategies ofhand, PEFCs are of ofintercept significant importance to analyze analyze and predict the system’s system’s Modeling research and strategies PEFCs are significant importance to predict the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, behavior and and also also to to optimize optimize its its output output performance performance [5]. [5]. In In Ahn Ahn and and Choe Choe [6], [6], the the PEFC PEFC dynamic dynamic stack stack behavior behavior and is behavior is improve the accuracy of heat demand estimations. improved using classic PID controllers for temperature regulation in a system model. In Lü et al [7], a FOPID controller

improved using classic PID controllers for temperature regulation in a system model. In Lü et al [7], a FOPID controller © 2017 The Authors. Published by Elsevier Ltd. * author. Tel.: 222 08; 46 Peer-review under responsibility the49 Committee of The 15th International Symposium on District Heating and * Corresponding Corresponding author. Tel.: +46 +46 46 46of 222 49Scientific 08; fax: fax: +46 +46 46 222 222 47 47 17. 17. Cooling. E-mail E-mail address: address: [email protected] [email protected]

Keywords: Heat demand; Forecast; Climate change

1876-6102 1876-6102 Copyright Copyright © © 2018 2018 Elsevier Elsevier Ltd. Ltd. All All rights rights reserved. reserved. Selection Selection and and peer-review peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the Applied Applied Energy Energy Symposium Symposium and and Forum, Forum, Renewable Renewable Energy Energy Integration with with Mini/Microgrids, Mini/Microgrids, REM REM 2018. 2018. Integration 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 10.1016/j.egypro.2018.12.017

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is used to enhance the dynamic performance and efficiency of PEFC. In Justesen et al [8], fuzzy logical control principle is utilized for optimization of PEFC system in high temperature condition. In Benchouia et al [9], good control effects are achieved by using an adaptive fuzzy logic controller (AFLC) for PEFC voltage control at the presence of fluctuations. Each controller mentioned above has been studied previously, but very limited research has been conducted comparing them. In this paper, a comprehensive mathematical model for PEFCs is developed, and more importantly, three different controllers, i.e., PID, fuzzy + PID, and FOPID are designed simultaneously to control the PEFC system to maintain a constant output voltage with an comprehensive comparison for their different features and advantages. This paper is organized as follows: Section 2 describes the mathematical model of the PEFCs and exhibits its simulation results. Three different control strategies and their control effects are presented in Section 3. Finally, conclusions are drawn in Section 4. Nomenclature Kp

proportion parameter

Kec deviation rate Kp* Kd*

Ki integration parameter

Kd

Ke deviation quantizing factor Vref

proportion parameter of the FOPID controller

differential parameter

λ

integrating order

reference voltage, V

μ

derivative order

Ki* integration parameter of the FOPID controller

differential parameter of the FOPID controller

2. Model definition 2.1. Electrochemical equations in static model In this paper, for more convenient analysis of the PEFC models, some necessary assumptions are considered, i.e., ideal reactant gases, pure hydrogen as fuels, uniform temperature in the whole fuel cell, steam neglected [10]. All the electrochemical equations used for characterizing PEFC static behaviors like voltage, power, efficiency, temperature variation are extracted from [11]. 2.2. Dynamic model There is a “charge double layer” phenomenon in fuel cells, which is extremely important for understanding the dynamic behaviors, i.e., when two different charged materials are in contact there is a charge accumulation on their surface or a load transfer. The charge layer on the interface electrode / electrolyte acts as a storage of electrical charges and energy, in this way it behaves as an electrical capacitor [12]. The equivalent circuit diagram is depicted in Fig. 1. The detailed information of the PEFC’s over the static and dynamic system parameters, its operating condition parameters and the experimental data used for validation are all extracted from [13].

Fig. 1 Equivalent circuit diagram

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3

2.3. Results for the static model Fig. 2 shows the PEFC’s static behavior. The supplied load current is gradually increased from 0 A to 35 A. It can be seen in Fig. 2 (a) that the simulated polarization curve presents a good agreement with the experimental data. At the beginning, the stack voltage falls fast due to the activation polarization, then it decreases linearly with the increased current due to ohmic polarization, finally as the current continues to increase, the voltage drops significantly. The power behavior is presented in Fig. 2 (b), and it can be observed that there is a peak with a value of 834 W at the current of 31 A. The stack efficiency presented in Fig. 2 (c) and it shows a similar behavior to that of voltage. The efficiency is high for low current and low power, which is important for PEFC’s system evaluation. 45

(a)

0.6

(b)

800

Simulation data Experimental data

(c)

35

30

400

0.5

0.4

200

25

20

600

Stack Efficiency

Stack Power (W)

Stack Voltage (V)

40

0

5

10

15

20

Current (A)

25

30

35

0

5

10

15

20

Current (A)

25

30

0.3

35

0

5

10

15

20

Current (A)

25

30

Fig. 2. Simulation results for PEFC static model

2.4. Result for the dynamic model Fig. 3 depicts the dynamic behavior of PEFC. In Fig. 3(a), the stack supplies 5 A to the load after 3 s and the current is at the same time increased to 15 A, which remains until the 6 s. Finally the load current is decreased to 5 A, until the end of the simulation at 10 s. The voltage curve is presented in Fig. 3(b) and it can be observed that there is a response delay as the load current has a sudden change. The voltage is 39.45 V before the current is increased, 35.05 when current is kept at 15 A, and again 39.45 V when the load is decreased. Fig. 3(c) shows the stack power response, with a peak at the load current’s first increase instant, with a maximum value of 580 W. At the current’s decrease instant, the power presents a minimum value of 180 W. The power has a steady-state value of 196.40 W for a current at 5 A, and 530 W with a current of 15 A. Fig. 3(d) shows the stack efficiency. The curve is just similar to the voltage curve, since they are directly related. The steady-state values for stack efficiency are 53% (HHV) for the current of 5 A and 46% (HHV) for a current of 15 A, i.e., one can see that there is a significant reduction in efficiency when load current is increased. This should be taken into consideration when a certain system is evaluated. 20

60

(a)

(b)

55 Stack Voltage (V)

Stack Current (A)

15

10

50 45 40

5

35 0

0

2

4

Time (s)

6

8

10

30

0

2

4

Time (s)

6

8

10

35

4

Yuanxin Qi et al. / Energy Procedia 159 (2019) 54–59 Author name / Energy Procedia 00 (2018) 000–000 600

1.0

(c)

400

300

200

100

(d)

0.8 Stack Efficiency

Stack Power (W)

500

57

0.6

0.4

0.2

0

2

4

Time (s)

6

8

10

0.0

0

2

4

Time (s)

6

8

10

Fig. 3. Simulation results for PEFC dynamic model

3. Voltage control 3.1. Control system The PID control is the most widely used form of feedback control in industrial applications due to its accurate and fast responsive correction to a control function. It is composed of three units: proportion, integration and differential. The parameters are obtained by an automotive tuning method [14]. The FOPID controller is a convenient fractional order structure that is employed for control purposes and it is characterized by five parameters: (1) the proportional gain, (2) the integrating gain, (3) the derivative gain, (4) the integrating order and (5) the derivative order. The two more units (4) and (5) suggesting its greater accuracy than the traditional PID controller, the FOPID method is based on Aleksei et al. [15]. The Fuzzy + PID controller combines the fuzzy logical control algorithm and PID control algorithm. It is capable for PID’s parameters on-line adjusting, which could greatly improve the controller’s performance [16]. A PEFC system is a nonlinear, complex and strong coupled system with many parameters that could easily affect its output voltage. In this paper, the hydrogen mass flow rate is adjusted by the controllers to stabilize its voltage. The structures of three different controllers and the whole control system are shown in Fig. 4. And all the related parameters are listed in Table 1.

Fig. 4. Structures of the controllers and whole control system

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Table 1. Parameters for PID, FOPID and Fuzzy + PID controllers. Parameter

Value

Kp

6.78

Parameter Ke

Value 6

KI

5.05

Kec

6

Kd

-0.72

Ki*

5

10

μ

0.93

Kd*

0.06

λ

0.89

Vref

45 V

Kp

*

3.2. Results for voltage control Using the parameters in Table 1, the three different controllers are designed and implemented according to Fig. 4 (d), with results shown in Fig. 5. In Fig. 5 (a), the input current is 3 A, and after 30 s, it is increased to 5 A, that remains until the end of the simulation. From Fig. 5 (b), it can be observed that all these three controllers are capable of describing the systematic disturbance, and maintaining the voltage at the given value. It is clear that the FOPID controller is slightly more effective than the PID controller with a smaller overshoot. The Fuzzy + PID controller exhibits the best performance with the smallest overshoot and fastest response. 6

46

(a)

(b)

PID Fuzzy+PID Fractional order PID

Stack Voltage (V)

Stack Current (A)

5

4

45

44

3

2

0

10

20

30

Time (s)

40

50

60

43

0

10

20

30

Time (s)

40

50

60

Fig. 5 Voltage control results

4. Conclusions In this paper, PEFC comprehensive mathematical models are developed, with PID controller, FOPID controller and Fuzzy + PID controller, which are designed to control PEFC’s output voltage by regulating the hydrogen mass flow rate. The use of FOPID controller is motivated by the fact that the presence of extra tuning parameter (fractional parameter) allows greater flexibility in achieving the design specifications, the Fuzzy + PID controller is selected because of its ability for PID’s parameters on-line adjusting, which will lead to a better control performance compared with classic a PID controller. The simulation results show that the developed model is well suitable to explain the PEFC steady-state performance as well as dynamic behaviour. It is also shown that the model predictions are in a very good agreement with experimental studies. All three controllers are effective in restraining system disturbance and tracking the reference voltage, but the Fuzzy + PID controller displays the best performance with a smaller overshoot and a faster response. The results presented in this paper can be used to further optimize the overall efficiency and cost of the fuel cells. 5. Acknowledgements The authors would like to acknowledge support from the Chinese Scholarship Council, grant number: 201706080005, Åforsk foundation, grant number: 17-331 as well as Vinnova, grant number: 2015-01485.

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6. References [1] M. Andersson, S. Beale, M. Espinoza, Z. Wu, W. Lehnert, A review of cell-scale multiphase flow modeling, including water management, in polymer electrolyte fuel cells, Applied Energy, 180 (2016) 757-778. [2] M. Andersson, S. Beale, U. Reimer, W. Lehnert, D. Stolten, Interface resolving two-phase flow simulations in gas channels relevant for polymer electrolyte fuel cells using the volume of fluid approach, International Journal of Hydrogen Energy, 43 (2018) 2961-2976. [3] M. Espinoza, M. Andersson, J. Yuan, B. Sundén, Compress effects on porosity, gas‐phase tortuosity, and gas permeability in a simulated PEM gas diffusion layer, International Journal of Energy Research, 39 (2015) 1528-1536. [4] S. Li, J. Yuan, G. Xie, B. Sunden, Numerical investigation of transport phenomena in high temperature proton exchange membrane fuel cells with different flow field designs, Numerical Heat Transfer, Part A: Applications, 72 (2017) 807-820. [5] M. Outeiro, A. Carvalho, MatLab/Simulink as design tool of PEM Fuel Cells as electrical generation systems, in: European Fuel Cell Forum, 2011. [6] J.-W. Ahn, S.-Y. Choe, Coolant controls of a PEM fuel cell system, Journal of Power Sources, 179 (2008) 252264. [7] X. Lü, X. Miao, Y. Xue, L. Deng, M. Wang, D. Gu, X. Li, Dynamic Modeling and Fractional Order PI λ D μ Control of PEM Fuel Cell, Int. J. Electrochem. Sci, 12 (2017) 7518-7536. [8] K.K. Justesen, S.J. Andreasen, S.L. Sahlin, Modeling of a HTPEM fuel cell using adaptive neuro-fuzzy inference systems, International Journal of Hydrogen Energy, 40 (2015) 16814-16819. [9] N.E. Benchouia, A. Derghal, B. Mahmah, B. Madi, L. Khochemane, E.H. Aoul, An adaptive fuzzy logic controller (AFLC) for PEMFC fuel cell, International Journal of Hydrogen Energy, 40 (2015) 13806-13819. [10] Z. Ural, M.T. Gencoglu, Mathematical models of PEM fuel cells, in: 5th International Ege Energy Symposium and Exhibition (IEESE-5), 2010. [11] R. Geethanjali, R. Sivakumar, Design of intelligent controller for PEM fuel cell, in: Science Technology Engineering & Management (ICONSTEM), 2017 Third International Conference on, IEEE, 2017, pp. 1050-1053. [12] A. Saadi, M. Becherif, D. Hissel, H. Ramadan, Dynamic modeling and experimental analysis of PEMFCs: A comparative study, International Journal of Hydrogen Energy, 42 (2017) 1544-1557. [13] J.M. Corrêa, F.A. Farret, L.N. Canha, M.G. Simoes, An electrochemical-based fuel-cell model suitable for electrical engineering automation approach, IEEE Transactions on industrial electronics, 51 (2004) 1103-1112. [14] D.E. Rivera, M. Morari, S. Skogestad, Internal model control: PID controller design, Industrial & engineering chemistry process design and development, 25 (1986) 252-265. [15] T. Aleksei, P. Eduard, B. Juri, A flexible MATLAB tool for optimal fractional-order PID controller design subject to specifications, in: Control Conference (CCC), 2012 31st Chinese, IEEE, 2012, pp. 4698-4703. [16] V. Rahmati, A. Ghorbani, A Novel Low Complexity Fast Response Time Fuzzy PID Controller for Antenna Adjusting Using Two Direct Current Motors, Indian Journal of Science and Technology, 11 (2018).