Modeling and Predictive Control of an Integrated Reformer

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Process Systems Engineering

Modeling and Predictive Control of an Integrated ReformerMembrane-Fuel cell-Battery Hybrid Dynamic System Pravin P S, Sharad Bhartiya, and Ravindra D. Gudi Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00688 • Publication Date (Web): 12 May 2019 Downloaded from http://pubs.acs.org on May 12, 2019

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Industrial & Engineering Chemistry Research

Modeling and Predictive Control of an Integrated Reformer-Membrane-Fuel cell-Battery Hybrid Dynamic System Pravin P S, Sharad Bhartiya, and Ravindra D Gudi˚ Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India E-mail: [email protected],[email protected],[email protected]

Abstract The main technological barrier in the commercialization of fuel cells lies in the difficulty of on-board hydrogen storage, especially for portable applications. The technology adopted in this paper to overcome this drawback is to indirectly store hydrogen in a hydrocarbon form. The stored hydrocarbon fuel can be converted to a hydrogen rich stream utilizing an auto thermal reformer. Pure hydrogen gas can be separated from the gas mixtures exiting the reformer by passing it through a palladium membrane based gas separation unit. The purified hydrogen gas can be fed to the fuel cell anode and air to the cathode to generate power. A battery unit is considered that serves as a supplementary power source to assist the fuel cell to deliver delay free power, in presence of uncertainties in the external load. This work basically focuses on the dynamic mathematical modeling and advanced, optimization based control of the integrated reformer-membrane-fuel cell-battery hybrid power system. This work is an ˚

To whom correspondence should be addressed

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

extension to an earlier work, where dynamic analysis and basic control studies of the integrated system without a battery unit, were examined. This paper includes a battery unit along with the fuel cell in order to meet the power demand especially during sudden load fluctuations and plant start-up. The presence of two energy sources to control the uncertainty in demand leads to the formation of a mixed logical dynamical (MLD) system. The control of such a MLD system has been attempted in a Model Predictive Control (MPC) framework in this paper. This resulting advanced control scheme has been implemented on the hybrid system to analyze the performance for a representative power application.

1 Introduction From the energy evolution view point, hydrogen is the fuel for future power generation applications. Hydrogen is the cleanest fuel available with much higher heating value compared to other commonly used fuels like petrol. The available methods for providing hydrogen to fuel cells is by either storing it in storage tanks, or by storing it indirectly in a hydrocarbon form and converting it into hydrogen using a fuel processor 1 . As hydrogen is not naturally available, there always exists a manufacturing cost associated with the hydrogen production from the available hydrocarbons. Another important bottleneck for use of hydrogen, especially in portable applications, lies in its direct storage 2 . This is due to the requirement of large composite vessels that can withstand high pressures of hydrogen because of its low volumetric energy density. This requirement might not be a problem for stationary applications and large heavy duty vehicles, but can be a challenging problem in portable and light duty automotive applications especially where space is a constraint. One notable drawback of hydrogen lies in the requirement of cryogenic temperatures for its storage. Another crucial issue with direct hydrogen storage is its flammability when exposed to air. There have been several research efforts to address these drawbacks. Gkanas et al. 3 has explored efficient hydrogen storage mechanism using metal hydride tanks using aluminium extended surfaces. A detailed review 2


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on the recent developments in fuel cell energy systems highlighting the metal hydride based hydrogen storage has been carried out by Lototskyy et al. 4 . A comparative study on the several available hydrogen storage technologies for fuel cell applications has been done by Ozaki et al. 5 . Another method to overcome the drawback of direct hydrogen storage, which is the principal focus of this paper, is to store hydrogen rich hydrocarbons on-board and suitably convert them into usable hydrogen fuel in-situ on an as needed basis. The most preferred technique to convert hydrocarbons to hydrogen is by using the commonly available method of reforming. The main motivation behind the present work is to avoid the drawback of direct hydrogen storage by exploring the possibility of storing a hydrocarbon fuel that is rich in hydrogen. The storage fuel rich in hydrogen is natural gas which already has an advantage of excellent infrastructure and ready availability. Mathematical modeling studies of an auto thermal reformer using methane as the fuel for hydrogen production has been done by Lu et al. 6 . The hydrocarbon fuel gets converted to a hydrogen rich stream and is fed as input to the fuel cell for power generation. A study on the dynamics of a methanol reformer for hydrogen production for use in fuel cells in automotive applications has been conducted by Varesano et al. 7 . Design and control of dry methane reforming of natural gas to produce synthesis gas has been done by Luyben. 8 Auto thermal reforming is chosen to be an attractive option for converting the hydrocarbon fuel to hydrogen. The resulting reformer output stream contains hydrogen gas along with a mixture of other gases like CO, CO2 , O2 , unconverted CH4 , H2 O (steam) and the inert N2 . Pure hydrogen gas can be separated from the gas mixture by passing it through a palladium membrane based gas separation unit. A detailed study on the palladium membrane based hydrogen separation along with the membrane properties have been carried out by Zhang and Way 9 . The output of the gas separation/purification unit contains pure hydrogen gas which can be fed as input to the polymer electrolyte membrane fuel cell (PEMFC) system. Daud et al. 10 have done an extensive review on the various control aspects related to a PEMFC

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system alone giving more attention to fuel starvation and water and heat management. The authors have discussed both conventional and advanced controller designs and the challenges faced while designing a controller for a PEMFC. The combined mathematical model of the resulting integrated reformer-membrane-fuel cell system has already been discussed in an earlier work 11 and several control related studies were also carried out on the system to study the system dynamics. The slow dynamics of the reformer represent a bottleneck of the overall integrated system. Additionally, the PEMFC dynamics is also unable to satisfy sudden changes in load power demands. To overcome this limitation, this work proposes the introduction of a battery unit that has much faster response times compared to a PEMFC while meeting power requirements. Thounthong et al. 12 investigated the feasibility of employing batteries, super capacitors and PEMFC as a hybrid power system. The authors have performed a detailed study on the energy management of the battery-super capacitor- PEMFC hybrid system and have realized the system using the experiments conducted with analog circuits. However, a formal study related to the controller design and analysis of switching between different power sources has not been reported. Depending on the various operating modes of the integrated power generation system, the MPC decides whether to use fuel cell alone or battery alone or both sources combined to meet the load power demand. Based on the various modes of operation formulated as constraints to the MPC, the controller is designed to make effective decisions to select between the various power sources. It is well known that in case of electric vehicles, recharging an electric battery takes considerable amount of time as compared to refueling a fuel cell hydrogen tank. Due to this, in the present work, battery is chosen only as a supplementary power source to assist the PEMFC in case of sudden load power demands, so as to achieve a delay free delivery of power. Hence, the resulting integrated system altogether consists of an auto thermal reformer as the fuel processing subsystem, a palladium membrane based gas separator as the fuel purification subsystem and a hybrid combination of PEM fuel cell and battery as the power

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generation subsystem. Due to complexity in the first principles model of the integrated reformer-membrane-fuel cell -battery hybrid system, a control relevant mathematical model of the integrated hybrid dynamical system (HDS) has been identified in this paper using a system identification approach. Identified state space model obtained using data is utilized for the predictions needed for MPC. On the other hand, the plant is based on a fundamental first principles non-linear model. The optimal control input moves are decided by the MPC using the identified state space model, while the control inputs are fed to the actual non-linear plant which is the first principles model. While stabilizing formulations of MPC exist in literature 13 , the work proposed in this paper is more aligned towards demonstrating the integration of power generators and storage units, and therefore we have not pursued these stability aspects in the present work. Bemporad and Morari 14 have proposed a detailed framework for modeling and controlling linear HDS governed by logic rules and operating constraints, generally termed as a mixed logical dynamical (MLD) system. The authors also gave an extensive idea of the various stability and optimal control aspects in case of a MLD system. Approaches to identify linear models as well as experimental validation for HDS have been widely reported 15–17 . In this work, the co-ordination between the various modes of power considered such as PEMFC, battery and hybrid PEMFC-battery is modeled as an MLD system. MPC is then implemented to achieve the desired targets in presence of various constraints. The main contribution of this paper are as follows: Building upon the previous work 11 involving modeling and control of an integrated reformer, membrane and fuel cell system, we introduce a battery unit in the overall scheme to react to fluctuating power demands in an efficient manner. To formally treat the resulting control problem, the logical decisions of (i) deriving power from the battery unit, (ii) proactive charging of the battery, (iii) monitoring the state of charge (SOC) of the battery (ie. SOCmin ď SOC ď SOCmax ), along with other control decisions related to reformer and fuel cell operations need to be taken into account.

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Because of this hybrid nature of the integrated reformer-membrane-fuel cell-battery system consisting of many switching logic rules and constraints, the system has been treated as a MLD system. In this paper, an advanced optimization based MPC control algorithm is implemented on the integrated HDS to optimize the overall system performance by calculating optimal control input moves. It is shown here that the MPC is able to optimally switch between battery and PEMFC based on certain switching rules or logical conditions which are formulated as a set of constraints for the designed MPC problem. This helps the controller to react to various power demands in an improved manner while preserving the SOC constraints to keep the battery healthy. The rest of the paper is organized as follows. A brief description of the integrated reformer-membrane-fuel cell-battery system is given in the next section. In section 3, an overview of the first principles model of each subsystem in the integrated system is discussed. The overall control problem of the integrated plant is given in the section 4 and a control relevant model of the integrated system is generated using system identification in section 5. Section 6 gives a brief overview of the MPC and discusses the MPC problem for a MLD system. Section 7 is divided into three subsections. In the first subsection, the performance of the designed MPC with two different prediction horizons, to track the set point for a generic power application is studied. Next subsection discusses the case study of the system being designed to deliver power for a realistic power application viz. a light motor vehicle and the last subsection compares the designed system performance with and without a battery subsystem in the loop followed by conclusions in section 8.

2 Plant description Direct hydrogen storage on-board in fuel cell applications is avoided by combining fuel processing, fuel purification and power generation subsystems to form an integrated assembly.

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Earlier work 11 exhibited a settling time of 0.4 s in the case of the integrated system revealing that there is always a small delay associated with the power demanded by the load and the power delivered. This delay can mainly occur during two scenarios, one in case of plant startup and other during sudden changes in the load power demand. In order to avoid this drawback, a battery module, that has much faster response times compared to fuel cells 12 is also considered along with the integrated system to form a hybrid power source for meeting the power demand. The main components of the integrated system consist of auto thermal reformer for fuel processing, palladium membrane for fuel purification and fuel cell-battery hybrid module for power generation. A block diagram showing the basic components of the integrated system with a battery back-up is shown in Figure 1. During the plant operation, appropriate amounts of stored methane, air and steam are mixed and fed to the auto thermal reformer. The output of reformer mainly consists of hydrogen gas along with other components like CO, CO2 , unreacted CH4 , N2 , O2 and H2 O psteamq. By utilizing palladium membrane based gas separation process, pure hydrogen gas gets separated from other gas mixtures. Pure hydrogen is fed as input to the fuel cell anode through control valve 2 and air is fed as input to the cathode side of the fuel cell to generate power. A non-return valve (NRV) is installed in order to avoid the possible back flow of hydrogen gas from control valve 2 to the palladium membrane. Based on some switching rules or logical conditions, appropriate control actions need to be taken to switch between the fuel cell and battery for a delay-free delivery of power to the external load.

Figure 1: Block diagram showing the integrated reformer membrane fuel cell system

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In this paper, the maximum power demanded by the external load is assumed to be 40 kW . For this study, the maximum current density delivered by a single fuel cell is assumed to be 1.5319 A{cm2 at a cell voltage of 0.53 V . For an electrode area per cell of 100 cm2 , the maximum power a single fuel cell can generate comes to approximately 0.08 kW . For generating a power of 40 kW , approximately 500 such individual cells connected in series constituting a fuel cell stack is essential.

3 First principles modeling The integrated system discussed in this paper mainly consists of four subunits viz. auto thermal reformer, palladium membrane, PEMFC and battery. Effective control of any system depends on the accuracy of the mathematical model available. Detailed mathematical models of each subsystem except the battery unit were already discussed in an earlier paper 11 . Therefore, only a brief overview of the mathematical model of the first three subsystems are provided in the upcoming subsections, whereas the fourth subsystem, viz. battery unit is presented in detail.

3.1 Auto thermal reformer unit Auto thermal reformer, considered in this study is a cylindrical reactor using Nickel as the catalyst material. Based on the opening of control valve 1 (u1 ), requisite amount of methane flows to the reformer inlet for hydrogen production. The mathematical model of the auto thermal reformer was adopted from Halabi et al. 18 . The mathematical model basically involves mass and energy balance equations. A total of seven main species (H2 , CH4 , N2 , O2 , CO, CO2 and H2 O psteamq) are considered for developing the model of the auto thermal reformer. Mass balance of each species in the gas phase resulted in seven partial differential equations. Mass balance in the solid phase involves an algebraic equation giving mass transfer from gas to solid. Energy balance on the gas and solid phase result in single partial differential

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equation, one for gas and other for solid. Overall, the model describes the dynamics of concentrations for the seven species along with the gas and solid phase temperatures. More details on the model equations and parameter values used can be obtained from Pravin et al. 11 .

3.2 Palladium membrane based separation unit The permeation of hydrogen gas across the palladium membrane has been modeled using Sievert’s law, which uses the difference in partial pressures of hydrogen gas at the upstream and downstream sides of the membrane 19 . The molar flow rate of hydrogen gas through the palladium membrane results in an algebraic equation which is a function of the membrane permeability. The membrane permeability is modeled using the Arrhenius law. Further details on the membrane modeling can be found in Pravin et al. 11 .

3.3 PEM Fuel cell unit During the fuel cell operation, pure hydrogen gas is fed to the anode side of the fuel cell through control valve 2 (u2 ) and air is fed to the cathode side. The mathematical model of PEMFC basically involves the consumption equations for each species involved in the electrochemical reaction. The mathematical model of the low temperature PEMFC was adopted from Methekar et al. 20 . Mass balance of the species involved in the electrochemical reaction is given by a set of quasi steady state ordinary differential equations. Another set of ordinary differential equations describes the balance of water in liquid and vapor form at both anode and cathode sides of the fuel cell. Equations governing the variation in anode gas, cathode gas and coolant temperatures are also described by a set of ordinary differential equations. The energy balance for temperature of the solid membrane is described by a partial differential equation. For further details, the reader is referred to Pravin et al. 11 .

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3.4 Battery unit Mathematical modeling of a battery is one of the important considerations while designing electric vehicles as well as hybrid electric vehicles. The fundamental part to be considered while designing a battery is the State of charge (SOC). It is defined as the ratio of the remaining capacity to the fully charged capacity of a battery 21 . Change in SOC of a battery for a time interval ∆T is given as follows,

SOCpt ` ∆T q “ SOCptq ´

Used capacity Total capacity

(1)

ż Used capacity “

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Parameter I indicate the charging or discharging current of the battery which assumes a negative value while charging and a positive value while discharging. Wehbe and Karami 22 have developed several equivalent circuit models that gives a relationship between the SOC of a battery and its terminal voltage. Used capacity is given by the integral of the current drawn from the battery, while total capacity is the rated Ah capacity of the battery 23 . In essence, it can be elucidated that SOC of a battery is one when it is fully charged while zero when it is discharged to a critical voltage. Critical voltage refers to a minimum voltage beyond which the battery life degrades as the voltage starts dropping very rapidly. The value of the critical voltage used in this study is 3V , which corresponds to a minimum battery state of charge of 0.2 or 20%. In this paper, batteries with a single cell capacity of 12 V and 2.2 Ah are considered. In an ideal scenario considering an efficiency of 100%, the total number of battery cells required to generate a power of 40 kW comes to be approximately 1516 cells. However, the efficiency of a battery often depends on many factors like the rate of charging/discharging as well as the current state of charge of the battery. Usually for design purpose, an efficiency level of around 85% is assumed 24 . Hence, for an 85% efficient battery,

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the total number of cells required for a power of 40 kW turns out to be approximately 1783 cells. The main parameters to be considered while designing a battery are the state of charge and the terminal voltage. Two additional inputs, u3 and u4 are introduced in the expression for SOC of the battery in this paper, where u3 denotes the battery charging current from the fuel cell and u4 denotes the battery discharging current to the external load. Modified model equation for SOC of the battery including both charging and discharging currents is as follows.

SOCpt ` ∆T q “ SOCptq `

u3 .∆T u4 .∆T ´ 2.2Ah 2.2Ah

(3)

where, ∆T denotes the sampling time of the process. In the model equation given in Eq.(3), a hard constraint is provided to make sure that the battery charging and discharging does not happen simultaneously (ie. u3 .u4 = 0). A detailed study of the available battery pack models were carried out by Li and Mazzola 24 , wherein several empirical battery models including electrochemical battery model and battery behavioral models were discussed. Battery terminal voltage is the actual voltage output from the battery unit and is considered as the third process output in this paper. The expression giving the relation of battery terminal voltage as a function of the battery state of charge is given as:

Vterm (t) “ 15 ˚ SOCptq

(4)

where, SOCptq and Vterm (t) are the battery terminal voltage and state of charge at any given time instant t respectively. The battery unit designed in this particular study has a rating of 12 V and 2.2 Ah. Relationship between battery voltage and state of charge has already been discussed by authors in 21 . In this particular study, for a maximum SOC rating of 0.8, the corresponding battery voltage needs to be 12 V and for a minimum SOC rating of 0.2, the battery voltage should be equal to 3 V (critical voltage). In order to represent this 11



operating condition of the battery, the expression in Equation (4) has been chosen that gives the relationship between the battery voltage and the SOC. By exploiting these combined power sources viz. fuel cell and battery to form a hybrid system, a delay free distribution of power to the external load can be achieved. Modeling of fuel cell stack and battery module with these many number of individual cells and batteries is beyond the scope of this paper. Hence in this paper, under the assumption that each individual cell behaves identically, modeling studies are carried out only for a single cell. As mentioned earlier, more details on the detailed first principles model of the integrated reformer membrane fuel cell system and the values of parameters used in the model can be obtained from an earlier paper 11 .

4 Control problem The first principles model of the integrated reformer-membrane-fuel cell-battery hybrid system involves many complex dynamic equations including some quasi steady state equations. Controller design for such plants with complex dynamics can be a challenging problem especially while designing model based controllers. In such cases, a control relevant model of the plant could be used for controller synthesis. Two main control problems were selected by Pukrushpan et al. 25 to control a fuel cell power generation system. The first problem was to control the air supply system for the fuel cell and the second was to control the fuel processor system. Golbert and Lewin 26 have designed a model predictive controller for fuel cell control considering current to be the manipulated variable and power output as the controlled variable. In this paper, the manipulated inputs chosen for the integrated reformer-membrane fuel cell-battery system are (1) molar flow rate of CH4 through control valve1 to the reformer inlet (u1 ), (2) molar flow rate of H2 through control valve2 to the fuel cell anode (u2 ), (3) battery charging current (u3 ) and (4) battery discharging current (u4 ). The associated controlled

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variables chosen are (1) molar concentration of H2 in the line pack (or line pack H2 pressure assuming ideal gas law) (y1 ), (2) PEMFC current density (y2 ) and (3) terminal voltage of the battery.

5 Control relevant modeling of the integrated system The dynamic behavior of any system can be studied by developing a detailed and accurate dynamic mathematical model of the plant. In order to implement MPC for the process plant under consideration, a simplified control relevant mathematical model is mandatory. Controller implementation usually utilises a simplified control relevant mathematical model of the plant. In the present study, we show a realistic situation where the plant is unknown and the controller has to be designed typically using a simplified plant model, which in most cases is identified from the input output plant data. For the case of the integrated system without the battery, a control relevant linear time-invariant state space model is developed from the perturbation data using system identification approach. The general structure of a state space model in the innovation form is,

xpk ` 1q “ Axpkq ` Bupkq ` Kepkq

(5)

ypkq “ Cxpkq ` Dupkq ` epkq

(6)

xp0q “ x0

(7)

where A, B, C, D, K and epkq denote the state transition matrix, input matrix, output matrix, direct coupling between input u and output y, state disturbance matrix and model plant mismatch respectively. Index k denotes the sampling instant and xp0q denotes the initial state of the system. In this paper, recognizing that the reformer-membrane-fuel cell constitutes one subsystem to deliver power, which is augmented by the presence of a battery, an approach to identify dynamic models individually for the reformer, PEMFC and battery

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subsystems, and then combining them to represent the overall system has been adopted. In the next section, we briefly discuss the identification of state space model of the first subsystem.

5.1 State space model of the integrated system without battery In this paper, model development for the integrated reformer-membrane-fuel cell assembly without the battery module is first carried out by choosing appropriate perturbations in the inputs and measuring the outputs. Multiple MISO models were identified for the reformer and fuel cell units by simultaneously perturbing the nonlinear plant with appropriate inputs ie. methane flow control valve (u1 ) and hydrogen flow control valve (u2 ) to record the corresponding outputs ie. hydrogen line pack pressure/molar concentration (y1 ) and PEMFC current density (y2 ) in order to generate an input-output data set. This input-output data was then used to develop control relevant linear perturbation models for controller synthesis.

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Figure 2: Input-output perturbation data for model identification Both methane and hydrogen flow rates are simultaneously perturbed and the corresponding hydrogen line pack pressure/molar concentration and PEMFC current density produced 14


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are measured and recorded to obtain an input-output data set. MISO state space models with different orders were identified using N4SID subspace estimation method available in system identification toolbox to check the percentage fit with the perturbation data. A first order state space model gave better fit for the output y1 (hydrogen line pack pressure/molar concentration) whereas a second order state space model gave better fit for the output y2 (PEMFC current density). The input-output perturbation data used for model identification is shown in Figure 2. The identification result showing the percentage fit between the simulated linear model output and the measured nonlinear plant output y1 can be seen in Figure 3 showing a fit of 74.98%. Similarly, the percentage fit between the simulated linear model output and the measured nonlinear plant output y2 can be seen from Figure 4 showing a fit of 89.81%. Although the percentage fit for output y1 , ie. hydrogen line pack pressure seems to be low, it is expected that the designed feedback controller, due to the fast sampling rates, can achieve improved closed loop performance.

Hydrogen line pack pressure (dev) [mol/m 3 ]

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0.6 Percentage fit = 74.98 %

Simulated linear model output Measured nonlinear plant output

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Simulated linear model output Measured nonlinear plant output

Percentage fit = 89.81 %

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Figure 4: Identified model percentage fit for PEMFC current density shows a percentage fit of 78.55% and 86.48% for outputs y1 and y2 as can be seen from Figure 6 and Figure 7 respectively. The model validation shown in Figure 6 and Figure 7 are based on infinite horizon prediction. As can be noticed from Figure 6, the open loop response of the hydrogen line pack pressure or concentration takes longer time to settle (approximately 200 seconds). This is due to the sluggish behaviour of the upstream reformer unit that converts methane to hydrogen. After generating individual MISO models for the reformer and fuel cell units, these models are combined together to result in a third order state space model for the integrated

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0.6 Simulated linear model output Measured nonlinear plant output

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Figure 6: Validated model percentage fit for output y1

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0.3 Simulated linear model output Measured nonlinear plant output

Percentage fit = 86.48 %

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Figure 7: Validated model percentage fit for output y2 reformer-fuel cell system as follows, »

fi

0 0 ffi —0.9936 — ffi ffi , A1 “ — 0 0.9571 0.1467 — ffi – fl 0 0.1342 0.5391 »

fi

0 0 ffi —6.29 C1 “ – fl , 0 2.537 ´0.9162

»

fi — 0.0013 ´0.0004ffi — ffi ffi B1 “ — 0.0009 0.0964 — ffi – fl ´0.0028 ´0.3025 » fi » fi 0 —0.1057 ffi — ffi 0 0 — ffi ffi D1 “ – fl , K1 “ — 0 0.07227 — ffi – fl 0 0 0 0.006815

(8)

5.2 State space model for the battery The equations for the battery as presented in Eq.(3) and Eq.(4) can be written in a state space form as follows, „ 

„



A2 “ 1 , B2 “ 6.313 ˚ 10´5 ´6.313 ˚ 10´5 „  „  „  C2 “ 15 , D2 “ 0 0 , K2 “ 0

18


(9)

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5.3 State space model of the integrated reformer-membrane-fuel cell-battery system To build the overall state space model of the integrated reformer-membrane-fuel cell-battery system, the individual models developed in sections 5.1 and 5.2 are combined to yield a fourth order state space model with four manipulated variables and three controlled variables. More details on the manipulated variables and controlled variables in the combined model of the integrated system are given in Table 1.

Table 1: Manipulated and controlled variables of the integrated system Manipulated variables

Controlled variables

u1 - CH4 flow through control valve 1

y1 - Line pack pressure/concentration

u2 - H2 flow through control valve 2

y2 - PEMFC current density

u3 - Battery charging current

y3 - Battery terminal voltage

u4 - Battery discharging current

Therefore, the overall discrete state space model of the integrated reformer-membrane-fuel cell-battery system can be obtained as follows.

»

fi 0.9936

— — — A“— — — –

0 0 0

0

0

0

ffi ffi 0.9571 0.1467 0ffi ffi ffi 0.1342 0.5391 0ffi fl 0 0 1

19


(10)


Page 20 of 49

»

fi 0.0013

0

´0.0004

0

— ffi — ffi — 0.0009 ffi 0.0964 0 0 — ffi B“— ffi —´0.0028 ´0.3025 ffi 0 0 – fl 0 0 6.313 ˚ 10´5 ´6.313 ˚ 10´5

»

fi

6.29 0 0 0 — ffi — ffi C “ — 0 2.537 ´0.9162 0 ffi , – fl 0 0 0 15

»

fi 0 0 0 0 — ffi — ffi D “ —0 0 0 0ffi – fl 0 0 0 0

»

(12)

fi 0.1057

— — — K“— — — –

(11)

0 0 0

0

0

ffi ffi 0.07227 0ffi ffi ffi 0.006815 0ffi fl 0 0

(13)

As already discussed in Section 5.1, multiple MISO models were identified which resulted in a single-state model for the reformer section and a two-state model for the fuel cell section. The linear state space MIMO model was obtained by stacking the two MISO models. The reformer was fitted with a single-state model and hence the measurement of line pack pressure depends only on the single reformer state. The fit based on the single state is approximately 75% and adequately fits the plant transients. On the other hand, the fuel cell model is based on two states with a percentage fit of approximately 90%. The stacking of the two MISO models shows the decoupled state to output structure. However, we would not like to make use of the state interpretation, since it cannot be generalized. The fourth state corresponds to the state of charge of the battery. The first state corresponds to auto thermal reformer unit, second and third states corresponds to the PEM fuel cell unit and the fourth state corresponds to the battery.

20


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5.4 Mixed logical dynamical (MLD) systems Combination of both the power sources viz. fuel cell and battery in any portable or stationary applications can lead to the formation of a general hybrid system. Hybrid dynamic systems, by one definition 14 refer to such systems that can be operated in several operating modes due to the occurrence of different events. In each operating mode, the system dynamic behavior changes or switches according to a predefined set of difference or differential equations. In some classes of hybrid systems, there can be changes in the values of state variables or even changes in the state dimension itself. In the case of integrated reformer-membrane-fuel cell-battery system, switching between battery and fuel cell based on certain switching rules or logical conditions can result in a hybrid power source that includes battery and fuel cell. MLD systems are special subclass of hybrid systems which are described by logic rules and operating constraints involving both real and integer variables. In the case of mixed logical dynamical hybrid systems, there exists a coupling between the continuous state system and the discrete state system. 14 The basic step to handle MLD system is to convert the logical statements that decide the system state into mixed-integer linear inequalities. For getting further details on the truth table and propositional logic statements, the reader is referred to the paper by Bemporad and Morari 14 . Two variables M and m can be introduced which denote the maximum and minimum value of a function f pxq, where X denotes a bounded set.

M “ max f pxq,

m “ min f pxq

xPX

xPX

(14)

MLD systems basically deals with logical inequalities consisting of both continuous variables and logical variables. By using the designed variables M and m, the equivalent inequalities

21



Page 22 of 49

for the expression y “ δf pxq can be obtained as follows.

y ď Mδ

(15)

y ě mδ

(16)

y ď f pxq ´ mp1 ´ δq

(17)

y ě f pxq ´ M p1 ´ δq

(18)

The set of logical binary variables used in the case of integrated reformer-membrane-fuel cell-battery hybrid system is given in Table 2. Table 2: Logical variables used in the integrated system Logical variables Value

Condition

δ1

1/0

Reformer is ON or OFF

δ2

1/0

Fuel cell is ON or OFF

δ3

1/0

Battery is ON or OFF

δ4

1/0

Battery is CHARGING or DISCHARGING

δ5

1/0

SOC ď SOCmax or SOC ą SOCmax

δ6

1/0

PL ď PF C or PL ą PF C

A set of all possible modes of operation through which the integrated hybrid system can pass is categorized in Table 3. Under the condition when all the necessary logical statements (represented by AND operation ‘^’) become active, the system switches to the corresponding operating mode as can be seen from the Table 3. Here, P1 , P2 , SOC, SOCmin , SOCmax , PF C , PL and µ represents the line pack hydrogen pressure, fuel cell anode inlet pressure, battery SOC, minimum required battery SOC, maximum battery SOC to be maintained, fuel cell power, load demand power and permissible tolerance value of pPF C ´ PL q respectively. It can be noticed from Table 3 that the line pack pressure P1 is compared with 1.3 times the fuel 22


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Table 3: Modes of operation of the integrated system

Condition

Operating modes

[P1 ă“ 1.3P2 ] ^ [SOC ă SOCmin ]

Battery OFF Fuel cell OFF

[P1 ă“ 1.3P2 ] ^ [SOC ą SOCmin ] ^ [pPF C ´ PL q ą µ]

Battery ON Fuel cell OFF

[P1 ą 1.3P2 ] ^ [SOC ă SOCmax ] ^ [pPF C ´ PL q ă µ]

Battery CHARGING Fuel cell ON

[P1 ą 1.3P2 ] ^ [SOC ă SOCmin ] ^ rPF C ´ PL q ą µ]

Battery IDLE Fuel cell ON

[P1 ą 1.3P2 ] ^ [SOC ą SOCmin ] ^ rPF C ´ PL q ą µ]

Battery ON Fuel cell ON

[P1 ą 1.3P2 ] ^ [SOC ą“ SOCmax ] ^ [pPF C ´ PL q ă µ]

Battery CHARGE FULL Fuel cell ON

cell anode inlet pressure P2 . This choice is made to ensure a sufficient driving force for the pressure driven flow of hydrogen from the line pack to the fuel cell anode inlet through the control valve 2. For this purpose, the pressure drop has been assumed to be 0.3 atm. No hydraulics calculations have been performed in this work. The discussed results will now be utilized to convert the possible logical expressions or statements of the integrated system to its equivalent linear inequalities, to describe specific instances of the overall system.

5.4.1 Condition for δ1 to be ON/OFF (For reformer) The logical variable δ1 decides whether the auto thermal reformer is ON/OFF. In other words, it can be interpreted that the value of δ1 decides whether the control valve 1 position (u1 for methane flow to the reformer inlet) is open or close. The value of δ1 is decided based on the line pack pressure (y1 ), which is one of the controlled variables. Hence in this scenario, the value of δ1 itself is decided by the designed controller based on the value of the line pack

23



Page 24 of 49

hydrogen pressure measured.

5.4.2 Condition for δ2 to be ON/OFF (For fuel cell) The logical variable δ2 decides whether the fuel cell needs to be ON/OFF. If the hydrogen pressure in the line pack becomes greater than or equal to 1.3 times the fuel cell anode pressure, the condition is favorable for control valve 2 to be open, which in turn indicates that fuel cell has sufficient hydrogen to meet the load demand. The logical statement for deciding the value of δ2 is given as

if P1 ě 1.3P2 ô δ2 “ 1

(19)

Converting the logical statement to linear inequalities results in set of following two equations.

1.3P2 ´ P1 ď M1 p1 ´ δ2 q

(20)

1.3P2 ´ P1 ě 1 ` pm1 ´ 1 qδ2

(21)

where, M1 and m1 denotes the maximum value of the function (1.3P2 - P1 ) and 1 indicates a small tolerance value.

5.4.3 Condition for closure of control valve 2 (u2 : H2 flow to fuel cell) If sufficient hydrogen is not present in the line pack, the corresponding logical variable δ2 will be forced to 0. Once δ2 becomes 0, then the control valve 2 should be fully closed. In logical statement, this situation can be represented as

if δ2 “ 0 ñ u2 “ 0

24


(22)

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Converting the logical statement to linear inequality result in the following equation.

´ δ2 ď ú2 ´ 0.5

(23)

5.4.4 Condition for battery discharging to be active or not If the battery is OFF due to insufficient state of charge (ie. SOC ă SOCmin ), the current delivered by battery to the external load (discharging current) should be zero. In logical statement form, it can be expressed as

if δ3 “ 0 ñ u4 “ 0

(24)


´ 1.7δ3 ď ú4

(25)

5.4.5 Condition for battery charging to be active or not If the battery is not getting charged from the fuel cell (ie. in case if battery was fully charged already or if the fuel cell does not have sufficient hydrogen to simultaneously meet the load power demand as well as charge the battery), then the current delivered by fuel cell to the battery (charging current) should be zero. In logical statement form, it can be expressed as

if δ4 “ 0 ñ u3 “ 0

(26)


´ 1.7δ4 ď ú3

25


(27)


Page 26 of 49

5.4.6 Condition for δ5 to be active or not (For monitoring battery SOC) If the state of charge of the battery is less than the maximum state of charge required (ie. SOC ă SOCmax ), then the battery should be charged and the corresponding logical variable δ5 should be one. In logical statement form, it can be expressed as

if SOC ă SOCmax ô δ5 “ 1

(28)

Converting the logical statement to linear inequalities result in the following set of equations.

SOC ´ SOCmax ď M2 p1 ´ δ5 q

(29)

SOC ´ SOCmax ě 2 ` pm2 ´ 2 qδ5

(30)

where, M2 and m2 denotes the maximum value of the function (SOC - SOCmax ) and 2 indicates a small tolerance value.

5.4.7 Condition for δ6 to be active or not If the power generated by the fuel cell is greater than the load power demand, the corresponding logical variable δ6 should be one. In logical statement form, it can be expressed as

if PF C ą PL ô δ6 “ 1

(31)

Converting the logical statement to linear inequality result in the following set of equations.

PL ´ PF C ď M3 p1 ´ δ6 q

(32)

PL ´ PF C ě 3 ` pm3 ´ 3 qδ6

(33)

where, M3 and m3 denotes the maximum value of the function (PL - PF C ) and 3 indicates a small tolerance value. 26


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5.4.8 Overall set of conditions for battery to be charging Battery can be charged if the following conditions are satisfied: Battery is OFF and fuel cell is ON and SOC is less than maximum SOC and fuel cell power is greater than the load power demand. In logical statement form, this conditions can be combinedly expressed as,

if δ3 “ 0 ^ δ2 “ 1 ^ δ5 “ 1 ^ δ6 “ 1 ô δ4 “ 1

(34)

Converting the logical statement to linear inequality result in the following set of equations.

δ2 ´ δ4 ď 0

(35)

δ5 ´ δ4 ď 0

(36)

δ6 ´ δ4 ď 0

(37)

´ δ3 ´ δ4 ď ´1

(38)

´ δ3 ´ δ6 ď ´1

(39)

5.4.9 Converting product form to linear inequalities By defining a new variable zpkq “ δpkq xpkq in discrete form, where k denotes the sampling time, the resulting product form can be converted to the following inequalities 14 . This converts the existing four continuous states (xi pkq, i “ 1, 2, 3, 4) of the integrated system to its corresponding discrete states (zi pkq, i “ 1, 2, 3, 4).

zi pkq ď Mi˚ δi pkq

(40)

zi pkq ě m˚i δi pkq

(41)

zi pkq ď xi pkq ´ m˚i p1 ´ δi pkqq

(42)

zi pkq ě xi pkq ´ Mi˚ p1 ´ δi pkqq

(43)

27



Page 28 of 49

where, Mi˚ and m˚i denotes the maximum and minimum values of the states of the system respectively.

5.4.10 Mixed logical dynamical system for the integrated system A mixed logical dynamical system can be generally represented by the following linear equivalent relation.

xpk ` 1q “ Ak xpkq ` B1k upkq ` B2k δpkq ` B3k zpkq

(44)

ypkq “ Ck xpkq ` D1k upkq ` D2k δpkq ` D3k zpkq

(45)

E2k δpkq ` E3k zpkq ď E1k upkq ` E4k xpkq ` E5k

(46)

The corresponding linear equivalent expression for the MLD system in case of the integrated hybrid system can be obtained by using the developed state space model of the system given in Eq.(10) to Eq.(13) and expressing it in the MLD form. The MLD form for the integrated system considered in this paper can be written in terms of state equation and output equation with all the constraints discussed in the previous subsections as follows.

x1 pk ` 1q “ 0.9936 z1 pkq ` 0.0013 u1 pkq ´ 0.0004 u2 pkq ` 0.1057 e1 pkq

(47)

x2 pk ` 1q “ 0.9571 z2 pkq ` 0.1467 z3 pkq ` 0.0009 u1 pkq ` 0.0964 u2 pkq ` 0.0723 e2 pkq (48) x3 pk ` 1q “ 0.1342 z2 pkq ` 0.5391 z3 pkq ´ 0.0028 u1 pkq ´ 0.3025 u2 pkq ` 0.0068 e2 pkq (49) x4 pk ` 1q “ x4 pkq ` 6.313 ˚ 10´5 u3 pkq ´ 6.313 ˚ 10´5 u4 pkq

(50)

y1 pk ` 1q “ 6.29 x1 pk ` 1q ` e1 pkq

(51)

y2 pk ` 1q “ 2.537 x2 pk ` 1q ´ 0.9162 x3 pk ` 1q ` e2 pkq

(52)

y3 pk ` 1q “ 15 x4 pk ` 1q

(53)

It can be noticed that Eq.(47) to Eq.(50) corresponds to the general MLD state equation as given in Eq.(44) and Eq.(51) to Eq.(53) corresponds to the general MLD output equation 28


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in Eq.(45). E1k to E5k represents the respective coefficient matrix for the variables upkq, δpkq, zpkq, xpkq and constant terms respectively.

6 Model predictive controller Model predictive controller (MPC) has the ability to predict the future response of the plant using its mathematical model by solving an online optimization problem. An important feature of the MPC lies in its ability to handle constraints in both inputs as well as outputs. The efficacy of the controller mainly depends on the accuracy of the mathematical model of the plant under control. Using the model, the MPC predicts the plant behavior, optimizes the system performance based on some predefined cost function, and calculates the optimal input moves to be fed to the plant. As already discussed, open loop simulations are carried out to obtain the input-output data set of the plant with which, a control relevant model is identified using system identification method. A general objective function in an MPC consists of mainly two terms, one that minimizes the error between the set point and the predicted output and other that minimizes the change in input moves given to the plant.

6.1 MPC for MLD systems The main objective of the controller designed for an MLD system is to track the reference trajectory or to stabilize the system to a desired or an equilibrium state. Because of the complexity of MLD systems, finding an optimal control law that minimizes the objective function is not an easy task 14 . As the MLD-MPC problem involves both continuous and discrete variables with the objective function being quadratic, the optimization problem can be formulated as a mixed integer quadratic programming (MIQP). The prediction equation for the system states and outputs can be obtained by successive substitution using Eq.(44) and Eq.(45) respectively. The general equivalent formulation of the MLD-MPC problem is given by 14 ,

29



Jpkq “ min V˜ pkq

Np ÿ

V˜ pkqT S1 V˜ pkq ` 2pS2 ` xpkqT S3 qV˜ pkq

Page 30 of 49

(54)

k“0

subject to F1 V˜ pkq ď F2 ` F3 xpkq where, S1 , S2 , S3 , F1 , F2 , F3 are appropriately chosen matrices and V˜ pkq is a vector containing all the inputs, outputs and the auxiliary variables as follows. V˜ pkq “ r˜ uT pkq y˜T pkq δ˜T pkq z˜T pkqsT

(55)

The resulting quadratic optimization problem given by Eq.(54) has been solved as a MIQP problem using TOMLAB optimization environment in MATLAB.

7 MPC implementation on the integrated system

Figure 8: Control structure of the integrated reformer membrane fuel cell system In an earlier work 11 , several multi-loop PID controllers were designed to control the integrated system without involving battery in the loop. In the present study, a battery unit is also added as an additional power source to the integrated system to form a hybrid system. 30


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Due to the slow charging time of a battery system, it is considered as the secondary power source and PEMFC as the main primary power source. The block diagram showing the control structure of the integrated reformer-membrane-fuel cell-battery system implemented with MPC is shown in Figure 8. The main task of the multi variable controller like MPC is to track the reference trajectory as well as to toggle between the battery and fuel cell based on the external load power requirement. Additionally, the MPC framework has the ability to predict the plant behavior and optimize the performance of the plant. Necessary set point reference trajectories are specified for the power demanded by the external load and the desired line pack pressure. With necessary constraints for the input moves, the optimization problem is solved to minimize the objective function. In the case of integrated system, expression for the total current delivered by the hybrid power source to the external load is given by

Itotal “ y2 ´ u3 ` u4

(56)

where, y2 is the current generated by the fuel cell, u3 is the charging current given by fuel cell to battery and u4 is the battery discharging current to the load. The critical objective of the designed MPC is to minimize the use of battery as recharging a battery system is more time consuming. At the same time, the error between the desired and the actual controlled variables of the system needs to be maintained as small as possible. For the integrated hybrid system, the objective function formulated has mainly three terms as given by Eq.(57)

J “ min

Np ÿ

pysp pkq ´ ypkqqT Qpysp pkq ´ ypkqq `

k“0

pSOCpkq ´ SOCmax pkqqT QSOC pSOCpkq ´ SOCmax pkqq ` ∆upkqT R∆upkq (57) where, the first term in the objective function indicates the error between the set point and 31



the predicted output, second term indicates the difference of SOC from the maximum SOC value (0.8 in this case), which minimizes the use of battery and the third term indicates change in the input moves. The associated constraints together with the switching constraints, as already discussed in the section 5.4 is formulated as a mixed integer quadratic programming problem and is solved using the miqp solver available in TOMLAB.

7.1 Result analysis and discussion 7.1.1

MPC performance on the fuel cell-battery hybrid system

This sections compares the performance variations of the designed MPC for different cases of control and prediction horizons. Both positive and negative step changes are given to the output load power demand to study the performance of the designed MPC to track the set point trajectory. Several combinations of the prediction horizon Np and control horizon Nc for the MPC were implemented to study the controller performance. A negative step change in the demand power from the external load is given at t = 5 seconds and a positive step change at t = 10 seconds. Irrespective of the changes in the power demand, the MPC should track the target power profile and at the same time maintain a constant hydrogen pressure in the line pack. It can be seen from Figure 9(a) and Figure 9(b) that the designed MPC could track the target power profile and also maintain a fixed line pack hydrogen pressure. It can be seen that for a higher value of Np , the controller anticipates the load power demand changes quite well in advance to start the control action. Based on the fluctuations in output load power demand, the MPC manipulates both the control valves (u1 and u2 ) in order to track the target power profile satisfying all the necessary constraints as can be seen from Figure 10(a) and Figure 10(b) respectively. It can be observed that the methane and in turn the hydrogen fuel usage is also optimized in the case of a larger prediction horizon. Based on the control valve 1 opening, the methane flow rate to the reformer starts fluctuating which in turn varies the hydrogen produced by the reformer. The molar concentration of hydrogen at the reformer exit varies as shown in Figure 11(a). Figure 11(b) shows the 32


Page 32 of 49

Page 33 of 49

(a)

Power [kW]

31

Set point Nc = 1, Np = 2

30.5

Nc = 1, Np = 5

30 29.5 29

Hydrogen line pack pressure [atm]

0

5

Time [s] (b)

10

15

10

15


1.914

Nc = 1, Np = 5

1.912

1.91 0

5

Time [s]

Figure 9: Performance of MPC tracking the target power profile and maintaining a constant line pack pressure

(a)

Control valve 1 opening [%]

60

Nc = 1, Np = 2

55

N = 1, N = 5 c

p

50 45 0

5

54


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Time [s] (b)

10

15

10

15

Nc = 1, Np = 2

52

Nc = 1, Np = 5

50 48 0

5

Time [s]

Figure 10: Percentage opening of the control valve 1 and 2

33



variation in molar concentration of hydrogen in the line pack, which is governed by the opening of control valve 2 due to fluctuations in the power demand. It can be noticed that for a higher prediction horizon, the controller is able to anticipate the plant output much better

at reformer exit [mol/m 3 ] in the line pack [mol/m ]

(a)

21.6

Nc = 1, Np = 2

21.55

Nc = 1, Np = 5

21.5 21.45 0

5

Time [s]

10

15

10

15

(b)

3

Molar conc. of H 2

and thus process only the requisite amount of methane fuel to produce hydrogen. Profile

Molar conc. of H 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 49

21.33

Nc = 1, Np = 2 Nc = 1, Np = 5

21.32

21.31 0

5

Time [s]

Figure 11: Molar concentration of hydrogen at reformer exit and in the line pack showing the variation in molar flow rate of hydrogen through the palladium membrane due to pressure difference in the upstream and downstream sides of the membrane can be observed from Figure 12(a). Due to changes in the control valve 2 opening, the molar flow rate of hydrogen through control valve 2 to the fuel cell also varies as seen from Figure 12(b). Based on the switching constraints, the MPC takes necessary actions to charge and discharge the battery. At the initial time, the battery SOC is assumed to be at a value of 75%. It can be noticed that at 5 seconds, the load power demand goes down and the extra power generated by the fuel cell is used to charge the battery (7 SOC < SOCmax ) as shown in Figure 13(a). During this time duration, the fuel cell alone will meet the power demand as well as charge the battery simultaneously. When the power demand goes high, the battery assists the fuel cell in meeting the demand and thus gets discharged as can be observed from Figure 13(b).

34


through control valve 2 Molar flow rate of H 2 to fuel cell [mol/s] through Pd membrane [mol/s]

2.5

(a)

×10 -5

Nc = 1, Np =2

2

Nc = 1, Np =5

1.5 1 0 1.7

5

Time [s]

10

15

10

15

(b)

×10 -5

Nc = 1, Np = 2

1.65

Nc = 1, Np = 5

1.6

1.55 0

5

Time [s]

Figure 12: Molar flow rate of hydrogen through Pd membrane and through control valve 2 to fuel cell

(a)

Battery charging power [kW]

0.04

Nc = 1, N p = 2

0.03

Nc = 1, N p = 5

0.02 0.01 0 0

5

10

15

10

15

Time [s] (b) Battery discharging power [kW]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Molar flow rate of H 2

Page 35 of 49

0.04 Nc = 1, N p = 2

0.03

Nc = 1, N p = 5

0.02 0.01 0 0

5

Time [s]

Figure 13: Battery charging and discharging power profiles

35



The variation in terminal voltage of the battery based on fluctuations in the battery charging and discharging cycles is shown in Figure 14(a). It can be seen that the MPC tries to maintain the terminal voltage of the battery close to the target value irrespective of changes in the load power demand. The change in state of charge of the battery is plotted in Figure 14(b) and the profile shows a direct relation with the discharging and charging cycles of the battery. It can be noticed that for a higher value of Np , the amount of discharge from the battery is less suggesting very less usage of battery, which is one of the objective of the designed controller. (a)

Battrey terminal voltage [V]

11.2501 11.25


11.2499

Nc = 1, Np = 5

11.2498 0

5

75.001

Battery state of charge [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 49

Time [s] (b)

10

15

75 Nc = 1, Np = 2

74.999

Nc = 1, Np = 5

74.998 0

5

Time [s]

10

15

Figure 14: Battery terminal voltage and state of charge profiles

7.1.2

Integrated fuel cell-battery hybrid system powering a light motor vehicle

For validating the potential of engaging the designed integrated system for a realistic power application, an associated drive cycle of a light motor vehicle with a maximum power rating of 60 kW , taking the transmission and DC/AC converter losses into account has been considered in this section. 27 Both slow and fast changing demand fluctuations have been considered to assess the performance of the designed controller in presence of hybrid power sources viz.

36


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fuel cell and battery. As already discussed in Section 2, the maximum current density rating for a single fuel cell is 1.5319 A{cm2 at a cell voltage of 0.53 V . Considering a maximum power from a single fuel cell to be 0.08 kW , approximately 750 number of such individual cells needs to be connected in series to meet the power demand. Also, in the case of battery, as discussed in Section 3.4, for generating a power of 60 kW , the total number of battery cells needed comes out to be approximately 2273 cells. For simulation purpose, it is assumed that the output electrical load power demand is assumed to exhibit slower dynamics for the first 65 s and extremely faster dynamics for rest of the time duration. As already discussed in the previous section, a 5 step ahead prediction controller gave better results compared to a 2 step ahead prediction controller for tracking the target power. Hence, in this study, we have focused the design only for a 5 step ahead prediction MPC controller to track the desired set point power profile. Based on the fast and slow changing power demands by the external load, the MPC anticipates this change and effectively switches among battery and fuel cell to deliver the requisite power as shown in Figure 15. It can be noticed that the designed controller perfectly tracks the demanded power without any offset in both slow and fast changing power demand scenarios. 60 58 56

Power demanded Power delivered

54

Power [kW]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


52 50 48 46 44 42 40 0

10

20

30

40

50

60

70

80

90

100

110

Time [s]

Figure 15: Profile showing power demanded by the load and power delivered by the integrated system

37



Depending on the demand fluctuations, the line pack hydrogen pressure also gets affected and the MPC controller regulates the methane inlet to the reformer to maintain almost a fixed pressure in the line pack. The profile showing the variations in the hydrogen line pack pressure is shown in Figure 16, indicating perfect control of the MPC offering an acceptable offset value from the set point. 1.93


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Set point Actual line pack pressure

1.925

1.92

1.915

1.91

1.905

1.9 0

10

20

30

40

50

60

70

80

90

100

110

Time [s]

Figure 16: Profile showing the hydrogen line pack pressure The changes in the methane flow rate to the reformer inlet is governed by the percentage opening of the control valve 1, which is manipulated by the MPC based on the hydrogen line pack pressure. The profile showing the variations in the control valve 1 position is shown in Figure 17. Similarly, the changes in hydrogen flow rate to the fuel cell anode inlet is governed by the percentage opening of the control valve 2, which is manipulated by the MPC based on the load power demand. The profile showing this variation of control valve 2 is shown in Figure 18. Based on the switching constraints formulated in the MPC problem, the controller effectively switches between the battery and fuel cell so as to deliver a delay free power to the external load. The profiles for the battery charging power supplied from the fuel cell to battery and the discharging power delivered by the battery to the load are given

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54 53.5


53 52.5 52 51.5 51 50.5 50 49.5 49 0

10

20

30

40

50

60

70

80

90

100

110

Time [s]

Figure 17: Percentage opening of the control valve 1

58 56 54


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


52 50 48 46 44 42 40 38 0

10

20

30

40

50

60

70

80

90

100

110

Time [s]

Figure 18: Percentage opening of the control valve 2

39



(a)

Battery charging power [kW]

0.6

0.4

0.2

0 0

10

20

30

40

Battery discharging power [kW]

50

60

70

80

90

100

110

70

80

90

100

110

Time [s] (b)

0.6

0.4

0.2

0 0

10

20

30

40

50

60

Time [s]

Figure 19: Battery charging and discharging power profiles

(a)

Battery terminal voltage [V]

11.256 11.254 11.252 11.25 11.248 11.246 0

20

40

60

80

100

80

100

Time [s] (b)

75.04

Battery state of charge [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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75.02 75 74.98 0

20

40

60

Time [s]

Figure 20: Profile showing variations in the battery terminal voltage and state of charge

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in Figure 19(a) and Figure 19(b) respectively. As already discussed, based on the battery charging and discharging profiles, the corresponding battery terminal voltage and the state of charge also varies accordingly. The profiles for the battery terminal voltage and the state of charge can be observed from Figure 20(a) and Figure 20(b) respectively. It can be noticed that during slow variations in the power demands (ie. till 65s), the battery usage is less, as compared to the fast varying power demands where the battery unit is used intensely. Because of this, the battery terminal voltage and state of charge can be seen to increase during the first section of the profile and decrease during the rest of the time instant.

7.1.3

Comparison of system performance with and without a battery unit

In order to study the advantage of including a battery unit into the integrated reformermembrane-fuel cell system, following simulations are carried out. MPC controller is implemented for controlling the plant in two different cases ie. with and without battery. The profile showing the power demand fluctuations and the performance of the designed controller to track the set point trajectory can be seen in Figure 21(a). It can be noticed (a)

Power [kW]

40

Set point Fuel cell alone Fuel cell + Battery hybrid

35 30 25 0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

2

1.916

3

Time [s] (b)

4

5

6

7

4

5

6

7

Set point Fuel cell alone Fuel cell + Battery hybrid

1.914 1.912 1.91 1.908 0

1

2

3

Time [s]

Figure 21: Performance of MPC tracking the target power profile and maintaining a constant line pack pressure

41



from Figure 21(a) that the controller is able to attain the desired target much faster in the case of hybrid system as compared to the case with only fuel cell. Controller in both the cases could start the control action a priory, but the hybrid case is seen to be reaching the set point with a lesser settling time of 0.2 s as compared to the case of fuel cell alone having a settling time of 0.4 s. Figure 21(a) shows the behavior of the closed loop system using MPC for tracking the target power profile. The fast dynamics (approximately 0.5 seconds) in Figure 21(a) indicates that the fuel cell can quickly deliver the desired load power, provided sufficient hydrogen is available in the line pack. The reduction in the settling times of hybrid case is because of the introduction of battery which can assist the fuel cell in case of sudden demand fluctuations. The hybrid case shows faster response to power demand fluctuations, which is an inevitable requirement especially in the case of automotive applications. The fuel cell alone case shows a smoother and sluggish response compared to the hybrid case. Figure 21(b) shows the variation in the line pack hydrogen pressure in response to the power demand fluctuations. It can be noticed that in the hybrid case, the amount of hydrogen used is less compared to the fuel cell alone case. Also, the controller is able to maintain a constant and safe line pack pressure in both the cases, but the deviation of line pack pressure from the target value is less in the case of the hybrid system. The corresponding control valve 1 and control valve 2 moves by the MPC based on the demand fluctuations can be observed from Figure 22(a) and Figure 22(b) respectively. It can be noticed that the amount of methane supplied to the reformer, which is governed by the percentage opening of control valve 1, is less in the case of hybrid system as compared to the fuel cell alone case. Similarly, due to the assistance of battery in the hybrid case, it can be noticed that the percentage change in the control valve 2 opening, that governs the amount of hydrogen feed to the fuel cell, is small as compared to the fuel cell alone case. This indicates that the amount of hydrogen fed to the fuel cell for meeting the demand is less in case of hybrid system and more in case of fuel cell alone system. The respective molar concentrations of hydrogen at the reformer exit and in the line pack

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Page 43 of 49

(a)


70 Fuel cell alone Fuel cell + Battery hybrid

60 50 40 0

1

2

3

Time[s]


4

5

6

7

4

5

6

7

(b)

80 60 40

Fuel cell alone Fuel cell + Battery hybrid

20 0

1

2

3

Time [s]

at reformer exit [mol/m 3 ] in the line pack [mol/m ]

(a)

21.7


21.6 21.5 21.4 0

1

2

3

4

5

6

7

5

6

7

Time [s] (b)

3

Molar conc. of H 2

Figure 22: Percentage opening of the control valve 1 and 2

Molar conc. of H 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


21.4


21.35 21.3 21.25 0

1

2

3

4

Time [s]

Figure 23: Molar concentration of hydrogen at reformer exit and in the line pack

43



can be seen from Figure 23(a) and Figure 23(b) respectively. This change is in response to the corresponding percentage variations in the opening and closing of control valves 1 and 2 respectively. As can be observed, the variation in molar concentrations is more in case of fuel cell only system as compared to the hybrid system. The variations in molar flow rate of hydrogen through the palladium membrane depends on the difference in hydrogen pressure at the upstream and downstream of the membrane. It can be noticed from Figure 24(a) that the change in molar flow rate is less due to very less pressure difference as compared to the fuel cell alone case. The change in molar flow rate of hydrogen through control valve 2 to the fuel cell, which is a function of the percentage opening of control valve 2 can be observed in Figure 24(b). It can be concluded that inclusion of a battery unit to the integrated reformer-membrane-fuel cell system can improve the performance of the overall system in

Pd membrane [mol/s] control valve 2 [mol/s]

Molar flow rate of H2 through

terms of speeding up the response and optimizing the utilization of hydrogen fuel.

Molar flow rate of H2 through

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3

(a)

×10 -5

2.5 Fuel cell alone Fuel cell + Battery hybrid

2 1.5 0

2.5

1

2

3

4

Time [s]

5

6

7

5

6

7

(b)

×10 -5

2 1.5


1 0

1

2

3

4

Time [s]

Figure 24: Molar flow rate of hydrogen through Pd membrane and through control valve 2 to fuel cell

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8 Conclusions The necessity of an auxiliary power source like battery was highlighted in an earlier work, where an integrated reformer-membrane-fuel cell system was designed for stationary and portable applications. This paper focused on the integration of a battery unit to the integrated reformer-membrane-fuel cell system to form a hybrid dynamical power system. The integrated system with battery in the loop has been modeled as a MLD system. The plant is controlled by an MLD based MPC controller that makes optimal decisions to switch between battery and fuel cell based on certain switching rules or logical conditions.

Acknowledgement The authors acknowledge financial support from the Dept. of Science & Technology, Govt. of India, Grant 13DST057.

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Graphical TOC Entry

49


Modeling and Predictive Control of an Integrated Reformer

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