Feed-forward control of a solid oxide fuel cell system with anode offgas recycle

Journal of Power Sources 282 (2015) 498e510

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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

Feed-forward control of a solid oxide fuel cell system with anode offgas recycle
a, *, Ralf Brandenburger a, Wolfgang Friede a, François Lapicque b, Maxime Carre Uwe Limbeck a, Pedro da Silva a a b

Robert Bosch GmbH, Department CR/AEB, Robert-Bosch-Straße 2, 71701, Schwieberdingen, Germany Laboratoire R
eaction et G
enie des Proc
ed
es, 1 rue Grandville, 54000, Nancy, France

h i g h l i g h t s
A feed-forward control for SOFC system with anode offgas recycle was developed.
The control strategy requires a limited number of variables and relations.
A prototype of SOFC system with anode offgas recycle has been started-up.
The start-up procedure does not require any liquid water feeding.
The prototype shows a gross electrical efficiency larger than 60%.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 November 2014 Received in revised form 31 January 2015 Accepted 9 February 2015 Available online 11 February 2015

In this work a combined heat and power unit (CHP unit) based on the solid oxide fuel cell (SOFC) technology is analysed. This unit has a special feature: the anode offgas is partially recycled to the anode inlet. Thus it is possible to increase the electrical efficiency and the system can be operated without external water feeding. A feed-forward control concept which allows secure operating conditions of the CHP unit as well as a maximization of its electrical efficiency is introduced and validated experimentally. The control algorithm requires a limited number of measurement values and few deterministic relations for its description. © 2015 Elsevier B.V. All rights reserved.

Keywords: Fuel cell Anode recycle Solid oxide fuel cell Control Steam to carbon Start-up

1. Introduction This article aims at demonstrating the possibility to operate a combined heat and power (CHP) unit based on the solid oxide fuel cell (SOFC) technology with anode (An) offgas recycle (Recy). A CHP unit is a system capable of producing heat and power at the same time. The CHP technology is a well accepted technology to increase the efficiency of the energy supply and thus to reduce CO2 emissions, [1]. Stationary Fuel Cell Systems (FCS) represent one type of CHP systems. The electric efficiency of such systems plays a crucial role for stationary applications, where the CHP unit is used as a

* Corresponding author.
). E-mail address: [email protected] (M. Carre http://dx.doi.org/10.1016/j.jpowsour.2015.02.053 0378-7753/© 2015 Elsevier B.V. All rights reserved.

power generator. The anode offgas recycle (AOR) is a way to increase the electrical efficiency of a fuel cell system. AOR actually consists in recycling a fraction of the hot anode offgas to the anode inlet. The concept of AOR has already been introduced, [2,3] and tested with success for large scale CHP units [4] over the fifteen past years. For the case of the SOFC technology, AOR possesses the advantage of the conventional steam reforming (higher electric efficiency than the catalytic partial oxidation with air) without sharing its main inconvenient: a tap water connection must be available or the temperature of the water cooling of the FCS's offgas must remain below a certain level. Indeed AOR makes use of the steam in the anode offgas to perform steam reforming reactions. First basic equations, defining the relations between the main variables of the CHP unit, are introduced. This part reveals that

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Nomenclature

gi,e

AOR APU AU CHP CPOx F FCS FU I MPC mCHP n_ nc NG r P&ID PG SOFC V_

gi,Ref

Vm

f Ge Gf GRef ge gi,C

Anode Offgas Recycle Auxiliary Power Unit Air utilization, e Combined Heat and Power Catalytic Partial Oxidation Faraday constant, C mol1 Fuel Cell System Fuel Utilization, e Drawn current, A Model Predictive Control micro Combined Heat and Power Molar flow, mol s1 Number of cells in the stack, e Natural Gas Recycle rate, e Piping and Instrumentation Diagram Protection Gas Solide Oxide Fuel Cell Volumetric flow rate, STP l min1 Molar volume under normalized conditions, STP l mol1 Oxygen to carbon ratio, e Coefficient related to the limitation for the constraint ! ,e fmin  f Coefficient use in the expression of the oxygen to carbon ratio f, e Coefficient use in the expression of the recycle rate r, e Average number of electrons per alkane molecule contained in a gas mixture composed of alkane molecules, e Number of C atoms contained in alkane i, e

algebraic deterministic relations are sufficient to describe comprehensively the FCS in spite of its complexity due to AOR. Subsequently a feed-forward control strategy based on the previous equations is examined. A CHP unit prototype with AOR has been built up and tested in our lab. The next section shows first experimental results, which prove that AOR increases the electric efficiency by more than 10 points in comparison to conventional FCS (Steam reforming or catalytic partial oxidation). The concept of AOR has first to be introduced as shown by Fig. 1. For the sake of simplicity only the relevant components are depicted in this figure. The usual elements of a CHP unit based on the SOFC technology are shown here. The additional component is labelled as “Recycle Blower”. As indicated in Fig. 1, a fraction of the anode offgas is recycled to be conveyed upstream of the Pre Reformer (Pre). It is now easier to explain, why this kind of CHP system is investigated in this paper:
One of the two electrochemical reactions in the anode produces water: H2þ O2 0 H2Oþ2e. As indicated in Fig. 1 the anode offgas, containing steam, is recycled upstream of the Pre Reformer. This steam can then participate in the reforming (Ref) reactions in the Pre Reformer. This means that no additional water source is needed for reforming of the alkane molecules in the Pre Reformer and in the anode. CO and CO2 molecules also participate in the reforming reactions but for the sake of

l jAir jI jNG jRecy Subscript An Bu C c e i in max min O Off NG Pre Recy Ref sat Sta sto

499

Number of electrons that alkane i can deliver for the electrochemical reaction in the anode, e Increase in molecule number due to steam reforming reaction of alkane i, e Stoechiometric air fuel ratio of burner, e Ratio between current air molar flow and nominal air molar flow, e Ratio between produced current and maximal produced current, e Ratio between current NG molar flow and nominal NG molar flow Ratio between current recycle molar flow and nominal recycle molar flow, e

Anode Burner Carbon atom cell electron Alkane i, i ¼ {CH4, C2H6, C3H8, C4H10} inlet of FCS maximum minimum Oxygen atom Offgas Natural Gas Pre Reformer Recycle Reforming saturated Stack stoichiometric

simplicity their influence is not explained (deliberately) in details at this stage of this study.
H2 and CO molecules are recycled too, which means that the anode is fed by recycled fuel molecules H2 and CO in addition to fresh alkane molecules coming from the Natural Gas (NG) source through the NG blower. Two fuel utilizations must be defined to describe the effect of the AOR: the system (Sys) fuel utilisation referring to the amount of natural gas fed through the NG blower and the stack (Sta) fuel utilisation referring to the amount of combustible gases fed to the anode. With AOR it is now possible to increase the system fuel utilisation for higher overall electrical efficiency, and simultaneously to maintain the stack fuel utilisation at a certain value to ensure the stack durability. The following part of this paper provides background information to understand the developed feed-forward control strategy in Section 3. 2. Basic equations describing a fuel cell system with anode offgas recycle Operation of a CHP unit with anode recycle can be modelled with various balances, which have to be introduced to understand all further argumentations on this topic. First the recycle rate is examined.

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500

NG

NG Blower

Air

Desulphurization unit

Cathode

SOFC Stack Anode

Pre Reformer

Air Blower

Recycle Blower

AC Power DC / AC Converter

Burner

Heat Exchanger

DC Power Fig. 2. Schematic view of the anode circuit with AOR for the establishment of the equation linking the recycle rate r with the recycle molar flow rate n_ Recy and the NG flow rate n_ NG and for the establishment of the equation linking FUSys and FUSta. I is the current produced in A, nc is the number of cells, and F is the faraday constant in C mol1.

Domestic hot water

Considering these three assumptions, the recycle rate can be expressed as:

Flue Fig. 1. Schematic of the studied SOFC CHP with recycle loop. The small grey circles refer to possible heat exchangers ensuring thermomanagement of the system.

2.1. Recycle rate

r¼

n_ Recy n_ Recy þ n_ NG GRef

with GRef ¼ 1 þ

P

(2)

xi;NG gi;Ref , where xi,NG is the molar fraction of

i

Fig. 2 represents a schematic view of the recycle part of the process, with the minimum number of components to understand the principle and how to calculate the recycle rate. The recycle rate is defined as the molar fraction of anode offgas that is recycled. The anode offgas is mixed to NG before entering the Pre Reformer:

r¼

n_ Recy n_ An;Off

alkane i (i ¼ CH4, C2H6, etc.) in the fresh natural gas. gi,Ref represents the number of moles created during the steam reforming reaction of one mole of the alkane i. Table 1 gives an overview of the possible steam reforming reactions in the Pre Reformer and in the stack. It can be read from Table 1 that coefficient gi,Ref is equal to 2 for methane, 4 for ethane, and in general, gCy H2yþ2 ;Ref ¼ 2y, where y is the number of carbon atoms in the alkane molecule. Coefficient GRef only depends on the properties of the natural gas.

(1)

The purpose of this section is to express the recycle rate as a function of controllable variables, n_ Recy and n_ NG . For the rest of this work such variables are called actuating variables. For calculation of the recycle rate it has to be assumed that:
Complete steam reforming of the alkanes is assumed downstream of the line of components “Pre Reformer þ Stack”: downstream of the anode no alkane molecules are present.
The result presented in equation (2) is valid for the configuration presented in Fig. 2. Location of compressors CRecy and CNG can be modified when required.
Only steam reforming reactions cause an increase in the molar flow. Because of their stoichiometry inside the anode the electrochemical reactions involving CO and H2 have no effect on the molar flow.

2.2. System fuel utilisation vs. stack fuel utilisation In this subsection the equation linking the system fuel utilisation (FUSys) and the stack fuel utilisation (FUSta) is established. The calculation is introduced by Fig. 3. For the sake of simplicity it is assumed that in any location of the anode circuit the molar electrons flux transferred to the anode to produce power can be Table 1 Steam reforming reaction of alkanes. Alkane

Reaction

Methane Ethane Propane In general

CH4 þ H2 O0CO þ 3H2 C2 H6 þ 2H2 O02CO þ 5H2 C3 H8 þ 3H2 O03CO þ 7H2 Cy H2yþ2 þ yH2 O0yCO þ ð2y þ 1ÞH2

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Fig. 3. Tertiary diagram indicating the formation of carbon deposition with respect to the temperature. The grey domain represents the domain where carbon deposition is expected at 750  C. Calculations were made using FactSage ® Software, version 6.3, compound database: FactPS.

calculated. These molar flows are indicated in Fig. 2 as n_ e;An , n_ e;NG and n_ e;Recy . For instance the molar flow n_ e;An takes into account the alkane molecules present in NG and the recycled molecules, H2 and CO, from the anode. Although present in the real circuit, the Pre Reformer is not shown in Fig. 2 because it is not involved in the calculation of the system fuel utilisation or the stack fuel utilisation as explained below. Steam reforming occurs in the Pre Reformer and does not consume in combustion any of the various fuels mentioned in Table 1. Thus the number of electrons available for the electrochemical reaction in the stack is not affected, so the Pre Reformer can be omitted for calculation of the fuel utilisations. First the stack fuel utilisation can be expressed as a function of the system fuel utilisation:

FUSta ¼

Inc=F Inc=F FUSys ¼ ¼ n_ _ _ ne;An ne;NG þ n_ e;Recy 1 þ n_e;Recy

(3)

e;NG

with:

FUSys ¼

F n_ NG

In P c i xi;NG gi;e

(4)

P and with n_ e;NG ¼ n_ NG xi;NG gi;e . gi,e is defined as the number i of electrons which are available at the anode by consumption of one molecule of alkane i. I is the current drawn from the stack, nc is the number of cells, and F is the faraday constant. Considering the reforming reactions in Table 1 and the electrochemical reactions occurring at the anode 2Hþþ O2 0H2O and CO2þþ O2 0 CO2, the coefficient gi,e can be defined as gCy H2yþ2 ;e ¼ 6y þ 2. Then a mass balance in the system at nodes A and B provides a second equation:

 n_ e;NG þ n_ e;Recy 

 Inc r ¼ n_ e;Recy F

Combining equation (3) and equation (5) yields:

(5)

501

Fig. 4. Schematic view of the anode circuit with AOR for calculation of the oxygen to carbon ratio.

FUSta ¼

ð1  rÞ FUSys 1  r FUSys

(6)

2.3. Oxygen to carbon ratio f The oxygen to carbon ratio f is introduced in this subsection. The ratio is defined at a certain point of the fuel cell system as:

f¼

n_ O n_ C

(7)

where n_ O is the O atom molar flow and n_ C is the C atom molar flow. The oxygen to carbon ratio f is considered here,1 as the parameter to adjust to avoid carbon deposition. A ternary diagram is a convenient representation to examine carbon deposition limit, [5,6]. The ternary diagram in Fig. 3 confirms the choice of the oxygen to carbon ratio as the parameter to set to avoid carbon deposition. Based on the calculation of thermodynamic equilibrium, the black curves in the graph indicate the limit of carbon deposition for pure carbon. All the gas mixtures composed exclusively of C, H, and O atoms located below one of the two curves, depending on the temperature, may generate carbon deposition. The star in the graph corresponds to a gas mixture composed of methane (CH4) and steam (H2O) with an oxygen to carbon ratio of 2. The yellow dotted line (in web version) corresponds to the value f¼2, whatever the gas mixture. Thus from the point of view of thermodynamics by choosing the correct oxygen to carbon ratio, carbon deposition can

1 The most-often used ratio is the S/C ratio, also called “steam to carbon ratio”. In numerous applications the amount of fed water molecules is equal to the amount of O atoms in the system. In this case it does not matter which ratio is used. In the present case no external water is fed into the system. The reforming reactions of the fresh alkanes contained in the natural gas only occur with CO2, CO, H2, and H2O present in the anode offgas. For this reason the oxygen to carbon ratio is used exclusively in this work.

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be prevented. However the graph in Fig. 3 should be considered with care. As a matter of fact, the black curves are actually valid for graphite. The carbon deposition observed on catalytic reformers or stacks is of another nature, producing pyrolytic carbon or whisker carbon, as reported in Ref. [7]. In such cases the black curves in the graph would exhibit a slightly different profile, [8]. Furthermore, as mentioned previously, the graph corresponds to thermodynamic calculation regardless of reaction mechanism. The kinetics of the carbon deposition plays an important role and had to be considered for, as done experimentally by Ref. [9], to determine the actual risk of carbon deposition. Fig. 4 introduces the calculation of the oxygen to carbon ratio. The circle with label f denotes the location in the gas circuit where the oxygen to carbon ratio is calculated. At this point the oxygen to carbon ratio is defined as previously introduced as:

l ¼

(8)

The only source of C atoms in the anode circuit is the natural gas P source, n_ C;in ¼ n_ NG xi;NG gi;C , where gi,C refers to the number of C i

atoms contained in one molecule of alkane i, e.g. 2 for C2H6. The only source of O atoms in the anode circuit is the flow of O2 anions passing through the electrolyte, i.e. n_ O;in ¼ I nc =2F. From a mass balance in the system presented in Fig. 4 it can be established that n_ C;Pre ¼ n_ C;in =1  r and n_ O;Pre ¼ r=1  r n_ O;in which leads to:

f ¼ r FUSys Gf P

(9) P

i xi;NG gi;e =2

i xi;NG gi;C .

2.4. Stoichiometric air fuel ratio l of the burner In this subsection the characteristic variable for the burner (Bu), the stoichiometric air fuel ratio l is examined. Fig. 5 shows the gas

n_ O2 n_ O2 ;sto

(10)

n_ O2 refers to the amount (in mol s1) of dioxygen flowing into the burner. This flow of dioxygen is then “available” for combustion reactions in the burner. The flow rate n_ O2 ;sto refers to the amount of dioxygen necessary to consume stoichiometrically the amount of combustible species flowing into the burner from the anode outlet. The mass balance on dioxygen in the cathode together with the mass balance on the combustible species in the anode in the system presented in Fig. 5 yield:

l ¼

n_ O;Pre f¼ n_ C;Pre

with Gf ¼

circuits, in particular with air flow to the cathode. Stoichiometric coefficient l is defined as

n_ NG

n_ Air xO2 ;Air ð1  AUÞ   P i xi;NG gi;O2 1  FUSys

(11)

where xO2 ;Air refers to the molar fraction of dioxygen in the air, gi;O2 refers to the number of dioxygen moles for stoichiometric consumption of one mole of alkane i, and AU is the air utilisation. Using the definition of the air utilisation:

AU ¼

Inc 4FxO2 ;Air n_ Air

(12)

together with that of the fuel utilisation system, see equation (4), P P and observing that xi;NG gi;e ¼ 4 xi;NG gi;O2 , equation (11) can i i be rewritten as follows: 1 1 l ¼ AU 1

(13)

FUSys

3. Feed-forward control strategy In the previous section the definitions of main criteria together with the basic equations defining the characteristic variables have been given in order to describe the operating point of the SOFC system. The present section describes the feed-forward control strategy developed to operate the system “in secure conditions”. The first subsection examines the operating domain in which the actuating variables (n_ Air , n_ NG , and n_ Recy ) have to be kept for this purpose. The following subsection demonstrates the possibility to adjust these actuating variables at desired coordinates by separating the variables from the equation set in this domain. 3.1. Authorized domain for the anode side 3.1.1. Limitation due to the oxygen to carbon ratio f As explained in Section 2.3 the oxygen to carbon ratio has to be kept above a certain limit fmin:

! fmin  f

(14)

Inequality (14) can be expressed with variables (n_ NG and n_ Recy ), as explained in this sub-section. Using equations (2) and (9), inequality (14) is transformed into:

! n_ Recy  Fig. 5. Schematic of the SOFC system path with burner.

fmin GRef n_ 2NG Ge Gf  fmin n_ NG

where Ge ¼ Inc =F

P

i xi;NG gi;e .

(15)

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3.1.2. Limitation due to the stack fuel utilization Each fuel cell has a maximum (max) authorized fuel utilisation in order to prevent the stack from possible degradation and even local fuel starvation. This requirement can be expressed as:

! FUSta  FUSta;max

n_ Recy 

  GRef n_ NG Ge  FUSta;max n_ NG FUSta;max ðn_ NG  Ge Þ

3.2. Authorized domain for the cathode side

(17)

3.1.3. Limitation due to the recycle rate The last limitation concerns the flow upstream of the Pre Reformer (see Fig. 3 showing the limit of oxygen to carbon ratio to avoid carbon deposition). Besides the limitation of the pump itself, the Pre Reformer and the stack cannot be fed by too a large molar flow to avoid that pressure exceeds, approx. 100 mbar(g), i.e. 10000 Pa. For this reason the molar flow upstream of the Pre Reformer, n_ Pre , must be limited under a defined level:

! n_ Pre  n_ Pre;max

(18)

A mass balance in the system shown in Fig. 2 yields:

! n_ Recy  n_ Pre;max  n_ NG

the right bottom corner of the graph, which makes the authorized domain smaller. In addition, as expressed above, too high flow rates result in too high pressure drop: in such case the limit n_ Pre;max has to be reduced, leading to downward shifting of the upper dotted curve, reducing then the authorized domain.

(16)

From the definition of the system fuel utilisation in equation (4), and using equations (2) and (6), inequality (16) becomes:

!

503

Similar to the anode side, it is possible to calculate the features of the “Authorized Domain” for the remaining actuating variable of the cathode side, i.e. n_ Air . For that purpose the two inequalities governing the molar flow through the cathode are considered. 3.2.1. Limitation due to the air utilisation The cathode has to be fed with air in excess for the production of the considered current:

! AU  AUmax

(20)

Similar to the fuel utilisation, this equation ensures that enough oxygen is always supplied to the cathode during power operation: local air starvation at the cathode can then be avoided. By using the definition of the air utilization, AU ¼ Inc =4FxO2 ;Air n_ Air , the following inequality is deduced:

! Inc  n_ Air 4FxO2 ;Air AUmax

(21)

(19)

3.1.4. Combination of the limitations Fig. 6 gives an overview of the authorized domain for the actuating variables if one considers the three constraints (16), (18), and (19). To introduce Fig. 6 variables jRecy and jNG must be defined: jNG ¼ n_ NG =n_ NG;nominal and jRecy ¼ n_ Recy =n_ Recy; nominal . The variable n_ Recy; nominal and n_ NG;nominal are the molar flows at full load with FUsta ¼ 70%. The solid dotted curve corresponds to equation (19): changing the generated current has no effect on this curve, whereas the two other curves corresponding to equations (15) and (17) move toward

3.2.2. Limitation due to the air fuel ratio l The stoichiometric air fuel ratio of the burner, l, has to be kept in a defined range:

! ! lmin  l  lmax

(22)

The left term of this inequality ensures that the fuel fed is entirely burnt: should oxygen (air) flow rate be too low for the combustion, only a fraction of the fuel will be burnt, leading to high CO concentrations in the exhaust gas. The right term of this inequality ensures that combustion can be sustained: if too much air is fed, the temperature in the combustion chamber will decay, forcing the combustion to be stopped. Using equation (13) and the definition of the air utilisation (12), inequality (22) can be rewritten in the following form:

!

Inc 4FxO2 ;Air

lmin

! ! 1  1 þ 1  n_ Air FUSys

(23)

and

! n_ Air 

Fig. 6. Graph in (JRecy, JNG) coordinates indicating the authorized domain for the anode side. The calculation was made with the following parameters: I ¼ 9 A, nc ¼ 25, Fmin ¼ 2, FUsta,max ¼ 70%, V_ NG;nominal ¼ 0.44 Nl min1 (7.33$106 Nm3 s1), V_ Recy;nominal ¼ 2.03 Nl min1 (3.38$105 Nm3 s1), and natural gas composition:xCH4 ¼ 95% xC2H6 ¼ 3 % and xC3H8 ¼ 2%.

Inc 4FxO2 ;Air

lmax

1 1 FUSys

!

! þ1

(24)

3.2.3. Combination of the limitations Fig. 7 shows the authorized domain for the cathode actuating variable n_ Air . This representation relies upon the two reduced operating parameters jI and jAir which are defined as: jI¼ I/IFull load and jAir ¼ n_ Air =n_ Air;nominal . The variable n_ Air; nominal is the molar flow at full load with AU ¼ 35%.

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r¼

f   f þ Gf  f FUSta

(25)

Then by incorporating once more equation (25) into equation (9) and by expressing the system fuel utilisation FUSys with respect to the current produced I and the molar flow of natural gas (see equation (4)) the actuating variable n_ NG is expressed as a function of the two setpoint variables and the current drawn:

I nc G f    n_ NG ¼  f þ Gf  f FUSta F ge

(26)

Then equation (26) is inserted in equation (2), which is again combined with equation (25). The recycle molar flow can finally be written as a function of the two setpoint variables and the cell current: Fig. 7. Graph in (JI, JAir) coordinates indicating the authorized domain for the cathode side. The calculation was made with the following parameters: nc ¼ 25, FUSys ¼ 84%, lmin ¼ 1.5, lmax ¼ 12, AUmax ¼ 50%, IFull load ¼ 9 A, V_ Air;nominal ¼ 10.76 Nl min1 (1.79$104 Nm3 s1), natural gas composition: xCH4 ¼ 95%, xC2H6 ¼ 3%, xC3H8 ¼ 2%, and minimal fuel for heating the fuel cell system V_ NG;min ¼ 0.2 Nl min1 (3.33$106 Nm3 s1).

The boundaries of the allowed domain are calculated assuming that a minimum fuel feed is required to maintain the fuel cell system at a sufficient temperature. In other words the variable FUSys may be reduced when the current is reduced. In the extreme case that no current is drawn from the cell minimal value for the natural gas flow must be defined. This correction is done stepwise, i.e. a constant FUSys is defined for all the operating points and this value is corrected at the only condition that the resulting natural gas flow is lower than a certain limit n_ NG < n_ NG;min . In that case the lower NG flow limit, n_ NG;min , is used and the corrected system fuel utilisation value can be calculated backwards. The stepwise correction of the NG flow can be seen in Fig. 7 in the curve l  lmax and l  lmin for the range jI 2 [0; 0.75]. 3.3. Separating the effects of the anode actuating variables n_ NG , and n_ Recy The three key molar flow equations are presented in equations (2), (6) and (9). These three equations will be used in this section to deduce the required expressions for actuating variables n_ NG and n_ Recy . In order to simplify the mathematical expressions calculated in the following section, coefficient ge is defined as follows: P ge ¼ xi;NG gi;e . After i algebraic arrangements the two actuating variables n_ NG and n_ Recy can be expressed as functions of the two setpoint variables FUSta and f. As explained in Section 2.3 the oxygen to carbon ratio is the key characteristic variable to avoid carbon deposition in the Pre Reformer or in the stack. The stack fuel utilisation (FUSta) is preferred over the system fuel utilisation (FUSys) because of its physical meaning for the stack: by controlling the stack fuel utilisation one can prevent stack degradation by local fuel starvation. Once these two variables are fixed, the values for variables r and FUSys can be calculated. The mathematical rearrangements are not described in details but the principle is given below. A detailed description of these rearrangements is given in Ref. [10]. First equation (9) is used to express the stack fuel utilisation with respect to variable r and parameter Gf. Substituting then the variable fuel utilisation in equation (11) by its expression obtained thanks to the rearrangement of equation (9), the recycle rate r can be expressed with respect to the two setpoint variables:

In G G f   c  Ref f    n_ Recy ¼  f þ Gf  f FUSta F ge Gf  f FUSta

(27)

Now it is possible to calculate the coordinates of the point in the authorized domain shown in Fig. 6 for the operating current I ¼ 9 A. The coordinates of the point will fall automatically in the authorized domain by choosing the characteristic parameters FUSta and f that fulfil inequalities (14) and (16) and using equations (26) and (27). 3.4. Feed-forward control strategy for the cathode actuating variable n_ Air Inequalities (21), (23), and (24) have to be fulfilled, so that safe operation of the fuel cell system is ensured by the feed-forward control strategy. The next paragraph describes the calculation steps in order to determine the air flow setpoint variable for the system as shown in Fig. 8. The equivalent control diagram shown in the right part of Fig. 8 is explained below:
The desired l variable is designated as lsetpoint in Fig. 8. This value is then limited by the saturation block. The upper limit for the saturation value lmax corresponds to the maximal authorized l value in the burner. The lower limit lmin is the result of the calculation explained in the next point of this list.
lmin is the maximal value of lmin,bu and lmin,AU. lmin,bu is the minimal value for l accepted for the combustion reaction in the burner. lmin,AU is the corresponding l value obtained when the system would be operated at the limit AUmax. The conversion from AU to l is operated in the block “AU to l ”. by using equation (13).
The saturated air fuel ratio, named as lsetpoint,sat in Fig. 8, is converted into an air molar flow, again using equation (13) and the definition of the air utilization, AU ¼ Inc =4FxO2 ;Air n_ Air . The desired air molar flow can be expressed as follows:

n_ Air;setpoint ¼

I nc 4FxO2 ;Air

lsetpoint;sat

!! 1 1 FUSys

(28)

The coordinates of a point in the authorized domain shown in Fig. 7 can be calculated. The coordinates of the point are to be in the authorized area by choosing the characteristic parameters l and AU that fulfil inequalities (20) and (22). Numerical calculation is then carried out with equation (28).
The calculated desired air molar flow n_ Air;setpoint is transmitted to an underlying closed loop control unit (not represented here), which sets the operating point of the compressor CAir, to obtain the desired air molar flow.

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505

Fig. 8. Schematic of the SOFC system with the equivalent control diagram for the cathode actuating variable.

Three more remarks can be made to complete the explanation of the cathode feed-forward control strategy:
A system with two air feeding circuits (one to the cathode and one to the burner) can be designed for separate investigation of the characteristic variables AU and l. However the compactness of the system is a significant aspect in CHP applications.
The value of lsetpoint can be the result of a preliminary calculation: the temperature of the stack is regulated over closed-loop control by setting the value of lsetpoint. Whatever the prior calculations are, the presented equivalent control diagram in Fig. 8 allows operation of the burner and the stack under secure conditions.
An equivalent feed-forward control strategy, i.e. fulfilling the three inequalities (21), (23), and (24), can also be established using the characteristic variable AU instead of l. The feed-forward control strategy presented in this section offers the advantage to consist exclusively in deterministic equations which can be easily implemented in a PLC: as a matter of fact with the help of equation (26) and equation (27) only few calculation steps are necessary to calculate the actuating variables n_ NG and n_ Recy . The cathode actuating variable requires a more complicated strategy, as shown in Fig. 8, but its complexity remains acceptable for standard PLC. The simplicity of the feed-forward control strategy does not remove basic security requirements: key characteristic variables, FUSta, AU, F and l stay under the necessary limits to ensure secure operation. 3.5. Comparison with the state of the art First literature sources treating control issues of SOFC systems with AOR are examined. In a second step the scope of the comparison will be enlarged and all class of SOFC systems are considered. Hottinen et al. in Ref. [11] propose a control strategy for SOFC with AOR, which is mainly characterized by a parallel online thermodynamic calculation of chemical equilibrium upstream of the stack/Reformer. Results of this calculation are then used to verify that the F ratio remains in a secure area. If necessary, the recycle rate is tuned up to set the F ratio to desired value. Dietrich et al. examine in Ref. [12] a SOFC with AOR: there the cathode air is used

to regulate the stack temperature. The presented FCS works with an injector nozzle instead of recirculation blower, which hinders to set up the F ratio through the recycle rate. The authors suggest, that the F ratio is maintained above a defined limit by feeding additional CO2. In previous mentioned works the F ratio can be controlled. However the control is linked to further calculations [11] or additional hardware [12]. The presented control strategy for the F ratio in this work is a feed-forward calculation and no extra hardware is necessary. Nonetheless the provided control strategy in this paper does not consider intermediate reforming states like in Ref. [11] and does not offer a direct actuating variable, with limiting impacts (Temperature, pressure drop) on the FCS, like in Ref. [12] with the extra CO2 feeding. Few or no indications about the control of FUSta are provided, which does not allow any valuable comparison to be made in this work. By extending the scope of the considered SOFC systems, several literature sources treating control issue can be found. First, mCHP applications are considered. The Japanese company Kyocera gives in Ref. [13] an overview of its low-level control strategy for a mCHP SOFC system. The considered SOFC system does not feature any AOR but direct steam feeding. The proposed feed-forward low-level control equations are very similar from those presented in this study: few deterministic equations linked key system variables, e.g. fuel utilisation, and actuating variables, e.g. natural gas molar flow rate. In addition to this, a higher-level control algorithm is presented in form of a state diagram to ensure safe operations during main operation phases of the SOFC system. Liso et al. proposes an interesting analyse of the heat-to-power-ratio (heat output/electrical output) of SOFCbased mCHP system in Ref. [14]. This study examines the benefit to modulate the heat-to-power ratio of a SOFC system (no AOR but direct steam feeding) in order to fit heat and power demands of various households in Europe. In this case, the modification of the heat-to-power ratio can be considered as an upper-level control routine to maximize the profitability of the SOFC-based mCHP system. This article gives insights into the consequences for the lowlevel control routines by modifying the heat-to-power ratio. Leaving the field of mCHP applications, many authors have considered the use of a modelling predictive control (MPC) under constraints to control a SOFC system. In most cases the MPC replaces at the same time the low-level control and high-level control. Sanandaji et al. presents in Ref. [15] a detailed model of a CPOx-based SOFC system. Then a simplification of this model is performed and

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the simplified model is used to develop a MPC for the SOFC-system. The MPC is then tested on the first detailed model and shows promising results: the SOFC system responds to the load demand by satisfying all the constraints. Further MPC under constraints applied to SOFC-systems are presented in Refs. [16,17]. MPC under constraints appears to be a meaningful complementary control algorithm to replace or extend any existing low-level control strategy, e.g. as presented in this study. Indeed MPC under constraints offers the possibility to limit the impacts of negative effects on the SOFC system, e.g. large temperature gradient within the stack. Braun et al. share a similar point of view in Ref. [18]. The authors mention an additional advantage of MPC: the possibility to estimate unmeasured variables (e.g. the fuel utilisation), which are crucial for control issue. Zhang et al. proposes in Ref. [19] an interesting method based on a transverse optimal operating point optimization to control SOFC-System under constraints. Similar to the aforementioned MPC, this type of control aims at responding to the load demand by satisfying different constraints. Finally Huang et al. presents in Ref. [20] a detailed review of the model-based control possibility for SOFC system. Here, “control” is defined as the task to follow the load demand by increasing the system efficiency, by regulating disturbance and by maintaining the SOFC system in safe operation limits. Two classes of model-based control are identified: the first class, named “univariate control”, aims at delivering constant power without changing the fuel utilization and the stack temperature. The second class, named “multivariate control”, aims at delivering constant power by respecting a series of constraint like temperature gradient in stack, dynamic limitation of the SOFC system, etc. 4. Experimental The previous feed-forward control strategy was tested with a SOFC FCS in a test bench. This FCS is composed of a SOFC stack and further components, which are presented in Fig. 9. The Piping and Instrumentation Diagram (P&ID) in Fig. 9 represents a CHP SOFC system with anode offgas recirculation. The main difference with flow diagram in Fig. 1 is the presence and arrangement of the heat exchangers (Reformate HEX and Air HEX). Four components have been added to allow start-up operation of the FCS: a catalytic

partial oxidation (CPOx) reactor, an air feeding unit for the CPOxreactor, a start-up burner, and a protection gas (PG) e.g. nitrogen feeding unit (CPG). The next paragraph describes the FCS arrangement presented in Fig. 9. The air circuit, represented in dark green lines (in web version) with “//” patterns, is composed of air compressor CAir and heat exchanger Air HEX: air is first compressed by CAir and then heated up by Air HEX. During power generation the air stream enters the cathode at approx. 750  C. The anode circuit, represented by the dark red lines (in web version) with “/” patterns in the figure, begins at node A, where fresh natural gas is mixed up with a part of anode offgas, also called recirculate. This gas mixture is conveyed with the help of the recirculation compressor CRecy through the remaining components of the anode circuit. During power generation the CPOx reactor is inactive: no air is present in the recirculate. Higher hydrocarbons of C2, C3 and C4 type are pre reformed at around 450  C in the Pre Reformer to avoid carbon formation in the stack at higher temperatures [3]. The partially reformed gas mixture flows into the anode, where a part of the combustible compounds are consumed in electrochemical reactions. After leaving the anode, the anode offgas is split into two streams. The first one is driven to the burner, as shown in Fig. 9, where the remaining combustible compounds are burnt. The heat is then transferred to the inlet fresh air over the air heat exchanger (Air HEX). The second part of the anode offgas flows through the recirculation compressor and is fed into the gas stream at node A. A way to heat up the FCS is to perform partial oxidation of natural gas in the CPOx reactor. A fraction of the combustible compounds is burnt in the CPOx reactor. Thus a heat source is present in the anode path, which allows heating up anode and cathode with a similar heating rate. The second advantage is the production of a hydrogen- and carbon monoxide-rich gas mixture upstream of the Pre Reformer and the anode. No liquid water is needed for start-up. This way of starting up the FCS is called waterfree mode. A start up procedure is detailed in the following section and in Fig. 10. The PG feeding unit CPG is used at the beginning of the water-free start-up procedure. The start-up burner boosts the start-up procedure by providing extra overheated air upstream of the burner.

Fig. 9. Piping & Instrumentation Diagram (P&ID) of the investigated FCS.

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the start-up burner. During the phase 0:00e2:10 h inert “protection” gas is fed into the anode circuit at 1 Nl min1 (1.66$105 Nm3 s1), and the electrical heater in the Pre Reformer is working to warm up the anode circuit. Phase 2 At time 2:10 h the CPOx reactor is ignited: the CPOx electric heater is started to elevate the CPOx temperature above 300  C. For this purpose a mixture of air and natural gas is fed through the anode circuit. The partial oxidation temperature is controlled by using the oxygen to carbon ratio F. The output temperature of the CPOx reactor is set to 530  C thanks to a temperature control. As soon as the partial oxidation reaction is started, the electric heater and the protection gas feed are stopped. The heating power is set by adjusting the natural gas flow. The recirculation pump is switched on and the recycle rate is then set to 50% in order to distribute the generated heat in the CPOx reactor over the whole anode circuit. After approx. one hour of operation of the CPOx reactor the electrical heater of the Pre Reformer is switched off. The stack is heated up by this procedure until time 8:00 h. Phase 3 Then the burner is ignited: the main cathode air feed is reduced to reduce the air fuel ratio l of the burner. This reduction can be seen in the time variations of the characteristic variables in Fig. 10. Besides, the natural gas feed to the anode is ramped up to 2 Nl min1 (3.33$105 Nm3 s1). After ignition of the burner, its temperature is observed to increase from time 8:00 h. From now on the temperature of the burner is regulated by the cathode air flow. The value of the air fuel ratio l is maintained within a certain domain by using the cathode air flow feed-forward control strategy presented in Fig. 8. The stack is further heated up this way till time 9:15 h.

Fig. 10. Water free start-up procedure of the fuel cell system with AOR.

5. Results and discussion Main results of operation of the CHP SOFC with anode offgas recirculation are presented in this section. First a water-free startup procedure is examined. A comparison with start-up procedures for SOFC systems found in the literature completes the analysis of start-up operations. Then a comparison between power operation with and without AOR is proposed: electric efficiency as well as stack voltage are examined. To conclude this section some improvements of the start-up procedure are suggested. 5.1. Experimental procedure for start-up Fig. 10 presents the most important variables during water free start up operation. The start-up procedure is divided into 4 phases. Phase 1 First the start-up burner is ignited. Its temperature is regulated at approx. 825  C during the whole start-up procedure as depicted in graph temperature, variable “T_StartBurner”. Around 2 Nl min1 (3.33$105 Nm3 s1) natural gas is fed into

Phase 4 Power is generated from time 9:15 h. The oxygen to carbon ratio F increases due to the additional oxygen source in the anode path generated by the electrochemical reaction. The temperature in the stack is only approx. 500  C. Generation of power is part of the start-up procedure and contributes to maintain the stack at a sufficient temperature. The anode natural gas feed is now controlled by setting the fuel utilization stack. The temperature closed loop control of the CPOx reactor is switched off. The variable F is set by adjusting the recycle rate, which is directly adjusted by regulating the flow passing through the recirculation compressor. From time 12:00 h the natural gas of the start-up burner is ramped down: the stack rises by the produced power and the contribution of the start-up burner becomes gradually less and less significant. At time 15:00 h no more natural gas is fed to the start-up burner, whose temperature decreases. At time 17:00 h the stack has reached its nominal temperature; so the FCS can deliver power at full load. The goals of the start-up procedure at this stage of the development are: 1. to bring the FCS to nominal temperature, so that power can be drawn, 2. maintain all key characteristic variables (F, FUSta, AU) in the allowed domain, 3. start the FCS without using liquid water, 4. start the FCS without protection gas, 5. Reduce the number of components to its minimum, 6. Start the FCS within less than 6 h.

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Important goals (1, 2 partly, 3) have been reached in the start-up procedure presented in Fig. 10. Nonetheless certain goals (2 partly, 4, 5, and 6) could be attained and possible improvements of the start-up procedure are examined in Section 5.3. The next paragraph presents an overview of the start-up procedure for SOFC system found in the literature. Rancruel et al. proposes a start-up procedure for a SOFC system with AOR in Ref. [21]. The start-up manoeuvre differs mainly from the one presented in this article by the use of a steam generator and by the use of buffer tanks (air tank, hydrogen tank, battery tank) to offer a more reliable gas and power delivery to the SOFC stack. Nonetheless the global concept of the start-up remains similar to the one proposed in this study: first natural gas is burned to bring the SOFC system to a high temperature level. In a second step power generation is started as soon as the stack temperature is high enough and the fuel and air feeding are in the correct range. A similar startup procedure is to find in Ref. [10]. Fontell presents briefly a start-up procedure for large SOFC CHP with AOR in Ref. [22]. From the unique graph presenting the startup operation it is possible to deduce the following key features: a steam generator is used to deliver a hydrogen rich gas to the stack before power operation. Power operation is started when the stack

temperature is high enough. Current is ramped up within 30 min. In the meanwhile steam generation is ramped down, but not stopped, and the O/C ratio can be maintained at a constant value: vapour from the anode offgas shall be recycled. The start-up procedure appears to be very similar to those presented in Refs. [10,21]. A start-up procedure for SOFC-based Auxiliary Power Unit (APU) is introduced by Sorrentino et al. in Ref. [23]. The APU works under direct steam feeding, i.e. without AOR. A pragmatic start-up procedure is proposed. The main focus is on reducing temperature gradient within the stack and on analysing the key parameters that influence the temperature gradient. The general concept of the start-up procedure is very similar to the one presented in this article, as well in Refs. [10,21,22]. 5.2. Operation with and without AOR Fig. 11 presents a comparison of two power operation modes: one with anode offgas recirculation and the other without anode offgas recirculation. This latter also called vaporizer mode could be carried out by means of a vapour feeding unit (not shown in Fig. 9). The considered gross electric efficiency is defined for this work as follows:

Fig. 11. Comparison of two operation modes: evaporator mode (no recy) and AOR (recy) a) (top) efficiency and fuel utilisation, b) (bottom) stack temperature.

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hel;DC;LHV

Pel;sta;DC ¼ Pin;NG;LHV

(29)

where Pel,sta,DC is the electric power measured directly at the stack current leads and Pin,NG,LHV is the power represented by the natural gas flow entering the FCS. The main result of this figure is focused on the comparison of the gross electric efficiency (hel,DC,LHV) in the two modes, see upper graph: the mode with AOR offers a higher efficiency than without recirculation. To generate results without AOR, a vapour feeding unit (not shown in the P&ID in Fig. 9) is used to create a mixture of natural gas and vapour. The CPOx reactor is in this case inactive. Fig. 11a shows the advantage of the AOR feature over a “classical” water feed system: the gross electric efficiency is above the one without AOR and confirms the conclusions reported in Refs. [12,24,25]. In recycle mode the fuel utilisation stack was 64% (not represented in Fig. 11). At full load, the stack temperature and the fuel utilisation stack are similar for the two modes. Thus a comparison of the two modes is possible at this operation point. At part load in evaporator mode, the stack temperature could not be maintained at 750  C because the endothermic reforming reaction in the stack reduces this temperature. This effect was rendered more visible by the decrease in the fuel utilisation stack. At part load under such conditions (low stack temperature, risk of stack starvation) it is recommended to maintain the fuel utilization stack as low as shown in Fig. 11 to avoid stack degradation. Thus at part load the comparison of the two modes is somewhat erroneous. Fig. 12 establishes one more comparison in terms of cell voltage fluctuations between the two operating modes. It can be seen that in evaporator mode the stack voltage varies in the range of ± 0.4% of the mean value at a frequency of approx. 0.1 Hz whereas the variations seem to be mainly due to measurement resolution: the recycle mode offers much more constant voltage behaviour than the evaporator mode which is certainly much safer for the longterm operations of the stack. Although this point cannot be demonstrated, irregular droplet evaporation in the evaporator, and so variations in the composition and pressure of the gas at anode inlet, is likely the cause of these voltage oscillations in evaporator mode. The low voltage oscillation amplitude in anode recycle mode indicates that the stack will be more preserved than in evaporator mode, which is to increase its lifetime.

as their surface temperature does not exceed approx. 300  C, [26]. Thus it be considered to recycle securely the gas containing oxygen in the anode circuit until ignition of the CPOx reactor. This possibility has been confirmed by Halinen et al. in Ref. [26].
The time required for start-up of the FCS presented in Fig. 10 (approx. 17 h) is largely too long for residential applications. The mechanical construction of the investigated prototype is not highly integrated and does not have appreciable low thermal losses and capacity. Improved design of each element in term of isolation, together with the ducts and connections between them can be highly improved. In addition the extra piping installed for analysis purpose inside the FCS - not represented in Fig. 9 - increases the mass of the system and favours some more heat losses. These various facts in the present e prototype e system contribute to extend in a significant manner the overall start-up time.
Another critical point is the level of the oxygen to carbon ratio F during the start-up procedure: during the whole procedure its value was far below 2, approx. 0.4, which is critical regarding carbon deposition. The level was fixed at such a low level to avoid overheating of the CPOx reactor. Considering a partial oxidation reaction, a relationship between the air fuel ratio l and the oxygen to carbon ratio F of the CPOx reactor could be established taking into account the definition of ratio F and ratio l for an exemplary combustion reaction involving methane and air:

F¼4l

(30)

Therefore it is possible to operate at partial oxidation (1 > l) while avoiding carbon deposition (2 < F). Increasing ratio F is to

5.3. Improving the start-up procedure The start-up procedure presented in Section 5.1 has the advantage that no liquid water is required, which avoids the technological issue of liquid water management. Nonetheless a couple of modifications can be suggested here to improve the above start-up procedure.
First, the start-up burner is an additional element and is partly redundant. At present state a start-up burner is absolutely required because the burner in the examined prototype cannot be started at cold state. In a long term view, it will be necessary to have a burner able to ignite at cold state, which could avoid the start-up burner and render the FCS much simpler.
Another optimization point concerns the use of protection gas at the beginning of the start-up procedure. For practical application in real conditions, e.g. production of heat and electricity for domestic use, no protection gas is available. A solution to this problem could consist in recycling the gas present in the anode when starting-up the system, even if this gas contains oxidizing molecules. Current catalyst materials resist to oxidation as long

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Fig. 12. Comparison of two operation modes for the stack voltage.

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result in increase in the temperature of the CPOx reactor: this undesired phenomena could be avoided by the use of an additional heat exchanger, which renders the conditions less favourable for practical applications. 6. Conclusion This work provides a novel feed-forward control strategy for stationary SOFC fuel cell system with anode offgas recirculation: feed-forward calculation steps are performed. From several setpoint variables, the actuating variables are calculated, which are necessary to manage steady-state and start-up operations. This feed-forward control strategy is characterized by its simplicity: two deterministic equations describe the relation between the anodic setpoint variables (fuel utilization stack and oxygen to carbon ratio) and the two actuating variables, namely natural gas flow and recycle flow. A deterministic equation combined with a couple of saturation functions, i.e. min and max function, establishes the relation between the air fuel ratio lambda of the tail burner and the cathode air flow. Furthermore this feed-forward control strategy offers secure operations of the fuel cell system whatever the load. A prototype of a fuel cell system with anode offgas recirculation was set up and could be started up without addition of liquid water. Then the fuel cell system was investigated in two modes: anode recirculation mode and evaporator mode (without anode offgas recirculation). At full load the fuel cell system operated with AOR exhibits a gross electric efficiency of 62%, whereas it is near 50% only in evaporator mode. DC LHV gross electric efficiency could be maintained above 60% at part load in the power operating range 50 %e100 %. The stack voltage exhibits a more stable profile e with far smaller fluctuations e in recycle mode. In evaporator mode oscillations in stack voltage are observed. They are probably related to water droplet evaporation in the evaporator and may reduce the lifetime of the stack. Finally, routes for possible technological improvement of the system are proposed. Acknowledgements We thank the company Robert Bosch GmbH, that funds this project.

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