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Control Strategies for Solid oxide Fuel cell voltage
Control Strategies for Solid oxide Fuel cell voltage
Control Strategies for Solid oxide Fuel cell voltage
Control Strategies for Solid oxide Fuel cell voltage
Control Strategies for Solid oxide Fuel cell voltage
Control Strategies for Solid oxide Fuel cell voltage
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Control Strategies for Solid oxide Fuel cell voltage

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This paper presents a comprehensive non-linear …

This paper presents a comprehensive non-linear
dynamic model of a solid oxide fuel cell (SOFC) that can be
used for transient behaviors studies. The model based on
electrochemical and thermal equations, accounts for
temperature dynamics and output voltage losses. The
relaxation time is strongly related to the transient temperature
distribution of the solid oxide fuel cell structure. Therefore,
it is in the order of some minutes depending on the design
parameters and the operating conditions. The model contains
the hydrogen, oxygen and water block separately. Other blocks
are concentration, activation and ohmic losses block. This
analysis is based on an integrated dynamic model of the entire
power plant using SIMULINK in Matlab. The analytical details
of how active and reactive power output of a stand-alone solid
oxide fuel cell power plant (FCPP) is controlled.

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  • 1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 Control Strategies for Solid oxide Fuel cell voltage 1 Kanhu Charan Bhuyan and 2Kamalakanta Mahapatra Dept of ECE, National Institute of Technology-Rourkela, India-769008 Email: kanhu2006@gmail.com, kmaha2@rediffmail.comAbstract— This paper presents a comprehensive non-linear controllers are designed for these purposes. The fuzzy logicdynamic model of a solid oxide fuel cell (SOFC) that can be control scheme is employed for the design of the twoused for transient behaviors studies. The model based on controllers.electrochemical and thermal equations, accounts fortemperature dynamics and output voltage losses. The II. PRINCIPLES OF FUEL CELL MODELrelaxation time is strongly related to the transient temperaturedistribution of the solid oxide fuel cell structure. Therefore, The fuel cell (FC) is an electrochemical device thatit is in the order of some minutes depending on the designparameters and the operating conditions. The model contains converts chemical energy of hydrogen gas ( H 2 ) and oxygenthe hydrogen, oxygen and water block separately. Other blocksare concentration, activation and ohmic losses block. This gas ( O2 ) into electrical energy. The solid oxide fuel cellanalysis is based on an integrated dynamic model of the entire consists of two porous ceramic electrodes separated by apower plant using SIMULINK in Matlab. The analytical details dense ceramic electrolyte. The cell produces electricity byof how active and reactive power output of a stand-alone solid the electrochemical reaction of fuel (hydrogen and / or carbonoxide fuel cell power plant (FCPP) is controlled. monoxide) and the oxidant (oxygen) across the solid electrolyte. Oxygen fed to the air electrode (cathode) acceptsIndex Terms— Fuel cell, FCPP, SOFC. electrons from the external circuit to form oxygen ions. The I. INTRODUCTION ions are conducted through the solid electrolyte to the fuel electrode (anode). At the fuel electrode, the ions combine Many researchers reported on of Molten carbonate fuel with hydrogen and/ or carbon monoxide in the fuel to formcell. Looking back, in 2004, Francisco Jurada presented a water and /or carbon monoxide. This reaction releasesmodel of ‘Solid oxide fuel cell’ without considering the electrons. Electrons flow from the fuel electrode (anode)temperature effect. The concept of molten carbonate fuel cell through the external circuit back to the air electrodeis exactly similar to solid oxide fuel cell. This comparison is (cathode).The overall reaction is exothermic; the cell producesgiven in [1] and [2]. The fuel input to the fuel cell is changing heat in addition to electricity.in steps in a paper in the literature [3]. Another very useful A typical fuel cell reaction is given below. The chemicalmodel is available in the literature in which was suggested reactions inside the cell that are directly involved in theby Kourosh Sedghisigarchi, [3] and [4] .This paper considers production of electricity are given asall the subsystems of fuel cell, that includes hydrogen block, At Anode:oxygen block, water block, activation and concentration block,and temperature block.. In temperature block, the relaxation H 2  O    H 2O  2 e time is closely related to the transient temperature distribution CO  O    CO 2  2 e  of the solid oxide fuel cell structure. The internal cell At Cathode:resistances are strongly temperature dependent. Thus, the relaxation time depends on the thermal properties, size and O 2  4e    2O2configuration of the cell, and operating conditions. In [5] and Overall:[3], SOFC model is given without considering thermal unit.However, in this paper, these structures are modified by the H 2  O2  CO  H 2O  CO2modeling thermal unit. A first comprehensive nonlineardynamic model of solid oxide fuel cell that can be used fordynamic and transient stability studies is developed by K.Sedghisigarchi, Ali Feliachi in 2004 [6]. The model based onelectrochemical and thermal equations, accounts fortemperature dynamics and voltage losses. The output voltageresponse of a stand-alone fuel-cell plant to a step change, afuel flow step change, and fast load variations are simulatedto illustrate the dynamic behavior of SOFC for fast and slowperturbations. Fig. 1 Basic operation of Fuel Cell This paper presents a SOFC model and designs the controlstrategies for the AC voltage control and the active/reactive The SOFC model consists of a) Electrochemical model-power control of the DC/AC inverter. Two separate component material balance equations. b) Thermal model-© 2011 ACEEE 50DOI: 01.IJEPE.02.03.14
  • 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011Energy balance equations. c) Nernst voltage equation d)Reformer model. e) Power conditioning unit model. f) Activeand reactive power control.A. Component material balance equation The change in concentration of each species that appearsin the chemical reaction can be written in terms of input andoutput flow rates and exit molarities  x i  due to the followingchemical reaction PV d in 0 r xi  N i  N i  N i . (1) RT i dt in 0where, V is compartment volume ( m3 ) , N i , , N i are molar Fig. 2 SOFC Dynamic Modelflow rates (mol/s) of i th reactant at the cell input and output B. Thermal modeling r The Nernst potential and loss mechanism are temperature(exit), respectively. N i is the reaction rate (mol/s) of the sensitive, the temperature throughout the cell must be knownreactant.is the cell temperature in degree Kelvin, is cell to accurately determine the cell’s electrical performance.pressure (atom), is the gas constant [(1 atom)/ (k mol degree In addition to the various types of heat transfer and theKelvin)]. sources, the thermal model also includes the variation of Molar flow of any gas through the valve is proportional material properties with temperature. The fuel cell power outputto its partial pressure inside the channel. The molar expression is closely related to the temperature of the unit cell. The heatis given by storage in the thin fuel unit or oxidant gas layer is neglected. The thin fuel unit or oxidant gas layers are lumped to the cell NH 2 N H 2O  KH2  K H 2O unit and gas layers are assumed to have the same temperature xH 2 xH 2O as the unit cell. E. Achenbach in [7] presents a relationship between twowhere, N H 2 is the hydrogen flow that reacts (k mol/s), K i is parameters S0 and F0 as given belowthe valve molar constant, xi is the molar fraction of species. F0  0.72 S0 1.1 (3)Applying the Laplace transformation to the above equationand isolating the hydrogen partial pressure, we obtain the t U j 1   following expression: where F0  C h 2eff and S0  heff p T 1 By simplifying the above eq. (3), we get KH2 xH 2  1   H 2s N in H2  2KrI  (2) F0 0.909  0.72S0 1 V F0 0.909  0.72 Y  T  1 (4)where ,  H 2  K RT ,where,  H 2 expressed in seconds, H2 U j 1   is the time constant associated with hydrogen flow and is Where, Y  heff the function temperature, K r is the constant dependent on U j is the power density (electric output),  is the efficiencyFaraday’s constant and number of electrons  N  in the of the fuel cell,  is the thermal conductivity, T is change ,reaction. in temperature N From the above eq. (4) we get, K r  4F 0.909 F0 Ywhere F is the Faraday’s constant. T  (5) 0.72 This is the increase in temperature from the initial condition after a relaxation time t .Assuming the relation between t, dt and temperature T . We can predict the temperature at on next simulation instant as  T  T  T  T0  T   in dt (6)  t © 2011 ACEEE 51DOI: 01.IJEPE.02.03.14
  • 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011C. Nernst voltage equation E. Active and Reactive Power Control Applying Nernst’s equation and ohmic law (taking into In synchronous machines, the power angle is notaccount ohmic, concentration, and activation losses), the measured, but the adjustment of the power angle occursstack output voltage is represented by following changes in steam input and rotor speed. In the FCPP, there is no speed control but the similar relationship Vdc  V0  rI   act   con (7) between output voltage phase angle and the flow of hydrogen  1  can be adopted as follows. Given that the load voltage Vs0  0 RT 0 x H 2 xO 2 2  V0  N 0  E  ln  is constant and the AC source voltage out of the inverter V ac  2F xH 2O  (8)   is given in (9), the angle  controls the power flow from theWhere, V0  is open-circuit reversible potential (in volts), fuel cell to the load, as in (10). The phase angle can be controlled using the input flow of hydrogen. The expressionE  is 0 standard reversible cell potential,  xi  is mole for , therefore, provides the relationship between the power output as a regulated quantity, and the amount of flow of fuelfraction of species, r  is ohmic resistances(in ohms), F  is input. This relationship is described by the following equations:Faraday’s constant (coulomb per kilo mole), T  is stack Assuming a lossless inverter, we gettemperature in Kelvin, N 0  is the number of cells in Pac  Pdc  V cell I (12) According to the electrochemical relationships, a relation-stack,  act is activation losses in volts,  con is concentration ship between the stack current and the molar flow of hydro-losses in volts,  I  is the stack current in amperes. gen can be written as N0ID. Power conditioning Unit Model qH2  (13) 2FU The power conditioning unit is used to convert DC output From equations (10), (12), and (13)voltage to AC. The power conditioning unit includes a DC/DC converter to raise DC output voltage, followed by a DC/ 2 FUX sin   qH2 (14)AC inverter to convert the DC bus voltage to AC. In this mV s N 0paper, only a simple model of a DC/AC inverter is consideredfor the following reasons: the dynamic time constant of Assuming a small phase angle sin    ; (14) can be writteninverters is of the order of microseconds or milliseconds. asThe time constants for the reformer and stack are of the order 2FUXof seconds.   qH2 (15) mV s N 0 A simple model of the inverter is given in [9], where outputvoltage and output power are controlled using the inverter Equation (15) describes the relationship between outputmodulation index and the phase angle  of the AC voltage phage angle  and hydrogen flow q H 2 . Equationsvoltage, V ac . The output voltage and the output power as a (10) and (15) indicate that the active power as a function offunction of the modulation index and the phase angle can be the voltage phase angle can be controlled by controlling thewritten as: amount of hydrogen flow. V ac  mVcell  (9) III. TS FUZZY CONTROLLER mV cell V s Pac  sin  (10) The proportional plus integral (PI) controller requires X precise linear mathematical models, which are difficult to obtain and may not give satisfactory performance under the transient conditions. The advantage of fuzzy logic controller Q  mV cell 2  mV cell V s cos   is that it does not require a mathematical model of the system. (11) X Here in the paper, TS fuzzy controller is incorporated becausewhere, V ac is the AC output voltage of the inverter [V], m is of its simple structure. The linguistic rule consequent is madethe inverter modulation index,  is the phase angle of the variable by means of its parameters. As the rule consequent is variable, the TS fuzzy control scheme can produce an infiniteAC voltage mVcell [rad], Pac is the AC output power from number of gain variation characteristics. In essence, the TSthe inverter [W], Q is the reactive output power from the fuzzy controller is capable of offering more and better solutions to a wide variety of non-linear control problems.inverter [VAR], V s is the load terminal voltage [V], X is the The deviations in the power error (error between referencereactance of the line connecting the fuel cell to the infinite and actual powers) are fuzzified using two input fuzzy sets Pbus [  ]. (positive) and N (negative). The membership function used© 2011 ACEEE 52DOI: 01.IJEPE.02.03.14
  • 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011for the positive set is where a  a1K , b  a2 K and  0 xi   L K  ( 1  K 2 2  K33  K 4  4 ) /( 1   2  3   4 )   x  L  P (xi)   i  L  xi  L As K is operating condition dependent, the effective value  2L (16)  1  xi  L of control gain varies widely during the control process. The values of a1, a2; K2; K3; K4 are given in APPENDIX-B. In theWhere, xi (k ) denotes the input to the fuzzy controller at the similar fashion TS fuzzy is incorporated to control reactivekth sampling instant given by power. This concept is given in [10]. x1 ( k )  e ( k )  Pacref  Pac (17)and IV. RESULTS AND ANALYSIS x 2 (k )   e (k ) (18) Fuel cell is designed for 320 V D.C. output voltage. Fig. 4For the negative set is shows the output voltage of fuel cell. Temperature of fuel cell is dependent on active power requirement. Consider that  1 xi   L active power is increased from 0.3 p.u. to 0.6 p.u at 1000 sec.   x  L  i and then decreased to 0.3 p.u at 2000sec. keeping reactive N (xi )    L  xi  L  2L (19)  0 xi  L power constant; the temperature of fuel cell is changed  accordingly as shown in Fig. 5. Fig.6 (a) and 7 (b) shows the active and reactive powers which are dependent on each other. The active power requirement is changed from 0.2 p.u to 0.6 p.u at 200 sec. and again it is change d to 0.4 p.u at 300 sec. From Fig. 6, it is seen that fuel cell is capable of providing the active power requirement. As active power demand is changed, the reactive power will also change Fig. 7 shows the capability of fuel cell to meet the reactive power demand. In order to make reactive power requirement independent of active power, a decoupled control theory is used. Consider that the active power is kept constant at 0.5 p.u. as shown in Fig.8 and reactive power demand is increased from 0.2 p.u to 0.6 p.u at 200 sec and then decreased to 0.4 p.u at 300 sec. Fig. 9 shows the capability Fig. (3) Membership function for (a) x1 and (b) x2 of fuel cell to meet reactive power requirement which is The membership functions for and are shown in figures controlled independently by applying decoupled control.(3) (a) and (b) respectively. The values of L1 and L2 are chosen Let initially rms value of active power is 30 KW and if theon the basis of maximum value of error and its integration. demand is that this rms value changes sinusoidally i.e., PacrefThe TS fuzzy controller uses the four simplified rules as changes at 200 secs. Fig. 10 shows that the fuel cell with PI controller is tracking the required reference power (Pacref),R1: If x1 ( k ) is P and x 2 (k ) is P then but it does not track the reference power perfectly.u1(k )  a1.x1(k )  a2 .x2 (k ) To overcome this problem, TS fuzzy controller is incorporated (discussed earlier). Fig. 11 shows the trackingR2: If x1 (k ) is P and x 2 (k ) is N then u2 (k )  K 2 u1(k ) performance of fuel cell with TS fuzzy controller. From Fig.R3: If x1(k ) is N and x 2 (k ) is P then u3 (k )  K 3 u1(k ) 11, it is seen that TS fuzzy controller is tracking the reference power perfectly. Now consider that reference active powerR4: If x1(k ) is N and x 2 (k ) is N then u 4 (k )  K 4 u1 (k ) changes (Pacref) shown in Fig. 12 and 13 shows theIn the above rules, represents the consequent of the TS performance of fuel cell with PI controller and Fig.13 showsfuzzy controller. Using Zadeh’s rule for AND operation and the performance with TS fuzzy controller. From these figures,the general defuzzifier, the output of the TS fuzzy controller it is seen that TS fuzzy controller can meet the power demandis. perfectly as compare to PI controller. In the similar fashion 4 the reactive power demand is changed and performance of  ( j ) u j (k ) fuel cell with PI controller and TS fuzzy controller is observed j1 u (k )  4 in figures 8.10 to 8.12. From these figures, it is seen that TS (20)  ( j ) fuzzy controller can track the required reactive power demand j1 perfectly as compare to PI controller.However for  =1, we get the centroid defuzzifier with u (k )given by u (k )  a x1(k )  b x2 (k )© 2011 ACEEE 53DOI: 01.IJEPE.02.03. 14
  • 5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 Fig. 4 Fuel cell output DC Voltage Fig. 11 Active powers with Fuzzy controller Fig.5 Temperature of fuel cell Fig.12 Reactive powers with PI controller Fig. 6 Active power Fig. 13 Reactive power with fuzzy controller V. CONCLUSIONS Fig.7 Reactive power The proposed SOFC dynamic model is developed along with the subsystems of concentration block, activation block, water, oxygen and hydrogen block. Thermal block is also incorporated in the SOFC dynamic model. The integrated model includes fuel cell and power conditioning unit. The mathematical equations facilitate modeling DC to AC converter. The proposed model is tested with its active and reactive power outputs being compared with the required Fig. 8 Active power (decoupled control) load demand. The dynamic behavior of SOFC model is analyzed by using PI and TS fuzzy controller separately. Here TS fuzzy logic controller is chosen because of its simple structure. It is observed that the dynamic performance of fuel cell with TS fuzzy controller is better in terms of tracking power demand as compared to the PI controller. REFERENCES Fig.9 Reactive power (decoupled control) [1] M.D. Lukas, K.Y Lee. And H.Ghezel-Ayagh, “Development of a stack Simulation model for Control Study on direct reforming molten carbonate Fuel Cell Power Plant,” IEEE Trans. Energy Conversion, Vol.14, pp.1651-1657, Dec.1999. [2] Wolfgang Friede, Stephane Rael, and Bernard Davat, “Mathematical Model and characterization of the Transient Behaviour of a PEM Fuel Cell,’’ IEEE Trans. on Power Electronics, Vol.19. No5, September 2004 [3] K.Sedghisigarchi, and Ali Feliachi, “Dynamic and Transient analysis of Power distribution systems with Fuel Cells- Part II: Fig. 10 Active Power with PI controller Control and stability Enhancement.© 2011 ACEEE 54DOI: 01.IJEPE.02.03.14
  • 6. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011[4] J.Padulles, G.W. Ault, and J. R. McDonald, “An integrated APPENDIX-A: Fuel Cell Operating DataS OFC plant dynamicmodel for power systemsimulation,” J. PowerSources, pp.399-408, Mar.1993.[5] M.Y. El-Sharkh, A. Rahman, M.S. Alam, A.A. Sakla, “Analysisof Active and Reactive Power Control of a Stand-Alone PEM FuelCell Power Plant,” IEEE Trans. on Power Systems, Vol.19, No. 4,November 2004[6] K. Sedghisigarchi, Ali Feliachi, “Dynamic and TransientAnalysis of power distribution systems with fuel cell,’’- Part IFuel-cell Dynamic Model IEEE Transactions on Energy Conversion,Vol, 19, No.2, June 2004.[7] E. Achenbach, “Three dimensional and time dependentsimulation of planar SOFC stack,” J.power Sources, Vol.49, 1994.[8] Y.H. Kim, and S.S. Kim, “An Electrical Modeling and FuzzyLogic Control of a Fuel Cell generation System,” IEEE Trans. OnEnergy Conversion, Vol.14, No.2, June 1999. APPENDIX-B[9] D.J Hal and R.G Colclaser, “Transient Modeling andSimulation of Tabular Solid Oxide Fuel Cell,” IEEE Trans. Energy For Active power control: a1=10, a2; =100, K2;= K3; =K4=1Conversion, Vol.14, pp.749-753, Sept.1999. For Reactive power control: a1=0.1, a2; =10, K2;= K3; =K4=0© 2011 ACEEE 55DOI: 01.IJEPE.02.03.14

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