The results of development and research of the simulator of fuel cells characteristics based on the operated pulse converter with direct current and digital alarm processor have been considered. The electrochemical model of fuel cell considering its static and dynamic characteristics is incorporated in the algorithm of the processor work. The specified simulator has on loading terminals the same characteristics of output capacity as a real system. It allows abandoning the use of both the elements and expensive accompanying systems at stages of research, design and realization of independent systems of power supply on the basis of fuel cells

Abramov, S. V.

Titov, V. G.

Electronic archive of Tomsk Polytechnic University

It is shown that use of correcting circuits allowsachieving phase shift uniformity at adjustment of powerattenuation. It is assigned that in modified Tshaped attenuator the phase shift change does not exceed 10° inattenuation range 2,5...8,2 dB in frequency band0,05...4,0 GHz; it is almost in 2,6 times lower than inattenuator without correction. In comparison with diode attenuators, the Tshaped bridge circuit does not give considerable advantages from the point of view ofphase shift minimum.In attenuator in the mode with adjusted slope of currentvoltage characteristic a minor change of phase shift– to 5° in the same range of frequencies and attenuations may be achieved. The obtained results are close tothe experimentally observed values.Power engineering93REFERENCES1. Stukach O.V. Condition of minimal dependence of phase shift onamplitude frequency characteristic in devices with variable conditions // Bulletin of the Tomsk Polytechnic University. – 2005. – № 4.– V. 308. – P. 157–160.2. Fieldeffect transistors on gallium arsenide. Principles of operationand manufacturing technique / Ed. by D.V. Di Lorentzo, D.D. Kadeluola. – Moscow: Radio and Communication, 1988. – 496 p.3. Tolstolutskiy S.I., Li A.I., Kazachkov V.V., Popov M.A., Tolstolutskaya A.V., Komor V.P. Solidstate fourbit microwave attenuator ongallium arsenide for the range 0–4 GHz / Microwave engineeringand telecommunication technologies (CriMiCo’2007): Writings ofthe 17th International conference in the Crimea. – September10–14, 2007, Sevastopol. – Sevastopol, 2007. – P. 85–86.Received on 07.12.2006Introduction In order to provide competitiveness with independent feed systems on the basis of well known sources ofelectric energy, the systems on the basis of fuel cells(FC) should operate with comparable efficiency [1].Such systems behavior in transients is one of the key issues at the stage of their design [2]. Simulator of FCcharacteristics is the device having at loading terminalsthe same characteristics of output power as the real system. In order to develop the simulator of FC characteristics the mathematical model of electrochemical generator directed to the analysis of the system bytechniques of automatic control theory and electricalengineering should be designed.Currently, the investigations in this field, introducedin domestic and foreign sources, may be conditionallydivided into two directions: the first one (given in themajority of works) is the investigation in the field ofelectrochemistry the aim of which is the development ofthe FC components (electrolytes, gasdiffusion electrodes etc.) and selection of optimal work areas on currentvoltage, parametric and other curves. Such models arebased on laws of electrochemistry of porous structures,thermodynamics and mechanics of gaseous and liquidmedia [3, 4]. They are not suitable for analysis of transients in FC system by the techniques of automatic control theory and electrical engineering.Another direction is the investigation in the field ofelectronics and microprocessor engineering allowingmodeling FC characteristics [5]. However, insufficientcoverage of these questions in scientific literature resulted in necessity of developing mathematical model ofclosedloop control of FC, designing physical modelcomputer control simulator of FC characteristics for experimental investigations of its characteristics; as well asdeveloping the control system allowing providing thespecified characteristics of the transients.The authors proposed a new device on the basis ofcomputer controlled pulse converter of direct currenton the basis of FC electrochemical model (software)included in it. The simulator on the basis of the mentioned converter has on its loading terminals the samedependence of output continuous stress on load currentas the real FC [6, 7].UDC 621.3SIMULATOR OF FUEL CELLS CHARACTERISTICS ON THE BASIS OF THE SEMICONDUCTOR CONVERTERV.G. Titov, S.V. AbramovState technical university, Nizhny NovgorodEmail: s.abramov@mail.ruThe results of development and research of the simulator of fuel cells characteristics based on the operated pulse converter with directcurrent and digital alarm processor have been considered. The electrochemical model of fuel cell considering its static and dynamic characteristics is incorporated in the algorithm of the processor work. The specified simulator has on loading terminals the same characteristics of output capacity as a real system. It allows abandoning the use of both the elements and expensive accompanying systems atstages of research, design and realization of independent systems of power supply on the basis of fuel cells.The principle of modeling FC characteristics by thesimulator consists in controlling voltage on the load according to the electrochemical model BFC included inDTS. The required value of voltage is formed by thechange of pulse ratio controlling pulse converter of direct current. Necessary operating conditions are computed by bundled software on the basis of data of currentand voltage sensors. The converter acts as the controlledsource of continuous voltage source providing the loadwith the same power as the real FC.The model describing static characteristics of fuel cellwith protonexchange membrane The fuel cell model used in the work is based on several basic equations given in the form of mathematicalblocks in Simulink package, and it is of the followingform:Uтэ=EНернст–ΔEом–Δакт–ΔEкон,where EНернст=1,23–8,5·10–4(T–298,15)++4,31·10–5·T(lnPH2+1/2·lnPO2),ΔEом= iТЭ·RM,ΔЕакт= –[ξ1+ξ2·T+ξ3·T·lnPO2ξ4·T·ln(iТЭ)],ΔEкон= –B·ln(1–J/Jmax),where EНернст is the opencircuit voltage of FC; ΔEом isthe ohmic drop on FC internal voltage; ΔЕакт is the voltage drop owing to anode and cathode activation; ΔEконis the voltage drop owing to decrease of reactive gas concentration; iТЭ is the FC load current, A; RM is the membrane equivalent resistance, Ohm; J is the current density of FC load, A/cm2; n is the number of FCs used ina battery; Т is the membrane temperature at work, К; Аis the membrane active area, cm2; l is the membranethickness; PO2 and PH2 are the partial pressures of oxygenand hydrogen, atm; RC is the equivalent contact resistance of the membrane, Ohm; В, ξ,ψ are the parametric coefficients.The expression for the equivalent resistance of themembrane:where ρM is the membrane specific resistance calculatedby the formula:A load characteristic (LC) of fuel cell in Fig. 1, a, represents a theoretical dependence of fuel cell outputstress on load current. In this case LC of a FC batterywas studied for comparison with the results of the experiment on training sample of Avista Labs SR12. The given LC describes only static behavior of FC battery aseach Xdirection point of the curve is obtained at achieving stable value.The experimental LC of FC battery is introduced inFig. 1, b; its parameters were taken as a principle at designing mathematical model for static mode of operation. Lowfrequency pulses on the obtained diagram aredescribed by low demands made to the quality of theoutput voltage used in the experiment of the trainingsample. Calculating the correlation coefficients of theoretical and practical LC the coefficients kU=0,91 andkР=0,89 for the curves of the output voltage and outputpower of FC battery, respectively, are obtained. This gives a reason to confirm that the stated electrochemicalmodel of FC reproduces correctly the behavior of thesystem in static modes of operation considering the accepted assumptions.Fig. 1. Theoretical (a) and experimental (b) load characteristicsof FCDynamic behavior of FC with protonexchangemembrane is based on a phenomenon of accumulationof charge double layer in the place of electrode andmembrane contact. If load current of FC changes thenthe charge needs some time for redistribution [7]. Oneof the simplest methods for modeling this situation consists in use of the equivalent circuit (astatic link of thefirst order) where the charge double layer would be represent in the form of condenser and resistors wouldcorrespond to internal resistances of FC. The circuit ismodeled in Simulink package and the results are introduced in Fig. 2, a.The assumptions accepted at design of this modelare the following: FC temperature and reactive gas pressure are constant during the whole transient. Load cur2,52181,6 1 0,03 0,062303.3030,634 3 exp 4,18FC FCMFCi iTA Ai TA Tρψ⎡ ⎤⎡ ⎤ ⎡ ⎤⎡ ⎤⋅ + ⋅ + ⋅⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦⎢ ⎥⎣ ⎦= ⎡ ⎤ ⎡ − ⎤⎡ ⎤ ⎡ ⎤− − ⋅ ⋅⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦⎣ ⎦,MMlRAρ=Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 494rent in the experiment changes in step from 0 to 25 Аand back. Sharp voltage fall is conditioned by close values of time constants in transfer function of the equivalent circuit. This fall can not be balanced by automaticcontrol system. This result shows that supplementarypower source is required for balancing voltage fall of FCat abrupt jumps of load. Long duration of the transientis conditioned by the value of equivalent circuit capacity making farad units. This capacity is proportional tothe area of a complex porous structure of the membranewhich exceeds in some orders its geometric area.Fig. 2. System response to load jump: a) modeled; b, c) experimentalThe response family of open loop to load currentjump at different initial and final current values obtained experimentally is given in Fig. 2, b, c. Calculatingthe correlation coefficient for the modeled and experimental results the coefficients kнаброс=0,88 andkсброс=0,85 for the curves corresponding to loadon andloadoff of FC battery, respectively were obtained. It gives the reason to confirm that the represented model fortransient condition of FC transfers correctly its behaviorin dynamic operation modes considering the acceptedassumptions.The simplest method of implementation of simulator strength part is the use of voltagedropping regulator,in the authors’ opinion. Its advantages are a simplemathematical model, linear dependence of output voltage on control PDMpulse ratio, possibility of applyingthis schematic solution for load feed with power to several kW.Block diagram of the proposed configuration of simulator with regulator is introduced in Fig. 3, a. BlockFCPEM (fuel cell with protonexchange membrane)represents the electrochemical model of FC in this Figure.Fig. 3. Block diagram of the proposed simulator configurationof FC characteristics (a) and time diagrams of closed system behavior (b)The proposed simulator configuration was introduced in the form of blocks of Simulink package and modeled for obtaining transient characteristics of the system at load current jump. The diagrams show the transient time less than 1 ms. After finishing the transients inthe system the perturbation is completely suppressedand levels of load current and voltage correspond to thespecified ones (рис. 3, b).For further investigation of simulator of FC characteristics the time constants of the airdelivery system toFC should be defined. They may be determined analytically or obtained experimentally. One of the experiPower engineering95ments described in scientific literature is examined as anexample [8]. In order to determine the KKP of airdelivery system in the experiment the compressor rotationalvelocity and pressure at compressor output as a functionof engine velocity signal was measured. Processing theresults of the experiment the program computes thecorrelation coefficient of a transfer function with theexperimental data.On the basis of the used experimental data the whole system was introduced in the form of links of the automatic control system. Synthesis of this model withmodels obtained before considering static and dynamicFC characteristics allowed making complete mathematical model of the closedloop control of electrochemical generator presented similarly in the form of links ofautomatic control system (Fig. 4, a). The block combining the direct current motor (DCM) and converter isgiven in Fig. 4, b.System input action is a signal of voltage assignmentand the output action is the measured voltage of fuel cellterminals. In order to determine the transfer characteristics of synthesized system it is introduced in the form ofblocks of Simulink package.Fig. 4. Block diagram of closed control system of electrochemical generator (a, b) and system response to load currentjump (c)The results of computer simulation are given inFig. 4, c. The closed system response to load currentjump is modeled in the experiment as an example. Theoutput voltage of the system is specified on the level of25 V.The first of three system responses corresponds tothe most unfavorable case when the load current jumpsfrom zero to peak value. In this case the transient duration amounts to 1,5 s and peak stress achieves 32 V exceeding stabilizing voltage by 28 %. The second and thethird system responses correspond to the jumps of loadcurrent from 5 to 20 А (excess of stabilizing level by16 %) and from 10 to 15 А (excess of stabilizing level by8 %) respectively. The transient time in all three cases isnearly the same. The output voltage stabilizes on the setlevel at the end of transient time.The abovementioned research is the base for physical implementation of FC simulator control on the basis of real time equipment dSPACE. After calculation ofparameters of simulator and compensator strength partthe computer simulation of the closed control systembehavior is carried out, the model of strength part isexchanged by real equipment. The regulator is given inthe form of Simulink blocks.The control algorithm is loaded in interface cardcontroller. The data from current and voltage sensorsenter the computer at virtual oscillograph through theanalogdigital converter. The device is controlledthrough the graphical user interface. It contains two oscillographs for measuring load current and voltage, twooscillographs for control signal and error voltage as wellas adjustments of proper regulator constituents and option dialog box.The control card of electronic power keys, cards ofamplifier prestages and filtering of measured signals ofthe experimental device are shown in Fig. 5. The outputLC filter is shown here as well.Fig. 5. Experimental device: card of control/measure and LF filterBulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 496In the series of experiments (Fig. 6) the load jumps.The diagrams correspond to minor change of load current (from 1,5 to 2,5 А and back) near the working point selected at regulator calculation.Comparing the obtained characteristics with the results of computer simulation one can note that the current overshoot is absent here as well and voltageovershoot does not exceed 10 %. Thus, the results of theexperiment coordinate with the data obtained at computer simulation. The transient time at the experimentamounted to less than 2 ms that exceeds slightly the predicted value; usually by the reason of analogdigital andreverse conversions introducing delay into a control circuit.Conclusion 1. The mathematical models considering static and dynamic properties of fuel cells applicable to wide range ofthese devices and intended for use in closedloop controlby simulator of fuel cell characteristics were developed.2. The closeloop control of electrochemical generatorwas designed. The computer analysis of transientson the device output terminal was carried out.3. A new semiconductor converter installation – simulator of fuel cell characteristics was developed andimplemented in the form of a model.4. A circuit solution of fuel cell power converter withpower battery, the flow of which is controlled according to the data of output current and voltage sensors was proposed.Power engineering97Fig. 6. Time diagrams of simulator of FC characteristics at load jumpREFERENCES1. Abramov S.V. Power converter for powersupply system on the basisof cells // Topical problems of electric power engineering: Materialsof the XXIIIth scientific and technical conference. – Nizhny Novgorod, December, 15, 2004. – NGTU, 2004. – P. 30–31.2. Abramov S.V., Vagin G.Ya., Titov V.G. Features of designing the independent system of power supply on the basis of fuel cell battery //State and perspectives of development of electrotechnics: Materialsof Матер. Междунар. scientific and technical conference (XII Benardosovskie Chteniya), Ivanovo, June, 1–3, 2005. – Ivanovo, 2005.– 179 p.3. Kuleshov N.V., Grigoriev S.A. Simulation of the processes in membraneelectrode block of fuel cell with solid polymer electrolyte //Bulletin of MEI. – 2003. – № 5. – P. 120–124.4. Larminie J., Dicks A. Fuel cell systems explained. – John Wiley &Sons, 2000. – 560 p.5. Zhu H., Kee R. A general mathematical model for analyzing the performance of fuel cell membraneelectrode assemblies // JournalPower Sources. – 2003. – № 4. – P. 124–136.6. Certificate for PM 39973 RF. Simulator of characteristics of fuel cellbattery / S.V. Abramov Stated 10.04.2004; Published 10.06.2004,Bulletin № 23. – 4p.: ill.7. Tsypkin М., Baranov I., Lizunov A., Samoilov D., Fateev V. Research and performance improvment of PEMFC electrode // Proc.of 14th Intern. Congress of Chemical and Process Engineering. –Praha, Czech Republic, 27–31 August 2000. – Praha, 2000. – P. 61.8. Bird J.P. Model of the Air System Transients in a Fuel Cell Vehicle //Proc. of Virginia Polytechnic Institute and State University. – Virginia, 2003. – V. 2. – P. 102–114.Received on 16.05.2007

Simulator of fuel cells characteristics on the basis of the semiconductor converter

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