Application of solid-oxide fuel cell in distributedpower generation

A.K. Saha, S. Chowdhury, S.P. Chowdhury and Y.H. Song

Abstract: A dynamic model of a solid-oxide fuel cell (SOFC) of 100 KW capacity has beendeveloped with a control action associated with it for application in distributed power generation.The SOFC system is chosen as a distributed energy resource (DER) because of its ability to toleraterelatively impure fuels. It also can be operated at a higher operating temperature. This dynamicmodel can be used to simulate and analyse the performance of such a system both in stand-aloneand integrated mode with other DERs to predict its dynamic behaviour and load-followingcharacteristics. With a control strategy developed to control the active power and inverter outputac voltage, it is highly efficient and capable of providing good dynamic behaviour andload-following characteristics while maintaining load parameters. The proposed model is used tosimulate a step change in power demand from the inverter-side controller to the SOFC-invertersystem. It uses two proportional-integral controllers separately with the SOFC system to controlfuel flow in accordance with power demand and to maintain the bus voltage constant at the setpoint value.

1 Introduction

Distributed power generation, at this point of time, isprogressively increasing in the power generation processesalong with the central power generation concept. Distributedgeneration (DG) has also achieved its importance as thepower demand is spiraling all over the globe day-by-day.Today, with the electricity restructuring, public environ-mental policy and expanding power demand, small distributedgenerators are in great need in order to satisfy on-site customerenergy needs [1]. From the customer’s perspective, distributedenergy resources (DER) may offer improved servicereliability, better economics and reduced dependence on thelocal utility. On the local utility’s perspective, the economicbenefits must be balanced against safety and operationalconcerns [2]. The DG schemes are located very muchnearer to the consumer site. DG uses distributed resourcesthat includes a variety of energy sources, such as microtur-bines, photovoltaics, fuel cells (FCs) and storage deviceswith capacities in the range 1 KW to 10 MW [3]. Moreover,FCs are attractive because they are modular, efficient andenvironmentally friendly [4]. FCs that generate electricityfromhydrogen by a chemical process can be used as a portablepower system [5]. DERs are finding their place in promisingway to meet the customer demand and also tailor-made.A number of literatures have been reported on theworks of

solid oxide fuel cell (SOFC). A general mechanistic modelconsidering all forms of polarisation and intricate indepen-dence among the electrode microstructure was described in[6]. Sedghisigarchi and Feliachi [4, 7] proposed a develop-ment of a nonlinear dynamic model of SOFC based on

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-rpg:20070025

Paper first received 21st April and in revised form 24th July 2007

A.K. Saha and S.P. Chowdhury are with Jadavpur University, Kolkata, India

S. Chowdhury is with Women’s Polytechnic, Kolkata, India

Y.H. Song is with Brunel Advanced Institute of Network Systems, UK

E-mail: akshay_ksaha@yahoo.com

IET Renew. Power Gener., 2007, 1, (4), pp. 193–202

electrochemical and thermal equations, and the control offrequency fluctuation and supply power were reported afterislanding distribution system to enhance the stability by con-trolling SOFC. Padulles et al. [8] proposed an approach tomodel different plant sub-subsystems including FC fromthe power system point view and described creation of ansimulation model of a SOFC-based power plant in [9].A lumped, nonlinear control oriented dynamic model forSOFC has been developed by Zhang et al. [10]. Hall andColclaser [11] reported the transient modelling of SOFCincluding electrochemical, thermal and mass flow elements.Qi et al. [12] presented dynamic model in the form ofnonlinear state space equations. Jurado et al. [13]implemented method for computing low order linearsystem model of SOFC from time domain simulation.A mathematical model at micro-scale level was developedin [14]. Wang et al. [15] discussed a numerical solutiontool for calculating planar SOFC. Wu et al. [16] presentedan SOFC model based on genetic algorithm-radial basisfunction neural network. A nonlinear modelling wasdescribed in [17] based on least square-support vectormachine. The control of SOFC for stand-alone mode withDC/DC boost converter and grid-connected mode withDC/DC converter along with a DC/AC inverter wereproposed in [5] using fuzzy logic. Jurado et al. [18] reportedthe development of SOFC system connected to a gridthrough the use of flux-vector controlled inverter. Miaoet al. presented dynamic models of SOFC and pulse-widthmodulation (PWM)-based inverter as interface in [19] andlinearisation of FC plant along with a supplemental controlscheme to improve the dynamic stability of distributionsystem in [20]. Li et al. [21] reported separate fuel inputcontrol and voltage control for an SOFC. The independentcontrols of active and reactive power were discussed in[22]. Mazumdar et al. [23] described SOFC powerconditioning system at the sub-system level. A thermodyn-amic model of a tubular SOFC stack was presented in [24]whereas system efficiency and operation under full and partload were presented in [25].

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It has been observed that the literatures were mainlyattempting the modelling of the SOFC system. Also,inverters with the SOFC system using different method-ologies and control techniques have been reported. But,no such literature was reported, which described indepen-dent active power control and inverter output ac voltagecontrol for an SOFC system. However, the DC powergenerated by the FC is to be supplied to the load throughthe interface of converter or inverter. Now, it is importantand worth noting that the inverter output ac voltage is tobe maintained at the desired constant value while supplyingrequired active power to the load. Therefore there must besome control action so that the required active power canbe supplied to the load maintaining the inverter voltagelevel at constant value. In this work, a control strategy hasbeen proposed and implemented, which can supply therequired active power to the load maintaining the ac busvoltage of the inverter of an SOFC system. This work issignificant in respect of providing means for independentcontrol of active power and the inverter ac bus voltage.Another advantageous point is that the controllers usedfor these purposes are relatively easier to install and reason-ably robust, which make the complete system very muchsimple and comprehensive.

2 FCs and SOFC

FCs are electro-chemical devices and are used to convert thechemical energy of a gaseous fuel directly into electricity[26]. In FC, a chemical reaction takes place to converthydrogen and oxygen into water, releasing electrons in theprocess. It can be said in other words that hydrogen fuelis burnt in a simple reaction to produce electric currentand water [26].The basic structure of FC can be illustrated as shown in

Fig. 1 [19]. A typical FC consists of two electrodes,anode and cathode, where the reaction takes place. Anodeand cathode are also the mediums through which thecurrent flow takes place. Most of the FCs do not use straighthydrogen as fuel and invariably are incorporated with areformer to convert the fuel being used into hydrogen.Fuels which can be reformed are methane, ammonia,methanol, ethanol, gasoline, propane, natural gas and soon [26].The following are the characteristics of FCs are [1, 19]:

† High efficiency of about 35–60%.† Very low emissions (CO2, NOX, SOX). The CO2

emission is about 50% less as compared to a conventionalpower generator that uses coal to generate same amountof power.† Very much quiet in operation.

Fig. 1 Basic structure of a fuel cell [19]

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† Quiet neat and clean ones.† Highly reliable in operation.† Limited number of moving parts.† Flexible and modular design to match versatile require-ments of the customers.† Cause less environmental pollution.

These are the features that lead to their use in powergeneration applications and many studies are beingconducted on them all over the world. The FC can serveas an emergency source of energy in the event of long-termoutage of power [5]. The FCs are used in stand-alonepurposes at homes, hospitals, industries and now findingtheir use in numerous vehicles [5]. Also, at present theyhave a wide of transportation and other stationaryapplications [26].Different types of FCs available at present are [27]:

1. AFC, Alkaline FC.2. PEFC/PEM, Polymer Electrolyte FC / Proton ExchangeMembrane.3. PAFC, Phosphoric Acid FC.4. MCFC, Molten Carbonate FC.5. SOFC, Solid Oxide FC.

Among different types of FCs classified by the type ofelectrolyte material being used in them, the SOFC isconsidered in this paper for DG application performanceanalysis under normal operating conditions because of itsfollowing features [26, 5]:

† SOFC can tolerate relatively impure fuel such as thosewhich can be obtained from gasification of coal.† It is used to operate at extremely high temperatures of theorder of 700 to 10008C.† Waste heat from the SOFC is of high grade which allowsthe use of a smaller heat exchanger.† There is a possibility of co-generation for additionalpower production.† The reformer system required for an SOFC is lesscomplex because an SOFC can use carbon monoxide asfuel along with hydrogen.† In an SOFC system, the operating temperature of thereformer and the stack are compatible.† The electrolyte is in solid state and hence does notrequire any hydration which makes water managementsystem easier.† Also, SOFC does not need costly catalysts. SOFC systemhas relatively simple design and they have significant timerequired to reach operating temperature.† Their response to load changes makes them suitable forlarge stationary power applications.† The technology is most suited to applications in the DG(stationary power).† SOFC do not contain noble metals.

SOFC systems are based on either tubular or planarelectrode configuration. In each case, the operating temp-erature permits internal reforming of hydrocarbon fuelsinto hydrogen-rich gas. The chemical reactions that takeplace inside the SOFC and directly involved in theproduction of electricity are as follows [4, 11].At anode (fuel electrode)

2H2 þ 2O2�! 2H2Oþ 4e� (1)

and

2COþ 2O2�! 2CO2 þ 4e� (2)

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At cathode (air electrode)

O2 þ 4e� ! 2O2� (3)

Overall cell reaction can be expressed as

H2 þ1

2O2 ! H2O (4)

The anode of FC is typically a porous nickel-zirconiacermet that serves as the electrocatalyst, which can beelectronically conductive. It allows fuel gas to reach theelectrolyte interface, and catalyses the fuel oxidationreaction.

3 FC power generation scheme

A power generation FC system has the following three mainparts to generate electrical power and supply to the load asshown in Fig. 2: 1. Fuel processor, 2. Power section and3. Power conditioning unit.The fuel processor converts the fuel into hydrogen and

by-product gases. The power section generates electricityusing a number of FCs. The power conditioner convertsdc power to ac power output and includes current, voltageand frequency control [27]. The power conditioning unitconsists of only a DC/DC converter or the two stages ofa DC/DC converter and a DC/AC inverter. The outputvoltage of FCs at the series of the stacks is uncontrolledDC voltage that fluctuates with load variations as well aswith the changes in the fuel input [5]. This is controlledby a DC–DC converter that converts the generated dcpower to regulated DC output and this regulated DC isconverted to ac power by the DC–AC inverter withcurrent, voltage and frequency control to meet thedemand as per requirement.

4 Dynamic model of SOFC

The following are the assumptions made while developingthe model [9, 26]:

† Nernst equation is applicable.† Gases are ideal.† FC is fed with hydrogen and oxygen.† FC temperature is stable.† Electrode channels are small enough so that the pressuredrop across them is negligible. The channels that transportgases along the electrodes have a fixed volume, but theirlengths are small, so that it is only necessary to define onesingle pressure value in their interior.† Ratio of pressures between the inside and outside of theelectrode channels is large enough to assume choked flow.Choked flow of a fluid is a fluid dynamic conditioncaused by the Venturi effect. When a fluid at a certainpressure and temperature flows through a restriction into alower pressure environment, under the conservation ofmass, the fluid velocity must increase for initially subsonicupstream conditions as it flows through the smaller cross-sectional area of the restriction. At the same time, theVenturi effect causes the pressure to decrease. Chokedflow is a limiting condition that occurs when the mass

Fig. 2 Fuel cell power generation scheme

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flow will not increase with a further decrease in thedownstream pressure environment.† Ohmic and activation losses are taken into consideration.

The model of SOFC is based on some control strategiesadded to obtain a modified one for dynamic performanceanalysis. A proportional-integral (PI) controller is used tocontrol the flow of hydrogen to respond with the changein power demand. The reasoning for PI controller is thatthey are still among most popular controllers as they arerelatively easy to install, reasonably robust and canremove steady-state error. PI controllers are universallyknown because of their flexibility combined with the rela-tively easy tuning. On the other hand, conventionalPI-derivative (PID) controllers do not work well for non-linear systems, higher order and time delayed systems andparticularly complex and vague systems that have noprecise mathematical models. The derivative action inPID controller reduces the magnitude of overshoot pro-duced by the integral component, but the controller willbe little bit slower to reach the set-point initially. As thedifferentiation of a signal amplifies the noise levels, thismode is highly sensitive to noise in the error term and cancause a noisy controlled process to become unstable. PIDcontrollers when used alone can give poor performancewhen the PID loop gains must be reduced so that thecontrol system does not overshoot, oscillate or hunt aboutthe control set-point value. This control strategy uses avoltage feedback from the FC stack.At the beginning, the choked flow equation is considered

[9, 26]

mf

pus¼ k

ffiffiffiffiffiM

p(5)

where mf is the mass flow rate, pus the upstream pressure, kthe valve constant and M the molar mass of fluid.The utilisation factor (Uf) is defined as the ratio of the

amount of hydrogen which reacts with the oxygen to theamount of hydrogen which enters the anode.

Uf ¼mf , H2, r

mf , H2, in(6)

where Uf is the utilisation factor, mf, H2, r the amount ofhydrogen which reacts with the oxygen ions and mf, H2,in the amount of hydrogen which enters the anode.The following equations can be derived considering the

molar flow of any gas through the valve to be proportionalto its partial pressure [9, 26].

qH2

pH2

¼KanffiffiffiffiffiffiffiffiffiMH2

p ¼ KH2(7)

qH2O

pH2O

¼KanffiffiffiffiffiffiffiffiffiffiffiMH2O

p ¼ KH2O(8)

where qH2is the molar flow rate of hydrogen, qH2O

the molarflow rate of water, pH2

the partial pressure of hydrogen, pH2O

the partial pressure of water, kan the anode valve constant,MH2

the molar mass of hydrogen, MH2Othe molar mass of

water, KH2the valve molar constant for hydrogen and

KH2Othe valve molar constant for water.

Now, from (6) to (8), (9) can be rewritten as

mf

pan¼ Kan (1� Uf )

ffiffiffiffiffiffiffiffiffiMH2

qþ Uf

ffiffiffiffiffiffiffiffiffiffiffiMH2O

qh i(9)

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4.1 Partial pressures

The partial pressures of the gases are calculated using theideal gas law which applies to all the gases [9, 26]. Forhydrogen

pH2Van ¼ nH2

RT (10)

where Van is the volume of anode channel, nH2the hydrogen

moles in the channel, R the ideal gas constant and T thetemperature of FC stack.Taking the first time derivative after isolating the partial

pressure

d

dtpH2

� �¼

qH2RT

Van

(11)

Dividing the hydrogen flow into three parts, theirrelationship can be expressed as

d

dtpH2

� �¼

RT qinH2� qoutH2

� qrH2

� �Van

(12)

where qinH2is the molar flow rate of hydrogen into the

channel, qoutH2the molar flow rate of hydrogen out of the

channel and qrH2the molar flow rate of hydrogen reacting

in the channel.The amount of hydrogen that reacts is estimated by

qrH2¼

NoI

2F¼ 2KrI (13)

where No is the number of cells in series in the stack, I thestack current, F the Faraday’s constant and Kr the modellingconstant.From (9), (3) and (4) in (7), the equation of partial

pressure can be written after taking the Laplace transform as

pH2¼

1=KH2

1þ tH2s

qinH2� 2KrI

� �(14)

where tH2is the system pole associated with hydrogen flow.

Similarly, the partial pressures for oxygen and water canbe expressed as

pO2¼

1=KO2

1þ tO2s

qinO2

� KrI� �

(15)

pH2O¼

1=KH2O

1þ tH2Os2KrI (16)

4.2 Stack voltage

Considering ohmic losses of the stack, activation voltageloss and mass transportation loss, the expression of totalstack voltage can be written as [9, 26]

V ¼ No Eo þRT

2FlnpH2

p0:5O2

pH2O

!" #� rI � B ln i

� m( exp (ni)) (17)

where V is the total stack voltage, rI the ohmic loss of thestack, B ln i the activation voltage loss, B the Tafel lineslope (constant), m(exp(ni)) the mass transportation loss,m, n the constants and i the current density.The output voltage of the stack is given by the Nernst

equation. The ohmic loss of the stack is because of theresistance of the electrodes and to the resistance of the

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flow of oxygen ions through the electrolyte. The activationvoltage loss is because of the sluggishness of the reactionsat the electrode surfaces. To move the electrons to theelectrodes a portion of the voltage is lost to drive thechemical reaction in the FC stack. Mass transportationlosses are because of the difference in concentration ofthe fuel as it passes through the electrode. The concen-tration becomes high when the fuel and air enter the elec-trodes. As they travel through, they get used up in thereaction. This concentration affects the partial pressure ofthe reactants and has an effect on the voltage that portionof the electrode can produce. Mass transportation losscan not be calculated analytically with enough accuracy.The expression for mass transportation loss has developedexperimentally and is accepted as a good approximation[9, 26].The total power generated by the FC is [26]

PFC ¼ NoVI (18)

5 SOFC system model

SOFC is, in fact, a complex system. In this work, theprimary emphasis is to understand and analyse the perform-ance of the system under different load conditions with thecontrol strategies for active power control and ac loadvoltage control. Owing to these, a comprehensive andreduced order model of SOFC power generating system isused. The SOFC model is based on [1, 9, 26] in respect ofexpressions for partial pressures of hydrogen, oxygen,water, Nernst’s voltage, ohmic loss, activation loss, masstransportation loss as illustrated in Section 4 and differentmodel parameters such as maximum fuel utilisation,minimum fuel utilisation, optimum fuel utilisation, fuelsystem response time, electrical response time and so on.(the parameters are listed in Table 1) and illustrated inFig. 3.Fuel utilisation is defined as the ratio between the fuel

flow that reacts and the fuel input flow [1]. Here, we have

Uf ¼qrH2

qinH2

(19)

Typically, 80–90% fuel utilisation is done [1].For a certain input hydrogen flow, the demand current of

the FC system can be restricted in the range [1]

0:8qinH2

2Kr

� I �0:9qinH2

2Kr

(20)

The optimum fuel utilisation factor is assumed to be 85%[1]. The real output current in the FC system can bemeasured, so the input fuel flow can be controlled tocontrol the fuel utilisation at the optimum value at 85%. So

qinH2

¼2KrI

0:85(21)

This dynamic model is not capable of providing the temp-erature response with change of load because thermal modelthat involves energy balance equations is not included in it.The model has been developed and simulated inMatlab–Simulink environment.The overall reaction of the FC is [1, 27]

H2 þ1

2O2 ! H2O (22)

Therefore the stoichiometric metric ratio of hydrogen andoxygen is 2:1. Oxygen excess is taken so that hydrogen can

IET Renew. Power Gener., Vol. 1, No. 4, December 2007

react with oxygen more completely [1, 27]. Theoxygen input flow is controlled by the hydrogen–oxygenratio rH–O With the change in the flow of reactants, ittakes time to change the parameters of the chemical reac-tion. Therefore the chemical response in the fuel processoris slow. This response is represented using a transfer

Table 1: SOFC model parameters

Parameters Values

absolute temperature, T 1273 K

faraday’s constant, F 96 487 000 C/kmol

universal gas constant, R 8341 J/(kmol K)

ideal standard potential, Eo 1.18 V

number of cells in series in the FC stack 384

constant, Kr ¼No/4F 0.99 � 1026 kmol/

(S A)

maximum fuel utilisation, Umax 0.9

minimum fuel utilisation, Umin 0.8

optimal fuel utilisation, Uopt 0.85

valve molar constant for hydrogen, KH28.43 � 1024 kmol/

(s atm)

valve molar constant for water, KH2O 2.81 � 1024 kmol/

(s atm)

valve molar constant for oxygen, KO22.52 � 1023 kmol/

(s atm)

response time for hydrogen, tH226.1 S

response time for water, tH2O 78.3 S

response time for oxygen, tO22.91 S

ohmic resistance, r 0.126 ohm

mass transportation constant, m 1 � 1023

mass transportation constant, n 8 � 1023

electrode area, A 0.5 m2

tafel line slope, B 0.002

fuel system response time, Tf 5 S

electrical response time, Te 0.8 S

hydrogen-oxygen ratio, rH–O 1.145

rated power, Prated 100 kW

reference power, Pref 100 kW

IET Renew. Power Gener., Vol. 1, No. 4, December 2007

function of first order with a time constant of Tf. Thedynamic electrical response is modelled using a first ordertransfer function with a time constant of Te. Electricalresponse is associated with the speed of the chemical reac-tion at which charge is restored, which is drained by load.The power output of the FC system is the product of stackcurrent and voltage. The pressure difference between theanode and channels is to be maintained below 4 KPaunder normal operating conditions and up to 8 KPa duringtransient conditions [1, 27].

5.1 System model parameters

The parameters of the system model are based on the par-ameters used in [1, 26] and given in the following asTable 1.

6 Power and voltage control strategy

Two separate PI controllers are used to control the fuel flowto the FC system to meet the power demand set by the userof the system and to maintain the inverter output ac voltageas shown in Fig. 4. From the FC system the voltage is takenas input to the control functions which generate inverterphase angle of the ac voltage and the modulation index.The above quantities are obtained using the followingrelationship.The ac voltage output of the inverter can be expressed as

Vac ¼ mVcell/d (23)

where m is the modulation index, Vcell the FC DC voltageand d the phase angle of the ac voltage mVcell.The inverter needs to control the flow of active and reac-

tive power between the source and the load. The activepower is predominantly dependent on the power angle (d)whereas the reactive power is dependent on the magnitudeof the output voltage of the inverter. The basic couplingequations of active and reactive power are of the form [3]

Pac ¼mVcellVs

Xsin d (24)

Qac ¼mV

2cell � mVcellVsCos d

X(25)

where Vs is the load voltage, d the phase angle of the acvoltage mVcell and X the external line reactance.

Fig. 3 Fuel cell system model

197

The inverter for the system has been modelled using (23),(24) and (25), which has three inputs FC DC voltage (Vcell),phase angle of the ac voltage mVcell (d) and modulationindex (m) with active power, reactive power and acvoltage as outputs.Assuming a lossless inverter

Pac ¼ Pdc ¼ VcellI (26)

where, Pdc is the DC power and I the FC current.Now, hydrogen flow can be controlled by measuring the

FC current and expressed as [27]

qH2¼

2Kr I

Uopt

(27)

where I is the FC rated current, Kr the constant (Kr = No/4F )and Uopt the optimum fuel utilisation.Now, considering (24) and (26), we obtain

mVcellVs

Xsin d ¼ VcellI (28)

Therefore the current can be written as

I ¼mVs

Xsin d (29)

Now, putting the value of current in (27), we obtain

qH2¼

2KrmVs sin d

Uopt X(30)

which can be rewritten as

sin d ¼UoptX

2KrmVs

qH2(31)

Fig. 4 Power and voltage control strategy

Fig. 5 Step change in power demand

198

Using the above relationship, the following expressionfor the phase angle of ac voltage can be written wherethis angle is very small

d ¼UoptX

2KrmVs

qH2(32)

This expression (32) provides the relationship by which thephase angle can be controlled by controlling the hydrogenflow to the FC.With the expressions of ac power and phase angle, it is

now possible to control the active power output by theuse of hydrogen flow. The active power controller is a PIcontroller, which takes Pref and Pac as inputs and controlsthe phase angle of the ac voltage as output.On the other hand, actual inverter ac voltage is given as

one input to the voltage controller to generate the modu-lation index (m) whereas the other input is the referencevoltage set by the user. The expression for controlling themodulation index can be expressed as

m ¼ Kp þKi

s

� �Vref � Vac

� �(33)

where Kp and Ki are the proportional gain and integralconstant of the voltage controller.

Fig. 6 Fuel cell system stack current

Fig. 7 Fuel cell system voltage

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Proportional gains and integral constants (Kp and Ki) forboth the controller are chosen accordingly to meet theproposed control strategy.

7 Simulation of the system

To analyse the dynamic behaviour of the system, step loadchange is applied to it at time t ¼ 50 and 1800 s with all theparameters set as in the Table 1. The step load change isfrom 50 to 100% load, that is, from 50 KW to 100 KW incase of first simulation and 50 to 100% in case of secondsimulation. The simulation at t ¼ 1800 s is performed con-sidering the start-up time, the system in order to be morerealistic as an SOFC system takes a start-up time of about20–30 min and all the parameters were observed.Simultaneously, the set point to the voltage controller isprovided to maintain the inverter output ac voltage at thedesired value. The simulation results obtained are shownin the following figures (Figs. 5–15 for t ¼ 50 s simulationand Figs. 16–19 for t ¼ 1800 s simulation), which illustratethe dynamic behaviour of the system under step load changecondition keeping the inverter ac voltage at constant level.The change in stack voltage, change in stack current,change in output power, inverter ac voltage, change inhydrogen flow, change in oxygen flow, the pressure

Fig. 8 Fuel cell system power output

Fig. 9 Fuel cell system hydrogen flow

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difference between anode and cathode were observed andare represented as obtained from the simulation:

8 Simulation results

The step changes in load, which are used to test the dynamicbehaviour of the system are shown in Figs. 5 and 16,respectively. The changes in FC system current are illus-trated in Figs. 6 and 17, respectively. From the responseof the currents, it is observed that the increase in powerdemand increases the current. The increase in the value ofcurrent in turn decreases the FC system output voltages inboth the cases, which are represented in Figs. 7 and 17,respectively. The increase in FC system current alsocauses hydrogen flow to increase accordingly, which aredisplayed in Figs. 9 and 18, respectively. As a consequence,oxygen flow also increases. The changes in oxygen flow areshown in Figs. 10 and 18, respectively. As the hydrogenflow increases to the FC system, its power output increases.The increase in power output of FC system is shown inFig. 8. Figs. 11 and 19, respectively, illustrate the pressuredifference between anode and cathode, that is, hydrogenand oxygen. The figures show that the pressure differenceincreases with increase in hydrogen and oxygen flow, butit decreases to about 0 kPa under normal operating con-dition. Those also show that the maximum pressure

Fig. 10 Fuel cell system oxygen flow

Fig. 11 Fuel cell hydrogen-oxygen pressure difference

199

difference occurred is well below the level beyond whichthe FC electrolyte may get damaged. The active poweroutputs of the inverter are found to increase with thechange power demand, which are shown in Figs. 12 and

Fig. 12 Inverter AC power output

Fig. 13 Inverter reactive power

Fig. 14 Inverter AC voltage output

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16, respectively. The inverter active powers are found totake a little time in following the load demand. This is asthe result of the time taken by the FC system to generatepower with increasing power demand. The increase ininverter reactive power supplied by the inverter with

Fig. 15 Inverter AC voltage phase angle

Fig. 16 Step input, inverter active and reactive power

Fig. 17 Inverter AC voltage, FC system voltage and current

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increase in current are illustrated in Figs. 13 and 16, respect-ively. The ac voltages at the inverter output are shown inFigs. 14 and 17, respectively. There is a little drop in theinverter output ac voltage with sudden increase in demandfor very short period of time after which goes on maintain-ing a constant value as desired. The phase angle of the acvoltage at the inverter output, which shows an increasewith increase in power demand is illustrated in Fig. 15.

9 Conclusions

The SOFC model has been implemented with the assump-tions made along with the simple inverter as powerconditioner. The response of the complete system asobserved from simulated results has been found to besatisfying the assumptions made while building the modelof FC system in respect of fuel flow, oxygen flow, partialpressures of hydrogen, oxygen, water, voltage, current andpower output including different losses. The pressure differ-ence between hydrogen and oxygen has also been found tobe within the range during steady-state and transient periodsas required preventing any damage to the FC electrolyte.With the inverter-side controllers for voltage and powercontrol, the response of the FC system to the step load

Fig. 18 FC system hydrogen flow and oxygen Flow

Fig. 19 Hydrogen and oxygen pressure difference

IET Renew. Power Gener., Vol. 1, No. 4, December 2007

change has been observed to be a good dynamic behavioursuch that both the controlled variables active power andinverter ac bus voltage are met as per the desired setvalues. The system can respond well to meet the powerdemand set by the user to active power controller and it iscapable of maintaining the ac voltage of inverter simul-taneously. Thus, the proposed model can work efficientlyas desired. Therefore the model can be used for individualperformance analysis, that is, stand-alone performanceanalysis as well as it can be used for integration withother systems to validate their dynamic characteristics. Bythis proposed model, it is possible to develop, verify andvalidate the application of such a system even if theactual FC system is not available. There are scopes ofwork for improvement in the areas like use of fuzzylogic-based or adaptive network-based fuzzy inferencesystem controllers in place of PI controllers to improvethe load following performance of the system as theyoffer high system stability and better performance. Theinverter used in this work is a simple one which can beimproved by the use of a PWM-based one or flux-vectorcontrol methodology. Also, fuzzy logic controlled invertercan improve the system performance. Thermal model invol-ving energy balance equations can be modelled to augmentwith the proposed system for obtaining the temperatureresponse during steady-state as well as transient periods.This will also allow the user of the system to analyse thethermal stress on the system. The difference between thepower demand to the system and power supplied by it isto be supplied by energy storage device like battery orultra-capacitor during the transient periods. Such energystorage device can be modelled along with necessarycontrol strategies and implemented with the proposedmodel to obtain an enhanced system model. There is alsoscope for modelling a transformer that is required for inter-connecting the system with an existing utility systemworking at some different voltage level than the FCsystem. This will facilitate the system to be simulatedunder grid-connected environment with other systems.The system can then be connected with a gas turbine orphoto voltaic system to provide a hybrid power systemenvironment. However, in this work, a control strategyhas been proposed and implemented which can supply therequired active power to the load maintaining the ac busvoltage of the inverter of an SOFC system. This work is sig-nificant in respect of providing means for independentcontrol of active power and the inverter ac bus voltage.Another advantageous point is that the controllers usedfor these purposes are relatively easier to install andreasonably robust, which make the complete system verymuch simple and comprehensive.

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