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Interconnection of a Fuel Cell to the power grid Francisco M. Sarmento Instituto Superior T´ ecnico, Portugal October 21, 2010 Abstract The concepts of microgrid and islanding opera- tion imply the use of control methods in order to maintain the voltage and frequency levels within acceptable limits. This is obtained using invertes with a conventional droop-control method which has the ability to operate in parallel with the util- ity grid or islanded. As this type of systems is usu- ally fed by batteries, the use of controllable loads and controllable power sources are indispensable to maintain the energetic balance of the microgrid. In this paper, a Proton Exchange Membrane (PEM) fuel cell model and the converters needed to con- nect it to the utility grid are described and sim- ulated. A 3 phase voltage source inverter with a droop-control method is also described, in which a voltage control with an internal current control to protect against overcurrent is proposed. Fi- nally, a microgrid operation is simulated. Voltage amplitude and frequency behavior, when islanding and reconnecting the microgrid with the MV grid, are also evaluated. Keywords: Fuel-cell, hydrogen, microgrid, VSI, is- landed network. I. Introduction M ICROGRIDS are low voltages distribution sys- tems with distributed low power generation, stor- age devices and controllable loads that can work con- nected to the MV distribution grid or in island mode. The most common microgeneration systems used in microgrids are photovoltaic panels, fuel cells, variable speed wind turbines, microturbins and energy stor- age devices like batteries and flywheels. Most of these systems are connected to the ac system with inverters. Therefore, the lack of inertia systems in the microgrid makes it difficult to maintain the frequency within ac- ceptable values [13]. In order to allow the microgrid to work in island mode, two conditions are needed: 1. Power generation and loads must be balanced; 2. Microgeneration dynamics must maintain the mi- crogrid synchronism after entering island mode as well as keep voltage amplitude and frequency within acceptable values. Inverters with droop-control method emulate the behavior of a synchronous generator with inertia, al- lowing the second condition above to be achieved. These are called voltage source inverters. However, the parallel connection of voltage source inverters is sensitive to voltage and frequency variations of the utility grid, and can be damaged by overcurrent. In order to keep the power generation and loads balanced, controllable power sources are needed. In this paper, a fuel cell, being one of the most clean and efficient technologies to produce electricity, is studied as a controllable power source. From the fuel cell models developed in [7,15], an air compressor model is developed and the cathode chan- nel dynamic is enhanced, taking on account the main three gases that constitute the air: O 2 , N 2 and H 2 O. Energy consumption associated with the air compres- sor and the refrigeration fan is integrated within this model. Energy consumed by these devices is supplied by the fuel cell itself, and interferes with the output voltage dynamic behavior. New simulation models are developed, enabling the simulation of inverters and inverter’s controls that convert DC voltage generated by the fuel cell into AC, thus enabling the connection of the microgenerator to the grid. Furthermore, a power control model and a Volt- age Source Inverter are developed, the latter using the droop method, and a microgrid operation is simulated. Voltage and frequency behavior, when islanding and reconnecting the microgrid with the MV grid, are also evaluated. Considering the low value for the power supplied by the fuel cell, its inverters are designed and studied con- sidering a single phase connection (monophasic). The VSI, which is three-phasic, is dimensioned considering the same fuel cell power per phase. II. PEM Fuel Cell Model Development A PEM fuel cell stack is constituted by several cells connected in series. Each cell has two electrodes, the anode (negative electrode) and the cathode (positive electrode). The anode is continuously fed by a reagent 1
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Page 1: Interconnection of a Fuel Cell to the power grid · Interconnection of a Fuel Cell to the power grid ... the voltage produced by the chemical reaction, ... 062 T 303 2 I cel A i 0;634

Interconnection of a Fuel Cell to the power grid

Francisco M. SarmentoInstituto Superior Tecnico, Portugal

October 21, 2010

Abstract

The concepts of microgrid and islanding opera-tion imply the use of control methods in order tomaintain the voltage and frequency levels withinacceptable limits. This is obtained using inverteswith a conventional droop-control method whichhas the ability to operate in parallel with the util-ity grid or islanded. As this type of systems is usu-ally fed by batteries, the use of controllable loadsand controllable power sources are indispensable tomaintain the energetic balance of the microgrid. Inthis paper, a Proton Exchange Membrane (PEM)fuel cell model and the converters needed to con-nect it to the utility grid are described and sim-ulated. A 3 phase voltage source inverter with adroop-control method is also described, in whicha voltage control with an internal current controlto protect against overcurrent is proposed. Fi-nally, a microgrid operation is simulated. Voltageamplitude and frequency behavior, when islandingand reconnecting the microgrid with the MV grid,are also evaluated.

Keywords: Fuel-cell, hydrogen, microgrid, VSI, is-landed network.

I. Introduction

MICROGRIDS are low voltages distribution sys-tems with distributed low power generation, stor-

age devices and controllable loads that can work con-nected to the MV distribution grid or in island mode.

The most common microgeneration systems used inmicrogrids are photovoltaic panels, fuel cells, variablespeed wind turbines, microturbins and energy stor-age devices like batteries and flywheels. Most of thesesystems are connected to the ac system with inverters.Therefore, the lack of inertia systems in the microgridmakes it difficult to maintain the frequency within ac-ceptable values [13].

In order to allow the microgrid to work in islandmode, two conditions are needed:

1. Power generation and loads must be balanced;2. Microgeneration dynamics must maintain the mi-

crogrid synchronism after entering island modeas well as keep voltage amplitude and frequencywithin acceptable values.

Inverters with droop-control method emulate thebehavior of a synchronous generator with inertia, al-lowing the second condition above to be achieved.These are called voltage source inverters. However,the parallel connection of voltage source inverters issensitive to voltage and frequency variations of theutility grid, and can be damaged by overcurrent.

In order to keep the power generation and loadsbalanced, controllable power sources are needed.

In this paper, a fuel cell, being one of the mostclean and efficient technologies to produce electricity,is studied as a controllable power source.

From the fuel cell models developed in [7,15], an aircompressor model is developed and the cathode chan-nel dynamic is enhanced, taking on account the mainthree gases that constitute the air: O2, N2 and H2O.Energy consumption associated with the air compres-sor and the refrigeration fan is integrated within thismodel. Energy consumed by these devices is suppliedby the fuel cell itself, and interferes with the outputvoltage dynamic behavior.

New simulation models are developed, enabling thesimulation of inverters and inverter’s controls thatconvert DC voltage generated by the fuel cell into AC,thus enabling the connection of the microgenerator tothe grid.

Furthermore, a power control model and a Volt-age Source Inverter are developed, the latter using thedroop method, and a microgrid operation is simulated.Voltage and frequency behavior, when islanding andreconnecting the microgrid with the MV grid, are alsoevaluated.

Considering the low value for the power supplied bythe fuel cell, its inverters are designed and studied con-sidering a single phase connection (monophasic). TheVSI, which is three-phasic, is dimensioned consideringthe same fuel cell power per phase.

II. PEM Fuel Cell Model Development

A PEM fuel cell stack is constituted by several cellsconnected in series. Each cell has two electrodes, theanode (negative electrode) and the cathode (positiveelectrode). The anode is continuously fed by a reagent

1

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(hydrogen) and the cathode by an oxidant (oxygenfrom the air). The equation (1) describes the reactionthat takes place inside the fuel cell.

2H2 +O2 → 2H2O + heat + electric energy (1)

In the anode, each molecule of hydrogen (H2) isdivided in two electrons (e−) and two protons (H+)with the help of a catalyst, a noble metal like platinum.

H2 → 2H+ + 2e− (2)

While the protons are conduced through an electrolytemembrane, the electrons are forced to travel aroundan electric circuit, thus generating electric current. Inthe cathode, the electrons and protons are recombinedwith the oxygen (O2), forming water molecules (H2O)[9].

2H+ + 2e− +1

2O2 → H2O + heat (3)

The output voltage of a single cell can be defined asthe voltage produced by the chemical reaction, denom-inated by open circuit potential or thermodynamic po-tential (Enernst), minus the voltage drop related tointernal losses. These voltage drops are due to theactivation of the anode and the cathode (Vact), whichhave a dominant role in low current density; Ohmicvoltage drop (Vohm) due to the resistance of the col-lectors plates and the electrodes to the passage of elec-trons and the resistance to the passage of the protonsthrough the PEM electrolyte membrane; and voltagedrop resulting from the decrease of pressure of the re-acting gases inside the anode and cathode, when thecurrent and thus the consumption of hydrogen andoxygen increases (Vconc), called concentration loss.

This last loss is related to the physical character-istics of the system, which input limits the maximumproduced current. The maximum current allowed cor-responds to the current produced when the air flowinjected in the fuel cell reaches its maximum and allthe oxygen is consumed in the reaction [4, 12].

As the physical characteristics are considered in thismodel, the pressure drop of the reagents are taken intoaccount so the concentration voltage drop Vconc is notconsidered in the equation.

VCel = Enernst − Vact − Vohm (4)

VPC = N × VCel (5)

The open circuit potential Enernst can by calcu-lated using the modified Nernst equation:

ENernst = −∆rG0

2F+

∆rS0

2F(T − Tref )+

RT

2F×(

ln(pH2

p) +

1

2ln(

pO2

p)− ln(

pH2O,ca

psatH2O

)

)(6)

where

∆rG0 - Variation of standard Gibbs energy (G0

H2O−

G0H2− 1/2G0

O2) ∆rG

0 = −237, 180 kJ/mol.∆rS

0 - Variation of standard entropy (S0H2O− S0

H2−

1/2S0O2

) ∆rS0 = −163.135 kJ/kmolK.

F - Faraday’s constant; F = 96485, 3 C/molTref - Reference temperature; T = 298 KT - Operating cell temperature; [K]R - Universal gas constant; R = 8, 31447 Jmol−1K−1

pH2- Hydrogen partial pressure [atm].

pO2- Oxygen partial pressure [atm].

p - Reference pressure; p = 1 atm.pH2O,ca - Water vapor partial pressure in the cathode.psatH2O

- Water saturation pressure.

The water saturation pressure in standard atmosphereunit is related to the temperature in degree Celsius(C) and can be calculated from (7).

psatH2O = 10−2,1794+0,02953T−9,1837×10−5T 2+1,4454×10−7T 3

(7)The active voltage drop is calculated using an em-

pirical method from [2], which is based on electro-chemical, kinetics, and thermodynamic laws of the re-action on the electrodes.

Vact = − [ξ1 + ξ2T + ξ3T ln(CO2) + ξ4T ln(Icel)] (8)

The parametric coefficients ξ1, ξ2, ξ3 e ξ4 are calcu-lated using a multiple linear regression model, basedon experimental data from the fuel cell stack NexaTM

Power Module from BALLARD, with 1, 2kW nominalpower.ξ1 = −1, 0347ξ2 = 6, 9023× 10−3

ξ3 = 2, 9536× 10−4

ξ4 = −1, 3316× 10−4

The ohmic voltage drop can be calculated by thefollowing equation:

Vohm = (Rc +Rm)Icel (9)

where Rc corresponds to the collectors plates and theelectrodes resistance and Rm to membrane resistance.

Rc = 0, 0003 Ω (10)

Rm = ρml

A(11)

l is the membrane thickness (l = 183× 10−4 cm) [10],A is the membrane active area (A = 74 cm2), ρm is themembrane specific resistivity, which can be obtainedby (12):

ρm =181, 6

[1 + 0, 03

(IcelA

)+ 0, 062

(T303

)2 ( IcelA

)][λ− 0, 634− 3

(IcelA

)]exp

(4, 18

[T−303

T

])(12)

2

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λ is a parameter related with the humidity of the mem-brane. In this model, it is used the value of λ = 23 [10].

The “charge double layer” phenomenon is also con-sidered in this model. This phenomenon is responsiblefor the dynamic behavior of the fuel cell voltage, dueto the first order delay on the activation voltage.

dvddt

=1

CIcel −

1

τvd (13)

vd represents the dynamic activation voltage, C isthe equivalent electrical capacitance (C = 0, 54) whichis obtained from experimental results, and τ is thetime constant associated to first order delay, that isobtained from (14):

τ = CRa = CVactIcel

(14)

where Ra is the equivalent resistance and Vact is theactivation voltage drop without the delay.

Considering the dynamic behavior, the voltage pro-duced by one cell is given by:

VCel = Enernst − vd − Vohm (15)

The figure 1 synthesizes the calculations to obtainthe fuel cell stack voltage.

Figure 1: Fuel cell voltage calculation model.

The flow rates of the reactants and products arealso evaluated in this model. The air compressor thatfeeds the cathode is simulated, considering the com-pressor inertia and the control system to keep the air-flow aligned with its reference value. The behavior ofthe compressor considering these facts, has impact onthe fuel cell response.

The compressor model used in this model is de-scribed on [14] and it is based on the thermodynamicprincipals.

Jcpdωcp

dt=

1

ωcp(Pcm − Pcp) (16)

where Jcp is the inertia of the compressor (Jcp =1, 6×10−6 kg/m2); ωcp is the rotational speed; Pcm isthe power delivered to the compressor; and Pcp is thecompressor power load.

The compressor power load is calculated by (17):

Pcp = −Ws =CpTamb

ηcp

[(pcapamb

) γ−1γ

− 1

]mcp (17)

where:

γ - heat capacity ratio of the air Cp/Cv; γ = 1, 40.

Cp - air heat capacity at constant pressure; Cp =1005 J/(kgK).

ηcp - compressor adiabatic efficiency; ηcp = 0, 80.

pca - pressure inside the cathode [atm].

pamb - atmospheric pressure; pamb = 1 atm.

Tamb - ambient temperature; [K].

mcp - compressor mass air flow [kg/s].

The compressor mass air flow is determined througha compressor flow map described in [14], which isa function of the ratio between the pressure up-stream and downstream and the rotational speed,mcp(pca/patm, ωcp).

A DC permanent magnet motor is considered tocalculate the power delivered to the compressor.

Pcm = ωcpηcmkmRa

(vcm − kmωcp) (18)

km = 2 × 10−3 V/(rad/s) is the torque constant ofthe motor and is a function of motor geometry andmagnet properties, Ra = 150 mΩ is the armature cir-cuit resistance and ηcm = 0, 80 is the motor efficiency.This values are taken from [6] as typical values to thiskind of motors. vcm is the voltage applied to the mo-tor, used to control the mass air flow according to itsreference value. A PI controller is used to obtain thevcm voltage:

vcm = Kp(mrefcp − mcp) +Ki

∫(mref

cp − mcp) (19)

where Kp = 2× 104 and Ki = 32× 104.The reference mass air flow mar ref is given by a

cubic equation, obtained by a basic fitting of experi-mental values.

mar ref = 4, 4× 10−8IPC3 − 3, 45× 10−6IPC

2+

1, 05× 10−4IPC − 2, 03× 10−5 [kg/s] (20)

The fuel cell potential depends on the partial pres-sures of hydrogen, oxygen and water vapor, which de-pend on the consumption rate of the reactants. Thus,

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the mass air flow is studied in order to obtain the dy-namic behavior of the fuel cell.

Using the principles of mass conservation, the massair flow of each reactant is obtained for the cathode.

dmO2

dt= mO2,in − mO2,out − mO2,reac (21)

dmN2

dt= mN2,in − mN2,out (22)

dmH2O,ca

dt= mH2O,in − mH2O,ca,out + mH2O,prod

(23)

From the integration of the reactants mass variationinside the cathode, the partial pressure of each elementcan be derived, applying the ideal gas law:

pi =RTPC

Vca

mi

Mi(24)

where i indicates the element; Vca = 3, 3 × 10−4 m2

is the cathode channel volume; R is the gas constant;TPC is the temperature of the fuel cell and the gas el-ements; mi is mass of each element inside the cathodechannel; and Mi is the molar mass of each element.

The partial pressure of hydrogen inside the anodechannel can be considered equal to the total pres-sure, since the input mass flow is 99% pure hydrogen.Acording to [14], the valve control responsible to keepconstant the pressure inside the anode channel has avery fast response, so it can be considered allways con-stant; pH2 = 1, 35 atm

Combining the Faraday’s law with the relation be-tween electric charge and current, the reactants con-sumption and product production mass flows can becalculated.

mO2,reac = MO2

IPC

4FN (25)

mH2O,prod = MH2OIPC

2FN (26)

mH2,reac = MH2

IPC

2FN (27)

where N = 47 is the number of cells and F =96485, 3C/mol is the Faraday’s constant.

The input mass air flow from the compressor canbe divided in each element mass air flow (oxygen, ni-trogen and water), based on the relative humidity ofthe air HRamb and the oxygen molar fraction xO2 .

First, the pressure of the air upstream the compres-sor is divided in dry air partial pressure and watervapor partial pressure.

pair = pdry,air +HRair psatH2O(Tamb) (28)

where psatH2Ois the water saturation pressure.

From these partial pressures, the mass fraction ofdry air and water vapor can be calculated. With theoxygen molar fraction, the mass fraction of oxygen andnitrogen of the dry air can be also evaluated.

ydry,air =pdry,airMdry,air

pdry,airMdry,air + pH2O,airMH2O(29)

yO2,dry air =xO2MO2

xO2MO2

+ (1− xO2)MN2

(30)

where Mdry,air = 28, 850 g/mol is the molar mass ofthe dry air and is calculated by:

Mdry,air = xO2MO2

+ (1− xO2)MN2

(31)

The input mass flow of each element O2, N2 andH2O can be calculated from equations (32) (33) and(34).

mO2,in = yO2,dry airydry,airmcp (32)

mN2,in = (1− yO2,dry air)ydry,airmcp (33)

mH2O,in = (1− ydry,air)mcp (34)

The mass outlet flow, formed by water vapor andoxygen depleted air, can be considered proportional tothe upstream and downstream pressure [14].

mca,out = kca(pca − pamb) (35)

kca = 13, 4× 10−3 kgs−1atm−1 is a typical parameterof the outlet valve and is obtained from experimentalvalues.

From the integration of the equations (21), (22) and(23), the mass fraction of each element inside the cath-ode is obtained. Therefore, the mass outlet flow ofeach element can be also derived from mca,out:

mO2,out =mO2

mO2+mN2

+mH2O,camca,out (36)

mN2,out =mN2

mO2+mN2

+mH2O,camca,out (37)

mH2O,ca,out =mH2O,ca

mO2 +mN2 +mH2O,camca,out (38)

The temperature of the fuel cell stack, reactantsand products is also obtained using a thermal modeldescribed in [15], based on the total power generatedby the fuel cell stack, electrical power produced, heatdissipation from the fuel cell surface and heat dissipa-tion by the cooling system.

QFC = Ptotal − Pel − Qsurface − Qcooling (39)

Ptotal =NIFC

2F∆H (40)

Pel = VFCIFC (41)

Qsurface =TFC − Tamb

Rt(42)

Qcooling = mairflow,maxCp∆TmaxFFV (43)

4

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Figure 2: Cathode flow mass calculation model.

where

∆H - Standard enthalpy of formation of water vapor;∆H = 241, 820 J/mol

Rt - Thermal resistance of the fuel cell, obtained bycomparison of simulated data with experimentaldata; Rt = 0, 020 K/W

mvent,max - Maximum mass air flow of the coolingsystem [kg/s] [3]; mvent,max = 0, 0747 kg/s

Cp - Heat capacity of air at constant pressure; Cp =1005 J/(kgK).

∆Tmax - Maximum difference of the cooling air tem-perature before and after cooling the fuel cell;∆Tmax = 17 K

In the fuel cell studied [3], the speed of the cooling fanis given by the system as a percentage of the maximumspeed. FFV is the cube of that percentage, since it isthe relation between power and rotational speed.

FFV = (%vcool,max)3 (44)

The values of %vcool,max are a function of the fuel celltemperature. A lookup table is derived from experi-mental values in [15] to obtain this value in the model.

The temperature is obtained from the integrationof QFC .

TFC =1

Ct

∫QFC dt (45)

III. Power electronics and Control Design

The fuel cell stack voltage varies with the powerload. To connect the fuel cell to the utility grid, a DCto DC chopper converter is used to stabilize the volt-age and an inverter is used to convert to AC. Due to

the low power of the fuel cell (1, 2kW ), a single phaseinverter is designed [1]. The connection is presentedon figure 3.

A power source controller with a current source con-troller is designed to maintain the active and reactivepower according to the reference values. As the volt-age amplitude is imposed by the grid and can be con-sidered constant, the active and reactive power areproportional to the amplitude of the in-phase currentcomponent and to the quadrature current componentrespectively, being called from now on as active andreactive currents.

A PLL is used to obtain a sinusoidal signal in phasewith the voltage and another in quadrature. Thesesignals are the base to set up the reference active andreactive currents. Two proportional and integral con-trollers are used to calculate the amplitude of eachreference signal (mP and mQ), based on the measuredand references active and reactive power difference.

iact = mP sin(wt) (46)

ireac = mQ sin(wt− π/2) (47)

The reference current signal is the sum of active refer-ence current component and reactive reference currentcomponent.

iref = iact + ireac (48)

In order to protect against over-currents and short-circuits, a limiter is used to limit the current between−15 and 15 amperes.

The output of the proportional integral current con-troller PIi is the input for the Pulse-Width Modula-tion (PWM) block, responsible to generate the controlpulses for the single-phase IGBTs two-arm bridge. Forthe DC-DC chopper converter, a simple PI voltagecontroller is applied. The output of the PI controlleris compared with a tooth saw shaped signal.

Figure 4 presents the block diagram of the proposedcontrol and table 1 presents the values used for eachvariable.

Table 1: Parameters of the Power Source Inverter.

param. value param. value

Cin 350 µF kPP 0.0023

Lchop 110 µH kIP 0.217

Cbat 1 F kPQ 0.0023

kPchop 0, 916 kIQ 0.217

kIchop 141, 17 kPi 0, 97

Linv 78, 4 µH kIi 2592, 4

rL 12, 0 mΩ VLink ref 24V

C 0, 7 µF freqchop 20 kHz

n2/n1 15 freqinv 20 kHz

5

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Figure 3: Power electronics to connect the fuel cell to the utility grid.

Figure 4: Block diagram of inverter control.

IV. Voltage Source Inverter and ControlDesign

A voltage source inverter (VSI) with a droop-control is also described in order to simulate a micro-grid entering islanding mode and reconnecting againto the MV grid. It must have the ability to adjustit’s output voltage and frequency to the ac-distributedgrid when the microgrid is connected to the MV gridand it must be able to maintain the output voltageand frequency between acceptable limits when the mi-crogrid is islanded from the MV grid. [5, 8]

Figure 5: Three-phase VSI scheme.

The droop-control method consists in emulating thebehavior of large power generators, which drop theirfrequencies when the power delivered increases. Theseadjustment over the output-voltage frequency and am-plitude of the inverter allows the VSI to work in par-allel with the ac-distributed system.

The relation between voltage frequency and ampli-tude between two nodes and the active and reactivepower transited between them, depends on the type

of line used. In high voltage the lines have a high in-ductive component. On the other hand, in low voltagethe lines are mainly resistive, which changes the rela-tion referred. Equations (49) and (50) presents theserelations:

P =UVSI

R2L +X2

L

[RL (UVSI − Ugrid cos δ) +XLUgrid sin δ]

(49)

Q =UVSI

R2L +X2

L

[−RLUgrid sin δ +XL (UVSI − Ugrid cos δ)]

(50)

where RL and XL are the resistive and inductive com-ponents of the line and δ is the power angle.

The power angle δ is usually small. Thus, the sim-plifications cos δ ≈ 1 and sin δ ≈ δ can be consideredin order to simplify the control design.

Assuming that in high voltage lines the resistanceRL can be despised and in low voltage lines the in-ductance XL can be despised, equations (49) and (50)can be simplified:

• High voltage line

P ≈ UVSIUgrid

XLδ (51)

Q ≈ UVSI

XL(UVSI − Ugrid) (52)

6

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Figure 6: Voltage droop characteristics used in this model.

Figure 7: VSI control block diagram.

• Low voltage line

P ≈ UVSI

RL(UVSI − Ugrid) (53)

Q ≈ −UVSIUgrid

RLδ (54)

These equations show that in high voltage the ac-tive power is related to the power angle δ and thereactive power is related to the VSI and grid voltagedifference (UVSI − Ugrid). In low voltage the oppositeis verified.

Since in this paper a low voltage microgrid is stud-ied, the relation for low voltage lines should by consid-ered. However, a voltage control with an inner loopcurrent control as shown in figure 8 alters these re-lations when referred to the reference voltage signal.Thus, the high voltage line equations can be used.

Table 2: Parameters of the Voltage Source Inverter.

param. value param. value

U 750 V kff 3 × 10−4radW−1

L 12 mH kPv 0, 007

C 0, 7 µF kIv 226, 8

fN ≡ f0 50 Hz kPi 0, 64

VN ≡ V0 230 V kIi 2421, 33

TP ≡ TQ 0, 1sec finv 20 kHz

The voltage droop characteristics used in this modelare described by equations (55) and (56):

f = f0 − kPP (55)

V = V0 − kQQ (56)

where kP e kQ are given by:

kP =0, 01× fN

PN(57)

kQ =0, 04× VN

QN(58)

Figure 6 presents the relation between active and re-active power and voltage frequency and amplitude.

The voltage reference signal for each phase is ob-tained from the droop control as shown in figure 7.For each phase, a proportional and integral controlcompares the voltage reference signal vi ref with thereal single phase voltage vi (where index i identifieseach phase). The output of the PI controller is thereference current that is imposed to the inverter.

Figure 8: Voltage control with current inner-loop control.

7

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V. Simulation Results

MATLAB R©-SIMULINK [11] was used to simulatethe fuel cell model and the connection to the utilitygrid with the inverter described. Characteristics of thefuel cell like the polarization curve and the influenceof temperature are presented in figures 9 and 10.

Figure 9: Fuel cell polarization curve.

Figure 10: Simulated fuel cell voltage, current and temper-ature compared with experimental results when the fuelcell is subjected to load varying.

Figure 11: Fuel cell voltage and current when connectedto an AC system. Power load varying from no load to halfload and nominal load.

The behavior of the fuel cell when connected to anAC system is also presented on figure 11, for different

values of power load. Since the low pass filters fromthe DC-DC chopper converter and inverter have cutfrequencies nearby or above 50Hz, the current fromthe fuel cell has a variation of 100Hz as the instanta-neous power provided by the inverter.

A very simple microgrid scheme presented on figure12 is simulated and the results are analyzed. The reli-ability of the microgrid when entering islanding modeis tested, including the fuel cell as a controlled powersource and the behavior of the VSI to maintain thevoltage amplitude and frequency in acceptable values.The line parameters used in the simulated microgridare shown in table 3.

Figure 12: Simulated microgrid scheme.

Table 3: Line parameters.

Line resistance reactance R/X

L1 0, 089Ω 0, 017Ω 5, 1L2A 0, 036Ω 0, 003Ω 13, 1L2B 0, 048Ω 0, 004Ω 13, 1L2C 0, 060Ω 0, 005Ω 13, 1

In table 4 the schedule of events are described. Sim-ulation results are presented on figures 13, 14, 15, 16,17, 18, 19, 20, 21 and 22.

Table 4: Schedule of events in the simulation.

Time Description

0 sec Start - VSI: V0 = 230 V & f0 = 50 Hz; Util. grid:Vgrid = 400/230 V & fgrid = 50 Hz; Loads: C1,2,3 =3 × 750 W ; Fuel Cells: Pref = 0 W e Qref = 0 va.

1 sec Fuel Cells: Pref = 3 × 1000 W .2 sec Loads: C1,2,3 = 3 × 1500 W .3 sec D1 is opened - Starting islanding mode.4 sec Loads: C1,2,3 = 3 × 750 W .5 sec Fuel Cells: Pref = 750 W .6 sec D1 is closed - Reconnection to the Util. grid: Vgrid =

1 pu & fgrid = 49.9 Hz.7 sec Simulation end.

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Figure 13: Frequency

Figure 14: Utility grid power.

Figure 15: VSI Power

Figure 16: VSI Voltage.

Figure 17: VSI current.

Figure 18: Voltage.

Figure 19: Fuel Cells power

Figure 20: Load Power.

Figure 21: Fuel Cells Current.

Figure 22: Utility grid current.

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VI. Conclusions

A complete mathematical model of a PEM fuel cellincluding auxiliary systems as the air compressor andcooling fan is proposed. A DC-DC chopper converterand an inverter are dimensioned and a control is de-signed in order to connect the fuel cell as a powersource to a microgrid. To allow the microgrid to workeither connected to the MV grid or islanded, a volt-age source inverter based on a droop control methodis developed.

The model developed for the fuel cell presents sim-ilar response as the real one studied, NexaTM PowerModule from BALLARD, in static and dynamic be-haviors.

Simulation results from the microgrid show that thefuel cell can be used as a controllable power source,and working together with a VSI allows a microgridto work in island mode within acceptable values ofvoltage frequency and amplitude. Besides, the droop-control method allows the VSI to work connected tothe utility grid or in parallel with other VSI, adjustingits reference voltage signal to the voltage imposed bythe MV grid.

References

[1] Jose Fernando Alves da Silva, Sistemas de energiaem telecomunicacoes: Textos de apoio, Departa-mento de Engenharia Electrotecnica e de Com-putadores, IST, 2006/2007. 5

[2] John C. Amphlett, R. M. Baumert, T. J. Har-ris, Ronal F. Mann, Brant A. Peppley, andPierre R. Robert, Performance modeling of theballard mark iv solid polymer electrolyte fuel cell.i: Mechanistic model development, Journal of theElectrochemical Society, vol. 142, no. 1 (1995),1–5. 2

[3] BALLARD, NexaTM power module user’s man-ual, 2004. 5

[4] Jeferson M. Correa, Felix A. Farret Farret,Jonas R. Gomes, and Marcelo G. Simoes, Simula-tion of fuel-cell stacks using a computer-controlledpower rectifier with the proposes of actual high-power injecion aplications, IEEE TRANSAC-TIONS ON INDUSTRY APPLICATIONS, VOL.39, NO. 4 (July 2003), 1136–1142. 2

[5] Dr.-Ing Alfred Engler, Applicability of droops inlow voltage grids, Der Journal no. 1 (2005), 1–5.6

[6] A. E. Fitzgerald, Charles Kingsley Jr., andStephen D. Umans, Electric machinery, sixth ed.,Mcgraw Hill, 2003. 3

[7] Nuno David Geraldo Pires, Modelos de regimeestacionario para pilhas de combustıvel do tipopem, Master’s thesis, Universidade Tecnica deLisboa - Instituto Superior Tecnico, 2007. 1

[8] Josep M. Guerrero, Luis Garcıa Vicuna, JoseMatas, Miguel Castilla, and Jaume Miret, Out-put impedance design of parallel-connected UPSinverters with wirless load-sharing control, IEEETransactions on Industrial Electronics, vol 52, no4 (2005), 1126–1135. 6

[9] EG&G Technical Services, Inc., Fuel cell hand-book, seventh ed., U.S. Department of Energy, Of-fice of Fossil Energy, Morgantown, West Virginia26507-0880, November 2004. 2

[10] F. Ronald Mann, John C. Amphlett, Michael A. I.Hooper, Heidi M. Jensen, Brant A. Peplley, andPierre R. Roberg, Development and application ofa generalized steady-state electrochemical modelfor a PEM fuel cell, Journal of Power Sources,no. 86 (2000), 173–180. 2, 3

[11] MATLAB R©, The MathWorksTM

, Version R2010a,February 5, 2010. 8

[12] Matthew M. Mench, Thermodynamics of fuel cellsystems, Fuel Cell Engines, John Wiley and Sons,2008. 2

[13] Carlos Coelho Leal Moreira, Identification anddevelopment of microgrids emergency control pro-cedures, Ph.D. thesis, Faculdade de Engenharia,Universidade do Porto, Porto, Julho 2008. 1

[14] Jay T. Pukrushpan, Anna G. Stefanopoulou, andHuei Peng, Control of fuel cell power systems:principles, modeling, analysis and feedback de-sign; advances in industrial control, Springer,2004. 3, 4

[15] Nuno Rodrigues and Pedro Daniel, Caracteri-zacao do comportamento de uma pilha de com-bustıvel, quando integradas em microsistemas deenergia electrica, Master’s thesis, UniversidadeTecnica de Lisboa - Instituto Superior Tecnico,2005. 1, 4, 5

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