Masters G.M. Renewable and Efficient Electric Power Systems

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218 DISTRIBUTED GENERATION

So, from (4.33),

max

G

H

−237.2kJ/mol

−285.8kJ/mol

= 0.830 = 83.0%

This is the same answer that we found in Example 4.9 using entropy.

4.6.6 Electrical Output of an Ideal Cell

The Gibbs free energy G is the maximum possible amount of work or electricity

that a fuel cell can deliver. Since work and electricity can be converted back and

forth without loss, they are referred to as reversible forms of energy. For an ideal

hydrogen fuel cell, the maximum possible electrical output is therefore equal to

the magnitude of G. For a fuel cell producing liquid water, this makes the

maximum electrical output at STP equal to

=|G|=237.2kJpermolofH

(4.34)

To use (4.34) we just have to adjust the units so that the electrical output W

will

have the conventional electrical units of volts, amps, and watts. To do so, let us

introduce the following nomenclature along with appropriate physical constants:

q = charge on an electron = 1.602 × 10

−19

coulombs

N = Avogadro’s number = 6.022 ×10

molecules/mol

v = volume of 1 mole of ideal gas at STP = 22.4 liter/mol

n = rate of ﬂow of hydrogen into the cell (mol/s)

I = current (A), where 1 A = 1 coulomb/s

= ideal (reversible) voltage across the two electrodes (volts)

P = electrical power delivered (W)

For each mole of H

into an ideal fuel cell, two electrons will pass through

the electrical load (see Fig. 4.26). We can therefore write that the current ﬂowing

through the load will be

I(A) = n



mol



· 6.022 × 10



molecules H

mol



2 electrons

molecule H

· 1.602

× 10

−19



coulombs

electron



I(A) = 192, 945n (4.35)

FUEL CELLS 219

Using (4.34), the ideal power (watts) delivered to the load will be the 237.2 kJ/mol

of H

times the rate of hydrogen use:

P(W) = 237.2(kJ/mol) × n(mol/s) × 1000(J/kJ) ·

J/s

= 237,200n(4.36)

And the reversible voltage produced across the terminals of this ideal fuel cell

will be

P(W)

I(A)

237,200n

192,945n

= 1.229 V(4.37)

Notice the voltage does not depend on the input rate of hydrogen. It should also

be noted that the ideal voltage drops with increasing temperature, so that at the

more realistic operating temperature of a PEM cell of about 80

◦

C, V

is closer

to 1.18 V.

We can now easily ﬁnd the hydrogen that needs to be supplied to this ideal

fuel cell per kWh of electricity generated.

Hydrogen rate =

n(mol/s) × 2(g/mol) × 3600 s/h

237,200n(W) × 10

−3

(kW/W)

= 30.35 g H

/kWh (4.38)

4.6.7 Electrical Characteristics of Real Fuel Cells

Just as real heat engines don’t perform nearly as well as a perfect Carnot

engine, real fuel cells don’t deliver the full Gibbs free energy either. Acti-

vation losses result from the energy required by the catalysts to initiate the

reactions. The relatively slow speed of reactions at the cathode, where oxy-

gen combines with protons and electrons to form water, tends to limit fuel cell

power. Ohmic losses result from current passing through the internal resistance

posed by the electrolyte membrane, electrodes, and various interconnections in

the cell. Another loss, referred to as fuel crossover, results from fuel passing

through the electrolyte without releasing its electrons to the external circuit.

And ﬁnally, mass transport losses result when hydrogen and oxygen gases

have difﬁculty reaching the electrodes. This is especially true at the cathode

if water is allowed to build up, clogging the catalyst. For these and other rea-

sons, real fuel cells, in general, generate only about 60–70% of the theoretical

maximum.

Figure 4.29 shows the relationship between current and voltage for a typical

fuel cell (photovoltaic I –V curves bear a striking resemblance to those for a

fuel cell). Notice that the voltage at zero current, called the open-circuit volt-

age, is a little less than 1 V, which is about 25% lower than the theoretical

value of 1.229 V. Also shown is the product of voltage and current, which is

power. Since power at zero current, or at zero voltage, is zero, there must be a

point somewhere in between at which power is a maximum. As shown in the

ﬁgure, that maximum corresponds to operation of the fuel cell at between 0.4

220 DISTRIBUTED GENERATION

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0.5 1.0 1.5 2.0 2.5

Cell Voltage (V)

Power (W/cm

)

Ohmic Loss Region

Activation

Loss

Region

Mass Transport

Loss Region

Current Density (A/cm

)

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Figure 4.29 The voltage–current curve for a typical fuel cell. Also shown is the power

delivered, which is the product of voltage and current.

and 0.5 V per cell. The three regions shown on the graph point out the ranges of

currents in which activation, ohmic, and mass-transport losses are individually

most important.

Over most of the length of the fuel cell I –V graph, voltage drops linearly

as current increases. This suggests a simple equivalent circuit consisting of a

voltage source in series with some internal resistance. Fitting the I –V curve

in the ohmic region for the fuel cell shown in Fig. 4.29 yields the following

approximate relationship:

V = 0.85 − 0.25J = 0.85 −

0.25

I(4.39)

where A is cell area (cm

), I is current (amps), and J is current density (A/cm

Example 4.11 Rough Parameters of a Home-Scale Fuel Cell Stack. A1-kW

fuel cell operating on a continuous basis would provide all of the electrical needs

of a typical U.S. house. If such a fuel cell stack generates 48 V dc with cells

operating at 0.6 V each, how many cells of the type described by (4.39) would

be needed and what should be the membrane area of each cell?

FUEL CELLS 221

Solution. With 0.6-V cells all wired in series, 48/0.6 = 80 cells would be needed

to generate 48 V dc. The current that needs to ﬂow through each cell is

I =

1000 W/80 cells

0.6 V/cell

= 20.83 A

Using (4.39) to ﬁnd the area of each cell yields

0.6 = 0.85 −

0.25

× 20.83 A = 20.83 cm

4.6.8 Types of Fuel Cells

To this point in this chapter, the fuel cell reactions and explanations have been

based on the assumption that hydrogen H

is the fuel, Eq. (4.18) and (4.19)

describe the reactions, and the electrolyte passes protons from anode to cathode

through a membrane. While it is true that these are the most likely candidates for

vehicles and small, stationary power systems, there are competing technologies

that use other electrolytes and which have other distinctive characteristics that

may make them more suitable in some applications.

Proton Exchange Membrane Fuel Cells (PEMFC) Originally known as

Solid Polymer Electrolyte (SPE) fuel cells, and sometimes now called polymer

electrolyte membrane fuel cells, these are the furthest along in their development,

in part because of the early stimulus provided by the Gemini space program, and

especially now since they are the leading candidates for use in hybrid elec-

tric vehicles (HEVs). Their efﬁciencies are the highest available at around 45%

(HHV). Currently operating units range in size from 30 W to 250 kW.

PEM cells generate over 0.5 W/cm

of membrane at around 0.65 V per cell

and a current density of 1 A/cm

. To control water evaporation from the mem-

branes, these cells require active cooling to keep temperatures in the desired

operating range of 50

◦

Cto80

◦

C. With such low temperatures, waste heat cogen-

eration is restricted to simple water or space heating applications, which is ﬁne

for residential power systems. One limitation of PEM cells is their need for very

pure hydrogen as their fuel source. Hydrogen reformed from hydrocarbon fuels

such as methanol (CH

OH) or methane CH

often contains carbon monoxide

(CO), which can lead to CO poisoning of the catalyst. When CO adsorbs onto

the surface of the anode catalyst, it diminishes the availability of sites where

the hydrogen reactions need to take place. Minimizing CO poisoning, manag-

ing water and heat in the cell stack, and developing lower-cost materials and

manufacturing techniques are current challenges for PEM cells.

222 DISTRIBUTED GENERATION

Direct Methanol Fuel Cells (DMFC) These cells use the same polymer

electrolytes as PEM cells do, but they offer the signiﬁcant advantage of being

able to utilize a liquid fuel, methanol (CH

OH), instead of gaseous hydrogen.

Liquid fuels are much more convenient for portable applications such as motor

vehicles as well as small, portable power sources for everything from cell phones

and lap-top computers to replacements for diesel-engine generators.

The chemical reactions taking place at the anode and cathode are as follows:

OH + H

O → CO

+ 6H

+ 6e

−

(Anode) (4.40)

+ 2H

+ 2e

−

→ H

O (Cathode) (4.41)

for an overall reaction of

OH +

→ CO

+ 2H

O (Overall)(4.42)

Signiﬁcant technical challenges remain, including control of excessive fuel

crossover through the membrane concern for methanol toxicity, and reducing

catalyst poisoning by CO and other methanol reaction products. The advantages

of portability and simpliﬁed fuel handling, however, almost guarantee that these

will be commercially available in the very near future.

Phosphoric Acid Fuel Cells (PAFC) These fuel cells were introduced into

the marketplace in the 1990s, and there are hundreds of 200-kW units built by

the ONSI division of IFC currently in operation. Their operating temperature

is higher than that of PEMFCs (close to 200

◦

C), which makes the waste heat

more usable for absorption air conditioning as well as water and space heating

in buildings.

The electrochemical reactions taking place in a PAFC are the same ones that

occur in a PEM cell, but the electrolyte in this case is phosphoric acid rather than

a proton exchange membrane. These cells tolerate CO better than PEM cells, but

they are quite sensitive to H

S. Although there are already a number of PAFCs in

use, their future will be closely tied to whether higher production levels will be

able to reduce manufacturing costs to the point where they will be competitive

with other cogeneration technologies.

Alkaline Fuel Cells (AFC) These highly efﬁcient and reliable fuel cells were

developed for the Apollo and Space Shuttle programs. Their electrolyte is potas-

sium hydroxide (KOH), and the charge carrier is OH

−

rather than H

ions. The

electrochemical reactions are as follows:

+ 2OH

−

→ 2H

O + 2e

−

(Anode) (4.43)

+ H

O + 2e

−

→ 2OH

−

(Cathode) (4.44)

FUEL CELLS 223

The major problem with alkaline fuel cells is their intolerance for exposure to

, even at the low levels found in the atmosphere. Since air is the source of

for the cathodic reactions, it is unlikely that these will be used in terrestrial

applications.

Molten-Carbonate Fuel Cells (MCFC) These fuel cells operate at very high

temperatures, on the order of 650

◦

C, which means that the waste heat is of high

enough quality that it can be used to generate additional power in accompanying

steam or gas turbines. At this high temperature, there is the potential for the

fuel cell waste heat to be used to directly convert, or reform, a hydrocarbon

fuel, such as methane, into hydrogen by the fuel cell itself. Moreover, the usual

accompanying CO in fuel reforming does not poison the catalyst and, in fact,

becomes part of the fuel. Efﬁciencies of 50–55% are projected for internal-

reforming MCFCs. With combined-cycle operation, electrical efﬁciencies of 65%

are projected, and cogeneration efﬁciencies of over 80% are possible.

In an MCFC the conducting ion is carbonate CO

2−

rather than H

,andthe

electrolyte is molten lithium, potassium, or sodium carbonate. At the cathode,

and O

combine to form carbonate ions, which are conducted through the

electrolyte to the anode where they combine with hydrogen to form water and

carbon dioxide as shown in the following electrochemical reactions:

+ CO

2−

→ H

O + CO

+ 2e

−

(Anode) (4.45)

+ CO

+ 2e

−

→ CO

2−

(Cathode) (4.46)

Notice the overall reaction is the same as that described earlier for a “generic”

fuel cell

→ H

O (Overall)(4.47)

MCFCs operate in a very corrosive environment, and the challenges associated

with devising appropriate materials that will operate with suitably long lifetimes

are signiﬁcant.

Solid Oxide Fuel Cells (SOFC) SOFCs and MCFCs are competing for the

future large power station market. Both operate at such high temperatures (MCFC,

650

◦

C; SOFC, 750–1000

◦

C) that their waste heat can be used for combined-

cycle steam or combined cycle gas turbines, and both can take advantage of

those temperatures to do internal fuel reforming. The SOFC is physically smaller

than an MCFC for the same power, and it may ultimately have greater longevity.

The electrolyte in an SOFC is a solid ceramic material made of zirconia and

yttria, which is very unlike the liquids and solid polymers used in every other

type of fuel cell. The charge carrier that is transported across the electrolyte is

the oxide O

2−

ion, which is formed at the cathode when oxygen combines with

224 DISTRIBUTED GENERATION

electrons from the anode. At the anode, the oxide ion combines with hydrogen

to form water and electrons, as shown below:

+ O

2−

→ H

O + 2e

−

(Anode) (4.48)

+ 2e

−

→ O

2−

(Cathode) (4.49)

Efﬁciencies for SOFCs of 60% for electric power and greater than 80%

for cogeneration are projected. When combined with a gas turbine, such as

is suggested in Fig. 4.30, electrical efﬁciencies approaching 70% (LHV) may

be achievable.

A summary of the main characteristics of these various categories of fuel cells

is presented in Table 4.7.

4.6.9 Hydrogen Production

With the exception of DMFCs, fuel cells require a source of hydrogen H

for

the anodic reactions. For those that operate at higher temperatures (MCFCs and

SOFCs), methane may be reformed to yield hydrogen as part of the fuel cell

system itself; but in general, obtaining a supply of hydrogen of sufﬁcient purity

and at a reasonable cost is a major hurdle that must be dealt with before large-

scale commercialization of fuel cells will be achieved.

Hydrogen as a fuel has many desirable attributes. When burned, it yields only

small amounts of NO

created when combustion temperatures are high enough to

cause the nitrogen and oxygen in air to combine, and when used in fuel cells, the

only end product is water. Given its low density, it readily escapes from conﬁned

environments so that it is less likely to concentrate into dangerous pools the way

that gasoline fumes, for example, do. It is, however, not an energy source. It is,

Reformer

Anode

Cathode

Blower

SOFC

Compressor

Air

Combustor

Exhaust Recuperator

Compressor

Turbine

Power

Inverter

Generator

Figure 4.30 Gas turbines with pressurized solid-oxide fuel cells may be capable of

nearly 70% LHV efﬁciency.

TA BLE 4.7 Essential Characteristics of Different Types of Fuel Cells

Type of Fuel Cell

Characteristic PEMFC DMFC AFC PAFC MCFC SOFC

Electrolyte Proton

exchange

membrane

Proton

exchange

membrane

Potassium

hydroxide

(8–12N)

Phosphoric acid

(85–100%)

Molten

carbonates

(Li, K, Na)

Solid oxide

(ZrO

–Y

)

Operating

temperature

50–90

◦

C 50–90

◦

C(≤

130

◦

50–250

◦

C 180–200

◦

C 650

◦

C 750–1050

◦

Charge carrier H

−

2−

Electrocatalyst Pt Pt Pt, Ni/NiO

Pt Ni/LiNiO

Ni/Perovskites

Fuel H

(pure or

reformed)

OH H

(reformed) H

and CO

reformed and

and CO

reformed and

Poison CO > 10 ppm Adsorbed CO, CO

CO > 1% H

S > 0.5 ppm H

S > 1 ppm

intermediates H

S > 50 ppm

Applications Portable,

transportation

Portable,

transportation

Space Power

generation,

cogeneration,

transportation

Power

generation,

cogeneration

Power

generation,

cogeneration

PEMFC, proton exchange membrane fuel cell; DMFC, direct methanol fuel cell; AFC, alkaline fuel cell; PAFC, phosphoric acid fuel cell; MCFC,

molten-carbonate fuel cell; SOFC, solid-oxide fuel cell.

Source: Srinivasan et al. (1999).

225

226 DISTRIBUTED GENERATION

like electricity, a high-quality energy carrier that is not naturally available in the

environment. It must be manufactured, which means an energy investment must

be made to create the desired hydrogen fuel.

The main technologies currently in use for hydrogen production are steam

reforming of methane (SMR), partial oxidation (POX), and electrolysis of water.

More exotic methods of production in the future may include photocatalytic,

photoelectrochemical, or biological production of hydrogen using sunlight as the

energy source.

Methane Steam Reforming (MSR) About 5% of U.S. natural gas is already

converted to hydrogen for use in ammonia production, oil reﬁning, and a variety

of other chemical processes. Almost all of that is done with steam methane

reformers. After some gas cleanup, especially to remove sulfur, a mixture of

natural gas and steam is passed through a catalyst at very high temperature

(700–850

◦

C), producing a synthesis gas, or syngas, consisting of CO and H

+ H

O → CO + 3H

(4.50)

The above reaction is endothermic; that is, heat must be added, which may be

provided in part by burning some of the methane as fuel.

The hydrogen concentration in the syngas is then increased using a water-gas

shift reaction:

CO + H

O → CO

+ H

(4.51)

This reaction is exothermic, which means some of the heat released can be used

to drive (4.50). The resulting syngas in (4.51) is 70–80% H

, with most of the

remainder being CO

plus small quantities of CO, H

O, and CH

. Final pro-

cessing includes removal of CO

and conversion of remaining CO into methane

in a reverse of reaction (4.50). The overall energy efﬁciency of SMR hydrogen

production is typically 75–80%, but higher levels are achievable.

Partial Oxidation (POX) These systems are based on methane (or other hydro-

carbon fuels) being partially oxidized in the following exothermic reaction:

→ CO + 2H

(4.52)

Since (4.52) is exothermic, it produces its own heat, which makes it potentially

simpler than the MSR process since it can eliminate the MSR heat exchanger

required to transfer heat from (4.51) to (4.50). After the partial oxidation step,

a conventional shift reaction can be used to concentrate the H

in the result-

ing syngas.

Gasiﬁcation of Biomass, Coal, or Wastes As mentioned in Section 4.4,

gasiﬁcation of biomass or other solid fuels such as coal or municipal wastes by

high-temperature pyrolysis can be used to produce hydrogen. In fact, that was

FUEL CELLS 227

the primary method of hydrogen production before natural gas become so widely

available. With the likelihood of relatively inexpensive technology to remove

from the resulting syngas, there is growing interest in coal gasiﬁcation for

hydrogen production, followed by capture and sequestration of CO

in deep saline

aquifers or depleted gas ﬁelds. Some researchers hope such carbon sequestration

may provide a w ay to continue to exploit the earth’s large coal resources with

minimal carbon emissions.

Electrolysis of Water In reactions that are the reverse of conventional fuel

cells, electrical current forced through an electrolyte can be used to break apart

water molecules, releasing hydrogen and oxygen gases:

O → 2H

+ O

(4.53)

In fact, the same membranes that are used in PEM cells can be used in low-

temperature electrolyzers. Similarly, solid-oxide electrolytes can be used for high-

temperature electrolysis.

A sketch of an electrolysis cell that uses a proton exchange membrane is

shown in Fig. 4.31. De-ionized water introduced into the oxygen side of the

cell dissociates into protons, electrons, and oxygen. The oxygen is liberated, the

protons pass through the membrane, and the electrons take the external path

through the power source to reach the cathode where they reunite with protons

to form hydrogen gas. Overall efﬁciency can be as high as 85%.

Hydrogen produced by electrolysis has the advantage of being highly puriﬁed,

so the problems of catalytic CO poisoning that some fuel cells are subject to is

not a concern. When the electricity for electrolysis is generated using a renewable

energy system, such as wind, hydro, or photovoltaic power, hydrogen is produced

without emission of any greenhouse gases. And, as Fig. 4.32 suggests, when the

resulting hydrogen is subsequently converted back to electricity using fuel cells,

O −> 4H

+ O

+ 4e

−

+ 4H

−> 2H

Anode Cathode

+−

Proton exchange membrane (PEM)

−

Water

Power source

Figure 4.31 A proton exchange membrane used to electrolyze water.