Int J. Hydrogen Energy. Vol. 16. No. 7, pp. 461~467, 1991. Printed in Great Britain.

036~3199/91 $3.00 + 0.00 Pergamon Press pie.

International Association for Hydrogen Energy.

THE COST OF ELECTROLYTIC HYDROGEN FROM OFF-PEAK POWER

S. STUCKI

Paul Scherrer Institute. CH-5232 Villigen PSI, Switzerland

(Received for publication 30 Januao' 1991)

A~tract--The cost of electrolytic hydrogen depends on the capacity factor of the plant and the cost of electricity. Both these parameters are correlated if off-peak power is to be used for hydrogen production. Based on assumptions regarding the correlation between the electricity price and the availability of electric power, optimizations were run using a simple cost model for the electrolysis plant. The current density at which the electrolysis plant would be run is taken as a variable for optimization as well as the annual time of availability of electric power. The results of the optimizations show for a number of hypothetical electrolyser types that the optimum operation time or electricity price do not depend much on the technology used. Production cost of electrolytic hydrogen can, however, be cut by 30% by using advanced electrolysis technology. If they can be run at very high current densities, advanced high efficiency electrolysers using more expensive cell components are economically comparable with electrolysers specifically developed for the exploitation of off-peak power.

NOMENCLATURE

A Electrode area, m 2 CA Area related costs (cells and modules), sFr Ca Specific area related costs (per unit electrode

area), Fr m -2 CE Energy costs, sFr ce Electricity costs, sFr kWh- c o Intersection of linearized electricity cost function

(cost of electricity at t = 0), sFr kWh- CH2 Production costs for hydrogen, sFr Ct Total investment costs, sFr Cop Operating costs, sFr cop Specific operating costs (per unit quantity of

hydrogen produced) sFr kAh- CR Rectifier costs, sFr CO Intersection of linearized rectifier cost function,

sFr C~ Systems costs, sFr C o Intersection of linearized systems cost function,

sFr F Faraday constant, kAh mol- I Total electric current, kA i Current density, kA m -2 N Total hydrogen production, Nm 3 R Ohmic resistance of electrochemical cells, mOhm

m 2 t Annual availability of power; annual operating

time of plant, h U ° Intersection of linearized current-voltage curve, V U Cell voltage, V V ° Molar volume of hydrogen at standard con-

ditions, Nm 3 mol-

Greek letters

ct Annuity factor Slope of linearized electricity cost function, sFr kWh- lh - I

t/~ current efficiency p Slope of linearized rectifier cost function, sFr

kW-I tr Slope of linearized systems cost function, sFr

kA

INTRODUCTION

Large scale hydrogen production by water electrolysis can only be competitive with petrochemical hydrogen production in those special situations where electricity supply is exceeding demand. This can be the case at remote electric power sources and/or at off-peak times in electric utility grids with a large proportion of base load generation. Depending on the specific supply and demand characteristics of a given power grid, cheap off-peak power is available at night, weekends and during the summer months. Most electric utility grids have a considerable amount of off-peak power available at prices which may become interesting for electrolytic hydrogen production. This is especially the case in countries with a high proportion of nuclear and hydro- electric power such as Switzerland and France.

If an electrolysis plant is operated at off-peak hours only, the price of electricity can be considerably lower than the average price paid by a normal user. The average electricity price for hydrogen production will therefore be a function of the annual time that this

461

462 S. STUCKI

power is available for the operation of the plant, i.e. the number of hours per year that the utility will provide the plant with the rated power [1]. The price and conditions for the delivery of electricity during a guaranteed annual time and at a given rated power is negotiated between the user and the utility. The price will obviously be higher the longer the time of guaranteed availability.

Given a monotonously increasing dependence of elec- tricity price on availability, reducing the yearly operating time of the plant (capacity factor) will reduce the specific energy cost for hydrogen production and at the same time increase the specific capital costs. Both capital and energy costs of electrolytic hydrogen production depend on the power density of the electrolysers which is proportional to the current density. Hence, designing an electrolysis plant running on off-peak power involves optimizing the capacity factor of the plant as well as the current density at which it should be run.

Models with varying degrees of sophistication for estimating the cost of electrolytic hydrogen have been proposed in the literature [2-4]. In the following a simple cost model of an electrolysis plant is set up which allows for a given electrolysis technology and a given depen- dence of electricity price on availability of electric power to find the optimum operating conditions. The findings of the model calculations should help to optimize the design and operation of water electrolysis plants running on off-peak power.

THE COST MODEL

The cost for producing a quantity of hydrogen per year by water electrolysis (CH2) can be separated into energy cost (CE), the annual capital cost on investment (CI multiplied by the annuity factor ct) and operating cost (Co~):

CH2 = CE + aCl + Cop- (1)

(a) Energy costs

The energy costs are given by the following expression

C ~ = U x l x t x ce, (2)

where U (V) is the cell voltage of a single electrolysis cell, I (A) is the total electrolysis current flowing through the sum of all cells, t(h yr 1) is the availability of power per year and ce is the electricity price. Electric power con- sumption for pumping and other auxiliary equipment within the plant is small in comparison to the consump- tion of the electrolysis process and therefore neglected. The plant is assumed to operate at the rated design current I during the operating time of t hours per year (no part load operation considered). The total current I depends on the amount of hydrogen N (Nm 3 y-~) that the plant should produce annually:

N x 2 F I (3)

t x V° x r/i

where F is the Faraday constant (96,500 As mol-l), V ° the molar volume of hydrogen at normal conditions

(0.0224 Nm 3 mol- ~) and r/i the current efficiency of the electrolysis process (i.e. the fraction of the current producing hydrogen according to Faraday's law).

The cost of electricity is assumed to depend linearly on the annual operating time t:

ce = c o + Et. (4)

The cell voltage of the water electrolyser is approximated by a linear current-voltage relationship:

U = U ° + R i (5)

where i is the current density (A cm-2), R the Ohmic cell resistance, and U ° the extrapolated cell voltage at zero current.

From equations (2) to (5) we obtain for the energy costs:

2 N F ( U ° + R i ) C E = (c o + et) (6)

V° ~i

The energy costs depend on both optimization variables, i and t.

(b) Inves tmen t costs

Electrolysis plants, being of modular design, show only little economy of scale. In order to take into account the different cost structure of the modular parts of an electrolysis plant (electrolysers and rectifiers) on one hand, and of the conventional process plant on the other, the investment costs are further split into different contributions:

c , = cA + Cs + c g (7)

where CA represents the area related costs, i.e. the investment costs which are directly related to the num- ber of electrolysis cells and/or modules in the plant; the costs of the rectifiers are given by CR, and Cs summarizes the costs associated with the peripheral system, including piping, gas- and water conditioning, and site specific infrastructural costs. The cost CA can be expressed as

CA = Ca X A (8)

where ca is the specific cost of the electrolysis equipment per unit area and A is the total cell area required:

,9,

CA shows no economy of scale. The costs for the rectifiers are assumed to be pro-

portional to the installed electric power and to show an economy of scale, expressed by the straight line with an intersection at C°:

Cg = C ° + p U I . (10)

THE COST OF ELECTROLYTIC HYDROGEN

Table 1. Technical and economic data for water electrolysis plants

463

Technology and reference

Cost Cost Energy Cost systems power Total consumption

modules and site supply investmets (kWh Plant size (kW -l) (kW -l) (kW -l) (kW -I) Nm -3) (Nm 3 h -x) Currencies, remarks

Lurgi [7] 531 113 83 727 5.0 20,000 Electrolyser [7] 500 135 635 5.0 20,000

Alsthom [6] 2100 5.0 4000

ABB [8] 533 133 233 900 5.0 300 Lurgi [2] 530 4.64 750 Norsk Hydro [2] 418 4.42 I 1,300 Electrolyser [2] 361 4.91 11,300 Electrolyser [2] 300 4.91 22,600 Electrolyser, adv. design [2] 98 65 57 218 4.45 23,000 Electrolyser [4] 870 4.67 2300 Electrolyser [4] 568 4.67 7900 Electrolyser [4] 505 4.67 23,000 "Present technology" [5] 1300 4.5 not specified "Advanced technology" [5] 650 3.95 not specified

DM (1987) DM (1987), *incl. rectifiers FF (1984) 2.4 MW pilot plant sFr (1989) Cans (1980) CanS (1980) CanS (1980) Cans (1980)

Cans (1980) CanS (1980) CanS (1980) Cans (1980) DM (1985) DM (1985)

The cost Cs is assumed to depend on the production rate or total current I and to show economy of scale:

Cs = COs+ aI. (11)

From equations (3), (5) and (7) to (11) we obtain for the investment costs:

c, "~ 2NF I CI= C°s + C° + T + p(U° + Ri)+e l t-f-)~q.. . (12) /] V qi I

(c) Operating costs The cost Cop is assumed to depend on the plant size

(expressed by the total current I) and the duration of operation t:

2NF Coo = Cop x I × t = cop (13)

V° q i"

The total cost of electrolytic hydrogen for a plant which is designed to produce a given quantity of hydrogen per year can then be expressed by:

0 [0 = (C e Cn2 ~(C°s+ CR)+ +Et)(U° + Ri)

~ (? +p(U°+Ri)+tr) + ]2NF + t Copj V0~/i • (14)

Using the above formula, the cost of electrolytic hydrogen can be calculated for a given set of the

constants describing the economic and technical charac- teristics of the plant as a function of the variables i (current density) and t (the annual time of operation).

INPUTS

The model requires technical and economical data on the water electrolysis technologies to be optimized as input parameters. While technical performance data of electrolysers, both of"conventional" and of"advanced" design, are readily available in the open literature and can be parametrized easily for the above model, the economic data are much more difficult to obtain and, especially for the advanced electrolyser designs which are not yet on the market for large scale applications, can only be guessed very roughly. A list of water electrolysis cost data from literature is giyen in Table 1. The specific investment cost data range from ~ 500 to ~ 1500 Swiss francs per kW for complete electrolysis plants. The data strongly depend on the technology, the plant size, and to what extent plant auxiliaries were considered in the estimates. Only little data is available on scaling laws for electrolysis plant costs. The literature data were used to set reasonable ranges of variation for the economic parameters to be fed into the model.

Since the aim of the present study has been to check the sensitivity of hydrogen production costs on the annual availability and the cost of the off-peak power, the calculations were based on technical and economic parameters which were chosen to cover the whole range of available and prospective water electrolysis technologies. This was done by combining three types of current-voltage curves (high, medium and low efficiency) with three values for the specific module costs (expensive, medium and cheap cell tech- nology) into nine hypothetical electrolysers. The system and site related cost parameters and the rectifier cost

464 S. STUCKI

12

lo 1 1

J ~ CaseA

8

6

4

0 0 2000 4000 6000 8000

Availability of Electric Power (h/y)

Fig. 1. Assumed dependence of electricity costs on annual availability of off-peak power as used for the cost calculations presented below. The electricity cost is given in Swiss currency (100 cts = 1 sFr). The data points marked by squares represent the electricity cost data given by Derive and Saumon [1] in their

analysis and converted to sFr.

p a r a m e t e r s were a s sumed to be the same for all n ine m o d e l technologies .

The ca lcu la t ions were m a d e using two different s lopes ( referred to as " C a s e A " and " C a s e B", c f Fig. 1) for the i inear ized d e p e n d e n c e o f the electrici ty cost on avail- ability. The cos t da t a f rom the l i tera ture [1] which are also inc luded in Fig. 1 indica te tha t a l inear approx i - m a t i o n o f the cos t func t ion is reasonable . The abso lu te values o f the l i tera ture da ta , however , seem unreal is t i - cally low f r o m the p resen t day perspect ive . Cases A and B are es t imates based on cu r r en t electr ici ty pr ices in Switzer land.

3.0

2.5

2.0

1.5

1.0

efficiency

J

~ efficiency

10 20 30

i (kA/m2)

Fig. 2. Assumed current/voltage characteristics of the electroly- sers considered in the present study.

Table 2 lists the p a r a m e t e r s for which op t imiza t ions wi th respec t to cu r ren t dens i ty a n d availabi l i ty were run. The c u r r e n t - v o l t a g e charac ter i s t ics tha t were used in this mode l l ing s tudy (Fig. 2) were based on d a t a f rom the l i tera ture [5] and cover the range o f technologies . The low efficiency t echno logy s t ands for a lkal ine electrolysers o f s t a n d a r d des ign ope ra t ing at 80°C wi th unca ta lysed e lec t rodes and cons ide rab le overal l o h m i c res is tances (BBC, Lurgi , Electrolyser) . The m e d i u m efficiency tech- no logy s t ands for an electrolyser wi th r educed O h m i c res is tance bu t w i t hou t catalyt ic e lec t rodes a n d ope ra t ing at slightly e levated t e m p e r a t u r e (e.g. the A l s t h o m elec- t ro lyser which was des igned for h igh cu r ren t dens i ty ope ra t i on and low inves tmen t cos t for the electrolysis d e m o n s t r a t i o n p r o g r a m m e o f the F r e n c h na t iona l util i ty

Table 2. Input parameter settings

Electrolyser type 1 (high efficiency, cheap)

U ° = 1.43 V R = 0.017 mf~m 2 ca = 2000 Fr m 2

Electrolyser type 4 (medium efficiency, cheap)

U ° = 1.55 V R = 0.05 mflm 2 c a = 2 0 0 0 F r m 2

Electrolyser type 7 (low efficiency, cheap)

U ° = 1.64 V R = 0.18 n ~ m 2 Ca = 2000 Fr m-2

Electrolyser type 2 (high efficiency, medium)

U ° = 1.43 V R = 0.017 rnIh~ 2 ca = 5000 Fr m -2

Electrolyser type 5 (medium efficiency, medium)

U ° = 1.55 V R = 0.05 mf~m 2 c a = 5 0 0 0 F r m 2

Electrolyser type 8 (low efficiency, medium)

U ° = 1.64 V R = 0.18 mf~m z ca = 5000 Fr m -2

Electrolyser type 3 (high efficiency, expensive)

U ° = 1.43 V R = 0.017 rn~m 2 c a = 10,000 F r m -2

Electrolyser type 6 (medium efficiency, expensive)

U ° = 1.55 V R = 0.05 mQm 2 c a = 10,000 Fr m -~

Electrolyser type 9 (low efficiency, expensive)

U ° = 1.64 V R = 0.18 mD, m 2 ca = 10,000 Fr m 2

c°=0.01 Fr kWh -1 = 6 x 1 0 6 F r kWh i h - i (caseA); 12x 10 6 F r kWh i h-J (caseB)

N = 15 x 106 Nm s qi = 0.98

C O = 2 × 106 Fr cr =0.12 Fr A i

c o = o p = 1 5 0 F r k W - I

=0.15 Cop : 0

THE COST OF ELECTROLYTIC HYDROGEN 465

60

E 50

~ 40 .o

"~ 30

20 0

I a Type 3 & Type 4

i Type 7

e t = _~e o14' - i @ # ~ - -

o i~ i '

13; , ; , , o ° o . . . . . °

AIL&A&&&AA

O o

o'°'Caso .,;

o e . l * e l i ' ; I l l i l l l l l n

_ i l i n nnlnn ~,Ii I i t

, , *** i*°Case A o } i O 0 0 ° O e _ . a i l l i l d l

2000 4000 6000 8000

Availability of Electric Power (h/y)

Fig. 3. Cost of electrolytic hydrogen production running at optimized current density, as a function of the availability of off-peak electricity for the two cost scenarios (Fig. 1) and for three electrolysers (types 3, 4 and 7 of Table 2).

Open symbols refer to Case A, filled symbols refer to Case B.

company EDF [6]). The high efficiency technology corre- sponds to the range of modern electrolyser designs using alkaline or membrane electrolytes. Some of the high efficiency technologies have been demonstrated and are currently being introduced on the market for small applications.

The cost parameters for the cells have been chosen between Fr 2000 and 10,000. The lower limit is given by the cell cost for simple uncatalysed electrolysers. It is then assumed that electrolysers with superior perform- ance (i.e. using catalysts and/or materials compatible with operation at higher temperatures, pressures and current densities) will cost up to a factor of five more.

The cost parameters for the peripheral systems and rectifiers were chosen such that the model yields the proportion of module to peripheral costs if applied to established technologies where all contributions to plant costs are known (e.g. Refs [7] and [8], Table 1).

RESULTS AND DISCUSSION

The costs of electrolytic hydrogen production under optimized operation conditions (current density) as a function of the time of availability of off-peak power are plotted in Fig. 2. For better clarity the results are shown for three selected electrolyser types only (type 3: high efficiency, expensive, typical high performance advanced design; type 4: medium efficiency, cheap, typical design for off-peak power applications; type 7: low efficiency, cheap, typical traditional design). The calculations were made with the parameter settings as indicated in Table 2. The slopes and the minima of the resulting curves are found to be grouped according to the assumed relation- ship between the electricity prices and the time of availability (case A and case B, cf. Fig. 1). The curves for a given electricity price scenario show only little differ- ences with respect to slope and optimum time of avail- ability (minimum production cost). Depending on the electrolyser technology, characterized by its current voltage relationship and its specific module costs, the

curves show an almost parallel shift along the cost axis. Essentially the same behaviour is found for all nine electrolyser types studied in these model calculations.

The results of the optimizations of the nine electro- lyser types and the two electricity cost functions are shown as a combined column graph in Fig. 4. The top row of columns in Fig. 3 shows the hydrogen production costs under optimized operating conditions. The hydro- gen production costs are composed of an energy (E) and a capital (C) cost contribution (the operating costs Coo were neglected). It is interesting to note that the ratio of energy cost to total cost is practically a constant for all electrolyser types and cases considered (between 54% and 57%). The high efficiency electrolysers show the least sensitivity to specific investment costs: due to the small slope of their current voltage curves (i.e. their small Ohmic resistance) high specific cost of the electrolyser can be offset by high current density operation without excessive penalties in efficiency. On the other hand, the costs of hydrogen produced by the low efficiency cells of the conventional designs of electrolysers are found to be very sensitive with respect to cell costs.

The optimized operation time of the plant (capacity factor) shows relatively little dependence on the tech- nology. It is obvious that with a steeper increase of electricity costs with annual operation time (as reflected by case B) the optimum shifts to shorter times.

The optimum current densities depend strongly on the technologies considered. The highest current densities have to be applied in electrolysers with highly efficient but expensive cells. The optimum current densities do not depend strongly on the electricity cost relationship. It must be noted at this point that the current-voltage curve of the hypothetical electrolysers (Fig. 2) were assumed to be linear over an unlimited range of current densities. In reality, however, most established electro- lyser types only have a limited range of current densities available for optimization. This is mainly due to heat removal, electrochemical corrosion or gas blockage problems. On the other hand, in laboratory experiments

466 S. STUCKI

ets/Nm3

h/y

60

50

40

30 7

0

500u

40(3O

3000

2000

Case A

9

10C0

0

30

kA/m2

20

10

Case B

::;:::~

ii!!iiii --

iiiiiii ~ -

q:i:i:

o3 o

r r LL E

"6

E

o

2000 5000 10000 2000 6000 10000 Specific Investment Cost for Electrolyzer (sFr/m2)

m High efficiency I ~ Medium efficiency ~ Low efficiency technology technology technology

Fig. 4. Summary of optimization results for the sets of parameters given in Table 2.

using membrane electrolyte cells it has been shown that for this type of advanced electrolysers very high current densities of up to 100kAm -2 can be applied and that the cell characteristics can in fact be approximated by a straight line up to these extreme current densities [9].

CONCLUSIONS

If the price of electric power is related to the annual availability, an optimum can be found with respect to time of operation or electricity price respectively. This optimum is found to be only a little sensitive on the performance and the specific cost of the electrolysis equipment used. The resulting cost of hydrogen, how- ever, depends on the electrolysis technology employed. The cost of electrolytic hydrogen varies by a factor of 2.25 from the best to the worst electrolyser types. Not all of the considered electrolyser types, however, are likely to occur in reality. The low performance electrolysers which are the ones which have been on the market for a long time and which use highly reliable technology, use

low cost materials for their cell components and there- fore only type 7 (low efficiency, low cost) is realistic. On the other end of the scale are the high performance electrolysers, where the low cost technology is rather unlikely since high performance usually means more expensive design and components. Assuming that the electrolyser types 2 to 7 represent the range of technol- ogies available now or in the near future, the spread of cost for hydrogen production reduces to a factor of about 1.4.

In order to exploit the off-peak power from nuclear power plants a French consortium consisting of Elec- tricit6 de France (EDF), Gaz de France (GDF), Alsthom and Rh6ne-Poulenc has demonstrated a low cost water electrolysis pilot plant which was specifically designed for off-peak power applications. The design is approxi- mated in the present model by electrolyser type 4 (medium efficiency, low cost). The cost of the hydrogen produced using this technology is in fact at the low end, between the technologies of types 2 and 3, i.e. medium to high cost, high efficiency electrolysers. The medium efficiency low cost electrolysers developed in France

THE COST OF ELECTROLYTIC HYDROGEN 467

seem to represent the best suited technology for hydro- gen production from off-peak power at the present time. Highly efficient but expensive advanced designs are superior for continuous operation using more expensive electricity (see intersection of the curves for electrolyser types 3 and 4 in the case B scenario, Fig. 3) and just about competitive in off-peak applications if they can be run technically at the postulated very high current densities. Laboratory results on high current density operation of membrane electrolysis cells [9] need to be confirmed on a technically relevant scale.

For the developers of electrolysis technology the find- ings of this study indicate that the highest possible flexibility with respect to applicable current densities is of prime importance in designing advanced electrolysis equipment for off-peak power applications.

R E F E R E N C E S

1. C. Derive and D. Saumon, Aspects economiques xle pro- duction d'hydrogene par electrolyse d'eau. Revug G~n~rale de l'Electricitk, 171 (1982).

2. M. Hammerli, When will electrolytic hyd/'ogen become competitive? Int. J. Hydrogen Energy 9, 25-51 (1984).

3. R. L. LeRoy and A. K. Stuart, Present and future costs of hydrogen production by unipolar water electrolysis. Proc. Syrup. Industrial Water Electrolysis, Vol. 78-4. The Electro- chemical Society, Princeton (1978).

4. G. A. Crawford and S. Benzimra, Advances in water electrolysis and their potential use in ammonia and other applications. Int. J. Hydrogen Energy 11, 691 (1986).

5. D. Behrens (ed.), Wasserstofftechnologie, Perspektiven fiir Forschung und Entwicklung, p. 125. DECHEMA, Frankfurt (1986).

6. Hydrogene Electrolytique, Pilote de 2.4 MW d'electrolyse advancee chez Rh6ne-Poulenc a Point-de-Claix. EDF Pub- lication Ref. 1.45-2-14/7.

7. Schlussbericht der Arbeitsgruppe, WASSERSTOFF- PILOTPROJEKT Untersuchungen zur Erzeugung, zum interkontinentalen Transport und zur Verwendung des sauberen Energietr/igers wasserstoff auf der Basis grosser und billiger Wasserkraftpotential. DECHEMA (Juni 1987).

8. ABB Dept. IS, Z/irich, Switzerland, personal communi- cation (1989).

9. D. Sievert, D. Winkler, G. Scherer, A. Marek and S. Stucki, Analysis of the cell voltage of BBC membrel water electro- lysis cells: implications on choice of materials and process parameters. Proc. Symp. Electrode Materials and Processes for Energy Conversion and Storage, p. 367. The Electro- chemical Society (1987).