A study of water electrolysis with photovoltaic solar energy conversion

Int. J. Hydrogen Energy, Vol. 7, No. 4, pp. 287-310. 1982. Printed in Great Britain.

0360-3199/82/040287-24 $03.00/0 Pergamon Press Ltd. International Association for Hydrogen Energy.

A STUDY OF W A T E R ELECTROLYSIS WITH PHOTOVOLTAIC SOLAR ENERGY CONVERSION C . CARPETIS

DFVLR-Institute for Technical Physics, D-7000 Stuttgart 80, Federal Republic of Germany

(Received for publication 18 June 1981) Abstract--The performance of the hydrogen production system consisting of the photovoltaic array and the water electrolysis unit is studied. The results of the calculation are compared with available experimental data and the performance of a hydrogen production plant by means of photovoltaic solar energy conversion is determined for two typical locations. A method for the estimation of the power matching conditions of the system solar array electrolysis unit is formulated to allow conclusions of general validity.

NOMENCLATURE A Ai, Aic c cc ec Ee Es Fc Fs H Hm Hm~x I la Ic IE le le~ IL It; Im Io Io~ lp i K KL Kt~ Ko Ko~ Kp¢ K~ k L Lc n P Pe Ps q Rs

Completion factor Coefficients for polynomial approximation The sum of theoretical electrolyzer voltage plus cathode and anode overvoltages The same as c for one single electrolysis cell Theoretical electrolysis cell voltage Electrical energy input to the electrolysis unit System energy input Electrolysis cell surface Solar cell surface Specific hydrogen production rate Measured hydrogen production rate Daily maximum of hydrogen production rate Current Solar array current Solar cell current Current at the selected "points of comparison", E (Fig. 1) Electrolysis unit current Electrolysis cell current Photocurrent (array equation) Photocurrent in the case of a single solar cell Solar array current at the point of maximum power Reverse saturation current (array equation) Reverse saturation current in the case of a single solar cell Current at the system operating point Array inclination Iteration number variable Photocurrent constant (array equation) Photocurrent constant for single solar cell Saturation current constant (array equation) Saturation constant for single solar cell Solar cell shunt resistance constant Solar cell series resistance constant Boltzman constant Array equation factor Solar cell equation factor Solar cell junction perfection factor Specific hydrogen system production Parallel strings of series connected electrolysis cells Parallel strings of series connected solar cells Electronic charge Total series resistance of the solar array 287

288 R~ Rsh

Rsh,c r re so ss S Sm T T1 /'2 T3 x ~, )~ Va Vc VE Vc V~ Vm Vp Wc fl r/a ~L r/i r/s Tlsi rh.m q0 to

C. CARPETIS Solar cell series resistance Shunt resistance (solar array) Solar cell shunt resistance Equivalent resistance (electrolyzer equation) Electrolysis cell resistance Number of series connected electrolytic cells (per string) Number of series connected solar cells (per string) Solar radiation Measured irradiation Temperature (K) Transmission factor Scattering factor Obscurement factor Variable x = Vm/Imin equations (15)-(17) Factors Solar array voltage Solar cell voltage Voltage at the selected "points of comparison", E (Fig. 1) Electrolysis unit voltage Electrolysis cell voltage Solar array voltage at the point of maximum power Voltage at the system operating point Total resistance of electrolysis cell for the unit of area Solar equation factor (fl = 1 + RJR,h) Solar array efficiency Electrolysis unit efficiency Ideal solar array efficiency System efficiency Ideal array efficiency related to junction area radiation Measured system efficiency Latitude Relaxation factor INTRODUCTION

HYDROGEN as an energy vector offers a great number of advantages. It can be used as a fuel in the residential and transportation sector; for industrial applications, etc. Its usage is, practically, non-polluting, since the combustion product is mainly water. Primary energy for hydrogen production can be obtained from nuclear or fossil sources, or by use of solar techniques. Hydrogen production by fossil energy sources may shift the pollution problem from the user to the production sector. A really "clean energy system" is established by solar hydrogen production. Photovoltaic water electrolysis (i.e. a system consisting of a photovoltaic array, electrolysis cells, and hydrogen storage unit) is very promising (both for centralized, and decentralized applications). Hydrogen storage methods to cover the diurnal and even the annual variation in production rate and demand are technically and economically feasible. As mentioned before, hydrogen can be used as an alternative fuel or it can be reconverted to electricity by means of fuel cells, as well as by using it for steam generation. Of course, the economics of the system have to be specified. It is not only obvious that the photovoltaic system costs must be further reduced, but also that the electrolysis plant must be technically and economically feasible for the purpose. Much work has been done in both photovoltaic and water electrolysis research and development, but few results have been published for the photovoltaic-electrolysis system. In any case, experimental work has already demonstrated system operation [1, 2], and recent experimental activity has been reported [3]. It is the purpose of this work to provide an analysis of a system, composed of a photovoltaic converter and electrolysis device, and to compare the results with available experimental data. Further, an outline of the expected system characteristics for some typical application cases is included.

Objective of the investigation and method of calculation The calculation should allow the determination of the hydrogen production rate of a specified

A STUDY OF WATER ELECTROLYSIS

289

system, for given insolation, and thus determine the system characteristics for a given time period (day, year) and insolation conditions (location, climatic conditions etc.) Although this calculation is not intended to be a substitute for experimental investigations (which are urgently needed for the examination of long period behaviour and dynamic system response), it could be valuable in many cases. Calculation of basic system characteristics is valuable in planning experiments, scaling results to other dimensions, determining hydrogen storage requirements, predicting the need for system components (like power conditioning etc.) and, of course, in outlining the costs. In the immediate future the cost of photovoltaic arrays for large scale experimental systems may be prohibitive for many investigators. Thus, reliable analytical methods would be useful in predicting system performance for a variety of locations and climatic conditions, and thereby provide a valuable tool for experimenters and planners. Basically, the computation can be performed when the voltage-current characteristics for both the solar panel and electrolysis unit are known. For photovoltaic panels the characteristic equation is an implicit voltage-current relation of the form la = S(Va, la) with the solar radiation, S, as a parameter. This relation can be determined with high accuracy--knowing five constants. They are usually determined from the data delivered with the solar panel specification or by means of experimental data (see next section). The voltage-current characteristic equation of an electrolysis unit is also a non-linear relation of the type Ve = E(Ie). The part of the characteristic, which is of interest for normal operation, can be closely approximated by the linear equation Ve = c + rle. For computation purposes, however, it is preferable to use the polynomial approximation, (1)

Ve = E(le) : A,, + ~ , A , , I ~ . m

When the solar array is connected to the electrolysis unit to build a hydrogen producing unit, the operation point (Vp, Ip) will be the intersection of the above mentioned characteristics, where Vp = Ve = Va and Ip = Ie = Ia. Thus, the point of operation, can be determined as the solution of the simultaneous equations I=S(V,I)

and

V=E(/).

(2)

This is easily found by iterative procedures. In this way, the hydrogen production can be found for given solar radiation. The computation program can be written to account for the diurnal variation of solar radiation for a given day, and to perform the calculation for all days of a year for a given location. Climatic conditions are taken into account by introducing the scattering, obscurance, etc., factors from known climatic statistics, or by using recorded data, if available. The calculation of system working conditions throughout a year not only delivers the annual hydrogen production (thus enabling the calculation of the unit costs of stored and delivered hydrogen), but also enables the study of the matching conditions of the solar array and electrolyzer characteristics: it aids in deciding which measures are necessary to achieve best annual efficiency, by managing the points of operation to possibly approximate the maximum power working conditions of the solar array. Photovoltaic converter characteristics

In this study the general form of the solar array characteristic equation (voltage-current relation) has been used I~ = S(Va, I~) = [IL

-

lo(exp(L(V~ + l~Rs))

-

1)

-

VJRsh]/fl.

(3)

In this equation fl = 1 + Rs/Rsh,

(4)

L = q/AkT,

(5)

and where q is the electronic charge, k the Boltzman's constant and T the temperature.

290

C. CARPETIS

The implicit relation between Ia and Va is determined when the array parameters, photocurrent It, reverse saturation current Io, the series and shunt resistances, R~ and R~h, and finally the completion factor A have known values. The photocurrent IL is proportional to the solar radiation and its dependence on the temperature T can usually be neglected. However, the saturation current is strongly dependent on the temperature. For the photocurrent the following relation can be used IL = K L S

(6)

where S is the solar radiation, W c m -2. For the saturation current the temperature dependence can be described by the equation Io = K o T 3 exp(-1.3 104/T).

(7)

Substitution of r, L, IL, and Io in equation (3), according to equations (4)-(7), shows that the implicit relation Ia = S(Va, Ia) is determined if the array constants KL, Ko, A, Rs, Rsu and the array temperature T are known. The determination of the five constants of the solar array can be accomplished by using five selected points from the experimentally determined voltage-current characteristic. Accurate results can be obtained by a variation of an earlier proposal [4]. One set of five selected points of the characteristic delivers five sets of (Va, L) values which must satisfy the relation I~ = S(Va, Ia, Ko, KL, A, Rs, Rsh, T) (8) according to equations (3)-(7). Five equations with five unknowns (the constants) Ko, KL, A, Rs, R~h are thus obtained, and their solutions are derived by using iteration procedures. The completion factor A used in the solar array characteristic equation is related to the number s~ of series connected cells by the relation A = n s , T h e "junction perfection factor" n is compensating for non-ideal cell junction behaviour, thus it must be that 1 ~< n < 2. This condition can be useful for deciding whether the resulting equation constants can be accepted. If the resulting value, n = A/ss, does not fulfil the above condition, some inputs (V,, I~) must be discarded. Usually, after some trials, the improper inputs can be localized. Most published experimental results on photovoltaic--electrolysis systems do not include temperature monitoring. In these cases the temperature T can be handled as an unknown quantity which requires iteration of six equations. Of course, in this case, one has to assume that at least for each characteristic (for constant radiation level S) the temperature has been constant. This assumption can be controlled by the fact that the results must satisfy equation (8) for all points of this characteristic. Also the condition 1 ~< n < 2 can be used (as mentioned before) to control the results. Another method for determination of the constants takes into account all (or a great number of) available test points, and is accomplished by applying the least square method [5, 6]. Even so, improper values for some (Va, Ia) points, result in values of the constants corresponding to unacceptable physical values: for example, high values of the reverse saturation current (Io), or n > 2. Therefore, a control to localize points introducing the error is necessary. In general, however, the information obtained from published experiments and manufacturer specifications for commercial solar arrays is adequate to determine the constants in equation (8) with sufficient accuracy for reliable use of the analytical methods described in the following sections. It is important to mention that results found for a certain solar array can be used to find the parameters, or the constants, of a single photovoltaic cell. Of course, the cell constants can also be used to find the constants of any complex array consisting of series and parallel connections of the same cells. The calculation is based on the simple relations summarized in Table 1. It is obvious that these relations account for the series-parallel connection scheme. Actually, they are not dependent on the details of the connection (e.g. on the size of the selected panels or subunits). The importance of the total number of the series-connected cells, s~, and of the parallel strings, P~, is that they relate the array voltage and current (V~, Ia) to those of the individual cell (V¢, I¢) according to the equations V~ = s~V~; L = Pd~.

A STUDY OF WATER ELECTROLYSIS

291

TABLE 1. Characteristic equation parameters of solar cells and arrays Solar cell equation:

Factor L~ = q / A k T = q / n k T (completion factor A = n; 1 ~< n < 2)

file = IL~ -- loc {exp[L~(Vc + I~R~)] - 1} - V~Rsh.~

Photocurrent IL~ -- 0.92 F~' (KL~ + 7.2 × 10 5 T) • S ~ 0.92 F~KLcS (S in Wcm :)

Solar cell surface: F~ cm 2

Saturation current lo~ = K~F~T3 exp(-1.3 104/T) Series resistance R~ = K~/F~ Shunt resistance R~h.~= Kw/F~

Solar array equation:

Factor L - Lc/s~ = q / A k T (completion factor A = ns~, 1 ~< n < 2)

ilia = IL -- lo{exp[L(V~ + I~RO] - 1} - V ~ / R ~ h

Photocurrent/rE = ILcPs (or IL ~ KLS with K L = 0.92 F¢KL~PO Saturation current Io = lo~P~ [Ko = K~P~ in equation (7)] Series resistance R~ = R~,,~jP~ + R¢ (Re = Total resistance connections) Shunt resistance R~h = R~h~cSs/Ps

of

Notes: (1) See Table 2 for typical values of the constants. (2) The number of series connected cells s~ and the effective number of parallel strings P~ relate the array voltage and current to those of the individual cell by the relations V~ = s~V~ and I~ = P~. I~. (3) The quantities n, KL¢, Ko~, R~, R~h.~are usually denoted as the cell constants, the quantities A, KL, Ko, R~, R~h as the array constants.

A l i s t o f t y p i c a l v a l u e s o f t h e a b o v e m e n t i o n e d p a r a m e t e r s a n d c o n s t a n t s is g i v e n i n T a b l e 2. Finally, the constants for a typical 30 kW array consisting of commercial modules (present technology), are also given.

Electrolysis

unit characteristic

T h e c u r r e n t f l o w i n g t h r o u g h a w a t e r e l e c t r o l y s i s c e l l is v e r y l o w , u n t i l t h e v o l t a g e r e a c h e s a c e r t a i n v a l u e c a l l e d t h e d i s s o c i a t i o n v o l t a g e . F o r h i g h e r v o l t a g e v a l u e s , t h e c e l l c u r r e n t Ie~ i n c r e a s e s s t e e p l y . I t s d e p e n d e n c e o n t h e c e l l v o l t a g e V~c b e c o m e s r a t h e r l i n e a r , i . e . i t c a n b e a p p r o x i m a t e d by the relation Ve~ -~ c¢ + rclec = ec + Vac -]- Vcc -}- r J e c ,

TABLE 2. Parameter and constants for solar silicon cells and arrays State of the art (commercial or near term commercial)

KLc = 0.32 (A W-~) (lL~ ~ 0.03 A cm-2 at S = 0.1 W cm-2) Ko¢ = 6 (Acm 2, K 3) (1~ ~ 2.5 × 10-11 Acm-2 at 300 K) K~ = 0.34 (ff~cm 2) Kp¢ = 2000 (fl cm:) Example for a 30 kW-array: L = 0.051 V -1 lL = 108.7 A (at 1000 W m 2); 10 = 9 x 10-8A (at 300K) Rs = 0.24 fl; R~h = 192 if2

Projected

KL¢ = 0.344 ( A W -I) Koc = 0.65 + 0.06 (Acm-2,K -3) K~ = 0.34 (f2 cm ~) Kw = 2000 (fl cm 2)

Note: See Table 1 for equation summary.

(9)

292

C. CARPETIS TABLE3. Characteristicequation parametersfor electrolysisceilsand units

Electrolyticcell

Linearapproximation Vec = c¢ + r~l~c

cc = ec + Vac+ Vcc ec theoreticalcell voltage Vac anodeovervoltage Vcc cathodeovervoltage r¢= Wc/F¢

Wc Fe

Electrolysisunit

unit cell resistance(~2cm:), incl. electrolyte diaphragm, electrodeand contact resistanceterms electrodesurface, cm2

Polynomialapproximation Vet = A0~ +Atcl~c+ A2~l~+ . . .

Ao~,A~¢,Ace,etc. are determined by polynomialfittingtechniques

Linearapproximation

c = c~s~

V~ = c + rle

r = r~sJp~

Polynomial approximation lie =A0 + A~le + A21~ + . . .

The coefficients are determined by polynomial fitting techniques or from the cell coefficients: Ao =Ao~s~, A1 = AI~s~/P~, A2 = A2c&/P~ etc.

Note: The number of series-connected cells s~ and the effective number of parallel strings relate the electrolysis unit voltage and current to those of the individual cell by the equations V~ = V~is~, 1o = I~Pc.

where: ec V¢¢ Vac rc

is the theoretical cell voltage; is the cathode polarization overvoltage (due to kinetic reaction limitations); is the anode overvoltage and is the cell resistance, depending on electrolyte conductivity, distance between electrodes, diaphragm and electrode conductivity etc.

For future water electrolysis cells, both decreasing the theoretical cell voltage (by working at higher temperatures and pressures) and decreasing the polarization overvoltages (by using catalytic electrodes, appropriate diaphragms and electrode configurations) is being attempted in order to increase the electrolysis efficiency. As mentioned in a previous section, it is preferable for the applications anticipated here to use a polynomial approximation of the real characteristic according to equation (1). A polynomial of 5th order has been found as adequate for a good fit of the real electrolysis characteristic. Practical electrolytic units are of course constructed by connecting a great number of electrolytic cells in series and the resulting strings in parallel in order to match the system performance to the available power source. The voltage-current characteristic of any electrolysis unit is easily obtained from this connection scheme, according to the relations given in Table 3. Optimal matching of the characteristic of a solar array is achieved by adjusting the electrolysis cell surface Fe, number of series connected electrolysis cells se and number of parallel connected strings P~ to the corresponding numbers (Fs, s~, Ps) of the solar array. Electrolysis thermal losses are usually managed by external heat exchange, thus, isothermal operation is normally anticipated for water electrolysis plants. In the case of solar electrolysis, the varying power conditions could imply the necessity to account for varying electrolyzer temperature. This can of course be managed by adding appropriate terms in equation (1) or (9). Nevertheless, the memory of modern computing units enables the use of several sets of factors for the polynomial approximation at discrete temperature levels and the use of interpolation techniques for the intermediate values. Table 4 gives some typical values of the constants mentioned above for present and future electrolyzers. Further, typical data for a 30 kW electrolyzer consisting of commercial solid polymer cells are also given.

A STUDY OF WATER ELECTROLYSIS

293

TABLE 4. Parameter values for electrolysis cells and electrolysis units State of the art (near term commercial)

SPE technology

cc = 1.575 (V) Wc = 0.25--0.3 (f~ cm2)

(1 up to 1 A cm 2)

Alkaline electrolyzers

cc =1.62(V) We = 0.5-0.7 (f~ cm2)

(1 up to 0.4 A cm 2)

Example for a 30 kW SPE-electrolyzer: Linear approximation coefficients

Projected

Polynomial approximation coefficients

c = 306.2 (V) r =0.539(f]) A0 = 284.16; A~ = 2.232 A2 = -4.9 x 10-2; A3 = 5.61 × 10-4 Aa = 2.222 x 10-6

SPE-technology

c¢ = 1.42 (V) W~ = 0.1 (flcm 2)

cc : 1.55(v)

Alkaline electrolyzers

W~ = 0.3 (~ cm 2)

(1 up to 2 A c m -2) (1 up to 0.5 A cm2)

Matching of the characteristics As mentioned before, when a photovoltaic array is connected to the electrolysis unit, the working conditions are determined by the intersection of the characteristics, which fixes the voltage V and current I of the system.

I--{KLS-lo(expL(V÷IRsl-1)-VIl~}~

(Solar array)

/

t

S=solar irradiation//---Locus of maximal power / 1 V.-ImIRs*llL[o expL(V..I.Rs))

EIVt,IEI ~l~-Nominat operation p'o'' L : Point of max. power

V=~÷rz

L

/ / \ /I /'/ /,J

E: Points for compQrison

(v~=v. or I~:I.)

~_ Voltage

V

-----

FIG. 1. T h e typical situation concerning the v o l t a g e - c u r r e n t characteristics of the solar

array, of the electrolyzer and of the locus of maximal p o w e r points (not scaled). The Vl-characteristic can be adjusted to closely intersect at the nominal or "design" point N. The limits of p o w e r mismatching at points P different f r o m N, can be d e t e r m i n e d by considering the points E as s h o w n in the figure (VE = Vm if Vm > Vp and IE = I m if Vm < Vp). F o r these points Vmlm > Vplp > VEIE. The ratio VE1E/Vmlm can be d e t e r m i n e d as a function of the characteristic e q u a t i o n p a r a m e t e r s , thus enabling the determination of the lower limit for Vplp/VmIm (i.e. the determination of the relation VpIp/Vmlm > f ( r , c, L, Io,

RO).

294

C. CARPETIS

For known solar radiation, the photocurrent IL is known (see equation (6)) and the V, I values are determined by the solution of the simultaneous equations I = S ( V , I) = {Ie - Io exp[L(V + IR~) - 1] - V/R~h}/~6,

(10)

V = E(/) = A0 + A~I+ A 2 1 z + . . . + A s I 5,

(11)

as described in the next section. Optimal operating conditions are achieved when the point of operation coincides with the maximum power point (V,~, Ira) of the solar array characteristic voltage-current equation. To preserve this condition under varying solar radiation conditions during the working time of the day the locus of the maximal power points of the solar array and the characteristic of the electrolysis unit should coincide. This condition cannot be exactly met by practical characteristics. Nevertheless, it is important that, using an optimal series---parallel connection scheme for the electrolysis cells, a remarkably good fit of the electrolyzer characteristic equation with the (Vm, /m)----locus of the solar array can be achieved. The typical situation is depicted in Fig. 1. Of course, the question remains, what is the power loss due to the mismatching when the point of operation does not coincide with the intersection point N? Many investigators assume that the use of power conditioning between solar array and electrolyzer will be necessary. Actually, this will be beneficial if the power conditioner losses (which are typically 10%) are lower than the losses due to the mismatching and, further, if the increase of hydrogen output overcomes the additional power conditioner investment. It is, therefore, important to closely investigate the matching conditions for the case where no power conditioner is used. The power P = V I is maximum if the condition d P / d I = 0 is satisfied. To evaluate the voltage and the current at the maximum power point of the array characteristic the derivative d P / d I of the power P = V I is set equal to zero: dl I + V~--~ = 0 The derivative d I / d V is easily calculated by differentiation of equation (10). Substituting in the above condition, and, further, setting V = Vm and I =lm for the voltage and current at the maximum power points (Pm~ = Vmlm) it follows Vim = RsLIo exp[L(Vm + Rs/Im)] + fl Im L l o exp[L(Vm + Rdm)] + 1/Rsh"

(12)

The locus of maximal power points (Vm, Ira) described by the implicit equation (12) is non-linear. However, it is a well known fact that in the current region of interest (i.e. excepting very low current values, less than about 10% of the nominal array current IN) the Im value increases very steeply with the Vm values. Thus, the locus of maximum power points is an "almost vertical line" in relation to the voltage axis, as shown in Fig. 1. In this region the influence of the terms, including the shunt resistance R~h, is negligible thus the following simpler relation can be used for describing the locus of maximal power points 1

Vm _ Rs +

Im

(13)

LIo exp L ( V m + Rdm)"

Denoting

Vm = Im

--

x,

(14)

it follows from equation (13) that Vm =

1

L(1 + R d x )

In

1

(x - R~) LIo"

(15)

A STUDY OF WATER ELECTROLYSIS

295

Although an explicit expression for the mismatching between the maximum power locus and the electrolyzer characteristic cannot be given, the upper limits of power mismatching can be estimated by using equation (15). Consider, for example, the intersections P of the solar and electrolyzer characteristics which determine the working conditions as shown in Fig. 1 for two cases (above and below the nominal point N). The corresponding points of maximal power are denoted by L. Further, the selected points E are of particular interest, because the power V J E can be easily determined and, in addition, because the relation Vmlm > Velp > VEIE,

can be used to determine the limits of power mismatching. Since, according to equation (9) VE = C + tie and, further, IE =Im and VE = Vm for the points of comparison below and above, respectively, the nominal point N, it follows: VpIp > VEI....~E_ r + cL gmlm Vmlrn x

1+

In (x

-

Rs)LIo

'

(16)

for all points below the nominal point N, and x 1 Vplp > VEIE____{I__ cL(1 + - ~ ) [ l n ( ( x _ R ~ ) L i o ) J Vmlm Vmlm - r

-1

}'

(17)

for all points above the nominal point N. The importance of the above relations is that they determine the lower limit of the system power Vflp in relation to the maximal possible power Vmlm a s a function of the constants c, r (electrolyzer) and Rs, L, Io (solar array). The region of the variable x can be easily determined as shown in the following example. The "state of the art" system considered here consists of a fiat solar array and electrolysis unit according to the data given in Tables 2 and 4. The solar array, consisting of a total of Ps parallel strings each having s~ series connected silicon solar cells of a active cell surface F~ (cm 2) could deliver about 0.025 P~Fs (A) at 1000Wm -2 radiation. The nominal operation point would be selected to be about 0.0185 P~Fs (A). According to the data given in Table 2, the following array parameters will be used for the considered nominal temperature ( T = 300K): L = 36/s~ (V-l), R~ = 1.25 sdP~F~ (Q), Io = 1.627 × 10 -11 PsF~(A). The electrolyzer, consisting of a total of Pe strings, each having se series connected electrolysis cells of SPE-type with an active cell surface Fe (cm2), should be matched to the solar array data s~, P~ and F~. From the "basic design condition"* s~ = sd3.57 it followst c = 0.42 s~ (V). Further, to accommodate the maximum possible system current with a current density of about 10,000 A m -2 in the electrolysis cell it should be that PeF¢ ~ 0.035 P~Fs. Thus, it follows r = 0.30 re/(P~F~) ~ 2.4 sdP~Fs. Excluding extreme high or low radiation values, most of the hydrogen production will take place in the system current region from about I p = 5 . 5 x 10-3 psF~ (A) to about I p = 2 6 . 5 × 10 -3 PsFs (A), corresponding to the linear part of the electrolyzer characteristic. The corresponding voltage region (according to the relation Vp = c + rip with c = 0.42 ss and r = 2.45 s d P ~ ) will extend from Vp --- 0.433 s~ to about 0.484 s~ (V). Thus, it follows that the region of interest for the variable x(x =Vm/Im ~ Vp/Ip ) will be x = 18.3 s~/P~F~ to about 78.7 sdPsFs Inserting the lower limit x = 18.3 s~/P~F~in equation (17) (since the corresponding point is located above the nominal point N) it follows (with the c, r, L, R~ and Io values given above), Vplp > 0.943 Vm/m,

(18)

* This condition fixes the ratio of series connected electrolyticcells to the series connected solar cells accordingto the voltages of the individualcells. In general, it must be that s~/s~= oc(VodV~), where ~r(o:<1) must be adjusted for optimal design (optimal characteristic matching). t See equations in Table 3.

296

C. CARPETIS

for t h e u p p e r r a d i a t i o n level. With the u p p e r limit x = 78.7 sJ(PsFs) it ~follows from e q u a t i o n (16), Vo/p > 0.938 Vmlm,

(19)

for the lower r a d i a t i o n level. T h e s e results show t h a t in the c o n s i d e r e d case ( T ~ 300) the p o w e r ratio VpldVmlm is h i g h e r t h a n a b o u t 9 4 % , i.e. the r e l a t e d p o w e r loss due to mismatching, (Vm/lm- Vplp)/Vmlm, is lower t h a n a b o u t 6 % for every r a d i a t i o n level within the limits of practical interest.* This is a satisfactory "direct m a t c h i n g " situation, which implies t h a t the use of a p o w e r c o n d i t i o n i n g interface b e t w e e n the solar array a n d the electrolysis unit could b e u n n e c e s s a r y , if t h e o p e r a t i o n is i s o t h e r m a l . U n f o r t u n a t e l y , the t e m p e r a t u r e of the solar array will n o t b e c o n s t a n t a n d the v a r i a t i o n of the solar cells t e m p e r a t u r e will cause r e m a r k a b l e changes in the m a t c h i n g conditions. This can b e d e m o n s t r a t e d by considering the v a r i a t i o n of t h e lower limit of the p o w e r ratio (i.e. VzlE/Vmlm) for varying array t e m p e r a t u r e , as s h o w n in Fig. 2. T h e q u a n t i t y VEIE/Vmlm is calculated according to e q u a t i o n (16) or (17) as e x p l a i n e d before. Note t h a t e q u a t i o n (16) is valid iflm > IE. A l t e r n a t i v e l y , e q u a t i o n (17) m u s t be used if Im < IE. T h e results are given for the two radiation levels c o n s i d e r e d

-

-

.......

1st Design c = 0,420 s$ 2 d DesKJn c=0,38$s,

-

i

;

I

>" 0,6

0.4 I

0,2

T< 297K

2:~3

280

[

z

T " 297K

290

r-

300 Solor

314K

/"t To ,7~.:"+ec+ra = • t",;" cutoff

310 3i0 ceLLs temperoture

- K

FIG. 2. The variation of the ratio VEIE/Vmlmas a function of the solar cells temperature. This quantity is the lower limit of the ratio of the operating power Vp/p to the maximal array power V=I= at the considered radiation level (i.e. it is Vplp/Vmlm= +7,/rl~> VEIE/ Vml=). Two design cases are considered. The first, c = 0.42 ss, has been used, also for the example leading to the relations (18) and (19). With the second, c = 0.385 Ss, the maximum of the ratio VEIpJVmImis positioned at a higher temperature level. The small figures (not scaled) are to demonstrate the reason for this behaviour. (M denotes the points of maximum power.)

* This kind of presentation has been prefered, in order to underline that the results according to the relations (18) and (19) are not dependent on the s,, Ps, Fs values, i.e. of series-parallel connection of the arrays. [For an example, use ss = 720, Ps = 150,/7+= 25 cm2, to get a "30 kW" system. The corresponding electrolytic unit should have se ~ 202 SPE-cells connected i n series, PcFc-~ 131 cm2 and its characteristic would be V = 302.4 + 0.5 1. The matching conditions would be in accordance with relations (18) and (19).]

A STUDY OF WATER ELECTROLYSIS

297

before. Note that with varying temperature the x-values are slightly varying (for constant radiation level Im remains practically constant, whereas the voltage Vm increases with temperature as does the open circuit voltage Vow). Nevertheless, the influence of the temperature dependence of the saturation current Io is overwhelming, resulting in the situation shown in Fig. 2. The important result is that the lower limit of the ratio Vplp/Vmlm first increases with the temperature up to the maximum value, which has been adjusted by the design parameters. However, further temperature increase results in a very steep decrease of the useful power level. This can lead to a cut-off of the electrolysis process within a few degrees of temperature increase. (The results shown in Fig. 2 can be explained as follows: For temperatures lower than the design temperature the open circuit voltage Voc increases, so that the working point remains at about the same position, whereas only the maximum array power increases, about in proportion to Voo For higher temperatures, however, the open circuit voltage decreases and the intersection of the solar characteristic with the electrolyzer characteristic deviates rapidly to low current values, whereas the Voc voltage becomes rapidly lower than the dissociation voltage. The rapid decrease of the lower limit of the ratio Vplp/Vmlm(indicating that the array efficiency, r/a = Vplp/S, decreases rapidly in relation to the maximal possible value ?~i Vmlra/S) is the most adverse consequence of the temperature variation. Obviously, this can be omitted, if the design maximum (for high radiation levels) is selected to take place at the highest possible temperature of the array, as shown in Fig. 2 by the dotted lines. However, this can be managed by reducing the c-value, i.e. by a "capacity reduction method", which means that the avoidance of the possible electrolysis cut-off at the high temperature level is achieved by abandoning a part of the power output at the extreme of low temperatures, i.e. by accepting a design with less electrolysis cells connected in series (resulting in a lower c-value). Consequently, it becomes obvious from Fig. 2 that the determination of the power matching conditions (in the case of direct coupling of the array with the electrolysis unit) is dependent on the temperature variation of the array throughout the year. If this variation is not large, proper design could enable operation with values of Vplp/Vmlm= 0a/r/i well above the 90% limit. (It must be underlined that the curves shown in Fig. 2 are the lower limits of this ratio.) The numerical calculation and the corresponding results given in the next sections, confirm that, for the temperature variation expected for the most part of the year, the power matching could be quite satisfactory. However, more experimental results concerning the expected temperature excursions throughout the year are needed. In general, the following alternatives should be taken into consideration: (a) direct coupling, (b) use for power conditioning interface throughout the year, (c) provision of power conditioning unit, but use of direct coupling during periods of advantageous power matching. The optimal method can be determined by a system performance calculation throughout the year. Besides the local climatic conditions, the power conditioner data (efficiency throughout the year and costs) will be decisive, and must be well defined. It is probable that a power conditioning interface should be used in most application cases. From a first inspection, however, it follows that a mean efficiency of the power conditioning unit less than about 93% would be adverse and the advantages of its use doubtful. Further, it must be underlined that the pursued, overall efficiency advantage (i.e. the increase of the annual hydrogen production), should outweigh the additional capital costs. For the considered system, the overwhelming part of the hydrogen production costs is due to the capital investment. Thus, roughly speaking, an overall efficiency increase of e.g. 5% would not be advantageous if the costs must be increased by the same proportion, i.e. by about 5%. Consequently, for the interfacing problem considered here, the costs of the system components could be decisive for the optimum results. =

The computation program The main routine of the computation program calculates, for given solar radiation, the hydrogen production rate corresponding to the given characteristics of the solar panel and electrolysis unit. Thus, it is able to predict the hydrogen production during a day or during a year for a given location and defined local climatic conditions. The program proceeds as follows:

298

C. CARPETIS

(1) For given time steps the solar energy input to the array surface is calculated or inputted from records. The instantaneous voltage and current of the system are calculated from the intersection of the instantaneous array characteristic with the electrolysis unit characteristic. This is accomplished by using the iteration scheme I r+l = S ( V K + w ( V t( -

V~:-'), i f ) ,

V K+I = E(Ir+~),

(20) (21)

for the simultaneous equations (10) and (11). In the above equations w denotes the relaxation factor. After convergence to the solution (V, /), the instantaneous hydrogen production rate is directly calculated from the electrolyzer current L Finally, the point of the maximum power (Vm, Ira) of the instantaneous solar array characteristic is also calculated, and it is used for the determination of the matching conditions of the characteristics. If a power conditioning unit is assumed to be in operation, the calculation of the hydrogen production rate is based on the maximum array power Vmlm. However, the power conditioner data needed for the determination of the power loss mechanisms are required as input. Although the equations for the solar array and the electrolysis unit are not linear, the operating voltage and current are in a linear relation to the voltage and current (Vc, L, V~c, /~c) of the individual cells, because of the linear relations introduced by the series-parallel connection scheme of identical cells. The result is that the surface related array data are not dependent on the power level and the connection details of the arrays. For the system solution (V,/) it will be V = s~V¢ = s~V~ and I = P~/~ = P d ~ ,

as can be expected for series-parallel connections of identical cells (see also Table 1). For another matched system (consisting of cells of the same type) with s" = ~ss and P'F" = yP~Fs, it must also be, that s" = ~Se and P'F" = yPeF~. Thus, the system voltage and current will be V' = $V and I' = yI, The total array surface F will be increased by the factor $y (F' = $~9F). Thus, the specific power, kW m -2, does not depend on the array size VI

V'I'

-

F

- - - constant. F'

(2) To calculate the daily hydrogen production, the sunrise and sunset times are calculated for the specified day, the sunshine duration is divided into a number of time steps and the calculation proceeds as mentioned above. The output of the calculation for every time step includes the corresponding hydrogen production rate, the efficiencies of the photovoltaic array and electrolysis unit and the total system efficiency. Further, the daily hydrogen production and the corresponding system efficiency are outputted and the results are compared with the maximum daily hydrogen production, which would be possible in the case of the ideal matching of the characteristics. The results are also edited as specific values (e.g. per m 2 of the solar array), because, as mentioned before, these values are not dependent on the power level and on the series-parallel connection scheme used to build up the solar array and the electrolysis unit (i.e. the specific results are of general validity for matched systems so long as the same kind of solar and electrolysis cells is used). (3) For results on a yearly basis the above calculations are repeated for all days of the year and then integrated correspondingly for yearly output. (4) A sub-program delivers information on the costs of the hydrogen produced by the system, including hydrogen storage costs.

A STUDY OF WATER ELECTROLYSIS

299

The influence of the local climatic conditions on the solar energy input can be determined by using the values of the transmission factor T1 (mainly depending on the sun horizontal height), of the local Mie-scattering factor T2 (having highest values for industrial, urban areas) and of the obscurement factor 7"3, which accounts for the cloud losses. The obscurement factor is usually given by meteorological statistics as a monthly value, but, of course, any other scheme giving higher accuracy can be inputted in the calculation for every time step. The solar energy inputted to the hydrogen production system is first calculated for cloudless conditions (by accounting for the instantaneous horizontal sun height by the factor 7"1 and for the local conditions by the factor Tz) and then modified by applying the obscurement factor T3 to the resulting "cloudless day radiation" value. Of course, if recorded data for the solar energy input are available, the program part for the calculation of the solar radiation conditions is skipped and the record is used as input. As mentioned before, no convergence problems have been observed when running the above described program. Also, the calculation is inexpensive in time, since adequate convergence to the operation point (V, I) is achieved in most cases, after few iterations.

Comparison with experimental results An interesting test for the described calculation program can be made by comparing results with the experimental data reported [1]. The evaluation of the solar array used for this experiment (consisting of two series connected panels, Model 260, of Solarex, having nominal 6 W peak power) provides the characteristic parameters given in Table 5. The reverse saturation current of the array is relatively high, but it is not unusual for panels delivered at the time of the experiment. The solar array characteristic registered for the day of the experiment is typical for non-isothermal operation of the solar array, but it can be closely fitted by determining the appropriate temperature variation of the solar cells during the experiment day. This temperature variation influences the saturation current according to equation (7) and the maximum power point (Vm, Ira) according to equation (12). The evaluation of the electrolysis unit used for the experiment (General Electric Solid Polymer Electrolysis Unit, Model 15 E H G 1 A consisting of two electrolyzer cells) delivers the parameters given in Table 5. The experiment has been performed in Albuquerque, New Mexico, thus the solar data for the experiment day (22 March 1976) correspond to the latitude q~ = 35°05 '. Further, the solar array angle to the horizontal was i = 47°. Figure 3 summarizes the comparison of the experimental data and calculated values. The incident solar radiation reported [1] implies a cloudless day with a slight obscurance at the afternoon hours. However, it has been preferred to calculate the radiation for constant factors (T1, T2, T3) in order to demonstrate that the lower hydrogen production rate in the afternoon is due to the temperature rise of the array, rather than to lower radiation. The temperature increase has been assumed to be about 4.6°Ch -1, the maximal array temperature having been reached at 15.00 h. As shown in the figure, the reported lower system performance in the afternoon can be accurately predicted under these conditions, even for "symmetrical" radiation values. Furthermore, the calculated hydrogen production rate reaches a maximum at approx. 09.00 h and levels off during the middle part of the day, in accordance with the measured values. The calculated curve of the system efficiency ~/$verifies the minimum measured at noon, which is substantially lower than the maximum TABLE5. Characteristic equation constants for the solar array and electrolyzer used in the experiment reported in [1] Solar array A = 12.013 KL = 0,0254 Ko =30x103 R~ = 1.1Q R,h=80~

Electrolyzer A0= 2.95 Al = 2.132 × 10-1 A2=4.51×10 2 A3= 5.148 x 10-3 A4=2.093x 10 4

300

C. CARPETIS

3

.~,~

.~_ aoo :

'i

,too

o,,

.~ 6oo-

~'o

~.~

/t

\,,~

-o,1

~00-

200

1,05

-0,05 ISnl

Locol solar fire----h

FIO. 3. Comparison of the results reported in [1i with the calculated results according to the presented computation method. The latter are given for constant weather conditions throughout the day, in order to reveal that the degradation of the system performance in the afternoon is mainly due to the array temperature increase continuing at practically constant rate in the afternoon. The measured values are denoted with the subscript m (S,~, Hr,, etc.).

effÉciency measured at about 09.00 h. Thus, the remarkable behaviour of the system (levelling of the hydrogen production rate and decrease of the system efficiency during the middle part of the day) is well predicted by the described calculation method. It is of particular interest to discuss in more detail the reason for this behaviour. The conclusion reached in [1] is that, according to the experimental results, the system was not at the optimum point (of maximum power matching). The argument refers to the comparison of the performance curves of the solar array and the electrolyzer, which shows clearly that these curves not only do not coincide, but also, they are sufficiently apart to justify the above mentioned assumption of mismatching. However, a close investigation by means of the calculated data reveals that the poor results during the middle part of the day are due to poor solar array performance (mainly due to high series resistance) and that the power matching is surprisingly good. To clarify this point, the efficiency T/a of the solar array is depicted in Fig. 4 as a function of the time. Note that r/~ = r/s/r/EL = Operating array power Incident radiation '

(22)

where r/eL denotes the electrolyzer efficiency. The ideal efficiency r/i, defined as ~i

=

Maximum possible solar array power at S (W m-2) Incident radiation S (W m-2) ,

(23)

is also shown in Fig. 4. The comparison of the two curves, shows that no difference higher than about 5% exists at any time. Instead, the main reason for the poor system performance is the levelling of the solar array maximum power despite increasing solar radiation towards midday and the resulting minimum of the ideal efficiency r/i. The operating system efficiency r/a follows ~/iwithin the above mentioned 5% limit. The poor performance of the solar array can be recognized to be

A STUDY OF WATER ELECTROLYSIS

1 Z

W

!

LocQt t i m e - - , -

h

FIG. 4. Comparison of the solar array efficiency r/a during system operation (for the experiment described in [1]) with the maximal array efficiency under ideal power matching conditions, r/i. The result shows that for most of the day the power matching was very close. However, the system performance is adversely influenced by the array temperature increase and the high series resistance. (r/s~ denotes the ideal array efficiency related to the junction area radiation only.)

~"

Locution Nr.1

i =P-lO°

i

~

z"

-~

800 >,

®

~

),1

1,0-.1,0

~00200- 1.05/

--

0,5-.0.5 ~.

6 8 10 12 1/+ Local sotor time ~

h

FIG. 5. Calculated results for the "state of the art" photovoltaic-electrolysis system at location 1 (q0 = 35°) during a midsummer day. It denotes r/a, the operating array efficiency (for direct coupling with the electrolysis unit), r/i the maximal (optimal matched) efficiency of the array and r/~ the system efficiency (kW hydrogen energy output/kW radiation on the array).

301

302

C. CARPETIS

due to the almost linear decrease of the array current for voltages above about 30% of the open circuit voltage. This behaviour, again, is, as is well known, a consequence of high series resistance (about 1.1 g2 according to Table 5). Nevertheless, the described decrease of the solar current, beginning at low voltages, and continuing almost linearly up to the open circuit voltage, is also the main reason for the relatively low power mismatch: the operation power decreases slowly around its maximum and, thus, the different positions of the maximum power locus and electrolyzer characteristic are not critical.* However, for solar arrays with better performance, the power decreases steeply around the maximum power point and, thus, the electrolyzer characteristic must be as close as possible to the maximum power locus. As will be shown in the next section, much better solar electrolysis performance can be achieved with components of recent technology. To summarize: the calculated performance is in good agreement with the measured values reported [1]. The degradation of the system performance observed in the afternoon hours is found to be due to the continuing array temperature increase. The minimum of the system efficiency towards midday is not due to power mismatching, but is a consequence of poor array performance, mainly due to high series resistance Rs.

Calculation results for typical applications The performance of photovoltaic electrolysis systems including components available today (i.e. systems working according to the presently achievable solar array and electrolyzer characteristics) will be presented for two typical locations of different latitude and climatic conditions. The result given here will not be referred to a specific power level (i.e. to a specific solar array), instead the results will be given as specific values (kW of hydrogen production power per m 2 of solar array, kWh of annually produced hydrogen per m 2 of solar array etc.). This presentation, which has the advantage of greater generality, is possible due to the modular nature of both solar arrays and electrolysis units. As shown in a previous section the specific power, VI/F (kWm-2), is not dependent on the number ss of the series connected cells and on the number P~ of the effective parallel strings. This means that the specific data are not dependent on the current and voltage level selected by the designer. However, for selected P~, s~ and Fs values, the corresponding data of the electrolysis unit must be adjusted for power matching according to the relations

ss = Ksse and P~F~ = KpPeF~, where Ks and Kp are the adjustment factors (which can be optimized for best power matching conditions). Thus, the specific results ( k W m -2, k W h m -2 etc.) are not dependent on the ss, Ps, se, Pe and Fe values under the condition that the power matching is the same in all cases, which means that

PW~

seS--~= constant and p--~ = constant, i.e. that the adjustment factors are constant. In general, because of the great number of single solar and electrolytic cells included, even in a relatively small system (in the kW region), there is no difficulty in determining the series-parallel connections for optimal power matching. As mentioned, the results presented are for current technology systems. The fiat solar array is assumed to be composed of commercial silicon cells producing about 0.45 V and 25 m A cm -2 at the radiation level of 100 m W c m -2 (AM1). More data and the typical values of the parameters are given in Table 2. The results given in the following have been calculated for an electrolytic unit composed of solid polymer electrolysis cells. The "state of the art" data for SPE-cells (General Electric type) according to Table 3 have been used. (Current technology alkaline electrolysis cells have both higher electrode polarization and resistive voltage loss. However, for the projected performance of alkaline cells the results would be practically the same as for the "state of the art" SPE* It is of interest, that the resistive voltage drop in the used SPE-ceUs was relatively high (estimated value: Wc= 1.25fl cm2). However,the unit resistanceterm (r = 1.25se/P¢Fc)has been made low by simplyoversizingthe cell active surface (Fc ~ 50 cm2): the SPE-systemworked at very low current densities(up to 0.1 A cm-1). With the "state of the art" technologythe same performanceshould be achievablewith about one fifth of this cell surface.

A,STUDY OF WATER ELECTROLYSIS

303

electrolyzer considered here. Of course, the alkaline type electrolyzer would operate with at least half the current density of the SPE-system, which should be compensated by less expensive technology and lower surface unit costs.) The results are given for two locations. Location 1 is assumed to have latitude q~ = 35 °, and a typical hot summer/mild winter climate. The selected data correspond to the conditions available in Albuquerque, New Mexico, U.S.A. Location 2 is assumed to have latitutude q~ = 48 °, and a typical Central European climate. The selected data correspond to the conditions typical in the southern part of Germany, e.g. in Freiburg. Some characteristic results are depicted in Figs 5-10. Representative plots obtained for location 1 are given for a summer and a winter day in Figs 5 and 6. For the same days of the year the results obtained for location 2 are given in Figs 7 and 8. The plots shown in these figures depict the solar radiation, the hydrogen production rate and the system efficiency as a function of the time of the day. Further, the efficiency of the solar array r/a as well as the ideal solar array efficiency r/i ( f o r ideal power matching) are plotted for comparison. As mentioned in the previous section, the comparison of these two curves provides information on the power mismatching. The two efficiencies are very close and only a small deviation (not higher than 5%) can be observed in the early morning and/or for noon-hours. Although the solar radiation has been calculated for constant climatic factors during the day, a reasonable solar cell temperature variation has been assumed for the results shown in Figs 5-8. In order to study the influence of this variation, no power conditioning has been considered. The results confirm that the adverse effect of the array temperature variation is rather low, if the temperature does not exceed the assumed maximal (design) value. The continuation of the curves shown in Figs 5-8 for the afternoon hours would be symmetrical for symmetrical array temperature variation. In general, however, the temperature maximum occurs in the afternoon. For the purpose of comparison pursued here, this specification has been omitted. The efficiency of the electrolysis unit, also depicted in Figs 5-8, shows a minimum at the noon hours. This occurs, because, with increasing electrolysis current, the cell voltage is also increasing. Thus, the electrolysis efficiency, which, by definition is Reversible voltage

r/EL = Operating voltage ' e-

Location Nr.1

t

~"

i--,-lo°

,,_

:-

i-o .-

>-

0'1

t~

S

I~

. _

-,-

"1,S

e-

.-~ 600' ~-

®

.m

~,1

a

'0,1

O

1,0--1,0 ~-

/~00"

~ '~o

o ~EL

"~ e-

-o,o5

o,s -o.s .~_

200-

~e-i

Local solar time ---- h FIG. 6. The same result as in Fig. 5 for a typical midwinter day at location 1.

304

C. CARPETIS

:+1+ t

~

gl ~._ ,o~o,oo ,:,_,ooHr., ~l =t

?

"8oo J ~

t/~

.~ 1,5

600-

•.~"°~00""0,I ~ ~o

200"

'

/

S ~\

/l H

"~¢~=

1,0"1,0 ~°"

0,5--0,5 .o'I

Local solar time----h FIG, 7. Calculated results for the "state of the art" photovoltaic-electrolysis system at location 2 (q~ = 47 °) during a cloudy midsummer day. Although the system efficiency r/s is practically the same as in location 1, the hydrogen production rate H does not exceed 1 g h -1 per m 2 of the array.

1

Location 1~.2 l

i=r-lO°

|

~"

N 800 ,,." e ~.

.~ 1,5 ®

600' o¢

~,10

~EL

1,0' "1,0 "~

~/,00.

b.

o

~200.

%

•0,05

S

O,5' '0,5

._~

Local solar time ~ h FIG. 8. The same results as in Fig. 7 for a typical midwinter day at location 2.

A STUDY OF WATER ELECTROLYSIS

2000..4.

f

,'~ ,,

1500,

-1,5

1000.

.1

500.~

,,~',/ ...... for i=l'÷10° -for i=r-10 °

,0,5

100 200 300 Day of the year N FIG. 9. Mean energy input Es and hydrogen production P for the "state of the art"

photovoltaic-electrolysis system throughout a statistically typical year at location 1. The mean variation of the daily maximum of the hydrogen production rate, Hmax, is also depicted. The electrical output of the solar array is denoted by Ec. The dotted lines are for array inclination equal latitude minus 10°, In this case the winter hydrogen production rate is higher, but the yearly output slightly lower (an optimal array inclination can be determined if the features of the hydrogen storage device and the hydrogen demand schedule are taken into account: it must be found whether a higher production rate or the use of stored hydrogen is more advantageous to cover the winter peak demand).

~.~ "=£ ~ "=

Location Nr.2 for i=r-10 °

-~

. . . . . for i= ~+10°

1500-3

1,5

Hr~x

Es

1000

500

-0,5

160 260 360 Day of the year N--4-

FIG. 10. Mean energy input Es and hydrogen production P for the "state of the art" photovoltaic-electrolysis system throughout a statistically typical year at location 2. The variation of the daily maximum of the hydrogen production rate,//max, and of the electrical output Ec of the array are also depicted.

305

306

C. CARPETIS

diminishes with increasing operating cell voltage (in other words, since the hydrogen production is proportional to the system current, I, and the input power equals VI, the efficiency is decreasing with the operating voltage). The solar array efficiency r/a as defined by equation (22), is related to the radiation incident on the total array surface. The coverage factor of the array, amounts, typically, to 80%. Thus, as can be seen from the results shown in the figures, the solar cell efficiency related to the exposed silicon area exceeds the 10% value, as is typical for present technology. The total amounts (integrated values) of the solar radiation, electric energy production of the array and the system hydrogen production are shown as a function of the day of the year in Fig. 9 for location 1 and in Fig. 10 for location 2. Further, in both figures, the mean maximum of the daily hydrogen production rate is depicted as a function of the day of the year, in order to demonstrate the seasonal variation of the system performance throughout the year. In all cases shown in Figs 5-10, the solar arrays are assumed to be located facing south at fixed angles i to the horizontal (as indicated in the figures), i.e. no tracking has been assumed. In order to demonstrate the influence of the array inclination, the curves of the yearly results in Figs 9 and 10 are plotted for two values of the inclination (corresponding to the latitude of the location -+ 10°). The results are similar for both locations: the influence of the array inclination is relatively low in regard to the total hydrogen production. L o w e r inclination delivers more hydrogen on the yearly basis (because it utilizes m o r e effectively the summer radiation conditions). H o w e v e r , higher inclination delivers more hydrogen during the winter days, e.g. the increase in hydrogen production rate amounts to about 15% at the winter radiation minimum, for location 2, if the inclination is varied from 38 ° to 58 ° It is, of course, desirable to maximize the hydrogen production during the days of maximum demand. Nevertheless, it is obvious that seasonal hydrogen storage

TABLE6. Summary of the results for photovoltaic hydrogen production system "state of the art" cases Array inclination

Location 1 (cp = 35°)

i = -10 °

i = +10°

4.43 2.0 × 10-3 7.03%

4,29 1,78 × 10-3 7.06%

8.9% 11.8%

8.98% 11.86%

5%

5%

Specific annual hydrogen production, kg(H2)m 2 (array) Peak production rate, kg(H2)m 2h-l Annual mean hydrogen production efficiency

2.22 1.55 × 10-3 7.1%

2.07 1.35 × 10-3 7.11%

Annual mean solar array efficiency: related to the array surface related to the silicon (junction) area Maximal deviation of the array deficiencyrelated to the maximal possible efficiency

8.54% 11.38% 5%

8.5% 11.33~ 5%

Specific annual hydrogen production, kg(H2) m-2 (array) Peak production rate, kg(Hz)m-2h-1 Annual mean hydrogen production efficiency Annual mean solar array efficiency: related to the array surface related to the silicon (junction) area Maximal deviation of the array efficiencyrelated to the maximal possible efficiency

Location 2 (q0= 47°)

Note: (1) The results are not very sensitive in regard to the array inclination. Higher annual hydrogen production is achieved with lower inclination, but, then, the difference in production rate between winter and summer becomes substantial. (2) The peak production rate given above corresponds to the optimal electrolysisunit size. (3) The results are for fixed arrays facing south.

A STUDY OF WATER ELECTROLYSIS

3(17

will be, in most cases, beneficial for solar-hydrogen production systems, and in this case more hydrogen production on a yearly basis could be more advantageous than higher production rates during the winter period. In any case, the answer to this optimization problem can be given only with regard to specific location, hydrogen consumption schedule and hydrogen storage concept. A summary of the results concerning the solar hydrogen production for both locations is also given in Table 6. For the above annual results, an optimal power matching has been assumed. A reasonable temperature variation of the array based on meteorological information has been used. Power conditioning with an efficiency of 95% has been assumed to be operating for the cases where direct coupling would deliver lower overall efficiencies. The results are rather optimistic from the interfacing point of view. However, less optimistic assumptions do not effect the annual values by more than about 5%. In any case, the related uncertainty is not higher than that introduced by other meteorological data (e.g. obscurement factor etc.) A comparison of the results for the two locations considered shows that the annual hydrogen production per m 2 of the solar array will be about twice as high at location 1 in comparison to location 2. Thus, substantial differences in the production costs of solar hydrogen should be expected for different locations. However, it should be kept in mind that the break even criteria for its use, also depends strongly on the local hydrogen utilization schedule.

Solar hydrogen production costs The prediction of the hydrogen costs produced by solar electrolysis is, at present, impeded by the fact that the costs of the most expensive system component, the solar cell array, are changing (fortunately decreasing) rapidly. Yor this reason, solar array costs over a wide range (from the short-term expected values to the long-term target values) should be taken into consideration. Furthermore, in order to optimally deliver solar hydrogen, a hydrogen storage system should be incorporated to the solar array-electrolyzer system. Thus, there are three interconnected subsystems (solar array, electrolysis unit and hydrogen storage unit) which should be optimized for minimum hydrogen costs, according to the local conditions and to the hydrogen utilization schedule. Since optimization results cannot be given within the present work, only a rough parametric consideration of the cost situation is given, in Fig. 11. The annual hydrogen production (kg hydrogen per m 2 of array surface) is used as parameter in the upper-right quadrant of the nomogram. The maximal hydrogen production rate is similarly used in the lower-left quadrant and corresponds to the selected electrolyzer size. The nomogram is entered at the lower quadrants with the equipment costs, and proceeded, as shown in the figure, to the upper right quadrant.* The resulting hydrogen production costs are based on the total investment. Because of the large variation of the equipment costs, cost positions like installation and field work, plant overhead and because O + M costs have been estimated on a per unit basis; only the indirect costs have been taken to be proportional to the system construction costs. For the previously discussed locations 1 and 2, the results are shown in diagram (b) of Fig. 11 (assuming 25 $/m 2 structure and installation array costs and a 13% fixed charge factor). The results of Fig. 10 show that the contribution of the electrolysis unit to the total costs is low. This fact implies that it would be beneficial to select units with highest efficiency, even at high equipment costs (in other words: expensive technology for electrolysis units could probably minimize the costs in solar hydrogen systems). The main information derived from the computation results described in the previous sections, which is needed for the use of the nomogram shown in Fig. 11, is, of course, the annual hydrogen production. In addition, the size of the electrolysis unit could optimally be defined from these results. A rough estimation of the annual hydrogen production can be made from the simple knowledge of the local annual insolation data and the solar cell efficiency level. But, as shown in * In the example shown by the dotted lines in Fig. 11, it can be recognized that the intersection point A determines the total investment costs (i.e. the sum of specific equipment and installation costs due to the solar array, the electrolysis unit and their accessories and interfaces). In the upper left quadrant the annual unit charge is determined for different annual charge rates. Finally, in the upper right quadrant the lines for different annual specific hydrogen production (kg H2 m -2) are used to specify the unit hydrogen production costs (unit annual charge/annual production).

308

C. CARPETIS

Annual " ~ 1 ~

1,0 5 ~ / ~/ / 53

(without 0+PIIJ . . . . . .

30

1

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FIG. 11. Hydrogen production costs for the photovoltaic-electrolysis system with "state of the art" components. The "nomogram" presentation of the cost situation (upper diagram) illustrates the influence of the main variables and parameters. The influence of the local conditions is represented by the calculated hydrogen production rate (lower left quadrant), i.e. by the electrolysis module size, and, further, by the total annual hydrogen production (upper right quadrant). The nomogram is entered with the equipment costs for the solar array and electrolytic unit. Installation material and field work auxiliaries, O + M costs, parasitic energy costs etc. are accounted with estimated values, not dependent on the equipment costs. However, the indirect construction costs are proportional to the plant construction costs. The lower diagram shows the resulting hydrogen production costs for the two previously considered locations as a function of the solar array (uninstalled) costs.

the previous sections, the solar array efficiency and also the electrolyzer efficiency vary during the day. Further, the influence of the varying power matching conditions during the day and also the cut-off of the electrolysis process in cases of low radiation must be taken into account. As a result, the calculation of hydrogen production costs is substantially more accurate when the hydrogen annual production is calculated as described in the previous sections. As shown in Fig. 11, hydrogen production at location 1 could cost as little as 0.14 $/kWht for solar array costs at 100 $/m.2 However, hydrogen storage will demand additional costs. According

A STUDY OF WATER ELECTROLYSIS

309

to [7], short-time (diurnal) hydrogen storage would add about 0.02 S/kWh, long-time (seasonal) storage up to 0.06 S/kWh on the hydrogen production cost. From the results of Fig. 11 it can be seen that the electrolysis unit costs contribute a relatively low part of the total costs. In the near future, the cost reduction for hydrogen produced by solar electrolysis can be expected, as a consequence of the solar array cost reduction. In the long term, further cost reduction could be expected by the use of more efficient solar cells and electrolytic units, if, of course, the higher performance is connected with acceptable additional investment. With lower production costs, the importance of low cost storage methods for solar hydrogen will become more important. The cost optimization and the break even conditions will depend not only on the solar array and electrolyzer performance improvement, but also on the location of the production and the hydrogen utilization schedule. Conclusions A study and performance prediction for the system composed of a photovoltaic converter and an electrolysis device for hydrogen production can be made by means of inexpensive computation methods. The comparison of the results to available experimental data shows that a very good agreement exists. When this computation method is well established for the performance prediction of photovoltaic-electrolysis systems, it can be very valuable for planning, system design and optimization, cost prediction, break even point determination etc. When solar radiation records for a time period at a certain location are available, the hydrogen production can be predicted with high accuracy. The computation method accounts for the instantaneous matching of the component characteristics, the cut-off conditions etc. Especially, the solar array performance characteristic can be modelled analytically, with high accuracy, even for varying array temperature. The influence of varying temperature and of rapid voltage variation (implied by varying radiation) on the electrolyzer characteristic, needs more experimental investigation. However, the results could be easily introduced into the computation program to increase the accuracy. The performance of the system, photovoltaic array-water electrolysis unit, both with present technology components, has been studied for two typical locations. In location 1 ((p = 35°, warm summer/mild winter) the hydrogen production amounts to 4.43 kgm -2 (annual mean value) and the production rate reaches a maximum of 2 × 10 -3 kg m -2 h -1 in the summer months. The annual mean of the efficiency (related to the radiation on the total array surface) amounts to about 7%. In location 2 (q0 = 48°, Central European climate) the efficiency is about the same, but the hydrogen production is about 50% of the annual hydrogen production at the first location. These results are for fixed solar arrays facing south with an inclination at the horizontal equal to the latitude -+10°. The variation of the inclination in both locations shows a relatively low influence on the annual hydrogen production. However, for a given hydrogen utilization schedule, an optimization of the inclination could be combined with the determination of the optimal hydrogen storage device to be connected to the system. An important result of the study is that it is possible to achieve a very effective adjustment of the characteristic of the electrolysis unit to the locus of maximal power points of the solar array for a given array temperature. However, this "design adjustment" (T/a/~/i~- 1) for optimal power matching should be made for the maximal radiation level at the maximal operating array temperature. The reason is that for higher temperature the efficiency diminishes rapidly, and electrolysis cut-off could occur within a few degrees of further temperature increase. For all array temperatures below this point the array efficiency T/a will diminish by less than 3% per 10K in comparison to the ideal (maximal) array efficiency T/i. Under these circumstances, the decision whether a power conditioning interface is advantageous or a direct coupling should be preferred, cannot be validly made for all applications. The result of the corresponding optimization not only depends on the local climatic conditions (and the resulting array temperature variation) throughout the year but also on the cost composition of the system. The calculation of the hydrogen production conditions throughout the year, according to the presented computation scheme, is also needed in order to define the optimal hydrogen storage device, which would be necessary for the accommodation of given hydrogen demand throughout the year. The costs of the hydrogen produced by the photovoltaic-electrolysis system has been roughly

310

C. CARPETIS

estimated. Since the above mentioned optimization problems cannot be handled here, a parametric presentation has been preferred. The resulting unit costs are appreciable as they are the costs of producing electricity by means of photovoltaic cells. The latter are expected to diminish substantially in the future. Thus, the solar hydrogen production costs are actually dependent on the time scale and, further, the crossover with (increasing) alternative energy costs is dependent yet on scenario assumptions. However, more extended experimental and analytical investigation of the system photovoltaic array-electrolysis unit is needed for the near future, as a synthesis of the advances on the photovoltaic and electrolysis technology. REFERENCES 1. K. E. Cox, Hydrogen from solar energy via water electrolysis, Proc. llth 1ECEC, pp. 926-932 (1976). 2. N. COSTOGUE& R. K. YASUI, Performance data of a terrestial solar photovoltaic experiment, Proc. Int. Solar Energy Society Conference, pp. 138-139 (1975). 3. D. EST~VE, C. GANIBAL,D. 8TEINMETZ• m. VIALASON,Performance of a photovoltaic electrolysis system, Proc. 3rd World Hydrogen Energy Conference, Tokyo, Vol. 3, pp. 1583-1603 (1980). 4. W. T. PICCIAnO,Determination of solar cell equation parameters, including series resistances from empirical data, Energy Conversion 9, 1-6 (1969). 5. F. J. BRYANT& R. W. GLEW,Analysis of the current voltage characteristics of cadmium sulfite solar cells under varying light intensities, Energy Conversion 14, 129-133 (1975). 6. A. BRAUNSTEIN,I. BANY & I. APPELBAUM,Determination of solar cell equation parameter from empirical data, Energy Conversion 17, 1-6 (1977). 7. C. CARPETIS, m system consideration of alternative hydrogen storage facilities for estimation of storage costs, Int. J. Hydrogen Energy 5, 423--437 (1980).