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Solar electricity storage systems
Applied Energy 7 (I 980) 45-66
SOLAR ELECTRICITY
STORAGE
SYSTEMS
J. JENSEN and C. PERRAM
Energy Research Laboratory, Odense University, Campusvej 55, 5230 Odense M, Denmark
SUMMARY
The principle of'converting solar energy directly into electricity is non' practically feasible. In order to obtain a reliable source of powerJ?om such an intermittent power supply as the sun, someJorm of storage is necessary. Several methods of storage are reviewed. The particular advantages ofusing battery storage for solar systems are discussed and a method oJ designing such a system is analysed. The expected demands on such a battery are discussed, along with the batteJ3' developments needed in order to satisJactorily meet such demands.
INTRODUCTION
Photovoltaic (PV) conversion technology for the direct conversion of the sun's energy into electricity was developed through, and used in, the American space programme. The development of the solar cell for terrestrial use--and the industry surrounding it--began in 1973 with major emphasis being placed on the development of the solar cell itself, since the main hindrance to terrestrial applications comes from the cost of the photovoltaic array. Photons from sunlight incident upon--and absorbed by--such materials as silicon, gallium arsenide and cadmium sulphide liberate electric charge carriers and hence produce electrical energy. These individual cells are then connected electrically in such a way as to provide useable power levels (Fig. 1). The present volume of production (1978) is of the order of 1 MWpk mostly in the form of silicon flat plate cells. (The peak watt (Wpk) is the peak power generated with a radiation level of 1 kW/m 2 at a temperature of 28°C, referred to as AMi conditions). The present production costs for the cells are $7 $15/Wpk and 45 Applied Energy 0306-2619/80/0007-0045/$02.25 .~" Applied Science Publishers Ltd, England, 1980 Printed in Great Britain
46
J. JENSEN, C. PERRAM
Fig. I.
Photovohaic cells in place for a stand-alone system experiment. Jydsk Telefon, Denmark, 1979.
$20-$40/Wpk for the cells installed in array. ~ The price goals and history are shown in Fig. 2. Panel life is expected to be at least 20 years and it is calculated 2 that the payback of solar panels in terms of fossil fuels used in manufacture is now ~ 4 - 7 years, dependent upon location of use. ~- BLOCK I 20.00
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Photovoltaic module/array. Price goals and history. (Source: Quoted in reference 1.)
S O L A R E L E C T R I C I T Y S T O R A G E SYSTEMS
47
The output of electrical energy (and current) is proportional to the incident radiation intensity. The overall efficiency of conversion in terms of total area utilisation is the product of both cell conversion efficiency and panel area utilisation. At present the panel packing is 60 70 ~,,,and the maximum conversion efficiency of each cell up to 14 ~o, resulting in an overall total panel efficiency of less than 10 o~,. Developments in both panel packing with square cells and cell conversion efficiency are important if utilisation of available area is to be increased. The properties of solar cells that make them a particularly attractive alternative energy producer are as follows. Their utilisation of a distributed source of energy so that power can be generated locally, thus avoiding the expense of distribution. The fact that they are attractive in remote regions, especially those with high insolations. Their modular system design. The fact that they are clean--i.e, there are no environmentally damaging waste products. The fact that they are largely maintenance-free. The fact that they provide a high quality energy source.
THE NEED FOR S T O R A G E
Although the energy available from sunlight is both reliable and inexhaustible, it has the obvious limitation of being variable. The diurnal and annual variations are complicated by the less determinable variations due to climate. These variations must be taken into account in systems design, but they show immediately the need for storage if power is to be available on demand (i.e. supply levelling). Thus, when used in combination with a suitable storage system, the solar cell becomes a highly reliable power source which can be used independently of any other supply. As well as supply levelling, the storage system results in a reduction in necessary panel area to cope with sudden surges in demand for electricity (peak lopping).
S T O R A G E SYSTEMS
There are a number of ways of direct or indirect electricity storage 3"4 but only a few are applicable to solar electricity. The various candidate systems will be briefly discussed. An evaluation of the technical and economic advantages and drawbacks will be made.
Mechanical storage Electricity, once converted into mechanical energy, can be stored as potential
48
J. JENSEN, C. PERRAM
energy--for example, via elevated weights in the gravitational field, pumped water, compressed air and springs. Also, mechanical energy in the form of kinetic energy (e.g. in flywheels) can be used. The energy content of mechanical systems can be calculated as the amount of work which can be released to an external system when a force, F, is applied over a distance, S: (1)
W= ~ Fds
The energy content of a mass, m, placed in the gravitational field, g, at a height, h, and moved down to a height, h o, is given by the amount of work, W, the system can release: W = ~ F d s = m g ( h - ho) = m g A h
(2)
This equation also applies to the pumped water systems currently used as large-scale storage by utilities. The system of elevated weights needs high ratio gearing systems and the overall efficiency, because of frictional losses, is therefore fairly low. Pumped water storage using reversible turbines is only economically viable in large units. Compressed air or gas systems are widely used as buffer systems. When a piston is used to compress a gas, energy is stored in the gas and can be released later by reversing the movement of the piston. Pressurised gas is, therefore, an energy store. In Fig. 3 is shown a cylinder with compressed gas at a pressure, P, defined as force, F, per unit area, A.
F v
d$ Fig. 3.
Gas at a pressure, P, moves a piston by applying a force, F.
The work released by the expansion of the gas is: W = ~r.ds
= ~P.Ads
= ~P.dv
(3)
Instead of the moving piston, a hydraulic motor/pump in connection with an accumulator with a rubber bag for separating the gas from the fluid, is often used (see Fig. 4). The total efficiency of this storage method is much too low to apply to the storage of solar electricity, not only because of the friction losses in the necessary gearing system but especially because of the heat losses of the compression process.
SOLAR ELECTRICITY STORAGE SYSTEMS
49
J
Item
Description
1 2 3 4 5 6 7 8
Shell Fluid Port Assembly Separator Bag M S Hyd Tube Schraeder Wllve Assy Gas Back up Bottle Perforated Tube "Tee' Connection
Fig. 4.
Compressed gas accumulator with rubber bag separator.
Mechanical springs are well suited to the storage of small amounts of energy. Most applications, however, are found in dynamic mechanical systems where the primary purpose is not to store energy. The calculation of the amount of energy stored in a spring is of the same kind whether it relates to a compressed or an expanded spring. The latter situation is shown in Fig. 5. An ideal spring exhibits a linear relationship between force, F, and distance of expansion, S = x - x 0. The work supplied in order to extend the spring to a distance of S can be derived by inserting F = K . g in the general mechanical work equation, K being the constant of elasticity. Then : W = ~ F d s = ~ K S . d s = ½KS 2
(4)
50
J. JENSEN, C. PERRAM
i
I
L ~
I
I
Xo X1 Fig. 5.
X2
Expansion of a spring by applying forces of different values.
The energy density of a spring system--or of any system with solid elastic material as the energy storage medium--is rather low and gearing systems are also necessary here. Spring systems will only find application as energy stores where the output energy required is mechanical energy with pulses of high power. In inertial storage systems, energy is stored as kinetic energy in the rotating mass of a flywheel. With angular velocity, ~o, and moment of inertia, I, the energy content is:
w = ½/~o 2
(5)
Two examples of flywheel design are shown in Fig. 6. When the expression for the moment of inertia, 1, is inserted into eqn. (5) the maximum energy density can be derived. The inertia of the flywheel, with the mass concentrated in the rim, is equal to the radius squared times the total mass, and it
Fig. 6.
Left: Flywheel with mass concentrated in the rim. Right: Proposed 'superflywheer.
SOLAR ELECTRICITY STORAGE SYSTEMS
51
follows that the maximum amounts of kinetic energy per unit volume, U~ot,and per unit mass, ~;,, respectively are: ~4~oI(max) = ½6m~x,
~;, (max) --
1 CSmax
2 p
(6)
Hence, optimum flywheel materials have a high tensile strength, 6, and low mass density, p. A number of advanced concepts have been proposed 5'6 but the technology is at the drawing board or laboratory stage. In order to achieve a low loss system with a long storage time, vacuum encapsuled rotors with magnetic bearings have to be developed. The need for auxiliary equipment means that there is a lower size limit for economic viability of flywheel systems. In conclusion, the potential energy storage systems are ruled out as technically economic ways of storing electricity from solar cells. Prospects for the use of advanced flywheel systems do exist, but further development is necessary and a size limitation due to costs is foreseen.
Storage in electrical and magnetic fields An electric capacitance, C, is a device which can take up charges, q, whereby an electric field, E, is established and hence energy is stored. Figure 7 shows a parallel plate capacitor with dielectric material described by the permittivity, e, separating the plates. Also shown is the series RC circuit where R is the total circuit resistance and V the applied voltage.
q lit)
\\ +
Fig. 7.
\\ ~ \
, -
Left: Parallel plate capacitor. Right: Series RC circuit.
The energy content of a capacitor Wc is: wc = kcv 2
(7)
The amount of stored energy is proportional to the material's constant • or, in other words, the material's ability to polaris• when placed in the electric field, E, between the plates of the capacitor. The volumetric energy density: Wva = 1 E E 2
(8)
52
J. JENSEN, C. PERRAM
is very low in practice, and capacitors as energy stores only find application where small amounts of energy are to be stored for a short time or where short pulses of high power are required as the outputs. Magnetic fields, too, can be used for energy storage. Figure 8 shows an electromagnet where a flux, ~b, through the magnetic material with cross-section area, A, results from a stationary electric current, 1~,, in the coil consisting of N windings.
0
v-i-
0 Fig. 8.
I t.
Left: The magnetic circuit. Right: Series RL circuit diagram.
The energy content is dependent on the self-inductance, L, and the electric current, /st: 1
w = ~LI~,
2
(9)
The expression of the energy density is analogous to the case of the electric field,/~ here being the permeability (the material's constant of the magnetic material) and H the magnetic field: WvoI ---- l ~ H 2
(10)
The major drawback of electromagnets as energy stores is that the electric current has to be maintained during storage. Heat loss occurs due to the voltage drop over the resistance, R, and so ordinary magnetic systems can be ruled out as possible energy stores. This problem is coped with in so-called superconducting coils where the current passes without any resistance and hence there are no losses during storage (Fig. 9). Present superconducting materials, such as inter-metallic compounds and alloys, have critical temperatures ranging from l0 to 20 K and the penalty paid for the zero resistance and compact character is the need to operate at liquid-helium temperatures with the associated problem of using vacuum insulated cryogenic containers. In general, this places a lower limit on the size of the device, below which the superconducting coil is not practical. In conclusion, the storage of electricity from solar cells in electric or magnetic fields is ruled out. One future exception, perhaps, is the superconducting coil applied only for very large energy stores.
SOLAR ELECTRICITY STORAGE SYSTEMS
53
cryogenic contoiner o,1o
[ ] [
power
supply
T Fig. 9.
o
inductonce
'
A
IoQd .
[
Simplified superconducting energy storage circuit.
Chemical storage Two systems will be considered in this section: (a) the electrolyser/hydrogen/fuel cell system and (b) secondary electric storage batteries. The first concept implies that hydrogen is stored either as gas or liquid or dissolved in a metal to form a so-called hydride. The mass and volume energy densities, w,, and Wvo~,are listed in Table 1. TABLE 1 ENERGY DENSITIESOF HYDROGEN IN VARIOUSFORMS
Gas at 150 atm (20°C) Liquid - 252 °C Metal hydride (including metal) Oil (for comparison)
Wm (kJ/kg)
Wvol (kJ/dm 3)
140000 140000 1400-11000 44000
1700 10500 17500-21000 40000
The principal disadvantages of gaseous hydrogen as a storage medium are its large space requirement and the difficulty of leak-free confinement. Liquid hydrogen storage implies expensive cooling equipment and hence only very large units are expected to be economically viable. These drawbacks of hydrogen are abolished in the hydride form and the important constraint here is the price of the 'host metal'. The chemical reaction of exothermic hydride formation from metal (Me) and hydrogen (H2) is as follows: charging (heat released)
H2 +
Me ~
~ hydride + heat
(11)
discharging(heat added)
Hydrogen storage is regarded as important when long storage times are needed. The electrolyser is already available but a reliable hydrogen-oxygen fuel cell is still at the development stage. Rechargeable electric batteries are at present the obvious choice for storing electricity from solar cells. 7 A common feature of batteries is that electricity is
54
J. JENSEN, C. PERRAM
-I
current
elect;6ns
anode
electrolyte
1. cathode
I
e-
[ransport
@%
Fig. 10. An electrochemical energy source during discharge.
c o n v e r t e d i n t o c h e m i c a l - b o u n d e n e r g y d u r i n g c h a r g i n g . F i g u r e 10 shows the electrochemical system during discharge. B a t t e r y m a n u f a c t u r e is still d o m i n a t e d by the lead acid a c c u m u l a t o r invented by P l a n t + in 1860 b u t a d v a n c e d b a t t e r y d e v e l o p m e n t s have increased c o n s i d e r a b l y in i n d u s t r i a l c o u n t r i e s recently.S T a b l e 2 s h o w s a c o m p a r i s o n o f a n u m b e r o f c a n d i d a t e batteries, the p r o p e r t i e s o f w h i c h are briefly discussed below. L e a d a c i d : T h i s b a t t e r y is c o m m e r c i a l l y a v a i l a b l e in large q u a n t i t i e s at relatively low cost. It has been widely used as a s t a t i o n a r y b a t t e r y for local small-scale p o w e r
TABLE 2 COMPARISON OF F'ROPERTIES OF A N U M B E R OF ( ' A N D I I ) A T E BATTERIES
Lead acid
Nickel cadmium
Nickel zinc
Nickel iron
Lithium TiS 2
Electrolyte
HzSO.,
KOH
KOH
KOH
Vo tage ] Opea c rcu t (V))-~ Discharge 2h Self discharge
2.08 I-9 Medium -20 + 50 500 +
1.35 1.2 Low -30 + 50
Various organic 2.5 2.0 2.2 1.7 Low <75
Operating temperature ("C) Life (to 80 '~,,discharge) cycles Energy cfficiency (charge-discharge) Cost Capital (£/kWh) £/kWh cycle
75 30 0.075
2000
70 200 ~0-13
1.71 1.6 Mcdium -30 + 40
1.37 1.2 High 10 50
400
2000
75 ~ 70 ~0"21
50 60 ~ 70 ~ 0-044
> 250
25 <0.13
These figures should be regarded only as guidelines since they differ with battery design and duty. Some are projections from cell performance only. The cost figures relate to batteries developed mainly for other purposes and low loss batteries for solar electricity may well be more expensive.
SOLAR ELECTRICITY STORAGE SYSTEMS
55
generation, telephone exchanges, emergency supply units, etc. The overall cell reaction is: discharge
Pb + 2H2504 + PbO 2 ( - - - - ¢ P b S O 4 + 2 H 2 0 + PbSO 4
(12)
charge
The key problem with lead acid batteries is the need for careful maintenance. The major maintenance operation is the addition of water to make up for that which is lost by evaporation, electrolysis and self-discharge reactions. The final answer to this problem seems to be a battery of completely sealed cells such as the Gates system. However, the conventional lead acid battery may find some application for solar electricity, but only for large installations where service is available. Nicke~eadmium." This battery is commercially available in cell capacities of up to several hundred ampere-hours in sealed maintenance-free versions. The accepted cell reaction is: discharge
2NiOOH + 2 H 2 0 + Cd ~
) 2Ni(OH)2 + Cd(OH)2
(13)
charge
The Ni/Cd battery is widely used in small electrical appliances and the prospects for a future market in small solar cell units are encouraging. The price, which reflects materials problems (concerned with scarcity resources, handling and fabrication), is prohibitive for the widespread use of very large batteries. Nickel-zinc: The Ni/Zn battery is superior to the Ni/Cd battery in lower material cost, higher cell voltage and less toxic material contained. The cell reaction is: discharge
2NiOOH + 2 H 2 0 + Zn ~
) 2Ni(OH) 2 + Zn(OH) 2
(14)
charge
The main drawback for solar applications is short cycle life but there are good prospects that research in progress will lead to improvements. Nickel-iron." The cost is comparable with the more expensive type lead-acid batteries and the cycle life is long. However, the high self-discharge and the low overall efficiency, together with the need for maintenance resulting from hydrogen evolution, make it unsuitable for solar installations. Lithium-titanium disulphide. This cell is based upon an organic liquid electrolyte, conductive to lithium ions. These electrolytes have a rather high resistance, but this is not a disadvantage in matching with solar cells. The cell reaction proceeds via insertion of lithium ions between adjacent sulphur layers in the dichaleogenide TiS 2. The reaction is: discharge
xLi + TiS 2 (
) LixTiS2 charge
(15)
56
J. JENSEN, C. PERRAM
The cell voltage varies from 2.5 V to 1.9 V. The system potentially has a number of outstanding features. These include high energy density and long life, a leakproof seal and excellent stability over a wide range of operating temperatures. In addition, the Li/TiS 2 cell has a unique feature in its ability to indicate the level of its charge. The 'sloping voltage', simply monitored, indicates the level of capacity left. For small units, batteries seem to be the only technically and economically viable means of storage. 9 The features that make them particularly well suited for use with PV arrays are: The system input and output is in the form of low voltage dc electricity. They respond immediately to supply and load variations and are very reliable. It is possible to match the internal resistance of the battery to load for maximum power output. Modular construction allows flexible sizing and easy battery exchange. Batteries have a short lead time in manufacture. These advantages of battery storage apply to all sizes of solar installation: Set against these advantages are the relatively high capital cost and short lifetime of present day rechargeable batteries. With larger array installations ( > 1 kW) it may become more economic to electrolyse water and store the energy for solar cells as hydrogen, which is then converted to electricity in a fuel cell. A drawback of batteries is their limited temperature range of efficient operation. The solar panel, however, is especially suited for use in cold conditions because of its lack of moving parts and it is actually more energy efficient at lower temperatures.
SYSTEM STUDY
Electricity produced by solar cells can be converted so that it can be fed into a mains supply system, or it can be used for stand-alone systems such as that modelled in Fig. 11. In the following we deal primarily with systems of the latter type. Economic optimisation of a PV system such as that shown in Fig. 11 requires the identification and selection of individual system components which minimise the overall cost of the power produced over a particular time period. The cost of the electrical power depends on the solar insolation at a given locality; the system efficiencies, the costs of components and the match between load and insolation. This latter is the determining Jactor Jor the size of the storage necessary if a standalone system is to supply the load with I00 '.)/oreliability. With the cost of the solar cell array at its present level ( ~ $10/Wpk ) it is of particular importance to have accurate data on solar radiation in order to best utilise this incident radiation. Climatological data are available from several stations in
SOLAR ELECTRICITY STORAGE SYSTEMS
57
inpuf
I
control(~ I
E~ load Fig. 11.
System model for a stand-alone solar cell/battery storage system.
Europe over a period of several years. The most frequently available data records are those of global and diffuse radiation measured on a flat collector by means of a pyranometer. Since we are mainly concerned with collectors which are tilted from the horizontal, in order that the insolation flux is increased, it is necessary to calculate the radiation falling on such an inclined surface. Such calculations are
4000
3000
~c
2000
B o
1000
E
insolation
W/m 2
Fig. 12. Histogram of the number of hours:year (averaged over 8 years) that the mean hourly insolation is within each 100W/m 2 interval. The left end column is the number of" hours with zero insolation.
58
J. JENSEN, C. P E R R A M
based on certain assumptions as to the isotropy of the distribution of diffuse light over the whole sky. In our particular study we have used the model of Liu and Jordan l° which has been shown by Klucher ~l to be accurate for levels of insolation of less than 50 m W / c m 2 but to be up to 6 ~o inaccurate for larger insolations. The distribution of hourly insolation levels from zero up to a m a x i m u m of l k W / m 2 for Denmark (56 °N) is shown in Fig. 12. The relatively small percentage of time with an insolation level of over 50 m W / c m 2 shows that the errors involved in the model used are not significant. Figure 12 also shows the fraction (I4/) of peak power (Wpk) that can be expected to be achieved, e.g. ~70~o of the time W < 1/5Wpk and ~90~o of the time W < 1/2 Wpk. We also note that Wpk can be expected for only a few hours each year in Denmark.
OPTIMISATION
We consider a device consisting of a solar cell panel of area A m 2 connected to an electric battery with maximum capacity B kWh. The whole system is to be designed to meet a sequence of loads l I . . . . . 1NW over the N time periods t 1..... tN hours. During these periods, amounts of output energy, e I . . . . . e NJ/m 2 from the panels are used (after conversion) to service the load or, in the case where there is excess over the load, to recharge the battery if it is not full. We have assumed an overall battery efficiency of 70% and a total panel efficiency of 10~o. For a given battery capacity, B, the panel area, A, must be sufficiently large so that: N
Load L (in joules) = 3600 ~
N
tklK < A ~
K=I
eK
(16)
K-I
As the total energy over the whole period ~ e K tends not to vary too widely (see Table 3) and the load constraint is determined in advance, in practice, eqn. (16) gives a TABLE 3 SOLAR INSOLATION ON UNIT AREA OF A SOUTH-FACING PANEL WITH 45 o TILT
Year
(a) (b) (c) (d) (e) (f)
1962 1967 1965 1966 1961 1963
Yearly insolation ( J i m 2) x 10 9
Daily average insolation ( J i m 2) × 10 7
Standard deviation ( J i m 2) x 10 7
4.33 3.96 4.17 3-69 4-52 4-17
1.19 1.08 1.15 1.01 1-24 1.14
0.79 0-79 0.85 0.81 0.84 0.83
S O L A R E L E C T R I C I T Y S T O R A G E SYSTEMS
59
lower limit, A mi n tO A. Before we can optimise the parameters of the system, we must first find, in the form of a constraint, restrictions on A, B such that, for all inputs, eK, the load is met. The objective function we wish to minimise is the total cost, C, of the system, which may depend on quantities such as the unit cost of batteries and panels, installation costs and maintenance and replacement costs over the envisaged useful life of the system. This we write as:
C=A~ap+B~bq p
(17)
q
where ap and bq are the costs associated with solar panels and batteries, respectively. Costs of electronic controls are included in the battery costs, but the non-linear term describing reduced battery life caused by deep discharge is omitted in this preliminary analysis. Before we can apply standard programming techniques to this cost function we must formulate a load constraint. This will be a constraint g(A, B) upon A and B such that, at each time, tK, the load, /K, must be met. We have determined the function by simulation since the distribution of %. is non-Poisson, and analytic queuing techniques 12 cannot be used with confidence. Using hourly data available over a ten-year period in Denmark, and a system model as described, a computer simulation of a solar cell/battery system was developed. Daily insolation patterns over one year are shown in Fig. 13 for a 20 m 2 panel with 10 ~/efficiency. The relationship between the diffuse and direct radiation components is clearly shown. Because only direct radiation can be concentrated, the benefit to be gained by concentration in most areas is not considered to be of significance in such high latitudes. It should be noted that, for Denmark and Northern Europe in general, a large percentage of the total energy available is diffuse energy and it is the conversion of such diffuse energy in the winter period which makes the use of PV conversion feasible. Taking suitable initial values for A, B and an initial value B~, being the battery charge level at the beginning of the first period and available energy e 1, we follow the time dependence, Bj over the period of the simulation. If, at any stage, B2 = 0 and the load cannot be met, the simulation is stopped and the value of A incremented. If the load is maintained for the whole simulation, the value of B is reduced and the simulation repeated. In this way a curve g(A, B) can be obtained (Fig. 14). The differences from year to year are clearly large and it is important for absolute reliability of design that the 'worst possible' cases be considered. Figure 15 shows the feasible solution space for the economic optimisation using the 'worst possible' case. Using the simplified objective function described above and present costs of panels and batteries, we obtain an optimal value at C on the c u r v e i.e. at present we should choose as large a battery as possible and hence the minimum
60
J. JENSEN, C. PERRAM
o.,
o
selnof
m
c~ o -
x:
c~
o
8 c~
a
=c3
saln0f
L
c _
_
L
c~
m
m L
i
(salnof)
~6JeUa u01~oJp~j ~uepm3ul
61
SOLAR ELECTRICITY STORAGE SYSTEMS
100 ¸
"',.,.-,~. ,.. "t ~
B0"
....
?. i o:;
'i'\,
....
;
60-
1,t2
,,
..
". 'k ' .
• ,~..~, ~.... , , ,..
,,
"...
' .......................................
20
1~
z~
~
oAYs
Fig. 14. Relationships between panel area and battery capacity g(A, B) (for a constant 100 W load. in order that the load is fully maintained) for six different years using insolation data for Denmark.
loo
=
~D
Am°i~
,..~7- .-7 ~-
VT--T
7-
L',, ,~(/~/,,.,,b~ J / _
-
..
soluti
%
- ,(~j//
Ami.
J J
t
i"..... ._
J"
2O
0 0
1 20
I L~O
l 60
t 80 kwh
Fig. 15. The hand drawn minimum envelope of curves shown in Fig. 14. This is used to find the optimal combination o f panel area and battery capacity. A: concave envelope of load constraints g(A,B). B: linearised load constraint A.
62
J.
JENSEN,
C.
PERRAM
panel area possible. As the costs of solar panels are reduced, the minimum will move to D, with the battery component of the system assuming the dominant cost role. It is also possible to calculate the battery state-of-charge. Figure 16 shows such a diagram in the limiting case where the battery just fails to empty over a two-year period.
10
"6 L I
05
"6 i
c o .m t~ t._ t.a_
1962
Bati'ery
1963
si'a'fe-of-charge
curve
for jan 1 9 6 2 - dec 1963
Fig. 16.
Load = 50W, pane] area = 15m 2, battery capacity = 25 kWh.
This clearly shows the high discharge rates which occur during periods of low insolation as well as the extremely large battery capacities which are necessary to cope with this. The battery storage needs to cover 20 30 days' supply to ensure that a constant load can be maintained without excessively large panel areas. Using battery equivalents to 2000 and 1000 hours' storage, comparisons were made of the minimum panel area necessary for a 100 W constant load in Denmark and Carpentras, France (44°N) (Fig. 17).
63
SOLAR ELECTRICITY STORAGE SYSTEMS 100 I
8O E
o E
"1
.~_ ._ E
.J 20
.J
~ 0
100
I 200
300
400
; 500
L 600
J 700
L
i
800
900
constant load (watts} Fig. 17. Relationship between m i n i m u m panel area required to maintain a constant load throughout the year and the load size. Curves are shown for two battery capacities and two locations. 1 Battery capacity 1000 hours" storage for Denmark (1961, 1966). I[ Battery capacity 2000 hours" storage for Denmark (1961, 1966). Ill Battery capacity 1000 hours" storage for Carpentras (only one year available). IV Battery capacity 2000 hours" storage ['or Carpentras (only one year available).
PRACTICAL SYSTEM DESIGN PROBLEMS
The general problem of matching the internal resistance, R i, of a power source to the resistance of the load, R/, in such a way that m a x i m u m power is delivered to the load also applies to solar cell/battery systems. With a linear relationship between voltage and current, the plot of power in the load (Pt) as a function o f the load resistance (R/) can be drawn as shown in Fig. 18 : P/max is obtained when R t = R i.
R[ = R i
Fig. 18.
R! {nl
Load power as a function of load resistance.
64
J. JENSEN, C. PERRAM
Although neither solar cells nor batteries exhibit linear characteristics (Figs 19 and 20) the simple linear model used to derive the above maximum conditions stresses the importance of matching R i and R~ to be of the same order of magnitude for maximum power output. Because the internal resistance of solar cells is several orders of magnitude higher than that of generally available batteries, a combination of solar cells in series (to match the battery voltage) and in parallel (to match the resistance) is necessary. Unfortunately, the high resistance and low voltage of a solar cell compared with most battery cells make this matching difficult to effect and hence a higher resistance battery cell may be necessary.
constant region _~
2.66
current
ISC~ 2.50
maximum . power point_
2.28 I/)
~~
~ 1.9o E
constant
\ region voltage
1.52 _ 2 "~ 1.14
_
+50 °C
L'28°C /-t~O°
0.76 0.38
Voc\ 1 5
10 15 20 25 array voltage, volts
30
Fig. 19. Solar array voltage-current characteristics. Array size: 36 series, 4 parallel strings of 2in diameter Si-cells for insolation 100 m W / c m 2, Csc = short circuit current, Voc = open circuit voltage. Source: reference 13.
Further, electronic power conditioning--which controls the transfer of energy from the panels to the batteries--is necessary as the power delivered by the cells fluctuates greatly, and thus power transfer efficiency can be significally reduced. Matching the load to the generator for maximum power tracking a4 can be achieved by the use of high efficiency transistor choppers to form a self-adaptive power flow control system.
65
SOLAR ELECTRICITY STORAGE SYSTEMS
25 Ah BATTERY
25%
'C,6(~i25 %
II 50% Chorged .. CURRENT
(A)
50mW/cm 2 25%
"~-~
10 mW/c m-~
25% I 4
"--~ I 8
j, i 12
\ /
~ 16
I 20
VOLTAGE Fig. 20.
Current voltage characteristic of 25 Ah storage battery.~5
CONCLUSIONS
If solar electricity is to become a viable alternative power source then the development of the storage system is as important as the development of the array system. Because of the particular properties of batteries outlined above they are the obvious choice for use in PV systems at present. The demands placed on batteries used in PV systems, particularly in areas of variable insolation such as northern Europe, are exacting. The requirements are for: reliability; high overall efficiency; long cycle life; low self-discharge; good charge retention and the ability to overcome deep discharge. These, along with low overall cost demands, are not fulfilled by any battery available at present. There is therefore need for the development of new batteries specifically designed for PV systems.
66
J. JENSEN, C. PERRAM
ACKNOWLEDGEMENTS The authors wish to acknowledge discussions with a number of colleagues within the Anglo-Danish advanced battery research programme. Support for this work was o b t a i n e d f r o m E E C C o n t r a c t s 315-78 E E ( D K ) a n d 3 1 6 - 7 8 E E ( U K ) a n d t h e D a n i s h Department of Energy.
REFERENCES I. P. RAPPAPORTand L. M. MAGID, Prospects and opportunities in photovoltaics, Proc. o/2nd EEC Photovoltaic Solar Energy Con/erence, April, 1979, Berlin, p. 21. 2. M. WIHL and A. SCHEININEA,Analysis and simulation of the energy source of the future: The solar breeder, Proc. o/ 13th IEEE Photovoltaie Con/erenee, 1978. 3. K. J. Euler, Methods of accumulating electricity, ESRO Summer School, August, 1968. 4. J. JtZNSEN, Energy storage, Newnes-Butterworths, London, 1979. 5. R. PosT and S. POST, Flywheels, Scientific American, 229 (December, 1973), pp. 17-23. 6. A. R. MILNER, A flywheel energy storage and conversion system for photovoltaic applications, International Assembly on Energy Storage, Dubrovnik, Jugoslavia, May, 1979. 7. J. JENSEN,C. PERRAMand R. M. DELL, Batteries for solar electricity, Proc. 1979 Photovoltaie Solar Energy Conference, Berlin 2~26 April, D. Reidel Publ. Co., 1979, pp. 610- 20. 8. B.C. TOF~ELD~R. M. DELL and J. JENSEN,Advanced batteries, Nature, 276(5685) (1978), pp. 217 20. 9. J. JENSEN, P. MCGEEHm and R. M. DELL, Electric batteriesfor energy storage andconservation--An application study, Odense University Press. 1979, pp. 225. 10. B. Y. L~u and R. C. JORDAN,Daily insolation on surfaces tilted towards the equator, ASHRAE Transaction No. 1762 (1962), pp. 526-41. I 1. T. KLUCHER, Variation of solar cell sensitivity and solar radiation on tilted surfaces, Proc. of 13th IEEE Photovoltaie Confi'rence, 1978. 12. HAMDYA. TAHA, Operations research, MacMillan Publishing Co., Inc., New York, 1971. 13. ABBASA. SAHM, Regulation and Control Array Power--A minimum Power Dissipation Approach, Proc. oJ 13th IEEE Photovoltaic Confi, rence, 1978, p. 121. 14. P. L. SWARTand J. J. rAY WYK, Source tracking and power flow control of terrestrial PV panels for concentrated sunlight, Proc. oJ 13th IEEE Photovoltaic Confi, renee, 1978, p. 700. 15. P. E. BAIKIL Battery storage in solar cell systems, UK Section ~1 the International Solar Energy Society, Technical Meeting. May 5, 1978.
SOLAR ELECTRICITY
STORAGE
SYSTEMS
J. JENSEN and C. PERRAM
Energy Research Laboratory, Odense University, Campusvej 55, 5230 Odense M, Denmark
SUMMARY
The principle of'converting solar energy directly into electricity is non' practically feasible. In order to obtain a reliable source of powerJ?om such an intermittent power supply as the sun, someJorm of storage is necessary. Several methods of storage are reviewed. The particular advantages ofusing battery storage for solar systems are discussed and a method oJ designing such a system is analysed. The expected demands on such a battery are discussed, along with the batteJ3' developments needed in order to satisJactorily meet such demands.
INTRODUCTION
Photovoltaic (PV) conversion technology for the direct conversion of the sun's energy into electricity was developed through, and used in, the American space programme. The development of the solar cell for terrestrial use--and the industry surrounding it--began in 1973 with major emphasis being placed on the development of the solar cell itself, since the main hindrance to terrestrial applications comes from the cost of the photovoltaic array. Photons from sunlight incident upon--and absorbed by--such materials as silicon, gallium arsenide and cadmium sulphide liberate electric charge carriers and hence produce electrical energy. These individual cells are then connected electrically in such a way as to provide useable power levels (Fig. 1). The present volume of production (1978) is of the order of 1 MWpk mostly in the form of silicon flat plate cells. (The peak watt (Wpk) is the peak power generated with a radiation level of 1 kW/m 2 at a temperature of 28°C, referred to as AMi conditions). The present production costs for the cells are $7 $15/Wpk and 45 Applied Energy 0306-2619/80/0007-0045/$02.25 .~" Applied Science Publishers Ltd, England, 1980 Printed in Great Britain
46
J. JENSEN, C. PERRAM
Fig. I.
Photovohaic cells in place for a stand-alone system experiment. Jydsk Telefon, Denmark, 1979.
$20-$40/Wpk for the cells installed in array. ~ The price goals and history are shown in Fig. 2. Panel life is expected to be at least 20 years and it is calculated 2 that the payback of solar panels in terms of fossil fuels used in manufacture is now ~ 4 - 7 years, dependent upon location of use. ~- BLOCK I 20.00
o -'-
o
~
~
H
~
,
,
-,
I
BLO 5.OO
,
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SILICON INGOI(CURR[NIII[CHNOLOGY
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f
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--
EXIENDED DEV[LOPMENT \ t THIN FILMS AND AOVANCFDC O N C E P I S - ~ , , . I
0.25
1
$0. 10-0.301WpGOAL" ~ 0.|0
I
I
l
I
15 76 11 18 D
I
I
t
80 P,I ~
I
I
i
I
I
l
t
83 84 85 86 81 118 89
t
90
CALENDARYEAR Fig. 2.
Photovoltaic module/array. Price goals and history. (Source: Quoted in reference 1.)
S O L A R E L E C T R I C I T Y S T O R A G E SYSTEMS
47
The output of electrical energy (and current) is proportional to the incident radiation intensity. The overall efficiency of conversion in terms of total area utilisation is the product of both cell conversion efficiency and panel area utilisation. At present the panel packing is 60 70 ~,,,and the maximum conversion efficiency of each cell up to 14 ~o, resulting in an overall total panel efficiency of less than 10 o~,. Developments in both panel packing with square cells and cell conversion efficiency are important if utilisation of available area is to be increased. The properties of solar cells that make them a particularly attractive alternative energy producer are as follows. Their utilisation of a distributed source of energy so that power can be generated locally, thus avoiding the expense of distribution. The fact that they are attractive in remote regions, especially those with high insolations. Their modular system design. The fact that they are clean--i.e, there are no environmentally damaging waste products. The fact that they are largely maintenance-free. The fact that they provide a high quality energy source.
THE NEED FOR S T O R A G E
Although the energy available from sunlight is both reliable and inexhaustible, it has the obvious limitation of being variable. The diurnal and annual variations are complicated by the less determinable variations due to climate. These variations must be taken into account in systems design, but they show immediately the need for storage if power is to be available on demand (i.e. supply levelling). Thus, when used in combination with a suitable storage system, the solar cell becomes a highly reliable power source which can be used independently of any other supply. As well as supply levelling, the storage system results in a reduction in necessary panel area to cope with sudden surges in demand for electricity (peak lopping).
S T O R A G E SYSTEMS
There are a number of ways of direct or indirect electricity storage 3"4 but only a few are applicable to solar electricity. The various candidate systems will be briefly discussed. An evaluation of the technical and economic advantages and drawbacks will be made.
Mechanical storage Electricity, once converted into mechanical energy, can be stored as potential
48
J. JENSEN, C. PERRAM
energy--for example, via elevated weights in the gravitational field, pumped water, compressed air and springs. Also, mechanical energy in the form of kinetic energy (e.g. in flywheels) can be used. The energy content of mechanical systems can be calculated as the amount of work which can be released to an external system when a force, F, is applied over a distance, S: (1)
W= ~ Fds
The energy content of a mass, m, placed in the gravitational field, g, at a height, h, and moved down to a height, h o, is given by the amount of work, W, the system can release: W = ~ F d s = m g ( h - ho) = m g A h
(2)
This equation also applies to the pumped water systems currently used as large-scale storage by utilities. The system of elevated weights needs high ratio gearing systems and the overall efficiency, because of frictional losses, is therefore fairly low. Pumped water storage using reversible turbines is only economically viable in large units. Compressed air or gas systems are widely used as buffer systems. When a piston is used to compress a gas, energy is stored in the gas and can be released later by reversing the movement of the piston. Pressurised gas is, therefore, an energy store. In Fig. 3 is shown a cylinder with compressed gas at a pressure, P, defined as force, F, per unit area, A.
F v
d$ Fig. 3.
Gas at a pressure, P, moves a piston by applying a force, F.
The work released by the expansion of the gas is: W = ~r.ds
= ~P.Ads
= ~P.dv
(3)
Instead of the moving piston, a hydraulic motor/pump in connection with an accumulator with a rubber bag for separating the gas from the fluid, is often used (see Fig. 4). The total efficiency of this storage method is much too low to apply to the storage of solar electricity, not only because of the friction losses in the necessary gearing system but especially because of the heat losses of the compression process.
SOLAR ELECTRICITY STORAGE SYSTEMS
49
J
Item
Description
1 2 3 4 5 6 7 8
Shell Fluid Port Assembly Separator Bag M S Hyd Tube Schraeder Wllve Assy Gas Back up Bottle Perforated Tube "Tee' Connection
Fig. 4.
Compressed gas accumulator with rubber bag separator.
Mechanical springs are well suited to the storage of small amounts of energy. Most applications, however, are found in dynamic mechanical systems where the primary purpose is not to store energy. The calculation of the amount of energy stored in a spring is of the same kind whether it relates to a compressed or an expanded spring. The latter situation is shown in Fig. 5. An ideal spring exhibits a linear relationship between force, F, and distance of expansion, S = x - x 0. The work supplied in order to extend the spring to a distance of S can be derived by inserting F = K . g in the general mechanical work equation, K being the constant of elasticity. Then : W = ~ F d s = ~ K S . d s = ½KS 2
(4)
50
J. JENSEN, C. PERRAM
i
I
L ~
I
I
Xo X1 Fig. 5.
X2
Expansion of a spring by applying forces of different values.
The energy density of a spring system--or of any system with solid elastic material as the energy storage medium--is rather low and gearing systems are also necessary here. Spring systems will only find application as energy stores where the output energy required is mechanical energy with pulses of high power. In inertial storage systems, energy is stored as kinetic energy in the rotating mass of a flywheel. With angular velocity, ~o, and moment of inertia, I, the energy content is:
w = ½/~o 2
(5)
Two examples of flywheel design are shown in Fig. 6. When the expression for the moment of inertia, 1, is inserted into eqn. (5) the maximum energy density can be derived. The inertia of the flywheel, with the mass concentrated in the rim, is equal to the radius squared times the total mass, and it
Fig. 6.
Left: Flywheel with mass concentrated in the rim. Right: Proposed 'superflywheer.
SOLAR ELECTRICITY STORAGE SYSTEMS
51
follows that the maximum amounts of kinetic energy per unit volume, U~ot,and per unit mass, ~;,, respectively are: ~4~oI(max) = ½6m~x,
~;, (max) --
1 CSmax
2 p
(6)
Hence, optimum flywheel materials have a high tensile strength, 6, and low mass density, p. A number of advanced concepts have been proposed 5'6 but the technology is at the drawing board or laboratory stage. In order to achieve a low loss system with a long storage time, vacuum encapsuled rotors with magnetic bearings have to be developed. The need for auxiliary equipment means that there is a lower size limit for economic viability of flywheel systems. In conclusion, the potential energy storage systems are ruled out as technically economic ways of storing electricity from solar cells. Prospects for the use of advanced flywheel systems do exist, but further development is necessary and a size limitation due to costs is foreseen.
Storage in electrical and magnetic fields An electric capacitance, C, is a device which can take up charges, q, whereby an electric field, E, is established and hence energy is stored. Figure 7 shows a parallel plate capacitor with dielectric material described by the permittivity, e, separating the plates. Also shown is the series RC circuit where R is the total circuit resistance and V the applied voltage.
q lit)
\\ +
Fig. 7.
\\ ~ \
, -
Left: Parallel plate capacitor. Right: Series RC circuit.
The energy content of a capacitor Wc is: wc = kcv 2
(7)
The amount of stored energy is proportional to the material's constant • or, in other words, the material's ability to polaris• when placed in the electric field, E, between the plates of the capacitor. The volumetric energy density: Wva = 1 E E 2
(8)
52
J. JENSEN, C. PERRAM
is very low in practice, and capacitors as energy stores only find application where small amounts of energy are to be stored for a short time or where short pulses of high power are required as the outputs. Magnetic fields, too, can be used for energy storage. Figure 8 shows an electromagnet where a flux, ~b, through the magnetic material with cross-section area, A, results from a stationary electric current, 1~,, in the coil consisting of N windings.
0
v-i-
0 Fig. 8.
I t.
Left: The magnetic circuit. Right: Series RL circuit diagram.
The energy content is dependent on the self-inductance, L, and the electric current, /st: 1
w = ~LI~,
2
(9)
The expression of the energy density is analogous to the case of the electric field,/~ here being the permeability (the material's constant of the magnetic material) and H the magnetic field: WvoI ---- l ~ H 2
(10)
The major drawback of electromagnets as energy stores is that the electric current has to be maintained during storage. Heat loss occurs due to the voltage drop over the resistance, R, and so ordinary magnetic systems can be ruled out as possible energy stores. This problem is coped with in so-called superconducting coils where the current passes without any resistance and hence there are no losses during storage (Fig. 9). Present superconducting materials, such as inter-metallic compounds and alloys, have critical temperatures ranging from l0 to 20 K and the penalty paid for the zero resistance and compact character is the need to operate at liquid-helium temperatures with the associated problem of using vacuum insulated cryogenic containers. In general, this places a lower limit on the size of the device, below which the superconducting coil is not practical. In conclusion, the storage of electricity from solar cells in electric or magnetic fields is ruled out. One future exception, perhaps, is the superconducting coil applied only for very large energy stores.
SOLAR ELECTRICITY STORAGE SYSTEMS
53
cryogenic contoiner o,1o
[ ] [
power
supply
T Fig. 9.
o
inductonce
'
A
IoQd .
[
Simplified superconducting energy storage circuit.
Chemical storage Two systems will be considered in this section: (a) the electrolyser/hydrogen/fuel cell system and (b) secondary electric storage batteries. The first concept implies that hydrogen is stored either as gas or liquid or dissolved in a metal to form a so-called hydride. The mass and volume energy densities, w,, and Wvo~,are listed in Table 1. TABLE 1 ENERGY DENSITIESOF HYDROGEN IN VARIOUSFORMS
Gas at 150 atm (20°C) Liquid - 252 °C Metal hydride (including metal) Oil (for comparison)
Wm (kJ/kg)
Wvol (kJ/dm 3)
140000 140000 1400-11000 44000
1700 10500 17500-21000 40000
The principal disadvantages of gaseous hydrogen as a storage medium are its large space requirement and the difficulty of leak-free confinement. Liquid hydrogen storage implies expensive cooling equipment and hence only very large units are expected to be economically viable. These drawbacks of hydrogen are abolished in the hydride form and the important constraint here is the price of the 'host metal'. The chemical reaction of exothermic hydride formation from metal (Me) and hydrogen (H2) is as follows: charging (heat released)
H2 +
Me ~
~ hydride + heat
(11)
discharging(heat added)
Hydrogen storage is regarded as important when long storage times are needed. The electrolyser is already available but a reliable hydrogen-oxygen fuel cell is still at the development stage. Rechargeable electric batteries are at present the obvious choice for storing electricity from solar cells. 7 A common feature of batteries is that electricity is
54
J. JENSEN, C. PERRAM
-I
current
elect;6ns
anode
electrolyte
1. cathode
I
e-
[ransport
@%
Fig. 10. An electrochemical energy source during discharge.
c o n v e r t e d i n t o c h e m i c a l - b o u n d e n e r g y d u r i n g c h a r g i n g . F i g u r e 10 shows the electrochemical system during discharge. B a t t e r y m a n u f a c t u r e is still d o m i n a t e d by the lead acid a c c u m u l a t o r invented by P l a n t + in 1860 b u t a d v a n c e d b a t t e r y d e v e l o p m e n t s have increased c o n s i d e r a b l y in i n d u s t r i a l c o u n t r i e s recently.S T a b l e 2 s h o w s a c o m p a r i s o n o f a n u m b e r o f c a n d i d a t e batteries, the p r o p e r t i e s o f w h i c h are briefly discussed below. L e a d a c i d : T h i s b a t t e r y is c o m m e r c i a l l y a v a i l a b l e in large q u a n t i t i e s at relatively low cost. It has been widely used as a s t a t i o n a r y b a t t e r y for local small-scale p o w e r
TABLE 2 COMPARISON OF F'ROPERTIES OF A N U M B E R OF ( ' A N D I I ) A T E BATTERIES
Lead acid
Nickel cadmium
Nickel zinc
Nickel iron
Lithium TiS 2
Electrolyte
HzSO.,
KOH
KOH
KOH
Vo tage ] Opea c rcu t (V))-~ Discharge 2h Self discharge
2.08 I-9 Medium -20 + 50 500 +
1.35 1.2 Low -30 + 50
Various organic 2.5 2.0 2.2 1.7 Low <75
Operating temperature ("C) Life (to 80 '~,,discharge) cycles Energy cfficiency (charge-discharge) Cost Capital (£/kWh) £/kWh cycle
75 30 0.075
2000
70 200 ~0-13
1.71 1.6 Mcdium -30 + 40
1.37 1.2 High 10 50
400
2000
75 ~ 70 ~0"21
50 60 ~ 70 ~ 0-044
> 250
25 <0.13
These figures should be regarded only as guidelines since they differ with battery design and duty. Some are projections from cell performance only. The cost figures relate to batteries developed mainly for other purposes and low loss batteries for solar electricity may well be more expensive.
SOLAR ELECTRICITY STORAGE SYSTEMS
55
generation, telephone exchanges, emergency supply units, etc. The overall cell reaction is: discharge
Pb + 2H2504 + PbO 2 ( - - - - ¢ P b S O 4 + 2 H 2 0 + PbSO 4
(12)
charge
The key problem with lead acid batteries is the need for careful maintenance. The major maintenance operation is the addition of water to make up for that which is lost by evaporation, electrolysis and self-discharge reactions. The final answer to this problem seems to be a battery of completely sealed cells such as the Gates system. However, the conventional lead acid battery may find some application for solar electricity, but only for large installations where service is available. Nicke~eadmium." This battery is commercially available in cell capacities of up to several hundred ampere-hours in sealed maintenance-free versions. The accepted cell reaction is: discharge
2NiOOH + 2 H 2 0 + Cd ~
) 2Ni(OH)2 + Cd(OH)2
(13)
charge
The Ni/Cd battery is widely used in small electrical appliances and the prospects for a future market in small solar cell units are encouraging. The price, which reflects materials problems (concerned with scarcity resources, handling and fabrication), is prohibitive for the widespread use of very large batteries. Nickel-zinc: The Ni/Zn battery is superior to the Ni/Cd battery in lower material cost, higher cell voltage and less toxic material contained. The cell reaction is: discharge
2NiOOH + 2 H 2 0 + Zn ~
) 2Ni(OH) 2 + Zn(OH) 2
(14)
charge
The main drawback for solar applications is short cycle life but there are good prospects that research in progress will lead to improvements. Nickel-iron." The cost is comparable with the more expensive type lead-acid batteries and the cycle life is long. However, the high self-discharge and the low overall efficiency, together with the need for maintenance resulting from hydrogen evolution, make it unsuitable for solar installations. Lithium-titanium disulphide. This cell is based upon an organic liquid electrolyte, conductive to lithium ions. These electrolytes have a rather high resistance, but this is not a disadvantage in matching with solar cells. The cell reaction proceeds via insertion of lithium ions between adjacent sulphur layers in the dichaleogenide TiS 2. The reaction is: discharge
xLi + TiS 2 (
) LixTiS2 charge
(15)
56
J. JENSEN, C. PERRAM
The cell voltage varies from 2.5 V to 1.9 V. The system potentially has a number of outstanding features. These include high energy density and long life, a leakproof seal and excellent stability over a wide range of operating temperatures. In addition, the Li/TiS 2 cell has a unique feature in its ability to indicate the level of its charge. The 'sloping voltage', simply monitored, indicates the level of capacity left. For small units, batteries seem to be the only technically and economically viable means of storage. 9 The features that make them particularly well suited for use with PV arrays are: The system input and output is in the form of low voltage dc electricity. They respond immediately to supply and load variations and are very reliable. It is possible to match the internal resistance of the battery to load for maximum power output. Modular construction allows flexible sizing and easy battery exchange. Batteries have a short lead time in manufacture. These advantages of battery storage apply to all sizes of solar installation: Set against these advantages are the relatively high capital cost and short lifetime of present day rechargeable batteries. With larger array installations ( > 1 kW) it may become more economic to electrolyse water and store the energy for solar cells as hydrogen, which is then converted to electricity in a fuel cell. A drawback of batteries is their limited temperature range of efficient operation. The solar panel, however, is especially suited for use in cold conditions because of its lack of moving parts and it is actually more energy efficient at lower temperatures.
SYSTEM STUDY
Electricity produced by solar cells can be converted so that it can be fed into a mains supply system, or it can be used for stand-alone systems such as that modelled in Fig. 11. In the following we deal primarily with systems of the latter type. Economic optimisation of a PV system such as that shown in Fig. 11 requires the identification and selection of individual system components which minimise the overall cost of the power produced over a particular time period. The cost of the electrical power depends on the solar insolation at a given locality; the system efficiencies, the costs of components and the match between load and insolation. This latter is the determining Jactor Jor the size of the storage necessary if a standalone system is to supply the load with I00 '.)/oreliability. With the cost of the solar cell array at its present level ( ~ $10/Wpk ) it is of particular importance to have accurate data on solar radiation in order to best utilise this incident radiation. Climatological data are available from several stations in
SOLAR ELECTRICITY STORAGE SYSTEMS
57
inpuf
I
control(~ I
E~ load Fig. 11.
System model for a stand-alone solar cell/battery storage system.
Europe over a period of several years. The most frequently available data records are those of global and diffuse radiation measured on a flat collector by means of a pyranometer. Since we are mainly concerned with collectors which are tilted from the horizontal, in order that the insolation flux is increased, it is necessary to calculate the radiation falling on such an inclined surface. Such calculations are
4000
3000
~c
2000
B o
1000
E
insolation
W/m 2
Fig. 12. Histogram of the number of hours:year (averaged over 8 years) that the mean hourly insolation is within each 100W/m 2 interval. The left end column is the number of" hours with zero insolation.
58
J. JENSEN, C. P E R R A M
based on certain assumptions as to the isotropy of the distribution of diffuse light over the whole sky. In our particular study we have used the model of Liu and Jordan l° which has been shown by Klucher ~l to be accurate for levels of insolation of less than 50 m W / c m 2 but to be up to 6 ~o inaccurate for larger insolations. The distribution of hourly insolation levels from zero up to a m a x i m u m of l k W / m 2 for Denmark (56 °N) is shown in Fig. 12. The relatively small percentage of time with an insolation level of over 50 m W / c m 2 shows that the errors involved in the model used are not significant. Figure 12 also shows the fraction (I4/) of peak power (Wpk) that can be expected to be achieved, e.g. ~70~o of the time W < 1/5Wpk and ~90~o of the time W < 1/2 Wpk. We also note that Wpk can be expected for only a few hours each year in Denmark.
OPTIMISATION
We consider a device consisting of a solar cell panel of area A m 2 connected to an electric battery with maximum capacity B kWh. The whole system is to be designed to meet a sequence of loads l I . . . . . 1NW over the N time periods t 1..... tN hours. During these periods, amounts of output energy, e I . . . . . e NJ/m 2 from the panels are used (after conversion) to service the load or, in the case where there is excess over the load, to recharge the battery if it is not full. We have assumed an overall battery efficiency of 70% and a total panel efficiency of 10~o. For a given battery capacity, B, the panel area, A, must be sufficiently large so that: N
Load L (in joules) = 3600 ~
N
tklK < A ~
K=I
eK
(16)
K-I
As the total energy over the whole period ~ e K tends not to vary too widely (see Table 3) and the load constraint is determined in advance, in practice, eqn. (16) gives a TABLE 3 SOLAR INSOLATION ON UNIT AREA OF A SOUTH-FACING PANEL WITH 45 o TILT
Year
(a) (b) (c) (d) (e) (f)
1962 1967 1965 1966 1961 1963
Yearly insolation ( J i m 2) x 10 9
Daily average insolation ( J i m 2) × 10 7
Standard deviation ( J i m 2) x 10 7
4.33 3.96 4.17 3-69 4-52 4-17
1.19 1.08 1.15 1.01 1-24 1.14
0.79 0-79 0.85 0.81 0.84 0.83
S O L A R E L E C T R I C I T Y S T O R A G E SYSTEMS
59
lower limit, A mi n tO A. Before we can optimise the parameters of the system, we must first find, in the form of a constraint, restrictions on A, B such that, for all inputs, eK, the load is met. The objective function we wish to minimise is the total cost, C, of the system, which may depend on quantities such as the unit cost of batteries and panels, installation costs and maintenance and replacement costs over the envisaged useful life of the system. This we write as:
C=A~ap+B~bq p
(17)
q
where ap and bq are the costs associated with solar panels and batteries, respectively. Costs of electronic controls are included in the battery costs, but the non-linear term describing reduced battery life caused by deep discharge is omitted in this preliminary analysis. Before we can apply standard programming techniques to this cost function we must formulate a load constraint. This will be a constraint g(A, B) upon A and B such that, at each time, tK, the load, /K, must be met. We have determined the function by simulation since the distribution of %. is non-Poisson, and analytic queuing techniques 12 cannot be used with confidence. Using hourly data available over a ten-year period in Denmark, and a system model as described, a computer simulation of a solar cell/battery system was developed. Daily insolation patterns over one year are shown in Fig. 13 for a 20 m 2 panel with 10 ~/efficiency. The relationship between the diffuse and direct radiation components is clearly shown. Because only direct radiation can be concentrated, the benefit to be gained by concentration in most areas is not considered to be of significance in such high latitudes. It should be noted that, for Denmark and Northern Europe in general, a large percentage of the total energy available is diffuse energy and it is the conversion of such diffuse energy in the winter period which makes the use of PV conversion feasible. Taking suitable initial values for A, B and an initial value B~, being the battery charge level at the beginning of the first period and available energy e 1, we follow the time dependence, Bj over the period of the simulation. If, at any stage, B2 = 0 and the load cannot be met, the simulation is stopped and the value of A incremented. If the load is maintained for the whole simulation, the value of B is reduced and the simulation repeated. In this way a curve g(A, B) can be obtained (Fig. 14). The differences from year to year are clearly large and it is important for absolute reliability of design that the 'worst possible' cases be considered. Figure 15 shows the feasible solution space for the economic optimisation using the 'worst possible' case. Using the simplified objective function described above and present costs of panels and batteries, we obtain an optimal value at C on the c u r v e i.e. at present we should choose as large a battery as possible and hence the minimum
60
J. JENSEN, C. PERRAM
o.,
o
selnof
m
c~ o -
x:
c~
o
8 c~
a
=c3
saln0f
L
c _
_
L
c~
m
m L
i
(salnof)
~6JeUa u01~oJp~j ~uepm3ul
61
SOLAR ELECTRICITY STORAGE SYSTEMS
100 ¸
"',.,.-,~. ,.. "t ~
B0"
....
?. i o:;
'i'\,
....
;
60-
1,t2
,,
..
". 'k ' .
• ,~..~, ~.... , , ,..
,,
"...
' .......................................
20
1~
z~
~
oAYs
Fig. 14. Relationships between panel area and battery capacity g(A, B) (for a constant 100 W load. in order that the load is fully maintained) for six different years using insolation data for Denmark.
loo
=
~D
Am°i~
,..~7- .-7 ~-
VT--T
7-
L',, ,~(/~/,,.,,b~ J / _
-
..
soluti
%
- ,(~j//
Ami.
J J
t
i"..... ._
J"
2O
0 0
1 20
I L~O
l 60
t 80 kwh
Fig. 15. The hand drawn minimum envelope of curves shown in Fig. 14. This is used to find the optimal combination o f panel area and battery capacity. A: concave envelope of load constraints g(A,B). B: linearised load constraint A.
62
J.
JENSEN,
C.
PERRAM
panel area possible. As the costs of solar panels are reduced, the minimum will move to D, with the battery component of the system assuming the dominant cost role. It is also possible to calculate the battery state-of-charge. Figure 16 shows such a diagram in the limiting case where the battery just fails to empty over a two-year period.
10
"6 L I
05
"6 i
c o .m t~ t._ t.a_
1962
Bati'ery
1963
si'a'fe-of-charge
curve
for jan 1 9 6 2 - dec 1963
Fig. 16.
Load = 50W, pane] area = 15m 2, battery capacity = 25 kWh.
This clearly shows the high discharge rates which occur during periods of low insolation as well as the extremely large battery capacities which are necessary to cope with this. The battery storage needs to cover 20 30 days' supply to ensure that a constant load can be maintained without excessively large panel areas. Using battery equivalents to 2000 and 1000 hours' storage, comparisons were made of the minimum panel area necessary for a 100 W constant load in Denmark and Carpentras, France (44°N) (Fig. 17).
63
SOLAR ELECTRICITY STORAGE SYSTEMS 100 I
8O E
o E
"1
.~_ ._ E
.J 20
.J
~ 0
100
I 200
300
400
; 500
L 600
J 700
L
i
800
900
constant load (watts} Fig. 17. Relationship between m i n i m u m panel area required to maintain a constant load throughout the year and the load size. Curves are shown for two battery capacities and two locations. 1 Battery capacity 1000 hours" storage for Denmark (1961, 1966). I[ Battery capacity 2000 hours" storage for Denmark (1961, 1966). Ill Battery capacity 1000 hours" storage for Carpentras (only one year available). IV Battery capacity 2000 hours" storage ['or Carpentras (only one year available).
PRACTICAL SYSTEM DESIGN PROBLEMS
The general problem of matching the internal resistance, R i, of a power source to the resistance of the load, R/, in such a way that m a x i m u m power is delivered to the load also applies to solar cell/battery systems. With a linear relationship between voltage and current, the plot of power in the load (Pt) as a function o f the load resistance (R/) can be drawn as shown in Fig. 18 : P/max is obtained when R t = R i.
R[ = R i
Fig. 18.
R! {nl
Load power as a function of load resistance.
64
J. JENSEN, C. PERRAM
Although neither solar cells nor batteries exhibit linear characteristics (Figs 19 and 20) the simple linear model used to derive the above maximum conditions stresses the importance of matching R i and R~ to be of the same order of magnitude for maximum power output. Because the internal resistance of solar cells is several orders of magnitude higher than that of generally available batteries, a combination of solar cells in series (to match the battery voltage) and in parallel (to match the resistance) is necessary. Unfortunately, the high resistance and low voltage of a solar cell compared with most battery cells make this matching difficult to effect and hence a higher resistance battery cell may be necessary.
constant region _~
2.66
current
ISC~ 2.50
maximum . power point_
2.28 I/)
~~
~ 1.9o E
constant
\ region voltage
1.52 _ 2 "~ 1.14
_
+50 °C
L'28°C /-t~O°
0.76 0.38
Voc\ 1 5
10 15 20 25 array voltage, volts
30
Fig. 19. Solar array voltage-current characteristics. Array size: 36 series, 4 parallel strings of 2in diameter Si-cells for insolation 100 m W / c m 2, Csc = short circuit current, Voc = open circuit voltage. Source: reference 13.
Further, electronic power conditioning--which controls the transfer of energy from the panels to the batteries--is necessary as the power delivered by the cells fluctuates greatly, and thus power transfer efficiency can be significally reduced. Matching the load to the generator for maximum power tracking a4 can be achieved by the use of high efficiency transistor choppers to form a self-adaptive power flow control system.
65
SOLAR ELECTRICITY STORAGE SYSTEMS
25 Ah BATTERY
25%
'C,6(~i25 %
II 50% Chorged .. CURRENT
(A)
50mW/cm 2 25%
"~-~
10 mW/c m-~
25% I 4
"--~ I 8
j, i 12
\ /
~ 16
I 20
VOLTAGE Fig. 20.
Current voltage characteristic of 25 Ah storage battery.~5
CONCLUSIONS
If solar electricity is to become a viable alternative power source then the development of the storage system is as important as the development of the array system. Because of the particular properties of batteries outlined above they are the obvious choice for use in PV systems at present. The demands placed on batteries used in PV systems, particularly in areas of variable insolation such as northern Europe, are exacting. The requirements are for: reliability; high overall efficiency; long cycle life; low self-discharge; good charge retention and the ability to overcome deep discharge. These, along with low overall cost demands, are not fulfilled by any battery available at present. There is therefore need for the development of new batteries specifically designed for PV systems.
66
J. JENSEN, C. PERRAM
ACKNOWLEDGEMENTS The authors wish to acknowledge discussions with a number of colleagues within the Anglo-Danish advanced battery research programme. Support for this work was o b t a i n e d f r o m E E C C o n t r a c t s 315-78 E E ( D K ) a n d 3 1 6 - 7 8 E E ( U K ) a n d t h e D a n i s h Department of Energy.
REFERENCES I. P. RAPPAPORTand L. M. MAGID, Prospects and opportunities in photovoltaics, Proc. o/2nd EEC Photovoltaic Solar Energy Con/erence, April, 1979, Berlin, p. 21. 2. M. WIHL and A. SCHEININEA,Analysis and simulation of the energy source of the future: The solar breeder, Proc. o/ 13th IEEE Photovoltaie Con/erenee, 1978. 3. K. J. Euler, Methods of accumulating electricity, ESRO Summer School, August, 1968. 4. J. JtZNSEN, Energy storage, Newnes-Butterworths, London, 1979. 5. R. PosT and S. POST, Flywheels, Scientific American, 229 (December, 1973), pp. 17-23. 6. A. R. MILNER, A flywheel energy storage and conversion system for photovoltaic applications, International Assembly on Energy Storage, Dubrovnik, Jugoslavia, May, 1979. 7. J. JENSEN,C. PERRAMand R. M. DELL, Batteries for solar electricity, Proc. 1979 Photovoltaie Solar Energy Conference, Berlin 2~26 April, D. Reidel Publ. Co., 1979, pp. 610- 20. 8. B.C. TOF~ELD~R. M. DELL and J. JENSEN,Advanced batteries, Nature, 276(5685) (1978), pp. 217 20. 9. J. JENSEN, P. MCGEEHm and R. M. DELL, Electric batteriesfor energy storage andconservation--An application study, Odense University Press. 1979, pp. 225. 10. B. Y. L~u and R. C. JORDAN,Daily insolation on surfaces tilted towards the equator, ASHRAE Transaction No. 1762 (1962), pp. 526-41. I 1. T. KLUCHER, Variation of solar cell sensitivity and solar radiation on tilted surfaces, Proc. of 13th IEEE Photovoltaie Confi'rence, 1978. 12. HAMDYA. TAHA, Operations research, MacMillan Publishing Co., Inc., New York, 1971. 13. ABBASA. SAHM, Regulation and Control Array Power--A minimum Power Dissipation Approach, Proc. oJ 13th IEEE Photovoltaic Confi, rence, 1978, p. 121. 14. P. L. SWARTand J. J. rAY WYK, Source tracking and power flow control of terrestrial PV panels for concentrated sunlight, Proc. oJ 13th IEEE Photovoltaic Confi, renee, 1978, p. 700. 15. P. E. BAIKIL Battery storage in solar cell systems, UK Section ~1 the International Solar Energy Society, Technical Meeting. May 5, 1978.