DESIGN OF HYBRIDPHOTOVOLTAIC POWER GENERATOR, WITH OPTIMIZATION OF ENERGY MANAGEMENT

Two parameters were used to characterize the role of the engine-generator: denoted SDM and SAR, they are, respectively, the battery charge threshold at which it is started up, and the st

1999 Elsevier Science Ltd

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Pergamon P I I : S 0 0 3 8 – 0 9 2 X ( 9 8 ) 0 0 1 3 9 – X All rights reserved Printed in Great Britain

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DESIGN OF HYBRID-PHOTOVOLTAIC POWER GENERATOR, WITH

OPTIMIZATION OF ENERGY MANAGEMENT

†

M MUSELLI , G NOTTON and A LOUCHE

Universite de Corse-URA CNRS 2053, Centre de Recherches Energie et Systemes, Route des Sanguinaires,

F-20 000 Ajaccio, France Received 26 February 1998; revised version accepted 14 October 1998

Communicated by ROBERT HILL

Abstract—A methodology is developed for calculating the correct size of a photovoltaic (PV)-hybrid system

and for optimizing its management The power for the hybrid system comes from PV panels and an engine-generator – that is, a gasoline or diesel engine driving an electrical generator The combined system is a stand-alone or autonomous system, in the sense that no third energy source is brought in to meet the load Two parameters were used to characterize the role of the engine-generator: denoted SDM and SAR, they are, respectively, the battery charge threshold at which it is started up, and the storage capacity threshold at which

it is stopped, both expressed as a percentage of the nominal battery storage capacity The methodology developed is applied to designing a PV-hybrid system operating in Corsica, as a case study Various sizing configurations were simulated, and the optimal configuration that meets the autonomy constraint (no loss of load) was determined, by minimizing of the energy cost The influence of the battery storage capacity on the solar contribution is also studied The smallest energy cost per kWh was obtained for a system characterized by

an SDM 5 30% and an SAR 5 70% A study on the effects of component lifetimes on the economics of PV-hybrid and PV stand-alone systems has shown that battery size can be reduced by a factor of two in PV-hybrid systems, as compared to PV stand-alone systems  1999 Elsevier Science Ltd All rights reserved.

1 INTRODUCTION the physical, technical and economical hypothesis,

in Section 2, in which the detailed sizing

meth-As opposed to the PV-only system, the PV-hybrid

odology is also explained Section 3 examines the system – consisting of a photovoltaic system

effect of the battery storage capacity on the solar backed-up by an engine-generator set – has

contribution and the effect of the engine-greater reliability for electricity production, and it

generator’s operating strategy on the energy costs often represents the best solution for electrifying

Finally, an economic study is reported that com-remote areas (van Dijk, 1996) The

engine-pares the roles of the various subsystems in generator set (or simply engine-generator) reduces

determining the lifetime of the total system the PV component size, while the PV system

decreases the operating time of the generator,

ment costs This study’s primary objectives have

2.1 System configuration

been (i) to develop a sizing methodology for

PV-hybrid systems that supply small and medium The system (Fig 1) consists of a PV array, a power levels to remote areas, and (ii) to study the battery bank, a back-up generator (3000 rpm or influence of load profiles and of certain engine- 1500 rpm) driven by a gasoline- or diesel-engine, generator parameters, such as their type, starting a charge controller, and an AC / DC converter threshold, and stopping threshold A case study of The engine-generator will be used only as a the approach developed is performed for Ajaccio, battery charger (this reduces its required rated

A brief description of the overall sizing meth- the nominal battery capacity, Cmax

odology is presented in Section 1 The paper gives

2.2 Description of the sizing method

The system must be autonomous, i.e the load must be totally met by the system at all times

†Author to whom correspondence should be addressed Tel.:

Such a constraint still permits an infinite number 133-4-9552-4141; fax: 133-4-9552-41 2; e-mail:

muselli@vignola.univ-corse.fr of possible system configurations From solar

143

Fig 1 Sketch of the PV-hybrid system studied.

radiation data and from assumed daily load pro- and have a higher price than conventional files, the system behavior can be simulated, and a appliances

system meeting the constraints can be sized In our study, two possible hourly DC-load profiles However, finding the best system must be done on have been chosen to represent the load The first, the basis of an overall systems approach First, the ‘Low Consumption’ profile (Fig 2), is based certain physical and technical constraints are used on ‘adapted’ loads It has a mean daily energy

to reduce the system parameters to a realistic consumption of 1.8 kWh per day and a peak domain Then minimizing the energy cost leads to

the optimal solution

3 OPERATING AND DESIGN SIMULATIONS

3.1 Solar irradiation and load profiles

The sizing of PV-hybrid systems for Ajaccio

will be based on 19 years of hourly total

irradia-tion on a horizontal plane, collected at the site

The PV modules will be tilted, and so hourly total

irradiation on tilted planes had to be computed,

and this was done using the models of Hay and

Davies (1980); Orgill and Hollands (1977) The

resulting errors (RMBE 5 1.4% and RRMSE 5 Fig 2 ‘Low Consumption’ load profile used in the study.

7% for Hay and Davies model; RMBE 5 2

2.41% and RRMSE 5 8.81% for the Orgill and

Hollands model) have been shown to be quite

small (Poggi, 1995) for the site In this way,

hourly values of solar irradiation, I (t), on the PVb

array were calculated for a tilt angle of 308, and

this data provided the input data of the

simula-tions

Two different types of load can be identified:

1 That provided by ‘conventional’ appliances

available on the market that typically have a

low energy efficiency and have been optimized

not from an energy point of view, but rather

from a quality–price point of view;

2 That provided by ‘adapted’ or ‘high efficiency’

appliances that are rather scarce on the market Fig 3 ‘Standard’ load profile used in the study.

Design of hybrid-photovoltaic power generator, with optimization of energy management 145

power demand of 170 W, which occurs in spring and for these supports, the average price falls to and autumn The second, the ‘Standard’ profile $US 0.83 / Wp (0.69 ECU / Wp)

(Fig 3), is based on the French utility data Battery bank: The battery bank can be char-(EDF), as reported by Eliot (1982) It has a daily acterized by its nominal capacity Cmax, its (maxi-average load of 3.7 kWh per day and a peak mum) depth of discharge DOD, taken in this study power of 680 W, the latter occurring in the to be 70% (Tsuda et al., 1994), and two

conver-summer For each profile, the consumption is sion efficiencies rch and rdch, respectively, for

represented by a sequence of powers P (t), eachc charge and discharge, which were taken to equal taken as constant over the simulation time-step, to 85% (Oldham France, 1992; Manninen and

Dt, which is normally taken as 1 h. Lund, 1989) The cost of the battery is quite

significant, because the initial investment is high and the battery has to be replaced several times

3.2 System characteristics

during the PV system lifetime The battery bank

3.2.1 Photovoltaic subsystem PV modules: typically accounts for about 40% of the total For the PV subsystem, we assume a constant PV system cost (Notton et al., 1996a) Costs of

efficiency hPV of 10% The PV power production batteries per kilowatt-hour stored capacity are

P (t) is then computed as the product of the PVp plotted in Fig 4, for the various battery types

efficiency, the hourly irradiation I (t) and the PVb marketed by several French suppliers The battery module area, as has been proposed by several cost is strongly affected by its type; in particular, works (Iskander and Scerri, 1996) The ‘peak- whether it is the stationary type used in many PV Watt’ (or ‘Wp’) price was used as a fixed econ- applications or the starter type more readily omic parameter, as has been done by several available in developing countries

Frequently-en-authors (Keller and Afolter, 1995; Biermann et countered are costs of $US 130 / kWh and $US

al., 1995) It was set equal to $US 5.8 / Wp (5 217 / kWh (110 and 183 ECU / kWh) Thus, an ECU / Wp), in accordance with the prices of the average price of $US 180 / kWh (150 ECU / kWh) French producer PHOTOWATT and others sup- may be used for estimating the battery cost The

Module supports: A literature survey shows such as the charge–discharge rate, temperature that the costs of module supports are in the range and maximum discharge; it is very difficult to

$US 0.35 / Wp (0.28 ECU / Wp) to $US 1.9 / Wp correlate the lifetime with these parameters Based

(1.5 ECU / Wp) (Imamura et al., 1992; Palz and on our own experiences, a battery lifetime equal Schmid, 1990) Using data collected from four to five years has been considered in this work

PV suppliers (Wind and Sun, Eurosolare, Photo- Charge controller: Regulator costs vary widely watt, Siemens), support costs per Wp versus the Not all regulators work on the same electronic number of modules per frame are equal to $US principle, and they can include special options, 1.63 / Wp (1.28 ECU / Wp) However, generally such as lightning protection, digital displays, etc

PV frames are used with four modules or more, We estimated the average price to be $US 0.65 /

Fig 4 Price of battery storage as a function of the nominal battery storage capacity.

Wp (0.55 ECU / Wp) (Iskander and Scerri, 1996), where PG and Q are the generator power (kW)v

which is close to the GTZ value (Biermann et al., and the hourly consumption (l / h), PG and Q arev

1995), and we based our model on this price respectively the rated power and the consumption Photovoltaic subsystem installation cost: There at this rated power, and PCI is the heating valuev

21

is considerable experience in the installation of of the fuel (PCIv / diesel510.08 kWh?l and

21 small PV systems In some PV-system projects in PCIv / gasoline59.43 kWh?l )

Corsica, the installation cost was 25% of the PV The ratio Q /Pv G is the specific consumption, panel cost, and this is in agreement with some defined as the fuel consumption required to

references (Illiceto et al., 1994; Paish et al., 1994; produce, at nominal power, one kilowatt-hour of Abenavoli, 1991) Thus this percentage was used energy Using a power law model for the

Photovoltaic subsystem O&M cost: Concerning have:

Q 5 0.7368.P (3)

PV system investment, and a PV system lifetime

and assuming a constant value of 0.3 l / kWh

of 20 years (Notton et al., 1998).

(Thabor, 1988; Calloway, 1986) for diesel

en-3.2.2 Engine-generator subsystem.

Engine-gines, allows the determination of the reduced generators may be compared using many different

consumption versus reduced power:

characteristics, including fuel consumption, motor

2 for diesel generators: 05 0.22 1 0.78 0

the faster the wear of the parts and the shorter the

(4) lifetime; thus, a 3000 or 3600-rpm engine can

v

]

2 for gasoline generators: 5

Qv

must also compare gasoline engines with 1500

P

]

G

indices of the engine-generator‘s role, at least so

As an example, g 50.22 and j 50.78 for all diesel far as the simulations are concerned SDM and

generators, and g 50.29 and j 50.71 for a 2-kW SAR are the thresholds in battery charge at which

gasoline engine We note the presence of a the engine-generator is switched on or off,

respec-consumption at zero load: 20% and 30% of the tively, each expressed as a fraction of the battery

full load for diesel and gasoline back-up capacity

generators These results are in agreement with Fuel consumption: A back-up generator is

recent works (Beyer et al., 1995a).

characterized by its efficiency h and its consump-c

By using data collected from back-up generator tion in relation to the produced electrical power as

manufacturers, we have computed the efficiencies follows:

for each type of generator, and summarize these

]]]

PCI Qv v Engine-generator price: The engine price

de-pends on nominal power, the price per unit kW,

]05g 1 j ]0

has been used:

PG PG PG

5 1 2F h PCI Q0G F1 h PCI Q0G P0 C 5 C (P )G 0 G (6)

(2) where CG is the cost per kW of engine-generator

0

Table 1 Nominal engine generator efficiencies (h ) c

Minimum Maximum Standard Average value (%) value (%) deviation (%) value (%)

Design of hybrid-photovoltaic power generator, with optimization of energy management 147 Table 2 Statistical coefficients for the prices of back-up generators (Eq (6))

capacity, C the cost coefficient, and a the scale0 way, 1986; Cramer et al., 1990; Energie Relais,

factor The coefficients in this equation, obtained 1995; Sandia National Laboratories, 1990;

by fits to data provided by French suppliers, are Energelec, 1995) are very different; we used a

3000-Components of the engine-generator: We have rpm and 1500-rpm engine generators respectively allowed for a fuel storage tank, at a price of $US Engine-generator installation cost: According to 1.7 / l (1.43 ECU / l), in accordance with literature Paish et al (1994); Calloway (1986), the

engine-from the French manufacturer GENELEC The generator installation cost is equal to 10% of the storage capacity is taken to be the equivalent of initial investment for the engine-generator This

20 h of continuous engine-generator operation (in includes bedding, exhaust, and automatic control fact the engine runs for only a few hours a day, on costs

The fuel price is strongly dependent on the the installation cost of an engine-generator system energy policy of the country A study (Hille and is relatively low, the annual O&M cost is rela-Dienhart, 1992) illustrated the diversity of fuel tively high It is often estimated as being propor-prices Prices range from $US 0.02 / l (0.016 tional to the total hardware cost (Biermann et al.,

ECU / l) to $US 0.75 / l (0.63 ECU / l), the last 1995; Paish et al., 1994; EGAT, 1990) The

figure representing that in developing countries proportionality constant ranges from 5% to 20% Transport costs can increase the fuel price by $US However, such an hypothesis must be considered 0.12–$US 0.23 / l (0.1 ECU–0.19 ECU / l) for prudently, because the more an engine-generator each 1000 kilometers of distance the fuel must be runs, the more costly is its annual maintenance; moved by ground transport, and this is increased thus, it is good to take into account the annual

by a factor of nearly 40, if air transport is used operating time of the engine-generator

We have considered a price of $US 0.55 / l (0.46 (Abenavoli, 1991; Calloway, 1986) Recently, ECU / l) and $US 1.15 / l (0.97 ECU / l) for diesel some authors have calculated the maintenance and gasoline fuels, respectively cost as a fixed cost per kWh, thus linking it to the Engine generator lifetime: The engine-genera- operating time (Benyahia, 1989)

tor lifetime is expressed as a function of the Faced with all these various assumptions in the operating hours Table 3 summarizes the predic- literature, we estimated the O&M cost based on tions available in the literature For gasoline the cost and occurrence of various maintenance engines, in accordance with the great majority of operations; thereby, the O&M cost (including oil authors (Sandia National Laboratories, 1990; changes) is linked to the operating time Our Energelec, 1995), we have used the mean value of assumptions are (i) that oil (costing 4.49 $US (3.8 the range, which is an engine lifetime equals to ECU) per l) is replaced every 100 h for all

3500 h For diesel engines, the 1500-rpm diesel gasoline and all 3000-rpm diesel engines, and lifetime is greater than the 3000-rpm diesel life- every 150 h for all 1500-rpm diesel engines; (ii) time, because of the reduced rotational speed of that skilled laborer costs are $US 21.8 / h (18.5 the generator The literature predictions (Callo- ECU / h); (iii) that each oil change, complete with

Table 3 Back-up generator lifetime in hours (literature)

Beyer et al (1995a) Diesel 30 000

Energie Relais (1995) Diesel 1200

Sandia National Laboratories (1990) Gasoline 2000 to 5000

Sandia National Laboratories (1990) Diesel 6000

Energelec (1995) Diesel 3000 8000

Energelec (1995) Diesel 1500 12 000

an air-filter cleaning, requires 40 min of skilled consumed energy L(T) over the same period.

labour, (14.80 $US or 12.5 ECU); (iv) that the oil Thus

after every two oil changes; (v) that the air-filter L(T ) 5OP (t).dt 5hc PV.SRef.H (T )b (11) (10.9 $US or 9.2 ECU), and the fuel filter (5.4

$US or 4.6 ECU for gasoline and 10.9 $US or 9.2

where H (T ) is the global daily irradiation inci-b ECU for diesel engine) and the spark plugs (4.6

dent on PV modules inclined with an angle b and

$US or 3.9 ECU for gasoline engine) are changed

the summation is taken over all the days in the after four oil changes Each of these operations

period T We then define the dimensionless PV

take 2 h (43.7 $US or 37 ECU) Accordingly, the

area SDim as the ratio of the actual module area to O&M costs (in ECU / h) are to be computed from

the reference area SRef the following equations:

We also define a dimensionless storage capacity

(i) for gasoline engines, CO& M5(0.4005 C, which is expressed in terms of days of

autonomy C is obtained by dividing the actual

1 0.1532.Pgene) 3 15.2 1 120.1/ 400 (7)

storage capacity by the annual mean of the daily load consumption:

(ii) for 3000 rpm diesel engines, CO& M

C

]]

Ldaily

(8)

3.4 PV-hybrid system behavior Simulation (iii) for 1500 rpm diesel engines, CO& M

calculations

5(0.242 1 0.3505.Pgene) 3 15.2 1 120.8/ 600

The system simulation is performed by consid-(9) ering a Loss of Load Probability equal to 0%; in other words, the system reliability is 100%,

Notton et al (1997) have shown that the above

leading to autonomy for the system

costing hypothesis is consistent with the findings

Given the values of irradiation on tilted planes

of several earlier studies

and the consumption patterns previously de-Battery charger: The nominal power of the

scribed, the system behavior can be simulated battery charger is related to its nominal storage

using an hourly time step-several workers (Man-capacity One must take into account that the

ninen and Lund, 1989; Beyer et al., 1995b)

electrical current produced by the generator must

having shown that the simulation of PV systems not be greater than one fifth of the ampere-hour

requires only an hourly series of solar data Based capacity of the battery (Sandia National

Lab-on a system energy balance and Lab-on the storage oratories, 1990):

continuity equation, the simulation method used

Cmax

Considering the battery charger output power

A battery charger’s efficiency hcharger is equal to

P (t), the PV output power P (t) and the load

power P (t) on the simulation step Dt, the battery

energy benefit during a charge time Dt is given

by (Dt ,Dt):

and the statistical errors associated are as follows: 1

C 51099, a 5 20.691, MBE5 2113 $US / kW,0

C (t) 5 r E [P (t) 1 P (t) 2 P (t)] dt (13)

Dt1 3.3 Relevant dimensionless variables

The battery energy loss during a discharge time Two dimensionless variables characterize the

Dt is given by (Dt ,Dt):2 2

PV-hybrid system: the PV module surface and the

battery storage capacity; both are independent of

1 the daily load For the PV area, we first define a

]]

C (t) 5 E [P (t) 1 P (t) 2 P (t)] dt

reference area, Sref as the PV module area (m ) rdch

Dt2 that will produce, over the simulation period T

Design of hybrid-photovoltaic power generator, with optimization of energy management 149

The state of charge of the battery is defined SOC is compared with the intrinsic parameters

Cmin the system is failing and if SOC(t).Cmax,

C(t) 5 C(t 2 Dt) 1 C (t) 1 C (t)1 2 (15) the system produces wasted energy.

By simulating many PV-hybrid systems having

If C(t) reaches SAR by an energy benefit C (t)1

the same load, one can, in principle, find an during the charge period with the

engine-genera-infinite set of physical solutions, each solution tor working, the generator has to be stopped and

being characterized by a PV module area SDim, a

the charge time Dt1 during Dt is calculated

storage capacity Cmax, and a nominal engine-assuming a linear relation:

generator power Each solution defines a ‘pair’

Dt1 SAR 2 C(t 2 Dt) (SDim, Cmax) Several technical constraints, for

]Dt 5U]]]]]C (t)1 U (16) example, the available products, reduces the

infinite number of solutions to a finite number of Moreover, if during the discharge period when the configurations For each configuration, some

engine generator is stopped, C(t) reaches SDM, physical variables are calculated by simulations: the motor is started and the discharge time Dt2 the wasted energy, the working time and the fuel during Dt is calculated by a linear relation as: consumption of the engine- generator, and the

times when certain subsystems need replacement

Dt2 C(t 2 Dt) 2 SDM

]Dt 5U]]]]]C (t) U (17) The energy cost is then computed for each pair,

2

and the minimization of this parameter yields the optimal operating configuration

As an input of a simulation time-step Dt (taken as

1 h), several variables must be determined: PV

output power, load power, battery state of charge,

4 SIMULATION RESULTS

and back-up generator state (ON or OFF) in the

previous time-step A battery energy balance

4.1 Operating mode

indicates the operating strategy of the PV-hybrid

To illustrate the battery energy state evolution system: charge (energy balance positive) or

dis-as a function of the engine-generator thresholds, charge (energy balance negative) Some tests are

we have plotted in Figs 5 and 6, which show, necessary to study the SOC variations as

com-respectively, the energy stored and the engine-pared to the starting and stopping thresholds If

generator operating hours as a function of time,

SOC(t) falls below SDM, the motor is started; and

over five days Assumed parameter settings for

if SOC(t) exceeds SAR, it is stopped So, the

the figures are as follows: C 5two days, the initial

charge and discharge times (Eqs (16) and (17))

charge on the battery5100% of capacity, dimen-must be calculated on the simulation time-step in

sionless PV module surface50.94, SDM530% order to compute the different energy flows in the

and SAR550%, 70% and 100% Also, the ‘Low system (Eqs (13) and (14)) Then, the battery

Fig 5 Evolution of the battery state of charge for several assumed values of the thresholds (SDM, SAR) governing the operation

of the engine-generator.

Fig 6 Plot of the back-up generator operating time for several assumed values of the thresholds (SDM, SAR) governing the

operation of the engine-generator.

Consumption’ load profile was used, and a nominal engine-generator power is undersized and

the remainder of this paper, only batteries with

4.2 PV-hybrid system sizing curves capacities greater than to two days will be

consid-Fig 7 presents the solar contribution (defined ered

as the percentage that the PV production is of the Fig 8 presents the sizing curve, as obtained total energy production) versus dimensionless assuming the Standard load profile, the SDM and storage capacities (one to six days) These plots SAR are equal to 30% and 80%, respectively, and have been parameterized using dimensionless PV a gasoline-driven engine The existence of some areas ranging from 0.81 to 1.44 We concluded ‘discontinuities’ in Fig 8 are due to the number of that it was not necessary to consider a PV-hybrid changes of the engine-generator with the decrease system with a storage capacity greater than two or in dimensionless PV areas The optimal configura-three days of autonomy Sidrach de Cardona and tion, i.e., the one corresponding to the lowest Mora Lopez (1992) have obtained the same energy cost, is determined for each sizing curve conclusion considering a PV-hybrid system in In Figs 9 and 10 (which apply to ‘Low Consump-which the back-up generator was applied directly tion’ and ‘Standard’ profiles respectively), we

to the load and to a battery charger, at the same have plotted the sizing curves parameterized by time The simulations demonstrate that for a the storage capacities (two to six days) for

Fig 7 Solar contribution (%) as a function of dimensionless storage capacities 2 to 6 days.

Design of hybrid-photovoltaic power generator, with optimization of energy management 151

Fig 8 Sizing curve of PV-hybrid systems for a gasoline engine, ‘Standard’ load profile, and SDM and SAR equal to 30% and

80%, respectively.

The lowest points on the curve define the (SDim50.97, 0.95 and 0.73 for the three cases in

optimal configuration Although the locations of Fig 11) The optimal size of the engine generator the lowest points are indistinct around the optimal is easily deduced from the optimal capacity (two point, the optimal configuration is always ob- days) and from Eq (10), by dividing the battery tained when the storage capacity equals two days charger rated power by the charger efficiency

of autonomy These findings have been confirmed hcharger

for other values of the starting and stopping For the combinations of SDM and SAR and for

To make these results more general, a sensitivi- combined the solar contribution curves obtained

ty analysis of the energy costs to various parame- for a battery capacity of two days to deduce ters must be performed A short sensitivity study optimal solar and fossil fuel contributions for each

presented in a previous paper (Notton et al., engine-generator type, and these are given in 1998) confirmed the main conclusions shown Table 4

al (1996b) applied such an optimization to a

4.3 Influence of the back-up generator hybrid-system, but without including the

engine-operating strategy generator behavior in the system simulation In

In accordance with the above results, a storage that work, the stand-alone PV system without the capacity of two days will be used for the analysis engine-generator had been sized for several

loss-of the back-up generator operating strategy Also, of-load probabilities, and then the energy deficit the energy cost has been calculated for various was supplied by the engine-generator This con-combinations of SDM and SAR, by varying them figuration has led to identical optimal

contribu-by steps of 10%, (i.e., SDM[[30%; 90%] and tions (75% solar and 25% fossil), whichever the SAR[[40%; 100%]) For each combination, we engine type In this study, the results have been computed the optimal pair leading to the lowest found to depend on the engine type The varia-energy cost Fig 11 presents the results for each tions in the contributions for the diesel 1500-rpm engine type and for both load profiles The type can be linked to its longer lifetime, which optimal configuration is obtained when SDM5 leads to reduced replacement costs The results 30% and SAR570%, regardless of the load are very dependent on the lifetime and mainte-profile and the engine-generator type nance of the engine, and have been calculated by Thus we have now demonstrated that the optimizing these two parameters (Notton et al.,

optimal size of the battery capacity is two days 1997)

and the best energy management is obtained when

4.4 Wasted energy

SDM and SAR are respectively equal to 30% and

70% of the nominal storage capacity The optimal We have also studied, over a given time period,

PV area for each configuration is close to unity say T, the influence of the engine-generator

Fig 9 Sizing curves obtained for a storage capacity ranging from 2 to 6 days of autonomy, for each engine type (The Low

Consumption load profile is assumed).