F. Lasnier and W. Y. Juen, The sizing of stand-alone pho- tovoltaic systems using the simulation technique. RERIC. International Energy Journal 12( l), 21-39 ...
Solar Energy,
Vol.54,
No. 2, pp. 99-104, 1995 1995 Elwier Science Ltd Printed in the USA.All rightsreserved
Copyright0
Pergamon
0038-092X/95 $9.50+ .OO 0038-092X( 94)00091-3
PHOTOVOLTAIC
SYSTEMS
SIZING FOR ALGERIA
A. HADJ ARAB, B. AIT DRISS, R. AMIMEUR, and E. LORENZO* Centre de Developpement des Energies Renouvelables, BP 62 Bouzareah, Algiers, Algeria; *E.T.S.I. de Telecomunicacion, 28040-Madrid, Spain Abstract-The purpose of this work is to develop an optimization method applicable to stand-alone photovoltaic systems as a function of its reliability. For a given loss-of-load probability (LLP), there are many combinations of battery capacity and photovoltaic array peak power. The problem consists in determining the couple which corresponds to a minimum total system cost. The method has been applied to various areas all over Algeria taking into account various climatic zones. The parameter used to define the different climatic zones is the clearness index KT for all the considered sites. The period of the simulation system is 10 years.
and maxima1 monthly clearness indexes (KT,,,,, and KT,,) for all the considered sites. The interval (KTmi”, KT,,,,,) is divided into five subintervals. The monthly average clearness index of each site is located in the corresponding interval. The five intervals obtained are: ?? 1st interval: 0.424 < KT < 0.486 ?? 2nd interval: 0.486 < KT < 0.548 ?? 3rd interval: 0.548 < KT < 0.609 ?? 4th interval: 0.609 < KT < 0.67 1 ?? 5th interval: 0.671 < KT =G0.733
1. INTRODUCTION
The design method is applied to areas all over the Algerian territory. The design of the photovoltaic system depends on the location of these sites. The diversity of the Algerian sites comes mainly from the influence of the sea and the latitude and altitude variations. The radiation at regions near the sea is influenced by the seasons. The zones of north Algeria are more sky-covered than those of the south. The Saharian regions receive a greater amount of energy but are characterized by higher air temperatures. These desert sites are better candidates for photovoltaic installations. The difficulties of conventional electrical grid extension or diesel power generation as suggested by Benyahia and Ait Driss ( 1990) are avoided because they are remote and cover a large area. The first studies that led to the definition of the climatic zones in Algeria were based on hygrothermal considerations. Detailed description of this definition is given by Bore1 ( 1962) and Boudiaf ( 1984). The present work uses another approach in dealing with photovoltaic systems. It is based on energetic considerations, mainly, the ground-level solar radiation. The design of a photovoltaic installation for an electric load supply with a minimal cost is a complex problem in which many parameters must be taken into account. These parameters include climatic data, components cost, and a temporal distribution of the electric load. The prediction of the stand-alone photovoltaic system performance requires the use of unpredictable, day-to-day variations of solar radiation and the load profile. Generally, it is not sufficient to use seasonal or monthly mean values for these parameters in the design of photovoltaic arrays with storage batteries. The choice of sites in this study is dictated by the radiometric data available and the geographic location (Table 1) . 2.
The sites are classified in Table 2 corresponding to their clearness indexes. The four zones are bound in the following limits: ?? 1st zone: KT < 0.548 ?? 2nd zone: 0.548 < KT G 0.609 ?? 3rd zone: 0.609 < KT G 0.671 ??
4th zone: KT > 0.671
The stations are shown in Fig. 1 with the different zones. 2.2 Determination of loss-of-load probability The method used for the estimation of the optimum couples of battery capacity (C’s) and photovoltaic array peak power (PC) is based on the determination of the loss-of-load probability (LLP). The way to calculate this probability is based on a simulation with real-time solar radiation data for a given photovoltaic array peak power, PC, and storage capacity, C’s. The disadvantage of this method is that it is necessary to know daily radiation data for a long period of time ( 10 years, for example). Unfortunately, measured radiation data cannot be provided for many sites over the world, and where they are available they are provided for a short time period. This inconvenience can be solved by using synthetic solar radiation data which are generated from monthly mean clearness index values as proposed by Aguiar et. al ( 1988). The design criterions are the installation cost and its reliability. For a given LLP there are many couple sets (Cs, PC). The problem consists on the determination of the couple (Cs, PC) which corresponds to a minimum total system cost. It is possible that the power requested by
METHODOF CALCULATION
2.1 Climatic zone distribution The method used to define the different climatic zones is based on the determination of the minima1 99
100
A.
HADJ ARAB et al.
Table 1. Geographical location of the station
no 1
2 3 4 5 6 7 8 9 10 I1 12 13 14 15 16
17 18 19 20 21 :22 23 24 25 26 21 28 29 30
Station Adrar Ain-sefra Algiers Annaba Batna Bechar Bejaia Beni-abbes Biskra Constantine Djanet Djelfa Chlef El-bayadh El-golea
El-oued Ghardaia In-amenas In-salah Laghouat Miliana Oran Ouargla Skikda Tamanrasset Tebessa Timimoun Tindouf Tlemcen Touggourt
Table 2. Climatic zones repartition
Latitude (Deg.)
Longitude (Deg.)
Altitude (m)
27.88N 32.75N 36.72N 36.80N 35.55N 31.62N 36.72N 30.13N 34.85N 36.27N 24.55N 34.68N 36.17N 33.68N 30.67N 33.37N 32.38N 28.05N 27.25N 33.8ON 36.30N 35.32N 31.95N 36.87N 22.78N 35.48N 29.25N 27.67N 34.93N 33.12N
0.28W 0.6OW 3.17E l.llE 6.18E 2.22w 5.08E 2.18W 5.73E 6.62E 9.48E 3.25E 1.35E 1.02E 2.88E 6.88E 3.67E 9.50E 2.4lE 2.88E 2.23E 0.65W 5.33E 6.90E 5.52E 8.12E 0.23E 8.1lW 1.32W 6.07E
263 1072 24 20 1052 172 9 499 124 694 1054 1144 101 1310 397 62 530 561 293 796 715 119 138 42 1377 813 312 401 810 69
the load is higher than the power delivered by the photovoltaic field, thus the batteries are discharged to their minimal admissible threshold. In these conditions, the
Zone
Sites
I
Algiers, Annaba, Bejaia, Constantine, Oran, Miliana, Skikda Batna, Djelfa, Chief, El-bayadh, Tebessa, Tlemcen Ain-sefra, Bechar, Bet&abbes, Biskra, El-oued, Ghardaia, Laghouat, Ouargla, Touggourt Adrar, Djanet, El-golea, In-amenas, In-salah, Tamanrasset, Timimoun, Tindouf
II III
IV
consumption is not satisfied and there is a shortage of electrical energy.
In this case, the loss-of-load probability is defined as being the yield between the shortage duration and the photovoltaic system duration. Assuming that the daily load L is constant and the mean daily energy A produced from the photovoltaic array to satisfy the load is obtained from the month which presents the lowest radiation during the considered period. The following ratios are defined: Storage capacity, Cs, over the load L (CT/L); and A over the load L (A/L). This ratio allows for one to draw conclusions for any case of load L, independently from its absolute value. This program used the daily solar radiation data Gd and the couples (A/L , C’s/L ) to generate the corresponding loss-of-load probability. The period of the simulation system is 10 years. The principle is shown in Fig. 2.
Fig. 1. Climatic zones repartition.
Photovoltaic systems sizing Gd A/L
Cs/L
I .
r
Simulation program
.
output
Fig. 2. Output and input of simulation program.
The generated matrix of (A/L, C’s/ L) pairs is shown in Fig. 3. For a given reliability, this matrix will allow us to determine the geometric position of all the couples (A/L, G/L) leading to the same LLP.
OF RADIATION
SEQUENCES
In the present study, we have developped a computer program for the generation of the daily radiation sequences, using the Markov Transition Matrices library (MTM) given by Aguiar et al. ( 1988). From the monthly average clearness index, this program allows for the generation of radiation sequences, whose statistical properties are similar to real sequences. Due to the unavailability of daily radiation values, the relative deviation (ER) of the monthly average values and the generated values of the clearness index are compared. ER is defined as: ER =
KT,
- KT,
MIN( KT, KT,)
* 100.
(1)
where KT, is the monthly average clearness index (calculated from the measured values); and KT, is the generated monthly average clearness index. The measured and generated values have been found to agree very well. The average relative deviation values vary between 1.49% and 4.06% (Table 3). 4. DETERMINATION CORRESPONDING
Table 3. Different relative deviations and daily average irradiance for various locations
LLP
Input
3. GENERATION
101
OF THE COUPLE
TO THE MINIMUM
(0/L, SYSTEM
A/L) COST
The daily average irradiance (DAI) on the array plane of the worst month at the different sites is given
Site
ERmini @)
ERmaxi (W)
ERaverage (%)
DA1 (kWH/m2)
Adrar Ain-sefra Algiers Annaba Batna Bechar Bejaia Beni-abbes Biskra Constantine Djanet Djelfa Chief El-bayadh El-golea El-oued Ghardaia In-amenas In-salah Laghouat Miliana Oran Ouargla Skikda Tamanrasset Tebessa Timimoun Tindouf Tlemcen Touggourt
0.61 0.14 0.09 0.09 0.76 0.31 0.17 0.25 0.01 0.30 0.05 0.12 1.31 0.18 0.45 0.60 0.02 0.98 0.38 0.27 0.00 0.06 0.15 0.32 0.35 0.17 0.15 0.14 0.08 0.58
5.28 4.54 4.54 8.54 7.19 3.47 8.30 3.98 4.69 6.15 4.82 3.57 8.46 6.34 4.77 3.90 3.66 4.01 5.59 6.36 9.10 7.10 5.21 7.57 3.45 4.80 4.89 3.87 5.67 5.55
2.67 2.41 2.41 2.69 2.48 1.70 4.06 1.84 1.85 2.31 2.09 2.02 3.06 2.58 2.62 2.19 1.52 2.58 2.28 2.37 3.88 2.28 1.53 2.69
6.602 5.497 4.523 3.917 4.904 6.232 4.354 6.123 5.472 4.205 6.586 4.799 4.546 4.985 6.416 5.654 6.001 6.280 6.109 5.696 4.370 4.872 5.739 4.132 6.033 4.479 6.511 6.194 4.950 5.977
1.49 2.43 2.40 1.87 2.22 2.56
in Table 3. The array tilt angle is taken equal to the latitude of the considered site. Figure 4 shows the isosatisfaction curves of needs for different sites. Each point on this curve represents a couple (Cs/ L, A/L). The system autonomy curve is taken as the one corresponding to the LLP equal to zero. Each curve divides the (0, G/L) (0, A/L) plan into two distinct zones. In the region above the curve, the shortage conditions corresponding to LLP are not respected. The region below the curve shows oversizing
2 3 J Cs/L 1 .A/L . . . . . ..__..........___.... .._....._._...._._......._._...._._..__.._._. _._._._ _..._._.___._ .__. _._...._____.._._.__.
1
LLP 11
LLP li!
LLP13
. .
, . .
LLPl
._._._-.
LL
J
1.1
1.2
......._
a*-.
_.._._..
*-.a
____.._._._.....
..-.---_._._.-----_
p
i
J
Fig. 3. Matrix of LLP values corresponding to (A/L, Cs/L) couples of data
. . . .
A.
102
HADJ ARAB
conditions. The energetic performance of the system is not improved in this region, as well. In the present study, a simplified economic ap preach (Table 4), proposed by Lasnier and Juen
Table 4. Data for cost analysis PV array cost
( 1990), was adopted. We considered two cases in the economic analysis: the first consisted in replacing the battery storage once during the simulation period of 10 years. The second case consisted in replacing the battery storage twice during the simulation period of 10 years. The optimal couples (G/L, A/L) from these cases are given in Table 5.
12 US$/PW 0 US$
Maintenance cost Battery cost Maintenance cost
120 US$/kWh 0 uss
Site:
.
et al.
5. CONCLUSIONS
The different LLP values used are 0, .Ol, and . 1. For each application there is a corresponding value of the LLP. The photovoltaic applications in Algeria are
Bechar
Site:
Bechar
\
a
Cs /
X”““““““” Average load
Cs /
i&-b”“““““““‘n
Average
Site:
4
load
Adrar
,,,,,,,,,,,,,,,,“,,,,,,,,,,,,,,,~,,~ .
Cs
/
AvGage
load
Average
load
I.70
B
Site:
-0
Djanet
8 e $lJo
a \ a
1
UP
MO&&, Cs /
Average
load
-
.,
a--
Cs /
Fig. 4. Iso-satisfaction curve of needs for different sites. (Continued on following page. )
Photovoltaic systems sizing
Cs
/
Average
load
Cs
/
Average
load
Site:
\
Cs
/
El-bayadh
a?-*““““““““’
Average
load
Fig. 4. Continued.
essentially oriented to telecommunication, cold storage, pumping, and rural electrification. For example, the cold storage of goods such as vaccines and serums in aride zones requires a small value of the LLP. On the other hand, in an electrification setup, we can admit a high value of the LLP. In general, the southern locations show lower optimum couples than the locations of the north, whose solar potential is lower. Also, we see that Cs/L decreases while A /L increases when the replacement rate of the storage battery is higher. This is the consequence of the storage cost which increases relatively higher
than the photovoltaic array cost. This shows the importance of an optimal choice of the battery capacity for an optimal energy transmission. Furthermore, the battery must be preserved from the hard operating conditions of desert areas to avoid a high number of replacements during their system lifecycle. This would avoid increase of the produced energy cost. It is obvious that the battery capacity decreases drastically when LLP is taken higher. Sites classified in the same climatic zone with relatively similar daily average irradiance (Table 2) do not necessarily have a comparable optimum couple
A. HADJ ARABet al.
104
Table 5. Gptimal couples (Cs/L, A/L) for candidate sites spread over the four climatic zones
One replacement Zone
1
2
3
4
Two replacements
Site
LLP
Cs/L
AIL
Cs/L
AIL
Algiers
0 0.01 0.1
3.95 2.30 0.35
1.18 1.12 0.95
2.25 1.25 0.20
1.24
4.10 2.90 0.65
1.17 1.09 0.92
2.35
Annaba
0 0.01 0.1
0.35
1.34 1.21 0.95
Oran
0 0.01 0.1
4.95 1.80 0.35
1.32 1.14 0.97
4.85 0.95 0.20
1.33 1.24 0.99
Djelfa
0 0.01 0.1
4.95 1.35 0.35
1.27 1.11 0.96
4.85 0.70 0.20
1.29 1.18 0.98
El-bayadh
0 0.01 0.1
4.95 1.30 0.35
1.31 1.13 0.97
4.85 0.70 0.20
1.33 1.20 0.98
0 0.01 0.1
4.95 2.05 0.55
1.24
Tebessa
3.90 1.10 0.30
1.37 1.26
1.03
Bechar
0 0.01 0.1
4.10 0.60 0.10
1.15
1.03
2.45 0.30 0.10
1.47 1.19 1.03
El-oued
0 0.01 0.1
3.95 0.60 0.10
1.21 1.10 0.98
2.30 0.30 0.10
1.42 1.14 0.98
Ghardaia
0 0.01 0.1
4.15 0.60 0.10
1.24 1.14 1.02
2.45 0.30 0.10
1.46 1.18 1.02
Adrar
0 0.01 0.1
1.50 0.45 0.10
1.26 1.15 1.04
0.80 0.25 0.10
1.36 1.17 1.04
Djanet
0 0.01 0.1
1.60 0.45 0.10
1.23 1.11 0.98
0.85 0.20 0.10
1.34 1.14 0.98
Tindouf
0 0.01 0.1
4.25 0.55 0.10
1.24 1.13 1.01
2.55 0.30 0.10
1.41 1.17 1.01
1.17 1.00
1.25
1.60
1.37 0.97
(see Table 5 of Adrar, Djanet, and Tindouf). The CsIL for Tindouf is nearly 2.5 higher than those of Adrar and Djanet. This is due to the time distribution
of the radiation at the different sites. Therefore, the use of simple methods of sizing can lead to a nonoptimum system causing a high installation cost. REFERENCES
R. J. Aguiar, M. Collares-Pereira, and J. P. Conde, Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices. Solar Energy 40,229-279 ( 1988). Z. Benyahia and B. Ait driss, Remote area power supply systems, Proceedingsof the 1st WorldRenewable Congress. Reading, UK, 23-28 September (1990). J. C. Bore& Etude justificative de la dtfinition des zones climatiques en Alg6rie. ch. C.S.T.B. n “456, Paris ( 1962). M. Boudiaf, Recueil de don&es meteorologiques a l’usage des architectes. E.P.A.U., Algiers (1984). F. Lasnier and W. Y. Juen, The sizing of stand-alone photovoltaic systems using the simulation technique. RERIC InternationalEnergy Journal 12( l), 21-39 (1990).
