wind installations in Tunisia through a mathematical model

Energy Conversion and Management 75 (2013) 398–401

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

New insights for renewable energy hybrid photovoltaic/wind installations in Tunisia through a mathematical model A. Colantoni a, E. Allegrini a, K. Boubaker b,⇑, L. Longo a, S. Di Giacinto a, P. Biondi a a b

Department of Agriculture, Forest, Nature and Energy (DAFNE), University of Tuscia, Via S. Camillo de Lellis snc, 01100 Viterbo, Italy Unité de physique des dispositifs à semi-conducteurs, Tunis El Manar University, 2092 Tunis, Tunisia

a r t i c l e

i n f o

Article history: Received 26 February 2013 Accepted 19 June 2013

Keywords: Hybrid photovoltaic/wind systems Optimization Renewable energy

a b s t r a c t A mathematical model is presented for outlining future insights and potentials of hybrid photovoltaic/ wind installations throughout the Tunisian territory. The developed algorithm takes into account the existing background in terms of energy generation, conversion, sustainability and management, as well as actual resources maps. Relevant data like solar radiation distribution and cumulative wind speed records have been exploited in order to implement an efficient meshing scheme of the accessible area. The algorithm yielded a confirmed and data-consolidated installation plan over a 30-years period. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Tunisia is situated between Europe and Africa in a strategic and advantageous position with a relatively low amount of fossil fuels and lax of natural gas reserve [1–4]. Its energy consumption has increased parallel to the technological development. Nevertheless, most of the electricity is still generated by thermal power plants exploiting fossil fuels and gas. Since renewable energy sources (RES) play an important role in targeting energy security, sustainable development, and environment preservation [5–9], wind and solar energy can be particularly alternatives hence have to be consistently investigated. In the early 1970s, the installed power station capacity in Tunisia totaled roughly 2900 GW. The mean annual peak load along this period was approximately 1.890 MW. The contribution of hydroelectric power plants and wind power installations did not exceed 60 MW and 10 MW, respectively. The remaining capacity was wholly accounted for by thermal power stations. In this region, the commercial use of wind power for generating electricity is still in its infancy. In the 1980s, some small wind energy plants have been used on a decentralized basis, for example for the desalination of brackish water or pumping water as part of field irrigation schemes in isolated zones. Some studies estimated wind potential at around 1000 MW, with a possibility of implementing 250 MWwind farms in the northern part of the zone [10–12,1]. In 2000, the trend toward combining Solar Photovoltaic systems with additional wind generators has been explained by both high supply reliability and large storage capacity. ⇑ Corresponding author. E-mail address: [email protected] (K. Boubaker). 0196-8904/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2013.06.023

In the present study, an attempt to identify optimal locations which can host hybrid photovoltaic/wind system is performed on the basis of previsions of the 2014–2030 periods. The paper is organized as follows: In Section 2, the Current state-of-the-art of renewable energy sources in Tunisia is presented along with primer analyses patterns. A synopsis on hybrid photovoltaic/wind installations is detailed in Section 3. Sections 4 and 5 describe the used optimization scheme and results, respectively. Last section is the conclusion. 2. Current state-of-the-art of renewable energy sources in Tunisia Tunisia has an important solar potential, boasting mean annual irradiation rates between 1.5 and 5.5 MW h m2 (Fig. 1). Concerning wind energy, a single wind farm has been built, in Sidi Daoud (Northen part) near Cap Bon. It has been working since 2000. Average annual wind velocity at this location is 8.4 m/s at 30 ma.g.l. The project was put out to tender in 1996 on the basis of a feasibility study which was drawn up between 1990 and 1992. The wind farm is equipped with 32 turbines each rated at 330 kW each. In 2002 it generated 30 GW h of electricity and later in 2003 it was expanded by the addition of 12 turbines with a capacity of 8.7 GW h [13,14]. On another hand, the Meteorology National Institute (INM), provided 10-year mean records of synoptic observations for several locations in Tunisia [13]. Wind speed has been assumed to be stationary within each month with a maximum of 5.0 ms1 at heights beyond 10 m. Records show that wind mean speed in Tunisia varies between 2.0 and 5.0 ms1.

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Nomenclature i, j, k, n, q indexes (integer) N0 prefixed integer Mi meshing scheme point B4j Boubaker polynomials values (dimensionless) rj Boubaker polynomials minimal positive roots (dimensionless) Hq real parameter

Greek symbols C prefixed integer nj real coefficients -j unknown pondering real coefficients u optimization function (dimensionless)

Fig. 1 gathers global wind speed levels along with solar radiation distribution. High irradiation rates in the southern part (Fig. 1) encouraged the use of solar panels in commercial and residential installations through important official subsidies and assistance. The unique implemented high scale plant is in El Borma at the Algerian southern frontiers, with a nominal power of 2.1 GW.

Consecutively, the optimization is carried out through the Boubaker Polynomials Expansion Scheme BPES [15–33] a standardized weight function u(N0, C) is set as:

3. A synopsis on hybrid photovoltaic/wind installations

where B4k are the 4k-order Boubaker polynomials, rj are B4j minimal  positive roots and -j j¼1...N are unknown pondering real coefficients.

Overall the world, escalating fossil fuel costs and toxicity have caused most agents to seriously start looking at alternatives to standard energy sources. Recently, hybrid Photovoltaic-Wind power systems have been proposed in order to increase the share of RES from 4% -in terms of total electrical installed power in 2010- to 16% and 40% in 2016 and 2030, respectively. With specific regard to power demand, this target corresponds to the implementation of approximately 5.4 GW throughout the territory. If all the resources and the projected plants (53–90 MW) are taken into account, the amount of annual required installation should be equal to 0.3 GW. The configuration of a standard hybrid photovoltaic/ wind is shown in Fig. 2. In this configuration Wind and solar energy are converted into electric energy which is either stored or transmitted to loads. The topology of hybrid energy system consisting of a permanent magnet generator along with a PV array. Two energy sources are connected in parallel to a common DC bus line through two autonomous converters.

The BPES protocol ensures the validity of the optimizing test thanks to Boubaker polynomials first derivatives properties:

uðN0 ; CÞ ¼ C

1

C X i¼1

"

0 1 X -j  B4j ðrj ~ni Þ 2N 0 j¼1

N

# ð2Þ

0

4. Optimization scheme Taking into account time and budgetary constraints, and in order to find out the optimal location for the above described hybrid plant in the territory, an optimization procedure is developed. The optimization protocol is based on two elements: the pondered meshing and the Boubaker Polynomials Expansion Scheme BPES [15–37]. The pondered meshing is constructed through the available given data. Several solutions have been proposed through the BPES in many fields such as numerical analysis [20–23], theoretical physics [23–26], mathematical algorithms [27], heat transfer [28], homodynamic [29,30], material characterization [31], fuzzy systems modeling [26,32–36] and biology [37]. Each point Mi in the meshing scheme map is consecutively indexed using an integer index iji¼1...C , where C is the size of the meshing scheme, and then introduced within a continuum coordinate system (Fig. 3).  At this stage, a given N0 of aggregates nj j¼1...N affects to each 0 point. These aggregates involve, among others, irradiation level, wind performance, area accessibility level, installation history and mean costs of different options. In a first step, and for standardizing purposes, each aggregate ni ji¼1...N0 which varies inside

Fig. 1. Global wind speed levels along with solar radiation distribution in Tunisia.

the range ½nmin ; nmax , is normalized using the following equations: i i

n

min

~ni ¼ ni ni Dn ¼ nmax  nmin ; i ¼ 1 . . . N0 i i Dn

ð1Þ

Fig. 2. Hybrid photovoltaic/wind setup scheme.

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systems. The plants have different capacities, from 38 MW (eastern-south Tunisia) to 182 MW (middle part of Tunisia), depending on the wind and solar potential of that area. The systems will be completed by 2030. Tunisia is also looking at the possibility of a transmission line running from Egypt to Morocco, whereby a feasibility study has already begun. A link between Tunisia and Italy is also being considered so that opportunities of commercializing energy can be developed between the two countries [38–40]. Transmission network in Tunisia involves 60 HV substations and about 5000 km of HV lines. With specific regards to interconnection network is connected to Europe through networks in Algeria and Morocco. Interconnection with Libya help to extend the synchronous zone to the orient, which means that interconnection from Syria through Libya, Egypt and Jordan would take place. These possibilities are scheduled for incorporation within the input parameters of the actual study. 6. Conclusion Fig. 3. Optimization meshing scheme.

8   N
x¼0

  N X  ¼ 2N–0; B4q ðxÞ  q¼1

¼ 0; x¼r q

and

8 N
4q ðxÞ

dx

    

x¼0

¼0

N X dB

4q ðxÞ

dx q¼1

with : Hn ¼ B04n ðr n Þ ¼

    

x¼r q

¼

N X Hq q¼1

! P 4rn ½2  r 2n   nq¼1 B24q ðr n Þ þ 4r3n B4ðnþ1Þ ðr n Þ

The BPES solution is obtained by finding out the set of the ponder ing real coefficients, -j j¼1...N which maximizes the standardized 0 weight function u(N0, C) and testing the rank i which gives minimal value of the first derivatives of u(N0, C). At this stage, the adequate hybrid photovoltaic/wind setup is affected to the location of this rank i and hence is eliminated from the meshing scheme.

The protocol optimization is an important tool to evaluate the possible use of renewable energy sources such as hybrid systems based on solar and wind technologies and to identify the optimal locations of these plants. In order to reach this goal, the potential of wind and solar energy is considered. The best solution is mostly a compromise between the solar radiation and mean wind speed values (however other parameters are taken into account in the procedure) for that area. The present paper demonstrated that Tunisia can decrease the dependence on fossil fuels and, as consequence, ensure a clean and sustainable future based on the use of renewable energy sources. The performed mathematical model used relevant data like solar radiation distribution and cumulative wind speed records in order to yield a feasible and promising data-consolidated installation plan over a 30-years period. Nevertheless, some aspects have to be considered: the development of hybrid plants need incentives to compete with fossil fuels, which still covers most of energy demand. Interconnection and other possibilities can be incorporated as input parameters for the actual model for enhancement purposes. References

5. Results and discussion The result of this algorithm consists of an optimized and well scheduled planning for implementing the net of hybrid elementary units plan under the given constraints (Fig. 4). The study, which was carried out by the useful optimization procedure, yielded definition of five different locations which can host the hybrid

Fig. 4. Result of the algorithm.

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