March 26-29
Non Linear Optimization Based Design Methodology of Wind/PV Hybrid Stand Alone System Rachid Belfkira, Pascal Reghem, Jacques Raharijaona, Georges Barakat, Cristian Nichita GREAH – Groupe de Recherche en Electrotechnique et Automatique du Havre, University of Le Havre, 25 rue Philippe Lebon, BP 540 76058 Le Havre, France E-mail:
[email protected],
[email protected] Copyright © 2009 MC2D & MITI
Abstract: This paper presents a methodology for the calculation of the optimum size of a stand-alone hybrid wind/photovoltaic (wind/PV) system. The collection of six months of data of wind speed, solar radiation and ambient temperature, recorded on every hour, were used with the manufacturer’s specifications of a wind turbine and a PV panel to calculate the average power generated by the wind turbine and the PV module for each hour of the day. A deterministic algorithm is used to minimize the life cycle cost of the system while guaranteeing the satisfaction of the load. The mathematical modeling of the principal elements of the hybrid wind/PV system is exposed showing the main sizing variables. The deterministic algorithm is presented and implemented to minimize the objective function. Keywords: Wind/photovoltaic energy system, power supply, energy storage, modeling, optimization. 1. Introduction The various oil crises of the early 1970s pushed the majority of the industrialized countries to carry the consideration to the renewable energies. During this decade, the blaze of the oil prices caused the very high oil bills, representing a heavy burden for the national budgets. Then, the exploitation of other energy sources like the wind and the photovoltaic energies becomes necessary and profitable. In the developing countries, this exploitation had beyond the lightening of the oil bill a vital range. The use of renewable energy technology to meet the energy demands has been steadily increasing over the years. Several research tasks concerning the design and the sizing of the hybrid systems were carried out. A methodology for optimal sizing the combination of a battery bank and PV array in a hybrid wind/PV system has been presented
by Borowy and Salameh [1], the system operation is simulated for various combinations of PV array and battery sizes and the Loss of Power Supply Probability (LPSP) is calculated for each combination. Then, for the desired LPSP, the PV array versus battery size is plotted and the optimal solution, which minimizes the total system cost, is defined on this curve. In [2], both the configuration of a PV-diesel system with AC loads and the control strategy are optimized using genetic algorithms. In [3] Koutroulis et al. have proposed an alternative methodology for the optimal sizing of stand-alone PV/WG. The objective of this proposed methodology is to suggest, among a list of commercially available system devices, the optimal number and type of units ensuring that the 20-year round total system cost is minimized subject to the constraint that the load energy requirements are completely covered, resulting in zero load rejection. The 20-year round total system cost is equal to the sum of the respective components capital and
maintenance costs. The decision variables included in the optimization process are the number and type of PV modules, WGs and battery chargers, the PV modules tilt angle, the installation height of the WGs and the battery type and nominal capacity. The minimization of the cost (objective) function is implemented employing a genetic algorithms approach. In this paper, the developed methodology is based on a dynamic evaluation of the wind and solar energetic potential. This dynamic evaluation is based on the collection of the hourly data of wind speed, solar radiation and ambient temperature of the site of production. The different stages of the developed optimization approach will be described in the following sections.
In function of this wind speed, the model used to calculate the output power, PWT(t) (W), generated by the wind turbine generator is as follows:
PWT
a.v 3 (t ) − b.PR (t ) = PR 0
v ci 0 during the charging process of the battery and PB(t) < 0 in the discharging process as calculated in the equation (6). Additional constraints to be imposed are i 1 ≤ N PV
1≤ 1≤
,p
i ≤ N PV
, p max
N Wj T ≤ N Wj T max k k N BAT , p ≤ N BAT , p max
(21)
where NiPV,pmax, NjWTmax and NkBAT,pmax were calculated according to the nominal power of PV panel, wind turbine and nominal capacity of battery, respectively, and the peak of the load demand.
3. Results and Discussion The hybrid renewable energy system is assumed to be installed in a site in Dakar city in Senegal. The collection of average hourly data of wind speed, solar radiation on horizontal plane and ambient temperature recorded for every hour of the day are plotted in fig. 3 and are used to calculate the power produced by the renewable resources. The hourly distribution of the consumer power requirements during a day is shown in fig. 4. In this application we chose to use two types of each component of the hybrid wind/PV system. The specifications and the related capital, maintenance and installation costs of each component type, which are input to the optimal sizing procedure, are listed in Tables 1-3. The maintenance cost of each unit per year and the installation cost of each component have been set at 1% and 10% respectively of the corresponding capital cost. The serial connection numbers of the two types 1 and 2 of the PV arrays and of the batteries which are determined by the operating voltage of the system which is chosen to be equal to a standard value of 48 V, take respectively the values: N1PV,S = 2, N2PV,S = 3, N1BAT,S = 4 and N2BAT,S = 4. The expected battery lifetime has been set at 3 years with proper maintenance, resulting in ykBAT = 6. Since the tower heights of wind turbines affect the results significantly, 30 meter high tower is chosen. Using all these data and parameters, the minimization of the system total cost is achieved by selecting an appropriate system configuration. The optimal sizing results, consisting of both the devices type and their number, are shown in table 4. From these results, one can deduce that the rate of penetration of the PV power is higher than that of the wind power; this is due to the solar radiation of the site of Dakar that is important compared to the speed of the wind. Figure 5 presents the variation of the system total cost (fitness function) during the optimization procedure. It can be noted that a near optimal solution was derived during the early stages of the function evaluations. The minimum value of the system total cost is obtained after a number of 8000 of function evaluations.
(a)
12
Table 2: wind turbines specifications Type
1
2
Power rating (W) vr (m/s) vci (m/s) vco (m/s) Capital cost (€) Installation cost (€) Maintenance cost per year (€/year) Tower capital cost (€ ) Tower installation cost (€) Tower maintenance cost per year (€/year)
10000 13.8 3.1 25 20682 2068.2
7500 13.8 3.1 25 16978 1697.8
206.82
169.78
741
741
7.41
7.41
74.1
74.1
10
Wind speed (m/s)
8
6
4
2
0
0
500
1000
1500
2000
2500
3000
3500
4000
Number of hour
(b)
1000 900
Solar radiation (W/m²)
800 700 600
Table 3: batteries specifications
500 400
Type
300 200 100 0
0
500
1000
1500
2000
2500
3000
3500
4000
Numbre of hour
(c)
35
Ambiant temperature (°C)
30
Nominal capacity (Ah) Voltage (V) DOD (%) Efficiency (%) Capital cost (€) Installation cost (€) Maintenance cost per year (€/year)
1
2
100
230
12 80 80 126 12.6
12 80 80 264 26.4
1.26
2.64
25
Table 4: optimization results 20
15
10
0
500
1000
1500
2000
2500
3000
3500
4000
Number of hour
Type
1
2
NPV,p NWT NBAT,p
13 1 2
2 0 2
Cost (€)
Fig. 3: Hourly mean values during a period of six months of meteorological conditions: (a) wind speed, (b) solar radiation and (c) ambient temperature.
57687
4500 4000 3500
Table 1: photovoltaic panels specifications Type
1
2
Voc (V) Isc (A) Vmax (V) Imax (A) NCOT (°C) Capital cost (€) Installation cost (€) Maintenance cost per year (€/year)
32.6 7.87 25.9 6.95 45.9 603 60.3
21 7.22 17 6.47 43 519.14 51.9
6.03
5.19
Pload(W)
3000 2500 2000 1500 1000 500 0
5
10
15
Number of hour
Fig. 4: Hourly demand power in a day
20
12
x 10
4
generator systems using algorithms,” Solar Energy, 2006.
11
[4] R. Belfkira, C. Nichita, P. Reghem, G. Barakat, “Modeling and optimal sizing of hybrid energy system,” in Proc. International Power Electronics and Motion Control Conference, ~EPE-PEMC 2008~, September 1-3, 2008, Poznań, Poland.
Total Cost (€)
10 9 8 7
[5] F. Lasnier, T. G. Ang, “Photovoltaic engineering handbook,” Bristol, England: A. Hilger, 1990.
6 5
genetic
0
1000
2000 3000 4000 5000 6000 Number of Function Evaluations
7000
8000
Fig. 5: The system total cost during the DIRECT optimization
4. Conclusion A methodology of sizing stand-alone hybrid wind/PV system using a deterministic approach (the DIRECT algorithm) is proposed in this paper. Firstly, the used models of the wind turbine, the PV panel and the storage unit composing the hybrid system, were presented. Afterwards, the main ideas of the DIRECT algorithm were explained and the proposed optimization procedure was exposed and finally, the developed sizing procedure was applied to optimize a hybrid system. This developed methodology is based on the use of long-term data for wind speed, solar radiation and ambient temperature for a site located in Dakar in Senegal. The optimum numbers of wind turbines, PV panels and batteries depend on the particular site, load profile and the specifications and the related cost. Acknowledgement This work was financially supported by the region of “Haute Normandie”, in France.
References [1] B.S. Borowy, Z. M. Salameh, “Methodology for optimally sizing the combination of a battery bank and PV array in a Wind/PV hybrid system,” IEEE Transactions on Energy Conversion, vol. 11 n. 2, June 1996. [2] R. Dufo-Lopez, J. L. Bernal-Agustin, “Design and control strategies of PV-Diesel systems using genetic algorithms,” Solar Energy, vol. 79, pp. 33-46, 2005. [3] E. Koutroulis, D. Kolokotsa, A. Potirakis, K. Kalaitzakis, “Methodology for optimal sizing of stand-alone photovoltaic/wind-
[6] T. Markvar, “Solar Electricity,” 2nd ed, J. Wiley & Sons, 2000. [7] H. Yang, L. Lu, W. Zhou, “A novel optimization sizing model for hybrid solarwind power generation system,” Solar Energy, vol. 81, pp 76-84, 2007. [8] J. Bernard, “Energie solaire: calculs et optimisation,” Ellipses-Paris, 2004, pp. 5393. [9] G. Seeling-Hochmuth, “Optimisation of hybrid energy systems sizing and operation control,” Dissertation in Candidacy for the Degree of Dr.-Ing, University of Kassel, October 1998. [10] J. Azzouzi, R. Belfkira, N. Abdel-Karim, G. Barakat, B. Dakyo, “Design optimization of an axial flux PM synchronous machine: comparison between DIRECT method and GAs method,” in Proc. International Power Electronics and Motion Control Conference, ~EPE-PEMC 2006~, August 30–September 1, 2006, Portoroz, Slovenia. [11] D.R. Jones, C.C. Perttunen, B.E. Stuckman, “Lipschitzian optimization without the Lipschitz constant,” J. Optim. Theory Appl, vol. 79, 1993, pp 157 – 181. [12] M. Björkman, K. Holmström, “Global Optimization Using the DIRECT Algorithm in Matlab,” AMO - Advanced Modeling and Optimization, vol. 1 n. 2, 1999.
