Category Archives: EuroSun2008-3

Impact on solar fraction

Table 1 summarizes the results of simulations with the five load matching cases described above together with a base case (case 0) with the default load and production shown in Figure 2 and theoretical limits to the solar fraction (daily and annual optimum).

Table 1. Annual and summer solar fraction for different load matching cases and relative system sizes for detached houses. Daily optimum refers to the theoretical solar fraction that would occur if each daily load and demand were optimally matched. Annual optimum refers to the solar fraction that would result from an optimal match of the total annual load and demand. The summer solar fraction is calculated over the

months of May, June and July.

Summer

Summer

Annual

Annual

Case

ALR 2

ALR 8

ALR 2

ALR 8

0

0.36

0.58

0.21

0.35

1a

0.36

0.65

0.21

0.38

1b

0.39

0.66

0.19

0.37

2a

0.39

0.64

0.23

0.41

2b

0.41

0.73

0.24

0.48

3

0.37

0.80

0.21

0.43

Daily opt.

0.41

0.98

0.24

0.65

Annual opt.

0.41

1.0

0.24

0.94

It is seen from the table that the summer and annual solar fractions for the smaller ALR system are rather close to optimum already in the base case, since the overproduction is not very substantial. For ALR 8 the difference between the orientation cases and the optimum limits is much greater. The re-orientation cases (1a and 1b) yield somewhat increased solar fractions, although the effect is relatively small. The DSM options (cases 2a and 2b) yield higher solar fractions throughout, although in case 2a for the summer the figures are comparable and somewhat higher for the re­orientation case. Although storage (case 3) is the most flexible of the options, the loss of energy that depends on the efficiency of the storage medium makes it in some cases slightly worse than both DSM and panel orientation options.

Sun tracking orientation

The Solar8 system is mounted on our laboratorial facilities with its tracking axis oriented in the East — West position. It is possible to simulate the received irradiation by a tracking surface both with the axis in East-West and North-South direction for several climates at different latitudes. The results are given in Table 3.

By the analysis of the results, one can conclude that it is always better to track the sun around an axis with North-South direction. This effect is even more relevant when the system is moved closer to the equator where the sun reaches higher altitudes and moves around the sky from East to West direction, mostly.

Table 3. Incoming beam and global irradiation onto a tracking surface with axis in East-West and North-South

direction for Stockholm, Lisbon and Lusaka.

Sun tracking orientation of the surface

Stockholm (lat=59.2°N)

Lisbon (lat=38.7°N)

Lusaka (lat= 15.4°S)

G

(kWh/m2,yr)

Gb

(kWh/m2,yr)

G

(kWh/m2,yr)

Gb

(kWh/m2,yr)

G

(kWh/m2,yr)

Gb

(kWh/m2,yr)

Tracking surface around North-South axis

1343.0

787.3

2187.0

1445.0

2594.0

1754.0

Tracking surface around East-West axis

1262.0

717.6

1973.0

1263.0

2289.0

1474.0

Ratio N-S/E-W tracking

1.06

1.10

1.11

1.14

1.13

1.19

Method and boundary conditions

The study has been performed with the simulation software HOMER developed by the National Renewable Energy Laboratory (NREL). HOMER can be used for the sizing of hybrid systems based on the Net Present Costs (NPC). The modeled systems supply the household electricity for single family houses. The load profile for the electrical consumption has been derived from usage patterns and the average yearly electricity consumption for single family houses in Sweden (about 6000 kWh). Two additional load profiles with 3300 kWh and 1800 kWh have been generated, assuming the application of power efficient appliances and other energy saving measures to reduce the annual electricity consumption. The system size has been limited to 6 kW PV power which corresponds approximately to the available area of the south roof of a single family house, 3.6 kW wind turbine power and a battery bank size of 120 kWh. For the simulation a Bergey XL.1 wind turbine with a hub height of 20 m was used (max. 3 turbines each 1.2 kW). Another variable has been the capacity shortage which defines the percentage of load that is accepted to be uncovered. The applied prices and other economic parameters have been identified for Swedish conditions

In total 11 locations have been studied from the very South to the very North of Sweden (Table 1) using the local annual solar and wind resources (Figure 2).

Table 1. Studied Swedish locations latitudes, longitudes, and altitudes

City

Latitude

Longitude

Altitude (m)

Kiruna

67.83°N

20.43°E

408

Lulea

65.55°N

22.13°E

17

Umea

63.82°N

20.25°E

10

Ostersund

63.20°N

14.50°E

376

Borlange

60.48°N

15.43°E

140

Karlstad

59.37°N

13.47°E

46

Stockholm

59.35°N

18.07°E

30

Norrkoping

58.58°N

16.15°E

43

Gothenburg

57.70°N

12.00°E

5

Visby

57.67°N

18.35°E

51

Lund

55.72°N

13.22°E

73

Kir Lul Ume Ost Bor Kar Arl Nor Got Vis Lun [4]

image047

In Figure 4 the Net Present Costs are compared for capacity shortages of 0, 5 and 10 percent. It can be seen that the costs are highest for locations in the North of Sweden with low winter radiation and low wind speeds. For these locations also the difference between the no capacity shortage and 5% capacity shortage allowance are most significant. If no capacity shortage would be allowed the NPC would amount between $23,000 and $49,000. In this case, for the most locations, the use of a small diesel backup generator would probably be more cost effective to provide the uncovered load than an increased systems size.

Simulations with the 1800 kWh load profile have been done to compare PV-Wind Hybrid systems with PV-alone systems. The results in Figure 5 show the hybrid systems to be consistently less expensive than the PV-alone system. Logically at locations with higher wind speed such as Lund and Gothenburg the difference is greater than for locations with lower wind speed such as Borlange. Using a Hybrid system is reducing the NPC by 36% (for Borlange) and 64% (for Lund).

$70 000

Подпись:$60 000

$50 000

Q $40 000 СЛ

3 $30 000 $20 000 $10 000 $0

Linear concentrators with active dissipation systems which generate thermal energy

In 1981 Florschuetz [4] remarked that the use of air as an active refrigeration system is not a viable alternative because of its low thermal capacity and diffusivity. He found that water is a fluid whose properties allow for a better thermal interchange and consequentially the achievement of higher concentrations without the negative effects of the temperature over the PV cell efficiency.

After this study, a group of authors developed a series of active cooling systems using water (Edenburn, O’Leary and Clements, Chenlo and Cid, Russell). Although each system used the water cooling device to optimise conditions for electricity production, none of them analyse the possibility of taking advantage of the thermal energy produced by the warming up the water.

At present, there are two principal systems which optimise both the electricity production and the thermal energy production:

• CHAPS (Combined Heat And Power Solar), developed at the Australian National University. It consists of a parabolic concentrator with a ratio of 37X which focuses radiation onto a PVT module. The module converts the radiation into thermal and electrical energy with efficiencies of 57% and 11% respectively. The prototype was initially designed as a photovoltaic system with active cooling, the idea later evolved to use the water to capture the thermal energy. Reference data of the thermal gain achieved by the collector is not mentioned in any of the reference publications for the system [5].

• BIFRES, developed at the University of Lleida, is a system which concentrates radiation by Fresnel reflection to a concentration factor of 22X. The hybrid module operates with a nominal thermal efficiency of 59%, permitting the c-Si photovoltaic cells to operate at an optimum efficiency of 11.9% [2].

Both systems positively satisfy the requirements of actively cooling the cells whilst acting as a thermal collector with acceptable efficiencies, above 50%. However, in both cases the PVT module design is not straightforward. Both groups have opted for a tube of circular cross-section appended to an absorber on which the photovoltaic cells are placed. The two systems have significant differences: the heat sink is made of aluminium in the CHAPS system and of copper in the BIFRES system, also the tube developed at the ANU is furrowed with the goal of improving convection into the fluid.

After analyzing these two systems, some improvements may arise: It is well known that rectangular sections have higher Nusselt numbers than circular or square sections. A section with a higher aspect ratio (a), permits a greater thermal interchange into the fluid, where (a) is defined as the quotient between the long and short side of the rectangle [6]. Besides, an attractive concept such as the architectural integration is not well solved in the majority of PVT systems. As a consequence of their dimensions, PVT systems are only suitable for installation on flat roofs.

In this research is proposed, with the same concentration ratio than in the other systems explained before, to reduce the dimensions of the concentrator and the absorber to facilitate the integration in buildings.

Supervisory System

The Scada system was developed over the platform Axeda Supervisor Wizcon for Windows & Internet V8.2 [16]. The SCADA system used to implement this monitoring and control strategy permits the selective access to the application, depending on the user’s responsibility degree. In this paper we developed three user levels: Operators, Supervisors and Administrators. Several SCADA menus were built. The main characteristic of a SCADA Menu is to be simple, explicit and quick on transmitting the information to the operator or to the System administrator.

One of the developed Graphical User Interfaces (GUI) is shown in fig 9. As this SCADA platform is web enabled, all the GUI displayed data is also on-line accessible through the internet.

In fig. 9 it is shown the developed main menu for the sun-tracker system. The on-line available information, referring actual data from the tracker unit is: actual position for both axis, actual PV — power generated, max. daily PV-power generated, actual efficiency ratio.

4. Conclusion

This paper proposed the optimization of the electric energy production by photovoltaic cells through the development of an intelligent sun-tracking system. The developed solution has many advantages in relation to similar existing devices, as this system is autonomous regarding the information needed to process the optimal orientation and is intelligent in a way that it performs on-line monitoring of the photovoltaic energy production.

An experimental prototype was built and field results have proven the good performance of the developed tracking system.

The observed increase in power generation, in relation to other PV-systems, without tracking devices, is of similar magnitude (ca. 25%) as for other usual tracking solutions. However, this system has a relative advantage, as it measures exactly the controlled variable: the actual PV — power generation.

Подпись: Fig. 8. Control Algorithm for the Tracking system Box0: After reset is activated, the system stores the PV — power generated in the actual position, Pactual, in the variable Pin. The system searchs its reference — null position. It moves until it finds the hardhome position (both external proximity sensors on). In this position the system assumes the absolute orientation angles for both axis equal zero (a1 = a2 = 0). The maximal Power, Pmax is set to zero. Both counters, C1, C2, are loaded;

Box1: After start is activated, the system iniciates the search for the maximal power generated in axis 1, with an angle increment a10. The system stores the power generated in variable P1.

Box2: If P1 < Pmax, the system goes to Box 4, and follows for a new position;

Box3: If P1 > Pmax, this position is stored in the variables: a 1max, a2max. The max. Power value, Pmax is actualized with the new Power value P1;

Box4: Counter for axis 1 is updated;

Box5: After all orientations for axis 1 are evaluated, regarding a fixed orientation for axis 2, axis 2 is positioned in a new position, with an angle increment a20, and axis 1 returns to its initial position a1=0. The system re-initiates the search for the optimal orientation of axis 1, regarding the new position of axis 2. The information flux returns to box 1.

Box6: After all orientations for axis 1 are evaluated, regarding all different positions of axis 2, the system compares the maximal power found (Pmax) with the initial Power generated, before the search process had begun (Pin). If the new Power value is greater than a pre-defined gain, this new correspondent orientation (a1max, a2max) is sent to all park panels. If the power gain is not enough, the new found position is not to follow by the other PV-panels.

Подпись: Fig. 9. Sun Tracker System: SCADA main Menu

Box7: After a pre-defined time interval (K) the tracker system initiates a new complete search process in both axis. The information flux returns to box 0.

Acknowledgment

This work was partially funded by the FCT through program POCTI-SFA-10-46-IDMEC, subsidized by FEDER and by the Project PETER — PIC Interreg IIIA SP6.E53/03.

References

[1] Buresch, M. Photovoltaic energy systems design and installation. New York. McGraw-Hill, 1983.

[2] German Advisory Council on Global Change, 2003 (http://www. wbgu. de)

[3] Atlas I, Sharaf A.; “A Fuzzy Logic Power Tracking Controller for a Photovoltaic Energy Conversion Scheme”; Electr. Power Syst. Res. J., 1992; 25 (3); pp. 227-238

[4] Atlas I, Sharaf A.; “A Novel on-line MPP search algorithm for PV arrays”; IEEE Trans. Energy Convers., 1996; 11 (4); pp. 748-754

[5] Hua, C., Lin, J.; “An on-line MPPT algorithm for rapidly changing illuminations of Solar arrays”; Renew Energy 2003; 28; pp. 1129-1142.

[6] Benlarbi K., Mokrani L., Nait-Said M., “A Fuzzy Global Efficiency Optimization of a Photovoltaic Water Pumping System”; Sol Energy 2004; 77; pp. 203-216.

[7] Hua C., Lin J.; “A modified tracking algorithm for maximum power tracking of solar array”; Energy Conversion and Management 2004, Vol. 45, pp. 911-925.

[8] Chen Y., Liu Y., Wu F.; “Multi-Input Converter with Power Factor Correction, Maximum Power Point Tracking, and Ripple-free Input Currents”; IEEE Trans. Power Electron. 2004, 19 (3), pp. 631-639

[9] http://solardat. uoregon. edu/ SolarPositionCalculatorhtml

[10] Hoppe D.; “Solar-Tracking Mirror with Radiation Sensor”; Publ. Nr. DE4425125; European Patent Office, esp@cenet database.

[11] F. R. Rubio, M. G. Ortega, F. Gordillo and M. Lopez-Martinez; “Application of new control strategy for sun tracking”; Energy Conversion and Management, Vol. 48, Issue 7, July 2007, Pages 2174­2184.

[12] Simatic Net — NCM S7 for Profibus/ FMS. SIEMENS 12/2001.

[13] System Software for S7-300 and S7-400 — Reference Manual, SIEMENS 08/2000; A5E00069892- 02

[14] Simatic S7 Prodave S7 — Toolbox for PGs and PCs, SIEMENS, 2001

[15] Simatic S7-300 — Ladder Logic (LAD) for S7-300, SIEMENS, 2001.

[16] Wizcom for Windows and Internet 8.2 User Guide, AXEDA Systems 2002

Measurement of the slope errors of a linear PV/T Fresnel reflector

B. Abdel Mesih 1* , J. I. Rosell 1 , J. Illa 2, D. Chemisana 1

1 Department of environmental and soil sciences, University of Lleida, Spain
2 Department of computer science and industrial engineering, University of Lleida, Spain
* Corresponding Author, bahy@macs. udl. cat

Abstract

The objective of this work is to measure the surface slope errors of the mirrors of the 22-
suns photovoltaic-thermal concentrator that is installed in the University of Lleida in Spain.

A set of photos are taken with a digital camera placed at a distance perpendicular to the mirrors plane which is oriented towards the camera. The analysis of the reflected pattern of the edges of a target on the mirrors shows the irregularities of the mirrors surface. The deformation of the observed pattern could be due to installation errors, misalignments, or bending of mirrors under to their own weight. A geometrical algorithm based on the principles of projective geometry is used with the aid of numerical software to analyze and detect the edges of the absorber. The aim is to find the distribution of actual normal vectors of each mirror strip and to calculate the root mean square error (RMSE). This work gives insight into the loss of optical quality due to reflector errors which affects both the electrical and thermal output of the concentrator severely.

Keywords: Solar concentrators, linear PV/T Fresnel reflector, surface slope errors

1. Introduction

The optical quality of reflectors in photovoltaic thermal concentrator systems affects both the electrical and thermal production drastically. Misalignments of the mirrors during the installation phase, problems with the holding structure, or surface dents, all contribute to both non-uniform illumination and temperature on the PV modules. The current produced by the PV cells, which are usually connected in series, is directly proportional to the incident radiation. Consequently, the cell that receives the least illumination is then the one that determines the power output of the whole PV module. The negative effect of non-uniform illumination on the performance of a whole concentrator system has been well shown by Franklin and Coventry [3].

There are several methods to quantify the slope errors of the reflector components of solar concentrators. Scanning Hartman Optical Tester (SHOT) and video-SHOT (VSHOT) have been used since the 1970’s with great success. There are a number of publications that focus on the principles of VSHOT and applications [4, 11-13]. Photogrammetry is another reliable method that is popular in the field of assessing the slope errors of solar concentrators [7-9]. The curvature of specular reflecting surfaces has been also addressed in a number of publications concerning deflectometry and deflectometric measurements [5, 6]. In this paper, a new approach presented by Ulmer et. al [10] is used to measure the surface slope errors of the PV/T generator installed in Lleida, Spain. The method is called the absorber reflection method (ARM). The method relies on the fact that an observer can easily detect the deformation in the reflecting surface when observing the irregularities in the reflection pattern of a target which has defined and known uniform
contours. The results obtained by the ARM shows big resemblance to the results obtained by photogrammetric methods in assessing the surface errors of parabolic troughs.

Load Prognosis

For an optimal operation of grids and cogeneration plants good prognoses of the expected loads (electric and thermal) and feed-in of fluctuating generation are essential. For this we suggest a statistic method with empiric formulas to fit the load. In several projects we tested an algorithm based on the method of multiple linear regression [4],[7]. The scheme of this algorithm is shown in Fig. 4.

Basis for this method is a database with a time horizon of at least one year, which contains the profile of the value y[t] to be predicted together with other data {z1[t], .., Zn[t]} that might correlate with y. These are calendar data (e. g. day of year) and weather data (e. g. temperature, global radiation). To keep the database as up-to-date as possible it is continuously actualised with the newest measurements

before the actual prognosis calculation. The method of multiple linear regression [8] estimates the given depended variable y[t] by a linear function y[t] = co + ci Xi[t] + c2 X2[t] + … + cn Xn[t] + e[t]

Подпись: Fig. 4. Scheme of the prognosis algorithm.

of the given independent variables {x1 [t], .., xn[t]}, where the factors {c0, .,cn} are unknown and e[t] gives the error for each time step.

The error is minimised with a least square estimation, which has got the advantage that it can be solved analytical with a linear set of equations. From experience we know, that the thermal load will not depend linear on the input variables. To integrate also nonlinear relations the variables xi[t] are introduced. They are defined as a function of the input data in the database {z1[t], .., zn[t]}:

xi[t] = f (zi[t],…,zJt]) (4)

In a pre-analysis we tested, which combination of input variables fits the load best and got for each hour a model equation. The regression analysis results in a specific formula for each hour of the day, e. g. hour = 13:

Pioad. iih = Cl + C2 • Sunday + c3 ■ doy2 + c4 ■ doy4

r, ump ■ r,,-hmp — r — limp’ <ч limp’ (5)

+C9 • sunrise + C10 • sunset

image120

For the prognosis the multiple linear regression routine calculates the coefficients {c1, …, cn} for the chosen equation by use of the updated database. The resulting model is used together with weather forecasts from a commercial meteorological service. Fig. 5 shows the curve of a thermal load of a real district heating system and the prognosis which was predicted one day ahead.

Impact on overproduced power level

From the grid point of view, the instantaneous level of the overproduced power is critical, since it affects voltage levels locally in the grid. An analysis involving mean load cannot give any detailed insights into grid issues, but an average response in power overproduction to load matching measures can be determined. As an example, Figure 3 shows a duration graph over the overproduced power for the base case (case 0) and the two DSM cases (2a and 2b).

For the ALR 2 setup, the overproduced energy is heavily reduced, for the more extensive DSM scheme (case 2b) almost entirely. For the ALR 8 setup the effect is smaller since the amount of shiftable energy is smaller compared to the overproduction. A comparison with the panel orientation cases (not shown here) suggests that the DSM option is more effective at ALR 2 while the orientation options are more effective at ALR 8, since they shift more of the heavy overproduction from midday. A more comprehensive analysis of the impact on the overproduced power will be covered in [15].

4.

image068

Conclusion

For large system setups, corresponding to high penetration levels of PV, energy storage has the greatest potential of obtaining a better match between load and production in terms of solar fraction, although both DSM and PV array orientation options have comparable impacts. At more moderate overproduction, orientation and DSM options seem slightly better, because of energy losses in the storage medium.

References

[1] N. I. Carlstedt, B. Karlsson, E. Kjellsson, L. Neij, O. Samuelsson (2007), Konkurrenskraft for natansluten solel i Sverige (Competitiveness of grid-connected solar electricity in Sweden), Elforsk Report 06:57.

[2] PV-UPSCALE (2007), Publications review on the impacts of PV distributed generation and electricity networks, http://www. pvupscale. org.

[3] J. V. Paatero, P. D. Lund, Renewable Energy 32 (2007), 216-234.

[4] M. Thomson, D. G. Infield, IET Renewable Power Generation 1 (2007) 33-40.

[5] J. Widen, E. Wackelgard, K. Ellegard, Modeling household electricity load from time-use data. International Scientific Conference on “Green Energy with energy management and IT” in connection with the Swedish National Energy Convention 2008, Alvsjo fair, Stockholm, 12-13 March 2008.

[6] J. Widen, M. Lundh, I. Vassileva, E. Dahlquist, K. Ellegard, E. Wackelgard, Constructing load profiles for household electricity and hot water from time-use data — modelling approach and validation. Manuscript submitted to Energy and Buildings.

[7] A. Capasso, W. Grattieri, R. Lamedica, A. Prudenzi, IEEE Transactions on Power Systems, 9 (1994) 957-964.

[8] K. Ellegard, M. Cooper, electronic International Journal of Time Use Research, 1 (2004), 37-59.

[9] Swedish Consumer Agency, http://www. konsumentverket. se.

[10] Satel-Light, The European Database of Daylight and Solar Radiation, http://www. satel-light. com.

[11] P. Bennich, A. Persson, Methodology and first results from end-use metering in 400 Swedish households. In Proceedings of EEDAL 06 International energy efficiency in domestic appliances and lighting conference, Gloucester 21-23 June 2006.

[12] J. A. Duffie, W. A. Beckman (1991), Solar Engineering of Thermal Processes, John Wiley & Sons, Inc.

[13] D. L. King, J. A. Kratochvil, W. E. Boyson, W. I. Bower, Field experience with a new performance characterization procedure for photovoltaic arrays, 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, 1998.

[14] Meteotest, http://www. meteotest. ch.

[15] J. Widen, E. Wackelgard, P. Lund, Options for improving the load matching capability of distributed photovoltaics at high latitudes, manuscript to be submitted to Solar Energy.

Static surface vs. tracking concentrating surface

Another issue to take into account is that concentrating solar systems, with concentration ratio C=10, can make use only of the beam irradiation plus 10% of the diffuse one, roughly. On the contrary, non­concentrating systems make use of the global irradiation coming from the sun. Thus, the received global irradiation by a non-concentrating static surface was compared with the beam irradiation plus 10% of the diffuse onto a tracking concentrating surface (Table 4).

Table 4. Incident irradiation on a static non-concentrating surface and on a tracking concentrated surface. Static surface inclination from horizontal is 40° in Stockholm, 30° in Lisbon and 20° in Lusaka.

Static surface vs. tracking concentrating surface

Stockholm

(lat=59.2°N)

Lisbon

(lat=38.7°N)

Lusaka

(lat=15.4°S)

Static non-concentrating surface G (kWh/m2,yr)

1170.0

1865.0

2164.0

North-South tracking concentrating surface Gb + 10%*Gdiff (kWh/m2,yr)

842.1

1518.2

1836.9

Ratio Static/Tracking concentrating surfaces output

1.39

1.23

1.18

The global irradiation incident on a static surface is higher when compared with the beam irradiation plus 10% of the diffuse towards a tracking concentrating surface. This means that a non-concentrating fixed collector receives more usable irradiation than a tracking concentrating one like Solar8. Closer to the equator, the beam irrradiation values are higher and this result becomes less accentuated.

Summary and conclusions

PV-Wind-Hybrid systems are for all locations more cost effective compared to PV-alone systems. Adding a wind turbine halves the net present costs (NPC) for the coastal locations in the south of Sweden and cuts the NPC by one third for a location as Borlange with low wind speeds. The load that has to be supplied has of course a large impact on the system size and costs. The results from the simulations show that the NPC for a hybrid system designed for an annual load of 6000 kWh will vary between $48,000 and $ 87,000. Sizing the system for a load of 1800 kWh/year will give a NPC of $17,000 for the best and $33,000 for the worst location.

However, theses values are calculated for a capacity shortage allowance of 10%. The question is of course if such a shortage is acceptable in a single family house and if not what means could be applied to supply the remaining 10% and what would this cost. These questions have not been studied but as Figure 4 shows for most location it would increase the cost significantly if the last 10% should be supplied with the PV-Wind system. The cost per kWh electricity produced by a PV-Wind-Hybrid system varies between 1.4$ for the worst location and 0.9$ for the best location.

References

[1] Borowy, B. S., and Salameh, Z. M. (1994). "Optimum photovoltaic array size for a hybrid wind/PV system." Energy Conversion, IEEE Transaction on, 9(3), 482-488.

[2] Celik, A. N. (2002). "Optimisation and techno-economic analysis of autonomous photovoltaic-wind hybrid energy systems in comparison to single photovoltaic and wind systems." Energy Conversion and Management, 43(18), 2453-2468.

[3] Koutroulis, E., Kolokotsa, D., Potirakis, A., and Kalaitzakis, K. (2006). "Methodology for optimal sizing of stand-alone photovoltaic/wind-generator systems using genetic algorithms." Solar Energy, 80(9), 1072-1088.

[4] McGowan, J. G., Manwell, J. F., Avelar, C., and Warner, C. L. (1996). "Hybrid wind/PV/diesel hybrid power systems modeling and South American applications." Renewable Energy, 9(1-4), 836­847.

[5] Protogeropoulos, C., Brinkworth, B. J., and Marshall, R. H. (1997). "Sizing and techno-economical optimization for hybrid solar photovoltaic/wind power systems with battery storage." International Journal of Energy Research, 21(6), 465-479.

[6] Berruezo, I., and Maison, V. (2006). "Electricity Supply with PV-Wind Systems for Houses Without Grid Connection," Master thesis, Hogskolan Dalarna, Borlange.

[7] Pazmino, V. (2007). "PV-Wind Energy Hybrid Systems Techno-Economic Feasibility Analysis for Different Swedish Locations," Master thesis, Hogskolan Dalarna, Borlange.