Finally we investigated the correlation between the photo current (PC) and the effective absorption (Aeff) by the utilization of one of our photovoltaic devices with the following setup: dITO=140nm, dPEDOT=140nm, dCuPC=30nm, dBBP-perylene=70nm. The photocurrent action spectrum was taken by the use of a halogen lamp using a Keithley 237 source measure unit. The analysis of the PC and the Aeff curve in dependence on the incident wave length let us gain a better understanding of the diffusion lengths of excitons.

One finds evident correlation between PC and the Aeff which leads to an understanding about the energy conversion efficiency of a photovoltaic device based on their absorption spectra (see Fig. 10-11). The diffusion length of the excitons in the active layers becomes investigable by the analysis of the absorption spectra for different extends of the effective absorption region. The results of those investigations will be published in a further paper.

3.

Conclusion

Modeling of the spatial distribution of the light absorption in photovoltaic devices was carried out. To localize the light absorption density in the region of the pn-junction of a bilayer solar cell is of elementary importance for the improvement of efficiency. One

could achieve this by the proper adjustment of the optical parameters: thickness, refractive index and the coefficient of extinction of every device layer. Simulations show distinct maxima of absorption density for special layer thicknesses of the active layers. The top-views of the thickness variation graphs provide the optimal thickness for given solar cell materials like a map. Parameter studies were presented, showing where to go searching for materials with optimal absorption efficiencies for coming solar cell setups. Supplementary absorption density spectra show correlation with photo current curves which allows the prediction of the photo current and as a consequence the power conversion efficiency of a photovoltaic device.

Acknowledgements

We gratefully acknowledge the financial support by the “Friedrich Schiedel Stiftung fur Energietechnik Austria!’.

Part of the research work of this paper were performed within project S.14 at the Polymer Competence Center Leoben GmbH (PCCL, Austria) within framework of the Kplus-Program of the Austrian Ministry of Traffic, Innovation and Technology with the contributions by the University of Leoben, Graz University of Technology, Johannes Kepler University Linz, Joanneum Research ForschungsgesmbH and Upper Austrian Research GmbH. The PCCL is funded by the Austrian Governments of Styria and Upper Austria.

A. Mellit1, M. Benghanem2, A. Hadj Arab3 and A. Guessoum4
(1,"> University Center of Medea, Institute of Engineering Sciences, Ain Dahab
26000,Algeria. Tel/Fax: (213) 25 5812 53 e-mail mellit_adel2001@yahoo. fr

(2) University of Sciences Technology Houari Boumediene (USTHB), Faculty of Electrical

Engineering, El-Alia, P. O.Box 32. Algiers 16111, Algeria
Phone/Fax: (213) 21 21 82 14, e-mail m. benghanem@caramail. com

(3) Development Center of Renewable Energy (CDER), P. O.Box 62, Bouzareah, Algiers

16000, Algeria Tel: (213) 21 91 15 03 e-mail: hadjarab@hotmail. com

(4) Ministry for the Higher Education and Scientific Research, Algiers, Algeria
Tel: (213) 21 91 11 04, e-mail: guessouma@hotmail. com

Introduction

Many authors use the feed-forward neural network networks for modeling and forecasting time series [1]. Modeling time series include the area of stochastic prediction. The optimal prediction of a signal sample (in a minimum mean square sense), give a finite number of past samples, is its conditional expectation [2], but the computation of the conditional expectation requires the knowledge of the joint probability of the current sample and the past simple, which is generally not known. Because of this the conditional expectation is in general non-linear, funding the solution is mathematically intractable signal. Therefore, the methods for designing the non-linear signal predictors are sub-optimal, and they can only attempt to approximate the conditional expectation of the current sample. These sub-optimal methods, like Markov chains [3] autoregressive (AR) [4], these methods based on simplifying statistical assumption about the measured data, which are not always satisfied. Others method based on fractal dimension give acceptable results [5]. Neural networks are widely accepted as a technology offering an alternative way to tackle complex and ill-defined problems. They can be trained to predict results from examples, and are fault tolerant in the sense that they are able to handle noisy and incomplete data. They are able to deal with non-linear problems, and once trained can perform prediction at very high speed. The neural network approach provides a good solution to such a problem, because its design is based on training and, therefore, no statistical assumption (modeling) is needed the source data. This method has been successfully applied in several areas like speech processing; image coding; forecasting sunspots prediction solar radiation data and sizing PV systems parameters [6,7]. The aim of this study is to present a new model for prediction and modeling the different signals coming from the monitoring of stand­alone PV system using the adaptive network combining between RBF network and IIR filter. Estimated signals allow to analyzing the performance of PV systems and the sizing of PV systems. Possible applications can be found in: Analyzing the performance of stand-alone PV systems; State prediction of stand-alone PV systems (1 day, 2 days,..); Sizing of stand-alone PV systems; Study of storage energy cumulated; Control of maximum power point tracker (MPPT)

()Corresponding author

Evacuation of the glazing can be performed either during assembly in a vacuum chamber or afterwards through stubs in the glass pane or rim seal. The diffusion coefficient of monolithic silica aerogel is in the range of 10-5 — 10-6 m2/s [8], [9] and it is the governing parameter with respect to evacuation time. Therefore the evacuation should take place at least from one surface of the aerogel in which case only the aerogel thickness determines the evacuation time and not the actual glazing area.

From the thermal analyses use of laminated plastic foils developed for vacuum insulation purposes seems as the most suitable solution for the rim seal in aerogel glazing. The big challenge was how to make an airtight connection between the foil and the glass panes. From a thermal point of view, the total rim seal thickness should be as thin as possible which can be obtained by the option shown in Fig. 3a, where the foil is wrapped around the aerogel edges. A butyl sealant is applied between the glass panes and the foil before evacuation of the aerogel glazing. During evacuation the atmospheric pressure will press the glass panes against the aerogel and the butyl sealant making a firm and airtight joint between the foil and the glass panes. The principle is in this way "self tightening”. This principle was developed in a previous European project [12].

The drawback is that the glazing will not be flat due to the additional thickness along the glazing perimeter, which is an aesthetical problem.

Furthermore, the bending of the glass panes results in tensile stresses at the glass edges and tempered glass is required to avoid breakage. This makes the aerogel glazing considerably more expensive. Also the process of wrapping the foil around the aerogel edges is difficult due to the fragility of the aerogel.

In the HILIT project [4] the drawbacks have been overcome by development of a principle, where the foil is folded around rods of polystyrene as shown in Fig. 3b. The height of the polystyrene is a few millimetres lower than the aerogel thickness making room for the butyl sealant. The polystyrene spacer is required as support for the foil and has compression strength large enough to ensure the necessary compression of the butyl sealant when the aerogel glazing is evacuated. By proper choice of the polystyrene dimension a flat glazing is achieved. Furthermore the handling of the foil and application of the butyl sealants can be done without touching the aerogel edges. The drawbacks are an increased thermal bridge effect of the rim seal solution and a more difficult corner solution with enhanced risk of leakages.

Prototypes

The investigations and developments described in the previous sections have been implemented in the laboratory in a process for making prototypes of aerogel glazing. The prototypes were primarily made for testing of thermal and optical properties and for testing the assembly process at a pre-industrial scale.

The core element is the Aerogel Glazing Evacuation Apparatus (AGEA) developed in a national Danish project [10]. The AGEA is a vacuum chamber that makes it possible to evacuate and assemble the aerogel glazing in few minutes as the evacuation takes place mainly from the top aerogel surface.

The rim seal is made as the method shown in Fig. 3b with polystyrene rods wrapped in the Mylar® 250 RSBL300 foil [6]. The process is as follows:

• The heat treated aerogel (T = 425 °C) is placed on the lower glass pane

• A butyl sealant strip is applied to one side of the polystyrene rods with foil, which are placed along the aerogel edges with the butyl facing the lower glass and pressed slightly in position.

• The corners are joined with butyl sealant and a butyl sealant strip is applied on top of the polystyrene rods.

• The top glass pane is centred in the vacuum chamber and small self-adhesive metal disk are placed on the top glass pane opposite to electro magnets in the vacuum chamber lid. The lid is closed and the magnets are activated in which way the upper glass is fixed to the lid in the right position.

• The vacuum chamber lid is opened and the lower glazing with aerogel and rim solution is placed in the vacuum chamber.

• The vacuum chamber lid is closed and the evacuation started. The evacuation is continued until a pressure of approximately 1 hPa has been maintained for 5 minutes. Total evacuation time is approximately 30 minutes.

• The upper glass pane is lowered and pressed firmly against the aerogel and rim seal solution to make an airtight connection between glass panes and rim seal.

• The chamber is gently vented and the atmospheric pressure further compresses the glazing securing the complete compression of the butyl sealing between the foil and the glass panes.

Results

Several prototypes have been made during the HILIT project [4] based on aerogel sheets made by Airglass AB following the optimised aerogel elaboration process developed

during the project on the basis of the previously patented route [11]. The aerogel thickness was 15 mm + 1.

The centre U-values of the optimised glazing prototypes have been measured by means of a hot plate apparatus. The average centre U-value is found to be 0.66 W/m2K + 0.03, which with the average aerogel thickness of 14.8 mm correspond to an estimated thermal conductivity of 0.010 W/mK.

This indirect determined thermal conductivity is in accordance with the measured material properties at a pressure level of 1-10 hPa.

Four of the optimised prototypes have been used for a test window (Figure 5) measuring 1.2 by 1.2 m2 designed for hotbox measurements of the overall U — value. The well-insulated framing system is made only for fixation of the four glazings and will not withstand exposure to real climate for longer periods. The measured overall U-value of the glazing is deduced from the measurements by subtracting the heat loss through the framing system. The result of an average total U-value of 0.72 W/m2K + 0.04 compared to the average centre value of 0.66 W/m2K confirms the very small thermal bridge effect of the developed rim seal solution.

The average direct solar energy transmittance for the four glazings was measured to 73% + 2. The total solar energy transmittance, the g-value, has not been measured but would be a few %-points

Application

For a new single family house in a Danish climate the annual energy savings amounts to about 2300 kWh/a (-16%) if conventional argon-filled triple glazing, (U-value = 0.5 W/m2K, total solar energy transmittance = 0.4) is replaced with aerogel glazing (U-value = 0.5 W/m2K, total solar energy transmittance = 0.75). For a low-energy house the savings are reduced to 1600 kWh/a, but in this case it corresponds to 25% of the annual heating demand. A high solar transmittance may result in high indoor temperatures during summertime even in colder climates and solar shading and enhanced venting may be needed.

However, the optical quality of aerogel glazing is not at the same level as conventional glazing units especially not if exposed to non-perpendicular direct radiation where some diffusion of the radiation in the aerogel occurs and makes the outlook hazy. But the optical quality has been improved considerably thanks to the research carried out as part of the European projects [4], [5], [12] to a level where almost no disturbance in the view through is present if shielded against direct radiation. This makes aerogel glazing an excellent option for improved daylight utilization combined with a fair outlook by placing large areas of aerogel glazing in north facades. Due to the very good insulation properties and the high solar and daylight transmittance this can be done without energy loss or even with energy gain (Figure 1), which cannot be obtained with any other known glazing or daylight component options. Furthermore, the daylight will be at a more constant as well as pleasant level during the daytime compared to a south orientation and the excess temperature problems will be reduced considerably.

So the application of aerogel glazings in new buildings will offer the possibility of increase the north facing glazing area and decrease the south facing one. Hereby, the capital cost for overheating prevention, e. g. shading devices, air conditioning, enhanced venting, etc., can be greatly reduced.

Despite the promising results already achieved, the research is still focusing on further improvement of the optical quality through detailed studies of the aerogel process and a post heat treatment aiming at an optical quality comparable to ordinary glass.

Conclusions

Within the present European projects HILIT/HILIT+ transparent and insulating plane monolithic silica aerogel tiles are elaborated at large-scale on the basis of a previously patented synthesis route.

Evacuated aerogel glazings of approximately 55 by 55 cm2 have been made — the size dictated by the production plant dimensions at Airglass AB.

A rim seal has been developed with the required barrier properties against atmospheric air and water vapour to ensure a theoretical lifetime of the glazing of about 30 years and with a limited thermal bridge effect. The rim seal is dimensioned so a completely flat glazing is obtained making it possible to use non-tempered glass.

The final assembling and evacuation takes place in a vacuum chamber. The evacuation time is approximately 30 minutes resulting in a final pressure in the aerogel of 5 hPa.

The solar and daylight transmittance of the aerogel glazing is optimised by means of low — iron glass covers with an anti reflection coating. The optical quality has reached a level with minimal disturbance in the view through except if exposed to direct non-perpendicular radiation where diffusion of the light becomes significant.

The measured centre U-value is 0.66 W/m2K. Including the thermal losses in rim seal an overall U-value for the 55 by 55 cm2 glazing is found to 0.72 W/m2K deduced from the hotbox measurements on a window with 4 aerogel glazings joined in an interim frame.

The direct solar transmittance is measured at laboratory conditions to more than 75%, making the aerogel glazings developed in this project superior to other highly insulating glazings on the market with respect to energetic performance in northern European or equivalent climates. The total solar energy transmittance, the g-value, has not been measured but will be 1 — 2 %-point higher than the direct solar transmittance.

Within the frame of the present HILIT+ project, current studies are aiming at optimising further the elaboration process by decreasing duration of supercritical drying of the aerogel panes.

Acknowledgements

This work was funded in part by the European Commission. The authors would like to thank the participants in the two projects on which this work is based:

P. Achard, A. Rigacci & Y. Masmoudi, Ecole des Mines de Paris, France; L. Gullberg & G. Petermann, Airglass AB, Sweden; M. Ryden, Air Liquide Gas AB, Sweden; B. Chevalier, CSTB, France; P. Nitz & W. Platzer, Fraunhofer ISE, Germany; B. Sunden, LTH, Sweden;

M.-A. Einarsrud, E. Nilsen & R. A. Strom, NTNU, Norway; M. Durant, D. Valette & P.-A Bonnardel, PCAS, France; S. Bauthier & G. M. Pajonk, Universite Claude Bernard Lyon 1, France.

The AGEA has been developed and build with support from the Danish Energy Agency.

The power supply needs to be highly reliable but also should be as economical as possible. Both requirements look like to be mutually exclusive, so there is a necessity for optimisation: Ensuring the desired degree of availability while keeping the investment and operation cost low.

This sizing and optimisation process has been done by a tool called TALCO which stands for technical and least cost optimisation. It works not only on investment cost but uses lifetime cost (comprising initial investment, operation, maintenance and replacement). Simulation time is up to 20 years of continuous operation. The tool developed by Fraunhofer ISE consists of detailed models for each power supply component and uses meteorological data for the desired location. Typically 20-30 parameters are varied during the genetic optimisation process and the design target is the minimum life-time cost for the system for a given period.

For the location of Madrid, assuming an interest rate of 5 % the production cost for the electricity was calculated to be 1.82 EUR/kWh with optimal sizing. The system then runs with a solar fraction of 93%. Cost for fuel cell and electrolyzer hardware as well as hydrogen storage materials have not been accounted for a full degree as they are still in a prototype state and therefore their prices are not able to be used. Nonetheless electricity from hydrogen is much more expensive than from PV. In a modified set-up, commercially available hydrogen from
bottles costs 2.5 EUR/kWh including the efficiencies of both fuel cell and DC/DC-converter, still neglecting fully the investment and maintenance cost for the fuel cell.

An important results from the optimisation process are the parameters for the operation of the systems. State-of-Charge (SOC) limits for the usage of the fuel cell as well as minimum PV power requirements and time slot definitions for the use of the electrolyser are outputs from the optimisation and are the rules the EMS follows in its control strategy.

Although NRES currently form only a relatively small part of the world’s electricity generation, their use is expanding and they have a contribution to make to the future diversity of energy mix. As a global trend, government’s central energy policy objective is to ensure secure, diverse and sustainable supplies of energy at competitive prices. One of these studies goes on to suggest that, an available resource from renewables of up to about half of current United Kingdom electricity consumption at prices below 3p/kWh is achievable in the longer term, assuming a development program can be successfully carried out.[4] The study of this case goes on to state that, scenario studies show that in the period up to 2010 and 2025 wastes, wind and energy could make the dominant contributions with modest contributions from landfill gas and hydro resources. In the longer
term, non-fossil sources may form an increasingly large proportion of electricity and energy systems and those of expanding economies, at competitive prices. Moreover, the cost of generative electricity from renewables has almost halved since 1990 and the more mature technologies now generate electricity at prices not far above the wholesale market price. The NRES are, on present projections, amongst the lowest cost ways of providing alternative options to gas fired generation.[5]

DG is a concept of installing and operating small electric generators, typically less than 20 MW, at or near an electrical load. The premise of DG is to provide electricity to a customer at a reduced cost and more efficiently with reduced losses than the traditional utility central generating plant with transmission and distribution wires. Other benefits that DG could potentially provide, depending on the technology, include reduced emissions, utilization of waste heat, improved power quality and reliability. New technologies like small-scale co­generation, gas engines, PV, wind turbines and fuel cells enable an increasing flexibility in energy distribution systems. One of the technologies for DG is the natural gas distributed generators. It is a powerful tool for commercial, institutional, and industrial customers needing a higher level of power supply security. Whether the issue is life safety, securing data processing information, or ensuring plant productivity, natural gas onsite power systems offer the potential for enhancing reliability. For over two decades, stationary natural gas turbines and gas engines used in power generation and combined heat and power (cogeneration) applications have shown a high level of reliability and availability. Another technology, Phosphoric Acid Fuel Cells (PAFC) have recently been introduced into the market and showing these same strong performance characteristics. Compared with the well-established conventional energy systems, most technologies being developed for DG applications are currently costly. However, it is anticipated that with advances in the technologies and a greater demand for DG, costs will be reduced and more installations will take place.[6,7]

HES combine different power generation devices or two or more fuels for the same device. When integrated, these systems overcome limitations inherent in either one. HES may feature lower fossil fuel emissions, as well as continuous power generation for times when intermittent renewable resources, such as wind and solar, are unavailable. Potential hybrid combinations include generators (e. g., fuel cells that use hydrogen; and natural gas — powered turbines, micro-turbines, and reciprocating engines) that work in conjunction with NRES. The cost and environmental advantages of these advanced power generation technologies can be improved by using "opportunity” fuels, such as bio-generated gases and biomass, to supplement or replace conventional natural gas. As applications fields, HES can be used in commercial power parks, industrial plants, renewable energy — integrated buildings and remote (off-grid) power sites.[8]

Based upon the above mentioned advantages of the three alternatives, combining them as a Hybrid Distributed Generation (HDG) can provide electricity grid support and stabilization, achieving higher reliability measures, improve the quality and availability of power. Nevertheless, the concept of HDG should not be taken as a grant; each time this concept is questioned to be added to existing power system, the performance of the modified system should be tested concerning well-known probable problems. This will lead to a scientific assessment behind adding HDG and to what penetration level. Therefore, this paper discusses one of the common problems in power systems; voltage collapse problem, and the effect that can be detected by introducing Dg to an existing power system.

The analysis of the optimal solution from experimental data essentially comprises of four parts: The fluid dynamics analysis, as in the use of Particle Image Velocimetry, PIV, and their outputted results; the electrical output analysis, in the form of readings and analysis carried out for varying electrical loads; heat flux measurements taken directly in experimentation and using Infrared Thermography; and the combined heat and fluid dynamics effectiveness analysis carried out as described by the publications on transpired solar collectors by researchers at the NREL in the US and at Waterloo University in Canada. The experimental test rig design is along the lines of those used by Murphy [14 ] and Jubran et al, [15 ].

PIV provides velocity data across the flow field, requiring tracer particles or seeding in the flow. The method’s particular advantages are that it is non-intrusive, has high spatial and temporal resolution [16].

Conclusions

Perforating PV panels has been demonstrated as a viable way of increasing cooling by previous testing, Murphy [13]. This is more likely due to the increase in contact area brought about by the hole itself, than the setting up of particular boundary layer flow regimes. Hole geometry and features such as pitch and density along with the
main parameters outlined earlier remain to be examined. Setting up flow regimes such as film cooling could lead to fruitful results, though film cooling effectiveness is a measure of the layers ability to eliminate heat transfer to the hot surrounding environment, rather than promote heat transfer, this could still be useful in the PV problem, at the top of a fagade where the air in the cooling duct would be heated considerably. To date only circular holes at 90° to the panel have been investigated. As shown by Botas et al [17], and Goldstein et al [18], varying the hole parameters will increase film cover effectiveness. Altering hole shapes, compound angles, pitches, densities, etc. have also lead to increased heat transfer depending on how the variable parameters are manipulated.

Depending on the size of the duct behind the panel and the pressure difference used to model the buoyancy effect in a building fagade, the free stream air speed tends to be quite low, <5m/s [1]. The best flow regime to promote heat transfer is turbulent flow. At low velocities, and low Reynolds numbers, this may have to be induced, as discussed in work published by Niami and Gessner [19]. Staggering, perforating and setting up ribbed-grooved walls were found to increase heat transfer by a factor of 3 and more, as well as reducing hot spots. lacovides et al [10], discussed how the inclination of the ribbed turbulators brings about a more evenly mixed flow and heat transfer. The use of ribs would also supplement the ideas of cooling the panels using extended fins to the rear, as carried out by researchers at Brown University, Providence, Rl, on hybrid PV collectors. Dimples have been found to give almost the same heat transfer as ribs with a much lower pressure drop.

In the area of analysis and modeling, conventional CFD mathematics must be carried out on the solution ideas. This will be backed up by CFD computer analysis done on Flotran. Heat transfer measurements are being made using the IR camera and heat flux sensors and thermocouples.

Master structures of micro prisms with a pitch of 100^m were made by precision mi­cro machining. The substrate is made in a replication process (figure 2). Organic thin films and the electrodes are deposited on the surface by spincoating and evapora­tion respectively. Cohesion and adhesion forces lead to an increased thickness of the polymer films in the grooves of the struc­ture. This effect makes the location of the metal grid in the grooves more adequate than on the tips of the structure because the probability of direct shunts between the two metal electrodes is decreased. The mi­crogrid structure is realised by evaporation under a certain angle. The microstructure itself functions as a self aligning mask. In the first step a 200nm sacrificial layer of LiF

is evaporated under an angle of 65° relative to the normal of the substrate. This leads to an uncoated region of about 10^m width in the grooves of the structure. Normal to the substrate a 8nm Cr layer to increase the adhesion and a 100nm gold layer are evap­orated. The Au-layer on top of the LiF is removed in a lift off process in di-water in an ultrasonic bath. All grid stripes are interconnected by finally evaporated Cr-Au-layers. Thin films from standard solutions with thicknesses comparable to the planar substrate could be deposited on the structured substrate by spin-coating. PEDOT-CPP 105D was coated @2000Upm for 60sec. The films had to be dried in a vacuum oven for 1h @ 80°C. The active layer P3HT/PCBM (1:2 by wt.) was spun under argon atmosphere for 60sec @500Upm.

Prior evaporation of the 100nm thick Al — electrode, the substrate was again dried in vacuum oven @50° for 10h. From SEM- investigations it could be seen that the large ratio between the dimensions of the mi­crostructure and the thickness of the or­ganic thin films allows a relatively homo­geneous coating of 3-dimensional structure (not shown). An increased thickness of the polymer films in the grooves of the struc­ture was observed. IV-characteristics were measured under argon atmosphere using a Steuernagel AM1.5 Solar simulator (fig­ure 6). However the efficiency of 1.1% is far beyond the best published results for an ITO-based device, these inititial experiments should be regarded as a proof of principle.

Higher efficiencies are expected from further optimising of the process parameters.

1.1 A Calculation model

We have performed rigorous coupled wave analysis (RCWA) calculation [8,9] to simulate the optical properties of the periodically microstructured surfaces. RCWA is a method to analyse the general 3D grating diffraction problem by solving the following Maxwell’s equations rigorously,

‘ V-(*e) = 0 V — H’ = 0 Vx E — — ikoH Vx H’- iko£E

here, E;electric field, H; magnetic field, h = ^eJm0h’ , k =x/2n, s; dielectric constant and X; wavelength. Assuming the Incident electromagnetic wave with wavelength of X, Incident angle 9, azimuthal angle ф and polarization angle ф, the electric and magnetic fields at the grating region is expressed by,

і E2 = ^SP, q (Z)ExP[-i(kx, pX + ку,,У)]

IH 2 = X £ UM (z )Exp[-i(kx, px + kMy)] ^

Here Sp, q^ Up, q is the electric and magnetic amplitude created by the diffracted wave with order of (p, q). The wave vectors and dielectric constant are expressed with the periodicity Лх and Лу,

kx p — k0 {nc sin в cos ф — p(Х/Лх)} I ky q — k0 {nc sin (9 sin ф — q(l/Ay)}

Here, nc is the refractive index of each region, and e’m. n is the (m, n)-th order of Fourier series.

As shown in the above formulation of RCWA, diffraction efficiency for each diffraction order is calculated with inputting the state of incident beam, structural profiles, and optical

constants (n, k) of materials. Any fitting parameters are not used and the accuracy of the solution computed depends solely on the number of terms retained in space harmonic expansion of electromagnetic fields, which corresponds to diffraction order N=(p, q). We have conducted calculations varying N up to 10 and confirmed that spectral feature mostly converge at N > 7. So we consider the diffraction orders up to +7th for x — and y — directions, respectively, and therefore diffraction efficiencies for 225 diffraction orders are calculated for each wavelength in this study. The literature data of optical constants for metals are used in the calculation.

Figure 2 shows schematic diagram of the calculation model in this study. For the ease of calculation, we restrict the grating shape to a simple 2D binary grating with rectangular cavities. Here we define some parameters to describe surface microstructures and the state of incident wave as periodicity Л, aperture size a and depth d. In this study, we set Ax = Лу = Aand ax = ay = a. Incident angle 9 and azimuthal angle ф are also defined as shown in the figure, and polarization angle is defined as у = tan^As/Ap), where As and Ap denote the amplitudes of the s — and p — polarization components of the incident wave, respectively.

The hybrid power generating system consists of wind turbine generator, PV array, storage batteries, and control unit. A typical autonomous wind-PV HPGS generating system is shown in Fig. 1.

PV Module Performance Model

The electrical characteristics of a PV module are short circuit current, open-circuit voltage and maximum power point. A typical PV module I-V curve is shown in fig. 2. Current and voltage depend on temperature and irradiance. The temperature coefficient for the open circuit voltage is negative and large, which is approximately equal to -2,3 mV/°C for an individual cell. On the other hand, the current coefficient is positive and small, that is approximately +6 pA/°C for a square centimeter of the module area (Markvart, 1994). The operating temperature of the cell, which differs from the ambient temperature, determines the open-circuit voltage. Operating temperature can be calculated using equation 1 for a given ambient temperature (Lorenzo, 1994).

PV module short-circuit current is proportional to the number of parallel connected PV cells and irradiance. PV module open-circuit voltage is a logarithmic function of current and proportional to the number of serial connected PV cells. The PV module’s current IM under arbitrary operating condition can be described as;

The necessary number of PV modules to be connected in series is derived by the number of modules needed to match the bus operating voltage.

V =Vм ■ N

PV OC SM (3)

The current output of a PV array at time t, Iм (t), is related to the number of parallel strings as follows:

Ipv (t) = Iм (t) • Npm ■ fMM (4)

Wind Turbine Performance Model

Manufacturers give the characteristic curves for wind turbines as power output versus wind speed at the hub height. The design parameters of a wind turbine generator (WTG)
determine the amount of energy it can harvest from the wind. A power curve, which is a plot of output power against the average wind speed, can be constructed for a WTG design as shown in Fig. 3.

WTG are designed to start generating at the cut-in wind speed, vci Fig. 3 shows that the power output increases nonlinearly as the wind speed increases from to the rated wind speed (vr) . The rated power is produced when the wind speed varies from to the cut out wind speed (vco), at which the WTG will be shut down for safety reasons. The electrical power generated hourly can be calculated from the wind speed data using the power curve of the wind turbine specified ratio, always dispatching wind energy to allow a maximum of its share. In this way, the useful capacity of the wind turbine can be calculated.

Wind turbines are usually only connected in parallel, not in series. Several wind turbines can be connected in parallel to match the system current requirements. This can be done with parallel strings of the same wind turbine type or with strings of a different wind turbine type. It is assumed here that at most two different turbine types are used at the same time in one system. Energy densities for wind are calculated using equation 5.

PwT-0,5. Cp. pair. V

The power output of the wind turbine array at time t,

pwt (t) — !wt (t) ‘vwt 0)- Npwt (6)

Battery Performance Model

Batteries in a hybrid system are connected in series to obtain the appropriate nominal DC bus voltage. Therefore the number of batteries connected in series for the same type of battery in a battery bank is calculated as follows;

N S Bat=VP V/VBat (7)

The hybrid system can have several battery banks, which typically consist of different battery types. The battery state of charge of a battery bank at time t is calculated based on adding the charge current (positive sign) or discharge current (negative sign) to the battery bank state of charge at the previous time instant. When adding the battery current to the battery state of charge, self discharge losses and battery charging losses need to be taken into account. (Seeling-Hochmuth, 1997)

BatB

XiSOCi(t) ‘ Qi + ^Bat(t) ‘ ^t ‘ ^i(Ikolbat(t)) J’ NPBat i=0

The inverter characteristics can be described by the inverter input-output relationship. Some of the power going into the inverter will be lost due to transformation losses that are named inverter efficiency losses. Efficiency losses of inverter depend non-linearly on the AC output power, and therefore non-linearly on the AC load current.

PIIP ‘Vi = PIOP, Vim = f (PIOP) (9)

Control Unit performance Model

The control unit provides an interface between all components of hybrid energy system, giving protection and control. The most frequently encountered components of control unit are blocking diodes, charge regulators, energy routing switches, measurement sensors and the controller. In fact charge regulators can be modeled as a switch which connects and disconnects generator to battery or load according to battery state of charge, temperature or load demand (Engin, 2002). The output power, PBCOP of the battery charger equals the input power PBCIP multiplied with the efficiency losses during the energy conversion. Efficiency losses depend non-linearly on the DC output power, and therefore non-linearly on the DC output current of the battery charger.

Pbcip -Vbc ~ Pbcop, Vbc ~ f (PBCOP) (10)

Efficiency losses can be calculated from efficiency losses versus output power curves that are given manufacturers. Energy routing switches position is defined by controller that was defined operation strategy. Efficiency losses of energy routing switches are small and can be neglected.

Costing Model of Hybrid System

The hybrid system life-cycle costs are sum of initial investment costs and discounted operation costs. Using equation 11, LCC can be calculated. The hybrid system operation costs are in general non-linear, and depend on component size and type. It also depends on how system is operated (Engin et al., 2002).

NumberofConpenents

Cc + / DiscountedCnp,

m

Selecting the settings at which the levels are to be set also needs to be addressed. The range of the settings needs to be broad enough to accurately represent the operating process. However if the level settings are outside the feasible range to produce sufficient products then the results will be confined.

The level settings carefully chosen for the experiment factors are shown below in table 1.