There are no existing solar design programs developed specifically for a non reservation

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1 - 1 - Solar Design Program There are no existing solar design programs developed specifically for a non reservation based Native American community (Bernal-Agustín et. al 2007). In addition there are no existing solar design programs that include negative refraction solar cells manufactured from metamaterials (Liu, 2011). These solar cells use a negative refractive lens that bends sunlight in the opposite direction to theoretically produce more solar energy output in the same area (Leonhardt & Philbin, 2008). Excel spreadsheets are one approach used to develop mathematical and computational or computer simulation modeling. Excel is not only a freely available program for anyone with a Microsoft Windows operating system but is also powerful and versatile (Barth et. al 2009). One example of an Excel based solar design program uses a time step simulation that calculates energy output at predetermined intervals such as 15 minutes. The energy output for each appliance is listed as well as the type of appliance (Richardson & Thomson, 2011). The simulation model is written in Visual Basic (VBA) and runs as a VBA macro within the Excel spreadsheet. It is open source, which means that programmers can add to the code or modify it as they require (Richardson & Thomson, 2011). An Excel based design program will be developed and tested in order to determine how effective a negative refraction solar power system will be. The simulation model will use a comparison analysis of a negative refraction solar cell manufactured with metamaterials to a solar cell manufactured with the traditional photovoltaic (PV) materials. Power outputs of both will be compared as well as estimated manufacturing and design installation costs. A portion of the simulation model will be written in Visual Basic for Applications (VBA), the programming language used for Excel spreadsheets. The format for the Excel design program is follows. There will be a graphical user interface(gui) that will be accessed through a web site on renewable energy. This site can be

2 - 2 - lined to the other sites or used in a customer service portal or enterprise planning system. The user will be given a series of inputs. These inputs consist of hours per day for lights, television, HVAC, radios, computers, refrigerators, washers and dryers, and monthly bills. The design program will then calculate the desired ilowatt solar system, the number of solar panels for both photovoltaic and metamaterial, the costs for each system, and the cost savings for photovoltaic and metamaterial compared to the utility bills. In addition the carbon emissions will be calculated and compared to how many gallons of gasoline and how many trees planted will the system equal over its lifespan. The data used for this portion of the model were obtained from and All geographical locations are assumed to be Prescott Valley, Arizona. This is the location of Northcentral University, and the principle researcher owns a home there. The VBA section of the design program will calculate the levelized cost of energy and the maximum power curve for the voltage output (Lu et. al 2007). The levelized cost of energy (LCE) is the total sum of the purchase cost and the maintenance costs over the lifespan of the system. This number is expressed as a ratio between the total the cost of the system over the total energy in ilowatts per year (Lu et. al 2007). It is an important calculation in determining the program of a renewable energy system. The equation is given as LCE = ( COi / yi )/ Ean = ( COpv / Ypv) / Eean( γ ) Where COi is the sum of capital and maintenance costs, yi is the lifespan of the system, Ean(γ) is the annual energy from the system, COpv is the initial cost of the solar system, and Ypv is the lifespan of the system (Lu et. al 2007). The LCE equation has been stripped down for grid tie PV system. The efficiency of system design is determined by calculating its maximum power point (MPP) (Boztepe et. al 2007). This MPP includes a variety of factors such as the predetermined

3 - 3 - efficiency of the panels, the average sun radiation (insolation) of a given geographical area, panel shading, and other factors such as temperature. The MPP corresponds to a point on a curve with current measured in amperes on the y-axis and voltage measured on the x-axis. The curve forms a horizontal line above the x-axis depending on the voltage and then forms a 90 degree bend downwards at the point of maximum power. The equations used to calculate an MPP is: V / I = dv / di And the total power measured in watts of the system is: P = V / I = dv / di where the voltage divided by the current equals the negative change of the voltage divided by the change in current(boztepe et. al 2007). The maximum power is calculated using standard test conditions (STC), with the temperature at 25º C and irradiance (solar radiation) is 1,000 W/M² (watts per square meter). The MPP equation is a differential equation, where the voltage changes with respect to the current (Olariu et. al 2005). Differential equations are the foundation for most physics and engineering research by describing the change in variables over time or space domains (Olariu et. al 2005). The order of the equation is the order of the highest derivative. The MPP is the simplest form of a differential equation nown as a first order ordinary differential equation (ODE) with only one independent variable (Boztepe et. al 2007). More complex differential equations are nown as partial differential equations (PDE) in that they describe partial changes in more than one independent variable with respect to dependent variables (Olariu et. al 2005). There are two basic methods for solving differential equations, analytically and numerically (Olariu et. al 2005). Solving equations analytically involves setting up a model based on the properties then solving the equation using calculus and algebra. Solving equations numerically also involves setting up a model, but this model involves adding up a series of

4 - 4 - numerical equations based on the original. Numerical methods are very effective and can solve equations with the help of computers that analytic methods cannot (Olariu et. al 2005). One popular numerical method for solving a first order differential equation is the Fourth Order Runge Kutta Method (RK4) (Hood, 2009). The RK4 method uses a Taylor series to sum up four different numerical values of the equation. A Taylor series is an algebraic method that incrementally sums numerical functions to approximate the total function (Hood, 2009). The RK4 equations are 1 = ( x y ) hf i, i ( x + h 2, y / 2) 2 = hf i / i + 1 ( x + h 2, y / 2) 3 = hf i / i + 2 ( x + h y ) 4 = hf i, i + 3 Where the values are the terms of the equations, the h values are the series increments, the x values are the dependent variables, the y values are the independent variables, and i is the iteration number or how many trials are performed (Olariu et. al 2005). The solution to the RK4 equations is y ( ) i + 1 = yi + / 6 1, By inserting the MPP equation into RK4 with V = y and I = x they become along with the solution 1 y ( dv di ) = h / i i ( d( y + 1 / 2)/ d( x / 2) ) 2 = h i i + h ( d y + / 2) / d( x / 2) ) 3 = h ( i 2 i + h ( d( y + 3 ) / d( x )) 4 = h i i + h ( ) i + 1 = yi + / 6 1, (Olariu et. al 2005).

5 - 5 - These modified RK4 equations are translated into VBA and used to build a macro to solve the MPP equation and graph it on a curve. This program is based on the research done by (Hood, 2009) using VBA for solving RK4 equations. The actual VBA code is based on a program written by Bourg and modified for the MPP equations (Bourg, 2006). The initial V and I values and the h value will be entered into designated cells on the spreadsheet that the program will used to run the calculations (Bourg, 2006). Another RK4 series will also be developed in the C++.NET language. This is a powerful and effective language for building mathematical and scientific simulation models (Olariu et. al 2005). The C++.NET platform runs within the Microsoft Studio development environment that be downloaded and used by any user with a current Microsoft Office license (Olariu et. al 2005). The VBA macros will be activated by the user pressing a button for each on the GUI. The levelized cost of energy and maximum power curve will then be calculated. There is a disclaimer on the GUI These costs are calculated based on experimental data and are used for simulation purposes only (Liu, 2011). The actual costs may vary and further testing and research will need to be performed in order to obtain more accurate data. Metamaterial solar cell design and manufacturing is still in the theoretical stage. The design program GUI, VBA code, Excel formulas, XHTML/Javascript for web site, as well as the Power Point presentation are listed in the appendices.

6 - 6 - References Barth, M., Fay, A., Greifeneder, J., Strube, M., & Weber, P.(November 5, 2009). Object oriented engineering data exchange as a base for automatic generation of simulation models. Industrial Electronics, doi: /IECON Bernal-Agustín, J., Contreras, J.& Dufo-López, R. (2007). Program of control strategies for stand-alone renewable energy systems with hydrogen storage. Renewable Energy, 32(7). p doi: /j.renene Bourg, D. (January 17, 2006).Excel scientific and engineering cooboo. O'Reilly Media, Inc. Print ISBN-13: Boztepe, M., Çola, M., Hiyama, T. & Karatepe, E. (November 4-8, 2007). Power controller design for photovoltaic generation system under partially shaded insolation conditions. The 14 th International Conference on Intelligent System Application to Power Systems, ISAP Retrieved January 03, 2010 from Hood, D. (October, 2009).Numerical solution of ordinary differential equation using an MS Excel spreadsheet. MSOR Connections, 9(3). Retrieved from Leonhardt,U.& Philbin, T. (June 07, 2008). Transformation optics and the geometry of arxiv: v2 light. Liu, Y.(May, 2011). Solar cell design using metamaterials. (Masters Thesis). Available from ProQuest (ID ) Lu, L., Yang, H., & Zhou, W. (2007). A novel optimization sizing program for hybrid solarwind power generation system. Solar Energy 81. p doi: /j.solener Richardson, I. & Thomson, M. (April 04, 2011). Integrated simulation of photovoltaic micro generation and domestic electricity demand: A one-minute resolution open source model. In: Microgen II. 2nd International Conference On Microgeneration And Related Technologies, Glasgow. Retrieved from Olariu, S., Salleh, S., Sanugi, B. & Zomaya, A. (2005). Numerical simulations and case studies using Visual C++.NET. John Wiley & Sons, Inc. ISBN: