Activity: Solar Panel Inclination

Calculating the Energy Produced by Solar Power

Photovoltaic (PV) systems are used to translate sunlight into energy, for residential and industrial use. Along with wind power and other sources, PV systems represent a renewable source of energy, though PV systems do require batteries to allow for a continuous supply of electricity.

One thing to consider with PV systems is just how much energy can be harnessed. We can use the following formula to estimate the average energy output (E) of a PV solar panel, measured under standard test conditions and expressed in kilowatt hours (kWh):

E = A × r × H × η

Where…

A is the total solar panel area in m².
r is the solar panel yield, expressed as a percentage (%).
H is the average annual available solar radiation, assuming a 90° tilt, in kWh ⁄ m²
η is the efficiency of the solar installation, factoring in losses. The typical range of values are [0.75…0.85].

Before proceeding, check out the following brief video regarding solar energy use in California:

Calculating the Solar Radiation Available

Calculations of solar panel capability often assume a 90° angle between sunlight and the solar panel; in other words, maximum energy can be achieved when the solar panel and sunlight are perpendicular. However, in reality, corrections to the panel’s incline need to be made based on geographic position, season, and even the day of the year. How do we determine the amount of solar radiation available to the panel on a given day?

Observe the following diagram, which depicts the relationship between the amount of solar radiation measured on a horizontal surface (S_h), the amount of solar radiation measured perpendicular to the sun (S_p), and the amount of solar radiation incident on a titled panel (S_i):

solar_graphic
Adapted from http://www.pveducation.org/

We can calculate the amount of solar radiation using the following formula:

solar_formula1

Where the elevation angle θ (in degrees) is calculated from:

solar_formula2

and where d is the day of the year; for example, January 20 would be day 20, whereas February 4 would be day 35. The angle β is the angle at which the solar panel is tilted. The sine function (“sin”) is a trigonometric function based on the concept of a right triangle; it computes the quotient of (length of side opposite the angle / length of hypotenuse).

C++ Activity: Computing The Impact of Tilt

This project will provide you with an introduction to the fundamentals of conditional repetition in C++. The focus of this project is on how to solve problems using the C++ “while” or “for” statements. In this project, you will…

Develop code to read data from the standard input and produce data to the standard output.
Write code that conforms to a programming style specified by the instructor.
Translate given mathematical expressions into equivalent syntactically correct programming statements.
Select and implement the appropriate control structure(s) for this problem.

As always, be sure to properly document your code. Consult the C++ Coding Guidelines document for proper coding standards. Use good design principles and design the solution before attempting to write code.

Create a program called SolarPanelInclination.cpp. This program will allow the user to enter two inputs, as follows:

S_h, the amount of solar radiation measured horizontally, in kWh/m²
β, the angle at which the solar panel is tilted, in degrees (range is [0-180])

You must validate the β input for the given range. Remember to include a descriptive error message, and follow the basic steps outlined in class.

Once the program has received the input, a table of solar radiation measured perpendicular to the solar panel (S_p) over a period of 31 days (days 150-180). You may assume that the latitude is 40.6306464, which is the latitude of Schuylkill Haven, PA. All values should be expressed with three digits of precision on the right of the decimal point. Note: The sin() function in C++, found in the <cmath> library, expects to be given an angle in radians, not degrees. The formula to convert an angle in degrees to an angle in radians is (angle in degrees) x (π/180). Use the value 3.14159265359 for π.

For example:

Please enter the amount of horizontal solar radiation (kWh/m^2): 30
You entered 30 kWh/m^2.

Please enter the angle of tilt, in degrees: 45
You entered 45 degrees.

       DAY      Sp
       ===   ========
       150    28.468
       151    28.407
       152    28.349
       153    28.293
       154    28.240
       155    28.191
       156    28.144
       157    28.099
       158    28.058
       159    28.019
       160    27.983
       161    27.950
       162    27.920
       163    27.892
       164    27.868
       165    27.846
       166    27.827
       167    27.811
       168    27.797
       169    27.787
       170    27.779
       171    27.774
       172    27.772
       173    27.773
       174    27.776
       175    27.783
       176    27.792
       177    27.804
       178    27.819
       179    27.836
       180    27.857
Press any key to continue . . .

Another example:

Please enter the amount of horizontal solar radiation (kWh/m^2): 30
You entered 30 kWh/m^2.

Please enter the angle of tilt, in degrees: 60
You entered 60 degrees.

       DAY      Sp
       ===   ========
       150    23.885
       151    23.810
       152    23.739
       153    23.671
       154    23.607
       155    23.546
       156    23.488
       157    23.434
       158    23.383
       159    23.336
       160    23.292
       161    23.251
       162    23.214
       163    23.180
       164    23.150
       165    23.123
       166    23.100
       167    23.080
       168    23.064
       169    23.051
       170    23.042
       171    23.035
       172    23.033
       173    23.034
       174    23.038
       175    23.046
       176    23.057
       177    23.072
       178    23.090
       179    23.111
       180    23.136
Press any key to continue . . .

Deliverables

See the instructor for submission instructions and due date(s).

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