Solar Power Efficiency: Model the efficiency of solar panels based on different environmental conditions (sunlight intensity, angle, temperature).

Application of math:

Geometry

Functions

Calculus

Interest: . As an aspiring environmental engineer, this study aligns directly with my career goals and passion for renewable energy. Growing up in Nairobi, a city focused on environmental protection, and being inspired by activists like Wangari Maathai, I have a strong commitment to sustainability. Additionally, my research on how environmental conditions affect solar panel efficiency can contribute to optimizing renewable energy solutions in the future, making a real-world impact. Overall, this topic integrates my background, interests, and aspirations, providing a comprehensive and meaningful project.

Solar panels are usually made from silicon, or another semiconductor material installed in a metal panel frame with a glass casing. When this material is exposed to photons of sunlight (very small packets of energy) it releases electrons and produces an electric charge.

This PV charge creates an electric current (specifically, direct current or DC), which is captured by the wiring in solar panels. This DC electricity is then converted to alternating current (AC) by an inverter. AC is the type of electrical current used when you plug appliances into normal wall sockets.

Objective: To model and analyze the efficiency of solar panels under varying environmental conditions using functions, geometry, and differentiation.

Conveting solar energy

Solar Panel Basics:

photovoltaic cells: a nonmechanical device that converts sunlight directly into electricity. Some PV cells can convert artificial light into electricity.

The photoelectric effect; phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation. The effect is often defined as the ejection of electrons from a metal plate when light falls on it.

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These factors include sunlight intensitiy, angle of incidence and temperature

factors affecting efficiency

Sunlight Intensity (I): Varies throughout the day, Measured in W/m².

Angle of Incidence (θ):Depends on the tilt of the solar panel, Affects the amount of solar energy received.

Temperature (T):Higher temperatures can reduce efficiency.

Angle of incidence: based on the position of the sun

Temperature: Variations of temperature during the day

sunlight intenstity: Eg: using time

Using geometry to find the optimal tilt for maximum efficiency

optimization

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