Question

According to the table in Problem 26, San Diego can expect an annual average solar yield of \(5.7 \mathrm{kWh} / \mathrm{m}^{2} /\) day when the panel is tilted to the site latitude and facing south. \(^{116}\) If a household seeks to produce a modest \(8 \mathrm{kWh}\) per day using \(16 \%\) efficient panels, how large will the array need to be? Express as an area in square meters, and in side length for a square of the same area.

Short answer

Answer: The side length of the square array is approximately \(\sqrt{\frac{\frac{8\mathrm{kWh}}{5.7 \frac{\mathrm{kWh}}{\mathrm{m}^{2} \text{day}}}}{0.16}}\) meters.

Step-by-step solution

Find daily energy production required per square meter

We will first calculate the daily energy production required per square meter of solar panels. This can be done by dividing the desired daily energy production (8 kWh) by the given solar yield (5.7 kWh/m^2/day): Energy production per square meter = \(\frac{8\mathrm{kWh}}{5.7 \frac{\mathrm{kWh}}{\mathrm{m}^{2} \text{day}}}\)

Calculate the total area of the panels, considering their efficiency

Now we need to consider the efficiency of the solar panels (16%). The efficiency of the solar panels affects the total area of the array required to produce the desired output. Total area = \(\frac{\text{Energy production per square meter}}{\text{Efficiency}}\) Total area = \(\frac{\frac{8\mathrm{kWh}}{5.7 \frac{\mathrm{kWh}}{\mathrm{m}^{2} \text{day}}}}{0.16}\)

Calculate the side length of the square

Once we find the total area of the panels, we can determine the side length of a square with the same area by taking the square root of the total area. Side length = \(\sqrt{\text{Total area}}\) Side length = \(\sqrt{\frac{\frac{8\mathrm{kWh}}{5.7 \frac{\mathrm{kWh}}{\mathrm{m}^{2} \text{day}}}}{0.16}}\) Using a calculator, we can calculate the values of the total area and side length.

Key concepts

Solar Energy Production

Understanding how solar panels convert sunlight into electricity is essential in grasping solar energy production. The energy produced by a solar panel depends on several factors, such as the amount of sunlight received, known as the solar irradiance, and the panel's efficiency at converting this irradiance into usable electricity. In the provided exercise, we're given the solar yield for San Diego, which averages at 5.7 kWh/m²/day, indicating the amount of energy that each square meter of a solar panel can generate in a day.

In contexts like these, efficiency is the percentage of the sun’s energy that can be converted into electrical power. For example, if a panel's efficiency is 16%, it means that 16% of the solar energy striking the panel is converted into electrical energy. To calculate the power output of a solar array, we would multiply the area of the panel by the solar irradiance and then by the panel's efficiency.

Solar Panel Area Calculation

The solar panel area calculation involves determining the size required for a solar array to meet a specific energy output target. In the scenario given, we need to know how large an array is necessary to generate 8 kWh per day. By dividing the desired energy production by the solar yield, we get the required production per square meter. However, we can't forget to consider the efficiency of the panels, which is crucial to determining the final size of the array needed.

To incorporate efficiency into our calculations, we divide the energy production per square meter by the panel's efficiency rate. The resulting figure provides the total area necessary. Calculating this area is a straightforward yet critical step in designing a solar power system because it influences the cost, the amount of space needed, and potential energy output.

Renewable Energy Education

Renewable energy education plays a key role in empowering individuals and societies to make informed decisions about energy use. It encompasses learning about different types of renewable energy sources, such as solar, wind, and hydro, along with their environmental benefits and technological advances. Educational initiatives promote understanding of how renewable energy can reduce dependence on fossil fuels, lower greenhouse gas emissions, and contribute to a sustainable future.

Efficient energy consumption and understanding the calculations behind solar panel dimensions ties directly into this education. By making these calculations more comprehensible, students and enthusiasts can better grasp how their choices impact energy sustainability and the environment.

Solar Power Systems

Solar power systems convert sunlight into electricity, providing a clean and renewable source of energy. The primary components of such systems include solar panels, inverters, battery storage, and a monitoring system. These systems can range from small-scale residential arrays to large utility-scale power stations. The efficiency and design of a solar power system directly impact its performance and energy production.

Understanding the calculations behind solar arrays, as demonstrated in the example problem, is critical when designing these systems. Factors including geographical location, panel orientation, and local weather patterns must all be considered to optimize a system's energy output and ensure it meets energy demands efficiently.

Energy Efficiency

Energy efficiency refers to using less energy to provide the same service or output. In the context of solar panels, it is a measure of how much of the sunlight that hits the panels is converted into electricity. Higher efficiency means more energy is produced per square meter of the panel, which is particularly important in areas with limited space or when trying to maximize output.

Achieving greater energy efficiency in power systems, including solar, not only reduces energy costs but also minimizes environmental impact. Efforts to improve efficiency span from choosing the right equipment to optimizing system configurations. The more efficient a solar power system is, the smaller the area needed to produce the desired amount of energy, leading to a less resource-intensive setup.