Question

On good locations in South Morocco and Southern California one finds DNI \(\geq 2500\) \(\left[\mathrm{kWh} \mathrm{m}^{-2} \mathrm{yr}^{-1}\right] ;\) on a horizontal surface this is smaller, at \(1440\left[\mathrm{kWh} \mathrm{m}^{-2} \mathrm{yr}^{-1}\right]\). (a) Convert these values to \(\left[\mathrm{Wm}^{-2}\right]\) and \((\mathrm{b})\) compare the first value to the total solar irradiance.

Short answer

DNI converts to 285.6 Wm^{-2}; it is much less than the solar constant (1361 Wm^{-2}).

Step-by-step solution

Understanding Units and Conversion

To convert energy received over a year given in \([\text{kWh}\cdot \text{m}^{-2}\cdot \text{yr}^{-1}]\) into power per unit area \([\text{Wm}^{-2}]\), we need to know that 1 year is equivalent to 8760 hours, and power in watts can be obtained by dividing energy (in kWh) by time (in hours). We will use these conversions.

Conversion for DNI Value

For DNI: \(2500\, [\text{kWh}\cdot \text{m}^{-2}\cdot \text{yr}^{-1}]\). Convert this to \([\text{Wm}^{-2}]\):\[\text{Power (on a DNI basis)} = \frac{2500\, \text{kWh}}{8760 \text{ hours}} \approx 0.2856 \text{ kW}\cdot \text{m}^{-2} = 285.6 \text{ W}\cdot \text{m}^{-2}\]

Conversion for Horizontal Surface Value

For the horizontal surface value: \(1440\, [\text{kWh}\cdot \text{m}^{-2}\cdot \text{yr}^{-1}]\). Convert this to \([\text{Wm}^{-2}]\):\[\text{Power (on a horizontal surface)} = \frac{1440\, \text{kWh}}{8760 \text{ hours}} \approx 0.1644 \text{ kW}\cdot \text{m}^{-2} = 164.4 \text{ W}\cdot \text{m}^{-2}\]

Comparison with Total Solar Irradiance

The total solar irradiance (often referred to as the solar constant) is approximately \(1361 \text{ W}\cdot \text{m}^{-2}\). The DNI value of \(285.6 \text{ W}\cdot \text{m}^{-2}\) is much smaller than the total solar irradiance value, highlighting the losses due to the atmosphere, angle, and location among other factors.

Key concepts

Direct Normal Irradiance (DNI)

Direct Normal Irradiance, commonly abbreviated as DNI, is a crucial concept in the realm of solar energy. It measures the solar radiation received per unit area by a surface that is always held perpendicular to the sun's rays. DNI is critical for technologies that require direct sunlight, such as concentrating solar power systems and high-efficiency photovoltaic panels.

Understanding DNI provides insights into how much potential energy can be harnessed from the sun. In areas like South Morocco and Southern California, DNI values can exceed 2500 kWh/m²/year, which implies high solar resource availability. This is particularly important for solar power projects that rely on maximizing energy capture.

Key points about DNI include:

• DNI accounts for direct sunlight only, excluding diffuse and reflected solar radiation.
• It varies depending on geographic location, weather conditions, and time of year.
• DNI is a critical parameter for assessing the economic viability of solar energy installations that depend heavily on direct sunlight.

By converting annual DNI values to power per unit area, as shown in our exercise solution, we can determine the average solar power available throughout the year.

Total Solar Irradiance

Total Solar Irradiance (TSI) represents the amount of solar energy received per unit area outside the Earth's atmosphere on a surface perpendicular to the sun's rays. It is essentially the sum of all types of solar radiation reaching the Earth's atmosphere. TSI is a fundamental measure, often referred to as the solar constant, with an approximate value of 1361 W/m².

While TSI is crucial for understanding the potential energy available from the sun, it should be noted that not all this energy reaches the Earth's surface unattenuated. During the path through the atmosphere, several factors such as absorption, scattering, and reflection can reduce the amount of solar energy available for practical use.

Important aspects of TSI include:

• TSI affects the Earth's climate by determining the amount of energy available to the planet's surface.
• It is an essential input for models predicting weather and climate patterns.
• The comparison of DNI and TSI helps illustrate the impact of atmospheric conditions on solar power viability.

Thus, comparing DNI with the total solar irradiance highlights the significant reduction in energy content due to atmospheric and environmental factors, as shown in our exercise.

Energy Conversion

Energy conversion is a fundamental process in the utilization of solar energy. It involves transforming the radiant energy from the sun into usable forms, such as electricity or heat. This conversion is accomplished through various technologies and methods, each suited to different applications and efficiencies.

In solar power systems, energy conversion typically involves photovoltaic (PV) panels or solar thermal collectors. PV panels directly convert sunlight into electricity using semiconductors, a process governed by the photovoltaic effect. On the other hand, solar thermal systems convert solar energy into heat, which can then be used directly for heating purposes or to generate electricity through steam turbines.

Key points about energy conversion in solar power include:

• The efficiency of energy conversion varies between technologies and geographic locations.
• Maximizing energy conversion involves optimizing the angle, orientation, and technology type relative to the solar resource.
• Both DNI and TSI values are crucial inputs for designing efficient energy conversion systems.

Understanding these energy conversion processes and their efficiencies is critical for developing reliable and cost-effective solar energy solutions, as energy output directly influences the economic feasibility of solar projects.