How to Selecting Azimuth and Tilt Angles for Solar panel

How to calculate the solar panel installation tilt Angle and azimuth

The design and installation of photovoltaic (PV) systems require consideration of several factors to ensure that the systems operate efficiently and safely. Among these, the azimuth angle and tilt angle of the PV modules are two critical parameters. This guide will detail how to choose these parameters, especially when installing PV systems on non-south-facing roofs.

1. Solar power station Azimuth Angle Selection

Azimuth angle is defined as the angle between the vertical plane of the PV module and true south. In the northern hemisphere, the sun is positioned due south at noon; therefore, when the vertical plane of the PV module is at an angle of 0° to true south, the solar radiation received is maximized.

1.1 True South Orientation

• Advantages:
  • PV modules oriented to true south can achieve maximum annual energy production, particularly in spring and autumn.
• Disadvantages:
  • If obstructed by the shadows of nearby trees or buildings, power generation may decline.

1.2 East Orientation

• Advantages:
  • East-facing modules produce higher energy output in the morning, making them suitable for households or businesses with peak electricity demand in this period. For example, data indicates that east-facing modules capture significant irradiance in the morning.
• Disadvantages:
  • Lower energy generation in the afternoon may result in lower total output throughout the day compared to south-facing modules.

1.3 West Orientation

• Advantages:
  • West-oriented modules excel in afternoon energy output, ideal for households or businesses with electricity needs concentrated in the afternoon. According to Pecan Street’s research, west-facing modules can reduce household electricity consumption by 65% during high electricity prices compared to 54% for south-facing modules.
• Disadvantages:
  • Lower production in the morning leads to an overall decrease in daily energy generation relative to south-facing systems.

1.4 North Orientation

• Advantages:
  • May accommodate architectural aesthetic requirements or spatial constraints.
• Disadvantages:
  • North-oriented modules typically provide significantly lower energy output than other orientations—installation is generally not recommended.

2. Solar Panel Tilt Angle Selection

The tilt angle is the angle between the PV module and the horizontal plane. Selecting an appropriate tilt angle can maximize solar radiation received, thereby improving energy efficiency.

2.1 Year-Round Maximum Energy Production

• Recommendation: It is generally suggested that the tilt angle equals the local latitude (e.g., if the local latitude is 38.9°, the recommended tilt angle is 38.9°).
• Reason: This configuration can maximize the solar radiation received throughout the year, particularly suitable for users seeking to maximize annual energy output.

2.2 Winter Maximum Energy Production

• Recommendation: For maximizing energy output in winter, the tilt angle is suggested to be the local latitude plus 10° (e.g., if the local latitude is 38.9°, the recommended winter tilt would be 48.9°).
• Reason: The sun’s altitude is lower in winter, and increasing the tilt angle facilitates better capture of solar radiation.

2.3 Non-True South Orientation

• Recommendation: For roofs not facing true south, the optimal tilt angle decreases as the azimuth angle increases. Specific recommendations include:
  • Azimuth angle 0°~10°: Optimal tilt angle is 30°.
  • Azimuth angle 20°~60°: Optimal tilt angle is 20°.
  • Azimuth angle 70°: Optimal tilt angle is 10°.
  • Azimuth angle 80°~90°: Optimal tilt angle is 0°.
• Reason: Adjusting the tilt angle can mitigate some of the energy losses due to poor orientation, thereby increasing overall system efficiency.

3. Optimization Recommendations in Practical Application

3.1 Air Circulation

• Recommendation: Maintain a gap of 15 cm to 20 cm between the mounts and the roof to ensure good air flow, reducing the surface temperature of the PV modules and improving energy output.

3.2 Load Analysis

• Recommendation: Installing a PV system will increase the load on the roof; therefore, a load analysis of the roof structure is essential to ensure it can support the additional weight. This is particularly important for sloped roofs, which may require structural reinforcement.

3.3 Lightning Protection Measures

• Recommendation: Roof-mounted PV systems need to have lightning protection devices and grounding to prevent damage from lightning strikes.

3.4 Software Assistance

• Recommendation: Utilize professional software like PVsyst for simulations, which can accurately determine the best installation angles and orientations. These software tools can select appropriate tilt angles based on specific project requirements throughout the year.

4.Solar power plant Case Studies from Abroad

4.1 USA Case Study

• Pecan Street Research Report:
  • West-oriented modules perform exceptionally well during periods of high electricity prices and grid load, potentially reducing household energy consumption by 65%, while south-facing modules only achieve a reduction of 54%.
  • East-oriented modules have higher energy outputs in the morning, making them suitable for households or businesses with morning electricity needs.
  • Installation of north-oriented modules is not recommended as their energy output is significantly lower than that of other orientations.

4.2 Germany Case Study

• Research Findings:
  • West-oriented modules can produce about 10% more energy than south-oriented modules in summer afternoons, making them ideal for high electricity price periods and high grid load conditions.
  • East-oriented modules have about 5% higher energy output in the morning during spring and autumn compared to south-oriented modules and are suitable for low electricity price periods.
  • North-oriented modules are generally not recommended due to their significantly lower output.

4.3 France Case Study

• Research Findings:
  • By adjusting the azimuth and tilt angles of PV modules, energy losses due to poor orientation can be partially mitigated. For instance, losses are relatively small within a ±30° range of the azimuth angle.

5. Specific Calculation Methods for the Azimuth Angle and Inclination Angle of Solar Panels

5.1 Extraterrestrial Radiation Calculation Formula

E = E_SC × (r₀/r)² × (sin(δ) sin(λ) + cos(δ) cos(λ) cos(ω))

• E: Extraterrestrial radiation (W/m²)
• E_SC: Solar constant, E_SC = 1367 W/m²
• δ: Declination angle (°)
• λ: Latitude of the measuring point (°)
• ω: Solar hour angle (°)
• (r₀/r)²: Correction factor for the distance between the sun and the earth

5.2 Solar Elevation Angle Calculation Formula

θ_s = arcsin(sin(δ) sin(λ) + cos(δ) cos(λ) cos(ω))

• θ_s: Solar elevation angle (°)
• δ: Declination angle (°)
• λ: Latitude of the measuring point (°)
• ω: Solar hour angle (°)

5.3 Declination Angle Calculation Formula

δ = 23.45 × sin(360 × (n – 81)/365)

• δ: Declination angle (°)
• n: Day number of the year

5.4 Solar Hour Angle Calculation Formula

ω = 15 × (t – 12)

• ω: Solar hour angle (°)
• t: Local time (hours)

5.5 Solar Radiation on Tilted Surface Calculation Formula

G_T = G_direct × R_b + G_diffuse × R_d + G_reflected × R_r

• G_T: Solar radiation on tilted surface (W/m²)
• G_direct: Direct solar radiation on a horizontal surface (W/m²)
• G_diffuse: Diffuse solar radiation on a horizontal surface (W/m²)
• G_reflected: Reflected solar radiation from the ground (W/m²)
• R_b: Correction factor for direct irradiance on a tilted surface
• R_d: Correction factor for diffuse irradiance on a tilted surface
• R_r: Correction factor for ground reflection on a tilted surface

5.6 Direct Irradiance Correction Factor on a Tilted Surface

R_b = cos(θ_s – β) / cos(θ_s)

• θ_s: Solar elevation angle (°)
• β: Tilt angle of the photovoltaic module (°)

5.7 Diffuse Irradiance Correction Factor on a Tilted Surface

R_d = 0.5 × (1 + cos(β))

5.8 Ground Reflection Correction Factor on a Tilted Surface

R_r = (1 – cos(β)) × ρ

• ρ: Ground reflectance, generally taken as ρ = 0.2

6. Installing PV Systems on Non-South-Facing Roofs

PV systems can still be installed on non-south-facing roofs, but appropriate azimuth and tilt angles must be chosen based on the specific orientation and geographic location to ensure optimal energy efficiency.

6.1 East Orientation

• Recommendation:
  • East-oriented modules have higher energy output in the morning, making them suitable for households or businesses with peak electricity needs during this period. The data shows that east-facing modules receive significant irradiance in the morning, thus the total daily irradiance will be highly affected by the irradiance situation during the day.

6.2 West Orientation

• Recommendation:
  • West-oriented modules produce higher energy outputs in the afternoon, which is suitable for households or businesses with afternoon electricity demands. According to the Pecan Street research report, west-facing modules can reduce household consumption by 65% during peak pricing and grid load while south-facing modules achieve only a 54% reduction.

6.3 North Orientation

• Recommendation:
  • Installing north-facing modules is generally not recommended due to their significantly lower energy output than other orientations. However, in certain specific circumstances, such as architectural aesthetics or spatial constraints, they might be considered, although the expected energy efficiency will be lower.

7. Conclusion

When selecting the azimuth and tilt angles for PV modules, consider the following factors:

• Geographic Location: The latitude and longitude of different regions will affect solar radiation distribution.
• Electricity Demand: Choose the appropriate orientation based on your main electricity usage times.
• Shade Obstruction: Consider potential shade caused by surrounding trees, buildings, etc.
• Architectural Aesthetics: In some cases, aesthetic requirements may influence the installation orientation of PV modules.

Through proper calculations and optimizations, efficient PV systems can be installed even on non-south-facing roofs. Using professional software like PVsyst for simulations can help accurately determine the best installation angles and orientations, ensuring the systems operate efficiently, safely, and reliably.