1.3 Shading Analysis and Solar Access

Shading Analysis and Solar Access

Shading is the single greatest environmental factor reducing energy yield in field photovoltaic systems. Because crystalline silicon solar cells are connected in series, a shadow cast across even a small portion of a module does not merely cause a localized loss of output—it can compromise the performance of the entire series circuit. Accurately assessing, modeling, and mitigating solar shading is essential for realistic financial forecasting and reliable system engineering.

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1. Principles of Photovoltaic Shading: Near-Field vs. Far-Field

To evaluate shading impact, designers categorize obstructions based on their proximity and the character of the shadow they cast.

Near-Field Shading

• Definition: Obstructions located on the roof or immediately adjacent to the array (typically within 30 to 50 feet), such as chimneys, plumbing vent stacks, dormers, air conditioning units, parapet walls, satellite dishes, and nearby tree branches.
• Characteristics: Near-field objects cast sharp, dark, high-contrast shadows with minimal umbra diffusion. Because of their proximity, even minor variations in solar azimuth create rapid movements of the shadow across modules.
• System Impact: Near-field shadows severely truncate the IV curve of series strings, forcing bypass diode activation, driving shaded cells into reverse bias, and creating localized thermal stress.

Far-Field (Horizon) Shading

• Definition: Distant obstructions located hundreds of feet or miles away, such as mountain ridges, tall city skylines, or distant forest tree lines.
• Characteristics: Far-field obstructions cast soft, diffuse shadows primarily affecting low solar elevation angles during early morning and late afternoon hours.
• System Impact: Far-field shading reduces the effective daylight hours during times when irradiance is already attenuated by high air mass. Its impact on annual energy production is generally uniform and predictable, making it straightforward to model using regional elevation data.

The Nonlinearity of PV Shading

A standard residential monocrystalline module produces current in direct proportion to the sunlight striking its cells. Because cells are wired in series, the current flowing through the string is physically restricted to the current generated by the lowest-producing cell in that series chain:

• If an obstruction shades 10% of a module's surface, but that shadow falls across a single cell in each internal series sub-string, the power output of the module can drop by 50% to 90% if not mitigated by bypass diodes or module-level power electronics.
• Think of a series string of PV cells as a water pipe: pinching the pipe at any single point restricts water flow throughout the entire length.

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2. Tools for Shade Assessment

Accurate shading analysis requires mapping surrounding obstructions onto the celestial sun path for the installation's specific latitude.

The Solar Pathfinder

• Operating Principle: A non-electronic, manual optical instrument featuring a transparent, convex reflective plastic dome mounted over a paper sun path chart.
• Workflow: The surveyor levels the instrument using an integrated bubble level, points the base True South using a built-in compass corrected for local declination, and looks directly down onto the dome from above. The shiny dome reflects a $360^\circ$ panoramic image of the surrounding skyline, trees, and buildings overlaid directly onto the latitude-specific sun path lines.
• Data Extraction: By visually tracing where reflections cross the chart's monthly sun paths and solar hour intervals, the surveyor tabulates solar access percentages for each month without requiring batteries or digital processing.

Solmetric SunEye

• Operating Principle: A handheld digital instrument incorporating a calibrated fisheye camera, internal electronic compass, tilt sensors, and an embedded processor.
• Workflow: The surveyor places the SunEye at the proposed array height and tilt, levels the device, and captures a digital fisheye exposure. The device instantly analyzes the high-contrast boundary between open sky and solid obstructions, calculating hourly, monthly, and annual solar access numbers.
• Reporting: Automatically computes Solar Availability, Tilt and Orientation Factor, and Total Solar Resource Fraction, exporting digital horizon files directly into production simulation software such as PVsyst, Helioscope, or Aurora.

LiDAR and Remote Aerial Modeling

• Technology: Light Detection and Ranging (LiDAR) data captured via aerial flyovers or satellite high-resolution photogrammetry, complemented by drone-based 3D point cloud mapping.
• Advantages: Enables detailed 3D site modeling without requiring physical roof access during preliminary design, accurately reconstructing tree heights, roof pitches, and dormer geometry.
• Limitations: LiDAR datasets may be several years old, failing to capture recent tree growth or newly erected structures. Trees also present seasonal variations (deciduous leaf loss in winter vs. full foliage in summer), which must be accounted for in shading simulations.

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3. Solar Resource Metrics: TOF, SA, and TSRF

Incentive programs (such as state clean energy rebates), utility interconnection reviews, and commercial performance guarantees rely on standardized metrics to quantify site solar quality.

Solar Availability (SA)

Solar Availability (SA), also referred to as Solar Access, represents the percentage of available solar radiation that strikes the array location after deducting losses caused by shading obstructions alone:

$SA = \frac{\text{Insolation received considering shade obstructions}}{\text{Theoretical insolation received with zero shade obstructions}}$

If an unobstructed site would receive $5.0 \text{ kWh/m}^2/\text{day}$, but nearby trees reduce incident insolation to $4.4 \text{ kWh/m}^2/\text{day}$, the Solar Availability is $4.4 / 5.0 = 0.88$ (or $88\%$).

Tilt and Orientation Factor (TOF)

Tilt and Orientation Factor (TOF) measures the efficiency of the array's physical orientation (azimuth and tilt) compared to the mathematically optimal orientation for that specific geographic location:

$TOF = \frac{\text{Shade-free insolation at actual tilt and azimuth}}{\text{Shade-free insolation at optimal tilt and True South azimuth}}$

In the continental United States, an array facing due True South ($180^\circ$ azimuth) at a tilt angle equal to local latitude achieves a TOF of $1.00$ ($100\%$). An array mounted on an East-facing roof slope ($90^\circ$ azimuth) with a $20^\circ$ tilt might achieve a TOF of approximately $0.85$ ($85\%$).

Total Solar Resource Fraction (TSRF)

The Total Solar Resource Fraction (TSRF) is the master metric that combines both geographic orientation efficiency and shading impact:

$\text{TSRF} = \text{TOF} \times \text{SA}$

Worked Example: Calculating TSRF

A rooftop array in New Jersey has the following audit characteristics:

• The array is installed on a roof slope facing South-Southwest ($210^\circ$ azimuth) at a $26^\circ$ pitch ($6:12$). According to solar tables for that latitude, this orientation yields a $\text{TOF} = 0.96$ ($96\%$).
• A digital shade analysis using a Solmetric SunEye indicates that mature oak trees to the southeast reduce morning solar access, resulting in a $\text{SA} = 0.89$ ($89\%$).
• The Total Solar Resource Fraction is calculated as: $\text{TSRF} = 0.96 \times 0.89 = 0.8544 \approx 85.4\%$

Many state rebate programs and commercial power purchase agreements mandate a minimum TSRF threshold (often $75\%$ or $80\%$) for an installation to qualify for financial incentives.

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4. Seasonal Shading Dynamics and Shadow Geometry

The length of a shadow cast by any obstruction is an exact trigonometric function of the solar altitude angle ($\beta$):

$\text{Shadow Length} = \frac{\text{Object Height}}{\tan(\beta)}$

Because solar altitude reaches its annual minimum on the winter solstice, shadows reach their maximum annual length on December 21. A 30-foot tall tree with a solar altitude of $25^\circ$ casts a shadow extending $30 / \tan(25^\circ) = 30 / 0.4663 = 64.3 \text{ feet}$. On June 21, with a noon solar altitude of $72^\circ$, that same tree casts a shadow of only $30 / \tan(72^\circ) = 30 / 3.0777 = 9.7 \text{ feet}$.

Seasonal Shading Impact Matrix

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5. Bypass Diode Activation Dynamics and Hotspot Prevention

When light strikes a photovoltaic cell, it generates an electrical current through the photoelectric effect. What happens when a cell is shaded while the rest of the string remains in full sun?

Reverse Bias and the Hotspot Hazard

1. In a series string, the same electrical current must pass through every cell.
2. When one cell is shaded, its capability to generate current drops sharply.
3. The fully illuminated cells in the series string force their full current through the shaded cell.
4. To pass this current, the shaded cell is driven into reverse bias (acting as a high-resistance load rather than a power generator).
5. The shaded cell dissipates energy as concentrated heat. If sustained, temperatures can exceed $150^\circ\text{C}$ to $200^\circ\text{C}$, melting the EVA encapsulant, scorching the backsheet, causing localized cell delamination, or starting a fire. This destructive phenomenon is known as a hotspot.

How Bypass Diodes Protect the Module

To prevent hotspot destruction and maintain string current continuity, module manufacturers integrate bypass diodes inside the module junction box:

• In a standard 60-cell module, cells are wired into three series sub-strings of 20 cells each. One bypass diode is connected in antiparallel across each 20-cell group.
• Normal Unshaded Operation: Each cell produces positive forward voltage ($+0.5\text{V}$ to $+0.6\text{V}$). Across a 20-cell sub-string, the total forward voltage is approximately $+10\text{V}$ to $+12\text{V}$. The bypass diode experiences reverse voltage, keeping it turned OFF (open circuit). All current flows through the cells.
• Shaded Cell Operation: When a cell is shaded, its voltage drops to negative values (reverse bias of $-10\text{V}$ to $-15\text{V}$). This pulls the entire sub-string voltage negative. As soon as the sub-string voltage drops below approximately $-0.7\text{V}$, the antiparallel bypass diode forward-biases and turns ON (conducts).
• The Result: The bypass diode shunts the string current around the shaded 20-cell sub-string. The unshaded 40 cells continue producing power, and the overall string current remains high while losing only one-third of the module's voltage.

Advanced Module Topologies and MLPE

• Half-Cut Cell Architecture: Modern modules cut cells in half (e.g., 120 half-cut cells), splitting the module into two parallel upper and lower halves, each equipped with bypass diodes. If horizontal shading covers the bottom row of cells, only the lower half is bypassed while the upper half continues generating full power.
• Module-Level Power Electronics (MLPE): DC optimizers and microinverters perform Maximum Power Point Tracking (MPPT) at each individual module, completely eliminating string-level mismatch caused by partial shading.