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Summary

When modules in a string are partially shaded, electrical losses can occur beyond the geometric beam shading. Shaded cells produce less current than unshaded cells, and because cells within a string operate in series, the lowest-current cell limits the entire string’s output. The magnitude of these losses depends on module technology and internal circuitry (cell configuration, series vs parallel connections, configuration): crystalline silicon (c-Si) modules are more sensitive to partial shading than thin-film technologies like CdTe. PlantPredict provides four electrical shading models that determine the effective applied to : None, Linear, Fractional, and Step-Fractional. None, Linear, and Fractional are available with all shading algorithms and software versions. Step-Fractional is only available in V12+ with the 3D Site Level shading algorithm.

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Inputs

NameSymbolUnitsDescription
Beam Shading FactorUshd,BU_{shd,B}—Beam shading factor (0-1), from selected shading algorithm
Fractional Shading Percentff%User-specified loss percentage for Fractional model
Number of Module RowsMM—Number of module rows per bay (modules high); used in Fractional model (pre-V12 only)
Number of Bay FractionsNN—Number of partitions per bay for Step-Fractional model (V12+ only)

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Outputs

NameSymbolUnitsDescription
Electrical Shading FactorUshd,B,elecU_{shd,B,elec}—Electrical shading factor (0-1), applied to beam irradiance

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Detailed Description

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Electrical Shading Models

The electrical shading models are applied after beam shading is calculated. Model availability depends on the shading algorithm:
  • None: Nullifies the effect of shading entirely. Available in all shading algorithms.
  • Linear: Total shading losses equal beam shading losses; no additional electrical effect. Available in all shading algorithms.
  • Fractional: When any shading occurs, applies a minimum loss of ff% to the bottom row of modules within the (or all modules if there is only one row), plus additional losses from beam shading. Available in all shading algorithms.
  • Step-Fractional: Losses increase in discrete steps based on number of bay partitions. Available only with the 3D Site Level shading algorithm (V12+).
In V12+ with the 3D Site Level shading algorithm, the electrical shading factor Ushd,B,elec,iU_{shd,B,elec,i} is calculated per bay ii from the per-bay beam shading factor Ushd,B,iU_{shd,B,i}, then averaged across the site for each time step: Ushd,B,elec=1Nbays∑i=1NbaysUshd,B,elec,iU_{shd,B,elec} = \frac{1}{N_{bays}} \sum_{i=1}^{N_{bays}} U_{shd,B,elec,i}

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None

The effect of shading is nullified entirely. No shading losses are applied. Ushd,B,elec=1U_{shd,B,elec} = 1 Behavior is identical across all shading algorithms.

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Linear

The electrical shading factor equals the beam shading factor. No additional is applied beyond the geometric shading. Ushd,B,elec=Ushd,BU_{shd,B,elec} = U_{shd,B} Behavior is identical across all shading algorithms. This model is recommended for CdTe modules, which exhibit a linear response to shading with minimal additional electrical losses.

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Fractional

Electrical mismatch can increase shading losses beyond the geometric beam shading. Ushd,B,elec=E⋅f+Ushd,B⋅(1−f)U_{shd,B,elec} = E \cdot f + U_{shd,B} \cdot (1 - f) where EE is the unshaded module row factor (fraction of module rows within the bay that remain fully illuminated). When Ushd,B≥0.99U_{shd,B} \geq 0.99, no additional electrical effect is applied: Ushd,B,elec=Ushd,BU_{shd,B,elec} = U_{shd,B}. The value of EE depends on the shading algorithm and system configuration: Site-Level 3D (V12+): E=0E = 0 always. The formula simplifies to: Ushd,B,elec=Ushd,B⋅(1−f)U_{shd,B,elec} = U_{shd,B} \cdot (1 - f) This means that when any shading occurs, a minimum loss of ff is applied, with additional losses from beam shading. Row-to-Row and Legacy 3D (pre-V12): EE depends on MM, the number of module rows within the bay (the number of “modules high” of the mounting configuration): E=M−⌈M⋅(1−Ushd,B)⌉ME = \frac{M - \lceil M \cdot (1 - U_{shd,B}) \rceil}{M} where ⌈⋅⌉\lceil \cdot \rceil is the ceiling function. This represents the fraction of module rows that remain unshaded.
  • For M=1M = 1 (typical single-axis trackers): E=0E = 0 when any shade is present, same behavior as V12+.
  • For M>1M > 1 (multi-row fixed-tilt systems): EE is a step function. Losses increase in steps as shade crosses each module row boundary.
Example (M=2M = 2, f=50%f = 50\%):
  • Ushd,B=0.7U_{shd,B} = 0.7: E=(2−⌈0.6⌉)/2=0.5E = (2 - \lceil 0.6 \rceil) / 2 = 0.5, so Ushd,B,elec=0.5×0.5+0.7×0.5=0.60U_{shd,B,elec} = 0.5 \times 0.5 + 0.7 \times 0.5 = 0.60
  • Ushd,B=0.4U_{shd,B} = 0.4: E=(2−⌈1.2⌉)/2=0E = (2 - \lceil 1.2 \rceil) / 2 = 0, so Ushd,B,elec=0×0.5+0.4×0.5=0.20U_{shd,B,elec} = 0 \times 0.5 + 0.4 \times 0.5 = 0.20
Relationship to other models: When f=0%f = 0\%, the Fractional model reduces to the Linear model (Ushd,B,elec=Ushd,BU_{shd,B,elec} = U_{shd,B}). When f=100%f = 100\%, the Fractional model becomes equivalent to the Step-Fractional model with N=MN = M partitions (Ushd,B,elec=EU_{shd,B,elec} = E). For ff between 0 and 100%, the model offers a continuous transition between these two behaviors. However, the Fractional model is not recommended for systems requiring sub-module partitions (half-cell c-Si modules or c-Si modules mounted in landscape); use the Step-Fractional model instead.

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Step-Fractional

Available only in Site-Level 3D (V12+). The bay is divided into NN partitions. When shading affects any portion of a partition, the entire partition is considered lost. This creates quantized (stepped) losses that are always greater than or equal to the beam shading losses. The underlying assumption is that shade progresses uniformly across the bay, parallel to the bottom edge of the bay, with equal-sized partitions. When Ushd,B<0.995U_{shd,B} < 0.995: Ushd,B,elec=1−⌈N⋅(1−Ushd,B)⌉NU_{shd,B,elec} = 1 - \frac{\lceil N \cdot (1 - U_{shd,B}) \rceil}{N} where ⌈⋅⌉\lceil \cdot \rceil is the ceiling function. This model is recommended for c-Si modules, which exhibit stepped losses under partial shading due to bypass diode activation and, in half-cell modules, parallel-connected module sections. Example (N=3N = 3, c-Si module mounted one-high in landscape with 3 bypass diodes):
  • Ushd,B=0.80U_{shd,B} = 0.80: Ushd,B,elec=1−⌈0.6⌉/3=1−1/3=0.67U_{shd,B,elec} = 1 - \lceil 0.6 \rceil / 3 = 1 - 1/3 = 0.67
  • Ushd,B=0.50U_{shd,B} = 0.50: Ushd,B,elec=1−⌈1.5⌉/3=1−2/3=0.33U_{shd,B,elec} = 1 - \lceil 1.5 \rceil / 3 = 1 - 2/3 = 0.33
Sensitivity to NN:
  • N=1N = 1: Entire bay lost if any shading occurs
  • N=2N = 2: Half-bay partitions
  • N=4N = 4: Quarter-bay partitions
  • As N→∞N \to \infty: Approaches Linear model (Ushd,B,elec=Ushd,BU_{shd,B,elec} = U_{shd,B})
Choosing NN for c-Si modules: Let MM be the number of module rows per bay (modules high). For typical c-Si modules with 3 bypass diodes:
  • Portrait, full-cell modules: N=MN = M
  • Portrait, half-cell modules: N=2×MN = 2 \times M (half-cell modules have two parallel halves per module)
  • Landscape: N=3×MN = 3 \times M (one partition per bypass diode per module row)