Analysis methodology

View-factor programs such as PVsyst and PlantPredict represent the rear-side illumination of bifacial systems through a small set of correction factors. SunSolve Yield extracts these factors directly from a full ray-traced model of the system by running a baseline simulation alongside several modified simulations, each of which isolates a single optical or electrical effect. Comparing the results of these simulations at every time step, and then energy-weighting over the year, yields the annual-average factors reported on the analysis results tab.

The factors that can be extracted are configured on the Analysis tab.

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Controlled simulations

Each modified simulation starts from the baseline scene and changes one or more aspects of it. The selection of factors on the Analysis tab determines which of these simulations are run; simulations shared by several factors are run only once.

Sim IDSimulationModificationUsed for

1, Baseline, The system exactly as configured., The actual system; the reference that the factors aim to approximate. Also the source of the mismatch factors f_M and f_MR.

2, Rear-omitted, Rear-side collection of the modules is blocked., Front-only reference for the bifacial gain g _B; also the source of the front mismatch f_MF.

3, Transparent structure, The mounting structure is made optically transparent., Reference (no structural shading) for f_S; also the spacing-present case for the transmission f_T.

4, No module spacing, The vertical gaps between modules are removed and the horizontal gaps are blocked with an absorber (in addition to the transparent structure)., Reference (no between-module transmission) for f_T; the configured-albedo case for the effective albedo f_A.

5, Albedo 0.3, The ground reflectance is fixed at 0.3 with no wavelength dependence (with no module spacing)., Calibration reference for f_A at 0.3 ground reflectance.

6, Albedo 0.2, The ground reflectance is fixed at 0.2 with no wavelength dependence (with no module spacing)., Calibration reference for f_A at 0.2 ground reflectance.

—, AM1.5g, The spectrum incident on the system (direct and diffuse) is replaced by the AM1.5g reference spectrum., Reference spectrum for the spectral correction f_λ.

The factors are computed by comparing the rear current I_R, the front current I_F, and the module DC power P between simulations. I_R and I_F are the rear- and front-side light-generated currents (the current produced by the absorbed light), not the short-circuit or operating current. Each is evaluated at the cell level and averaged across the cells of a module; when the unit system contains more than one module, it is then averaged across the modules. As with the other quantities, the same currents are used regardless of the selected solve type.

In the equations below, the subscript identifies the simulation by the number shown in the table above: 1 = baseline, 2 = rear-omitted, 3 = transparent structure, 4 = no module spacing, 5 = albedo 0.3, and 6 = albedo 0.2. So I_R1 and I_F1 are the baseline rear and front currents, I_R3 is the rear current with a transparent structure, and I_R4, I_R5, and I_R6 are the rear currents with no module spacing at the configured, 0.3, and 0.2 albedos respectively. The power terms P₁ and P₂ are the module DC power from the baseline and rear-omitted simulations; P_noM1 and P_noM2 are the corresponding powers with each cell solved independently, that is, with no electrical mismatch from non-uniform irradiance.

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Factor equations

Transmission factor

Derived from the rear current with and without the lateral spacing between modules. This also accounts for the change in the total ground area available in the 3D scene.

$$f_T=\frac{I_{R3}-I_{R4}}{I_{R4}}$$

SunSolve’s automated analysis determines f_T from light passing between modules only. In PVsyst, f_T also includes light passing through the module itself. For semi-transparent modules, through-module transmission can be included, but this requires the manual process using a custom complex module in which transmission through the panel is blocked.

Rear shading factor

Derived from the change in rear current between the actual structure and a transparent-structure configuration. It represents the shading and reflection caused by the mounting structure on the rear side.

$$f_S=\frac{I_{R3}-I_{R1}}{I_{R3}}$$

Effective albedo factor

The effective broadband albedo is found by comparing simulations with two known reflectances (0.3 and 0.2).

$$f_A=0.2+(I_{R4}-I_{R6})\times \frac{0.3-0.2}{I_{R5}-I_{R6}}$$

f_A is the equivalent wavelength-independent albedo that reproduces the response obtained with the system’s wavelength-dependent albedo. If an albedo with no wavelength dependence is used, this calculation (and the simulations it requires) can be skipped, as it has no effect on the final result.

Electrical mismatch factors

Mismatch arises when cells receive unequal irradiance. The total mismatch factor f_M compares the baseline power with and without mismatch, and the front mismatch factor f_MF does the same for the rear-omitted (front-only) simulation:

$$f_M=\frac{P_{noM1}-P_1}{P_{noM1}}$$ $$f_{MF}=\frac{P_{noM2}-P_2}{P_{noM2}}$$

The rear mismatch factor combines these with the ratio of front to rear current:

$$f_{MR}=(f_M-f_{MF})\times (1+\frac{I_{F1}}{I_{R1}})$$

This is the form required by PVsyst 7.4.6 and later, which the automated analysis targets. Earlier versions of PVsyst used a variant that also multiplied by the bifaciality factor f_B.

These mismatch values are factors, not direct losses. The rear mismatch factor can be negative; a negative value indicates that the non-uniformity of the rear irradiance counteracts that of the front irradiance. It can also be negative at times where the overall power is very low and stochastic noise dominates the result.

Further discussion on the sources of electrical mismatch, and which are accounted for in SunSolve, is described in sources of electrical mismatch

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Evaluation metrics

Bifacial gain

The bifacial gain g_B is the relative increase in module DC power from rear-side illumination, obtained by comparing the baseline simulation with the rear-omitted simulation:

$$g_B=\frac{P_1-P_2}{P_2}$$

Here P is the module-level DC power output with cell mismatch included (the same quantity used for the mismatch factors); when the unit system contains more than one module, it is the total summed across all modules. The powers are summed over every time step before the ratio is taken, giving an energy-weighted annual value, and the same quantity is used regardless of the selected solve type.

Spectral correction

The spectral correction f_λ quantifies the difference in result when the site spectrum is used instead of the AM1.5g reference spectrum. It can be evaluated from either the module short-circuit current or the module maximum power, as selected on the Analysis tab:

$$f_{\lambda }=\frac{I_{sc,1}}{I_{sc,1,\text{AM1.5g}}}\text{or}{f}_{\lambda }=\frac{P_1}{P_{1,\text{AM1.5g}}}$$

Both quantities are taken at the module level:

• In short-circuit current mode, I_sc is the module short-circuit current.
• In module max power mode, P is the module DC power at the maximum power point, accounting for cell mismatch and, in tandem devices, mismatch between sub-circuits.

If the unit system contains more than one module, f_λ is computed from the sum of the I_sc or P across all modules. Summing gives the same result as averaging, because the module count cancels in the ratio.

f_λ is evaluated at two levels. At each time step it is the instantaneous ratio of the chosen quantity between the baseline and AM1.5g simulations; these per-time-step values are written to the downloaded CSV file and are the values used for the best-fit calculation. The single annual figure reported on the analysis results tab is obtained by summing the chosen quantity over all time steps for both simulations before taking the ratio, giving an energy-weighted average.

In both modes the same quantity is used regardless of the selected solve type (i.e. it never uses the output of the string or inverter, nor does it account for inverter effects such as clipping).

In the AM1.5g simulation, the spectrum incident on the system, both its direct and diffuse components, is set to the AM1.5g reference spectrum. The spectrum that is actually incident to the panels can still differ from AM1.5g, because the wavelength-dependent reflectance of the ground and structures alters the spectrum within the scene.

Spectral model coefficients

View-factor programs often do not accept a full time series of f_λ; instead they reproduce the spectral behaviour from a small set of coefficients that describe how f_λ varies with atmospheric conditions. To make its spectral results usable in those tools, SunSolve fits the per-time-step f_λ values to two established empirical models and reports the fitted coefficients on the analysis results tab.

Both fits use the same source data: the per-time-step spectral correction f_λ (the instantaneous baseline-to-AM1.5g ratio described above), paired with the atmospheric conditions recorded for that time step. Only generating time steps contribute; intervals where either the baseline or the AM1.5g output is zero (for example, at night) carry no spectral information and are excluded. Each model is then fitted independently by ordinary least squares, minimising the sum of squared differences between the modelled and simulated f_λ across all contributing time steps.

Sandia model

The Sandia model [King2004] expresses the spectral correction as a fourth-order polynomial in the absolute (pressure-corrected) air mass AM:

$$f_{\lambda }=a_0+a_{1}AM+a_{2}A{M}^2+a_{3}A{M}^3+a_{4}A{M}^4$$

The five coefficients a₀ … a₄ are found by a standard polynomial least-squares fit of f_λ against air mass. At least ten contributing time steps are required for the fit to be reported; with fewer points the coefficients are not returned.

First Solar model

The First Solar model [LeePanchula2016] describes the spectral correction as a function of both the absolute air mass AM and the precipitable water vapour W (in cm):

$$f_{\lambda }=b_0+b_{1}AM+b_{2}W+b_3\sqrt{AM}+b_4\sqrt{W}+b_5\frac{AM}{\sqrt{W}}$$

Because it depends on two variables, this is a multivariate least-squares fit rather than a single-variable curve fit. The six coefficients b₀ … b₅ are obtained by forming the normal equations for the six basis terms and solving the resulting linear system. The fit requires precipitable water vapour to be present in the weather data and to vary across the time steps; a constant or missing water-vapour series does not carry enough information to constrain the water-dependent terms, and the coefficients are not returned.

The reported coefficients can be entered directly into other tools that implement these models, so that the resulting spectral correction will more closely agree with the SunSolve-derived values.

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Bifaciality factor

The bifaciality factor f_B is a dimensionless parameter that characterizes the relative electrical performance of the rear side of a bifacial PV module compared to its front side. It is a property of the module rather than a result of the analysis.

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Energy weighting

The factors are calculated at every simulation time step. Daily and annual values are then obtained as energy-weighted averages of the time-step results, so that periods of higher production contribute more to the reported figure. This produces the energy-weighted annual averages shown on the analysis results tab, which are suitable for direct entry into PVsyst or PlantPredict.

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For full derivations and discussion of each equation, refer to the white paper linked from determining PVsyst bifacial inputs with SunSolve.