Irradiance Optimization

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Summary

Irradiance Optimization is a tracker angle calculation method that maximizes total plane-of-array irradiance rather than simply minimizing angle of incidence. PlantPredict implements two irradiance optimization modes: a built-in optimization algorithm (available since Version 11) and integration with the ArrayTechnologies external service. The built-in algorithm evaluates candidate tracker angles to find the angle that maximizes total POA irradiance, accounting for tracker movement penalties and hesitation factors.

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Inputs

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Outputs

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Detailed Description

Irradiance optimization operates after the base tracking angle is calculated and overrides that angle when conditions warrant. When enabled, irradiance optimization receives the tracker angle from the base tracking algorithm (single-axis tracking with optional backtracking) and evaluates whether an alternative angle would provide higher total POA irradiance. If wind stow is also enabled, wind stow has higher priority and will override the irradiance-optimized angle when wind thresholds are exceeded.

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PlantPredict Built-In Optimization

PlantPredict’s built-in irradiance optimization algorithm evaluates multiple candidate tracker angles to identify the angle that maximizes total POA irradiance. The algorithm operates only when GHI is non-zero.

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Step 1: Calculate Baseline POA Irradiance

Calculate total POA irradiance at the standard tracking angle $\alpha_{calc}$: $$G_{POA,calc} = I_b^{POA} + I_d^{POA} + I_r^{POA}$$ where the beam, diffuse, and reflected components are calculated using the configured transposition model.

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Step 2: Evaluate Candidate Angles

For each candidate angle $\alpha_i$ between 0° and $\alpha_{calc}$ (in integer degree increments), calculate the total POA irradiance: $$G_{POA}(\alpha_i) = I_b^{POA}(\alpha_i) + I_d^{POA}(\alpha_i) + I_r^{POA}(\alpha_i)$$ The candidate angle range depends on the sign of $\alpha_{calc}$:

• If $\alpha_{calc} > 0$: evaluate angles from $0°$ to $\alpha_{calc}$
• If $\alpha_{calc} < 0$: evaluate angles from $\alpha_{calc}$ to $0°$

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Step 3: Identify Ideal Angle

Select the candidate angle with maximum POA irradiance: $$\alpha_{ideal} = \underset{\alpha_i}{\arg\max} \, G_{POA}(\alpha_i)$$

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Step 4: Apply Optimization Logic

Irradiance optimization is applied only if both conditions are met:

1. The ideal angle provides higher POA irradiance than the calculated angle:

$$G_{POA}(\alpha_{ideal}) > G_{POA,calc}$$

2. (Version 12 and later) The ideal angle magnitude is less than the calculated angle magnitude:

$$|\alpha_{ideal}| < |\alpha_{calc}|$$ If these conditions are not met, the calculated angle is retained: $\alpha_{opt} = \alpha_{calc}$.

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Step 5: Calculate Movement Penalty Factor

The movement penalty accounts for energy lost during tracker rotation: $$\phi_{movement} = |\alpha_{ideal} - \alpha_{calc}| \times \frac{\omega}{\Delta t \times 60}$$ where:

• $|\alpha_{ideal} - \alpha_{calc}|$ is the angular traversal distance
• $\omega$ is the rotation speed (degrees/second)
• $\Delta t$ is the weather time interval (minutes)
• Factor of 60 converts minutes to seconds

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Step 6: Adjust Hesitation Factor

The hesitation factor $\eta$ represents control system inertia or reluctance to deviate from the calculated angle. It is constrained so that combined penalties do not exceed 1: $$\eta_{adj} = \begin{cases} 1 - \phi_{movement}, & \text{if } \eta + \phi_{movement} > 1 \\ \eta, & \text{otherwise} \end{cases}$$

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Step 7: Calculate Optimized Angle

The final optimized angle is a weighted combination: $$\alpha_{opt} = w_{ideal} \cdot \alpha_{ideal} + w_{traversal} + w_{hesitation} \cdot \alpha_{calc}$$ where the weights are: $$w_{ideal} = 1 - \phi_{movement} - \eta_{adj}$$ $$w_{traversal} = \phi_{movement} \times \frac{1}{2}(\alpha_{ideal} + \alpha_{calc})$$ $$w_{hesitation} = \eta_{adj}$$ If the corrected angle equals zero, the original calculated angle is retained.

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ArrayTechnologies External Optimization

When configured to use ArrayTechnologies mode, PlantPredict sends site parameters, tracker configuration, and weather data to an external API. The service performs proprietary optimization calculations and returns time-series of optimized tracker angles. PlantPredict applies the returned angles directly, bypassing internal tracking and optimization calculations. The ArrayTechnologies algorithms are proprietary and not documented here.

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Physical Interpretation

Irradiance optimization is most beneficial when:

• High diffuse fraction (cloudy or partly cloudy conditions)
• High ground albedo (snow-covered or reflective surfaces)
• Low sun angles (morning, evening, high latitudes, winter)

In these conditions, reducing the tracker angle from the ideal AOI-minimizing position can increase total POA irradiance by capturing more diffuse and reflected radiation, despite slightly worse beam incidence angle. The hesitation and movement penalty factors prevent excessive tracker movement for marginal irradiance gains, accounting for mechanical wear and the energy required for tracker actuation.

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References

• Kelly, N. A., & Gibson, T. L. (2011). Increasing the solar photovoltaic energy capture on sunny and cloudy days. Solar Energy, 85(1), 111-125.
• Marion, B. (2013). Comparison of predictive models for photovoltaic module performance. NREL/CP-5200-58057.
• Narvarte, L., & Lorenzo, E. (2008). Tracking and ground cover ratio. Progress in Photovoltaics, 16(8), 703-714.