POAI Diffuse-Direct Decomposition

​

Summary

When (POAI) is provided in the weather file, PlantPredict can reverse-decompose it into horizontal irradiance components (, , ) using the GTI-DIRINT algorithm. This is activated by the Frontside POAI toggle in Simulation Settings. When enabled, the standard GHI decomposition models (Erbs, Reindl, DIRINT) are bypassed—the horizontal components derived from the GTI-DIRINT algorithm feed into the normal pipeline for each DC field.

​

Inputs

---

​

Outputs

---

​

Detailed Description

PlantPredict POAI Diffuse-Direct Decomposition model is based on the GTI-DIRINT algorithm described by Marion (2015), which derives horizontal irradiance components from measured POAI. The algorithm iteratively applies a tilted variation of the DISC-DIRINT decomposition model and checks its results by transposing back to the tilted plane, adjusting the clearness index $K_t$ until the modeled POAI matches the measurement. Because POAI is typically measured by a sensor at a specific location in the power plant, its mounting configuration (tilt, azimuth, GCR, etc.) may not match any particular DC field—for example, DC fields can have different GCR or tracker settings. The algorithm therefore uses the mounting and tracking parameters defined at the weather-file level, which describe the sensor’s own configuration, rather than any DC field’s parameters. The derived GHI, DNI, and DHI are then re-transposed downstream for each DC field using that field’s actual parameters and the standard transposition models.

​

Algorithm Rationale

The DISC-DIRINT decomposition model was calibrated on horizontal irradiance data. Its central input is the clearness index: $$K_t = \frac{GHI}{DNI_{extra} \cdot \cos\theta_z}$$ which characterizes atmospheric transmittance through empirical relationships. Substituting GTI for GHI and AOI for $\theta_z$ produces a “tilted” $K_t$ that does not map cleanly to these relationships. A tilted surface sees a reduced fraction of the sky dome, receives ground-reflected irradiance that has no horizontal equivalent, and the beam projects through $\cos\theta_{AOI}$ rather than $\cos\theta_z$. The mismatch grows with tilt angle. The iterative procedure compensates for this mismatch. For a given timestep, the other inputs to the DISC-DIRINT model—pressure-corrected airmass, extraterrestrial irradiance, and zenith angle—are independent of the surface orientation. $K_t$ is the input that carries the orientation error. The iteration therefore targets $K_t$: starting with the measured POAI as an initial proxy $GTI_i$, the algorithm computes $K_t$ from $GTI_i$, runs the full DISC-DIRINT decomposition to estimate DNI and DHI, then transposes those components back to the tilted plane using the Perez model. The difference between modeled and measured POAI reveals how far $K_t$ was from its correct value, and is fed back into $GTI_i$ to refine $K_t$ on the next pass. The loop converges when the modeled POAI reproduces the measurement to within 1 W/m². The relaxation factor $C$ decreases with iteration count because DISC and DIRINT select coefficients from discrete lookup-table bins rather than continuous functions. A full-step correction ($C = 1$) works well when far from the solution, but near convergence it can overshoot and oscillate across bin boundaries. Progressively damping the step size ensures stable convergence.

​

Mounting Angle Calculation

Before decomposition, the algorithm computes the (AOI) and surface tilt for each timestep using the weather file’s mounting configuration. For fixed-tilt systems, the tilt is used as-is and the AOI is calculated from the fixed tilt and azimuth combined with the solar position (see Incidence Angle). For single-axis trackers, the tracking angle is calculated using true tracking or backtracking (selected during weather file import), assuming horizontal ground, and the AOI is derived from the resulting tilt and azimuth.

​

Timestep Classification

The algorithm handles two cases separately based on AOI:

• AOI < 90°: The beam component can reach the front surface. An iterative procedure solves for DNI and DHI.
• AOI ≥ 90°: The beam cannot reach the front surface directly. A simplified non-iterative procedure is used.

Timesteps where $POAI \leq 0$ are zeroed out: $GHI = DNI = DHI = 0$.

​

Case 1: AOI < 90° (Iterative)

The algorithm runs the full DISC-DIRINT decomposition using a tilted clearness index $K_t$ derived from an intermediate variable $GTI_i$, initialized to the measured POAI. At each iteration, $K_t$ and $GTI_i$ are used to estimate DNI, DHI, and GHI, which are then transposed back to the tilted plane to produce a modeled POAI. The difference between modeled and measured POAI is multiplied by a relaxation factor and used to adjust $GTI_i$ for the next iteration. The process converges when the difference falls within 1 W/m², or 30 iterations are reached. Each iteration performs the following steps: 1. Compute tilted clearness index: $$K_t = \frac{GTI_i}{DNI_{extra} \cdot \max\!\left(0.065,\, \cos\theta_{AOI}\right)}$$ 2. Estimate DNI using DISC + DIRINT correction: The DISC model computes an initial DNI estimate from $K_t$ using atmospheric transmittance factors (same formulation as in the GHI decomposition). The DIRINT correction coefficient $C_{DIRINT}$ is then looked up from a four-dimensional table using the modified $K'_t$, temporal stability $\Delta K'_t$, solar , and precipitable water (defaulted to unavailable): $$DNI = DNI_{DISC} \times C_{DIRINT}$$ 3. Derive DHI and GHI: $$DHI = K_t \cdot DNI_{extra} \cdot \max(0.065,\, \cos\theta_z) - DNI \cdot \max(0.065,\, \cos\theta_z)$$ $$GHI = DNI \cdot \cos\theta_z + DHI$$ 4. Transpose back to the tilted plane and compare: If DNI ≥ 0 and DHI ≥ 0, the derived horizontal components are transposed to the tilted plane using the Perez model (for sky diffuse) and an isotropic model (for ground-reflected diffuse): $$G_{ground} = GHI \cdot \rho \cdot \frac{1 - \cos\beta}{2}$$ $$GTI_{model} = DNI \cdot \cos\theta_{AOI} + G_{sky,tilt} + G_{ground}$$ where $G_{sky,tilt}$ is the Perez-transposed sky diffuse component. 5. Update and converge: The residual $D = GTI_{model} - POAI$ is computed. The intermediate variable is updated with a damped Newton step: $$GTI_i \leftarrow GTI_i - C \cdot D$$ where $C$ is a relaxation factor that decreases with iteration count to improve stability: The algorithm converges when $|D| \leq 1$ W/m². If convergence is not reached within 30 iterations, the result with the smallest $|D|$ is used. The converged $K'_t$ values for these timesteps are stored for use in Case 2.

​

Case 2: AOI ≥ 90° (Non-Iterative)

When the beam cannot reach the front surface, the measured POAI consists entirely of diffuse irradiance (sky and ground-reflected). The algorithm uses a simplified non-iterative approach: 1. Estimate $K'_t$ from nearby timesteps: The modified clearness index is taken as the average $K'_t$ from same-day timesteps (same morning/afternoon half) where $65° \leq AOI \leq 80°$. This provides a representative atmospheric state without requiring direct beam information. 2. Reverse $K'_t$ to $K_t$ and estimate DNI: $$K_t = \frac{K'_t}{1.031 \exp\!\left(-\frac{1.4}{0.9 + 9.4/AM'}\right) + 0.1}$$ DNI is estimated using the DISC + DIRINT procedure. 3. Derive DHI from an isotropic diffuse model: Since the beam does not reach the front surface, the POAI is assumed to be entirely diffuse (sky + ground). Solving for DHI: $$DHI = \frac{2 \cdot POAI - DNI \cdot \cos\theta_z \cdot \rho \cdot (1 - \cos\beta)}{1 + \cos\beta + \rho \cdot (1 - \cos\beta)}$$ DHI is floored at zero. GHI is then computed from the .

​

Downstream Processing

The derived GHI, DNI, and DHI are written back to the weather data and processed through the standard transposition pipeline. Each DC field may have different mounting parameters than the weather file, so the horizontal components are re-transposed per DC field using the selected transposition model (Hay-Davies or Perez).

---

​

References

• Perez, R., Ineichen, P., Moore, K., Kmiecik, M., Chain, C., George, R., & Vignola, F. (2002). A new operational model for satellite-derived irradiances: Description and validation. Solar Energy, 73(5), 307–317.
• Marion, B. (2015). A model for deriving the direct normal and diffuse horizontal irradiance from the global tilted irradiance. Solar Energy, 122, 1037–1046.