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High-Precision Solar Tracking Controller Powered by Bourges + Wang Algorithm

06 Nov , 2025

1. International High-Precision Astronomical Algorithms

These algorithms originate from astronomy and offer extremely high accuracy (arcsecond level). They are mainly used in scientific research, satellite tracking, meteorology, and precision photovoltaic (PV) control. However, their computational load is heavy, making them less suitable for embedded controllers.

Algorithm Institution / Author Accuracy Features Applications
SPA (Solar Position Algorithm) NREL, U.S. National Renewable Energy Laboratory, Reda & Andreas, 2008 ±0.0003° (~1.1 arcsec) Most authoritative algorithm; includes precession, nutation, aberration, and atmospheric corrections High-end PV tracker controllers, irradiance calibration
Grena Algorithm (2012) Grena, Solar Energy 2012 ±0.01° Accuracy close to SPA, but faster Tracker control, simulation
NOAA Algorithm U.S. National Oceanic and Atmospheric Administration ±0.01° Publicly available source code, easy to integrate General control and meteorological systems
Michalsky Algorithm Michalsky, 1988 ±0.02° Simplified astronomical model Legacy tracking systems, research reference
Meeus Algorithm Jean Meeus, Astronomical Algorithms (1991) ±0.001° General astronomical ephemeris algorithm High-precision systems, time ephemeris software
PSA (Photovoltaic Solar Algorithm) Commonly used in IEC standards ±0.02° Industrial-grade simplified model PV controllers
ESRA (European Solar Radiation Atlas) ESRA Team ±0.02° European standard for building and PV design PV and building simulation

2. Engineering-Grade Simplified Algorithms (for Embedded PV Trackers)

These algorithms trade some accuracy (±0.05°–0.2°) for much faster computation and lower power consumption, making them ideal for MCUs, PLCs, and DSPs. They are the most widely used in the PV industry today.

Algorithm Author / Source Accuracy Description
Bourges Algorithm (1985) B. Bourges ±0.03° Empirical Fourier expansion for solar declination (δ)
Wang Algorithm / Operator Method (1989) Wang Chunhua (Chinese Meteorological Society) ±0.05° Empirical operator method for δ, hour angle (H), azimuth (A), and altitude (h)
Cooper Algorithm (1969) Cooper ±0.1° Classic sine-based model; foundation for many later methods
Iqbal Model (1983) Iqbal, An Introduction to Solar Radiation ±0.05° Used mainly for irradiance models but includes geometric computation
Duffie–Beckman Algorithm (1991) Duffie & Beckman ±0.1° Widely used in thermal energy systems and embedded PV controllers
Kasten–Young (1989) Kasten & Young ±0.1° Empirical relation for solar altitude
Gueymard Algorithm (2001) Gueymard ±0.02° Lightweight irradiance model with geometric accuracy
Nann & Riordan (1991) Nann & Riordan ±0.05° Used in PV performance simulation (early PVsyst versions)

3. Lightweight Control Algorithms (Customized by Manufacturers)

Many commercial PV tracker manufacturers (e.g., NEXTracker, Array Technologies, Soltec, Good Future, TrinaTracker, Huawei, etc.) develop proprietary “control-level astronomical algorithms”. Typically, they combine several techniques:

  1. Base Algorithm: Use Bourges or Cooper for declination (δ)
  2. Hour Angle Correction: Wang operator method or linear correction
  3. Local Time Synchronization: Longitude/time zone and sunrise–sunset adjustments
  4. Real-Time Compensation: Sensor feedback (light, tilt, or irradiance)
Manufacturer Algorithm Strategy Features
NEXTracker (USA) NOAA + Grena hybrid Balance between precision and responsiveness
Array Technologies (USA) Bourges + Wang Operator Method Stable, anti-interference, ideal for large-scale arrays
Soltec (Spain) Grena + empirical calibration High accuracy, suited for bifacial PV
TrinaTracker / Huawei Tracker Simplified SPA + real-time light sensor correction Self-correcting high-precision system
Good Future / Chinese Controllers Bourges + Wang hybrid Efficient embedded algorithm, error < ±0.05°

4. Typical Algorithm Combinations (for PV Trackers)

Combination 1: Bourges + Wang Operator Method (Classic Model)

  • δ: computed by Bourges formula
  • H, A, h: computed by Wang method
  • Pros: Fast, high precision (<0.05°), ideal for embedded MCUs
  • Applications: Good Future, Array Technologies

Combination 2: Grena + NOAA Correction

  • Includes δ, Equation of Time (EoT), and H corrections
  • Pros: Stable throughout the day, suitable for high latitudes
  • Applications: NEXTracker, Soltec

Combination 3: Simplified SPA

  • Accuracy: ~0.001°
  • Pros: Extremely high precision, requires double-precision floating-point support
  • Applications: Scientific research, SCADA-level control systems

5. Algorithm Selection Guide (by Project Type)

Application Scenario Recommended Algorithm Accuracy Notes
Real-time PV tracking (MCU) Bourges + Wang ±0.05° Fast, stable
PV simulation / high-latitude use Grena / NOAA ±0.02° Requires higher processing power
Sensor-assisted control (light or tilt feedback) Wang Operator + Sensor Feedback ±0.1° Redundant safety design
Research / solar path analysis SPA / Meeus ±0.001° Highest accuracy, slower computation

6. Summary Table

Accuracy Algorithm Type Examples Typical Applications
⭐⭐⭐⭐ High-precision astronomical SPA / Grena / NOAA Simulation, research, high-end control
⭐⭐⭐ Engineering-grade simplified Bourges / Wang / Cooper PV tracker controllers
⭐⭐ Empirical / fast estimation Duffie–Beckman / Iqbal Engineering rough estimates, energy yield
⭐ Hybrid sensor-based Wang Operator + Feedback Cost-sensitive systems

 

 


solar tracking

 

How Good Future Solar Keeps Every Ray Working for You

The Good Future Solar Tracking Control System is designed to keep every solar module perfectly aligned with the sun — all day long.

Precision Tracking for Maximum Energy Output

Turning every ray of sunlight into clean, efficient energy. The Good Future Solar Tracking Control System ensures every solar module remains perfectly aligned with the sun all day long. Through real-time position correction and high-precision astronomical algorithms, your solar farm can achieve maximum sunlight absorption and superior overall system performance.

Feature Specification
Tracking Range ±60°
Tracking Accuracy ±1° (algorithmic precision < ±0.05°)
Solar Positioning Real-Time Azimuth & Altitude Correction
Algorithm Embedded Bourges + Wang Hybrid

Key Benefits

  • Up to 20% more energy generation compared to fixed-tilt systems
  • Higher ROI and lower LCOE
  • Seamless performance in diverse site conditions and climates

Reliable Performance for Every Project

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Technical Highlight: Bourges + Wang Algorithm

  • Bourges Formula: Calculates precise solar declination (δ) for any day of the year.
  • Wang Operator Method: Computes solar altitude (h) and azimuth (A) efficiently in embedded controllers.
  • Result: MCU-level tracking with < ±0.05° error, ensuring maximum energy yield with minimal hardware load.

Why It Matters: High-precision solar tracking reduces shading, optimizes module tilt dynamically, and increases daily and seasonal energy harvest.

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