Harmonic Summation Method for Wind Field Simulation with MATLAB

To simulate wind fields using the harmonic summation method in MATLAB, we need to implement a multidimensional approach that accounts for spatial effects. The harmonic summation method mathematically represents the wind field as a superposition of multiple harmonic components with different frequencies, amplitudes, and phases. In MATLAB implementation, this typically involves: - Defining frequency vectors using `linspace()` or `logspace()` functions - Generating harmonic components with `sin()` and `cos()` functions combined with amplitude modulation - Applying spatial correlation through covariance matrices or spectral density functions - Using matrix operations for efficient superposition of harmonic components Key implementation aspects include: 1. Wind spectrum modeling (e.g., Kaimal or von Karman spectra) using `pwelch()` for power spectral density estimation 2. Spatial coherence functions to account for correlations between different points in the wind field 3. Terrain effects implementation through height-dependent wind profiles using logarithmic or power law functions 4. Multidimensional array handling with `meshgrid()` for spatial coordinate generation The spatial effects consideration involves modeling how wind speed and direction vary across the wind farm terrain, which can be achieved through: - Topography data integration using `gradient()` for slope calculations - Wake effects modeling between turbines using analytical or empirical models - Boundary layer development simulation with height-dependent parameters This MATLAB-based harmonic summation approach provides a computationally efficient method for generating realistic wind field simulations that capture both temporal variations and spatial correlations, making it valuable for wind energy system analysis and turbine placement optimization.