Algorithm for Latin Hypercube Sampling in Power Flow Calculations

In power systems, probabilistic power flow calculation serves as a critical technique that helps engineers evaluate system reliability and stability. Latin Hypercube Sampling (LHS) is a widely-used stochastic sampling method applicable for solving probabilistic power flow problems. The algorithm operates by: 1) Performing stratified random sampling of input variables using uniform distributions, 2) Generating sample points through Latin Hypercube techniques that ensure full coverage of the input space with minimal samples, and 3) Executing probabilistic power flow calculations using these representative sample points. Key implementation aspects include: - Dividing the cumulative distribution function into equal-probability intervals - Randomly selecting one value from each interval without replacement - Applying permutation techniques to avoid correlation between variables - Integrating with power flow solvers (e.g., Newton-Raphson method) for batch processing Thus, the LHS algorithm finds extensive application in power systems, not only enhancing the accuracy of probabilistic power flow calculations but also significantly improving computational efficiency through its space-filling properties and reduced sample size requirements compared to traditional Monte Carlo methods.