Main Program for Stochastic Power Flow Calculation Using Semi-Invariant Method

The main program implements stochastic power flow calculation using the semi-invariant method, which has been thoroughly verified and demonstrates seamless integration with Matpower. This computational approach is particularly valuable for analyzing power systems containing uncertain variables that exhibit time-varying characteristics. The algorithm operates by decomposing random variables into their semi-invariants (cumulants), enabling efficient propagation of uncertainties through the power flow equations. Key implementation features include handling correlated random variables through covariance matrix transformation and utilizing Gram-Charlier series expansion for probability density function reconstruction. The method significantly enhances calculation accuracy compared to conventional deterministic approaches and provides probabilistic assessments of system stability. Additionally, the program facilitates identification of potential system vulnerabilities and weak points by generating probability distributions of bus voltages and line flows, enabling more effective planning and mitigation strategy development. The code structure includes modules for input data processing, semi-invariant calculation, linearized power flow solution, and probabilistic output analysis.