Single Machine Infinite System Dynamic Process Simulation using Implicit Trapezoidal Integration Method

This MATLAB program simulates the dynamic behavior of infinite systems using the implicit trapezoidal integration method for solving differential equations. The implementation focuses on numerical stability and accuracy when modeling continuous systems where components form an interconnected whole. The core algorithm employs iterative matrix operations to handle the implicit nature of the trapezoidal rule, which maintains numerical stability for stiff differential equations commonly encountered in power system dynamics. Key implementation features include: - Newton-Raphson iteration for solving nonlinear algebraic equations at each time step - Sparse matrix handling for efficient computation of large-scale systems - Adaptive time-stepping control based on local truncation error estimates - State variable initialization and boundary condition management The program structure comprises: 1. System parameter initialization (machine parameters, network configuration) 2. Differential equation formulation using state-space representation 3. Implicit trapezoidal integration with predictor-corrector scheme 4. Convergence checking and solution output This simulation tool finds applications across multiple domains including power system transient stability analysis, mechanical system dynamics, financial modeling, and physical system simulations where accurate long-term dynamic behavior prediction is crucial. The method's A-stability property makes it particularly suitable for systems with widely varying time constants.