MATLAB Implementation of Interior Point Method for Optimal Power Flow

Implementation Approach of Interior Point Method for Optimal Power Flow The interior point method is an efficient numerical optimization algorithm for solving optimal power flow problems. Its core concept involves introducing barrier functions to incorporate inequality constraints into the objective function, gradually approaching the optimal solution within the feasible region. In power system optimization, optimal power flow typically requires consideration of generation cost minimization, node voltage constraints, and line power limits. Problem Formulation The optimal power flow problem can generally be formulated as a nonlinear programming problem, containing an objective function (such as generation cost), equality constraints (like power flow equations), and inequality constraints (such as generator output limits). MATLAB implementation requires establishing a mathematical model first, including variable definitions (voltage magnitudes, phase angles, generator outputs), power flow equations (established using Newton-Raphson method), and relaxation treatment of inequality constraints. Key Steps of Interior Point Method Implementation The implementation of interior point method primarily involves these critical steps: Initialization: Provide a feasible starting point (must strictly satisfy inequality constraints), set barrier parameters and convergence tolerance. Barrier Function Construction: Handle inequality constraints using logarithmic barrier functions, integrating them into the objective function. KKT Conditions Solving: Iteratively solve correction equations (typically using Newton's method), updating primal and dual variables. Step Size Control: Ensure iteration points remain within the feasible region through backtracking line search. Termination Criteria: Stop when dual gap and constraint residuals fall below preset tolerance. MATLAB Implementation Key Points In MATLAB, you can utilize symbolic computation toolboxes (like `fmincon`) or manually implement interior point method logic. Manual implementation requires attention to: Using sparse matrix storage for Jacobian matrices to improve computational efficiency. Applying preconditioning techniques to accelerate linear equation system solutions. Appropriately selecting barrier parameter reduction strategies (such as fixed ratio reduction). Extension Directions Parallel Computing: For large-scale power grids, combine with MATLAB's Parallel Computing Toolbox to accelerate iteration processes. Robust Optimization: Introduce uncertainty models (like wind power fluctuations) to improve traditional optimal power flow. Interface Extension: Integrate with power system simulation tools like OpenDSS for practical scenario validation. The application of interior point method in optimal power flow balances computational speed and accuracy, making it an essential tool for power system economic dispatch. By adjusting barrier parameters and step size strategies, it can further adapt to optimization requirements of different-scale power grids.