Single-End Fault Location Algorithm Using Quadratic Equation Solving Method

The Single-End Fault Location Algorithm Using Quadratic Equation Solving Method is a technique for fault distance calculation in transmission lines. This algorithm utilizes voltage and current data measured from a single terminal, combined with line parameters to establish a mathematical model, enabling precise calculation of fault distance through quadratic equation solving.

In practical implementation, the method first captures voltage and current signals during fault conditions, extracting relevant electrical quantities (such as positive-sequence, negative-sequence, or zero-sequence components). The algorithm then establishes relationship equations between fault distance and measured electrical quantities based on distributed parameter models of transmission lines. Since these equations typically take quadratic forms, mathematical methods can be applied to obtain analytical solutions for fault distance. Key implementation involves solving the quadratic equation ax² + bx + c = 0 using discriminant analysis to determine valid roots.

PSCAD, as a power system simulation tool, can validate this algorithm's effectiveness. Simulation environments can be configured with different fault types and locations, where the algorithm processes simulation data and compares calculated results with actual fault distances to evaluate location accuracy. This integrated approach allows for algorithm parameter optimization and performance testing under various complex operating conditions. Implementation typically involves creating custom modules in PSCAD/EMTDC using component-based programming to simulate fault scenarios and verify calculation logic.

The algorithm's advantage lies in requiring only single-end data, making it suitable for lines without dual-end communication capabilities. Core challenges involve minimizing impacts from inaccurate line parameters and mutual inductance effects on location results. Future improvements could explore multi-algorithm fusion techniques or intelligent optimization approaches using machine learning to enhance robustness, potentially implementing adaptive parameter adjustment through iterative optimization algorithms.