Transmission line fault location by solving line differential equations

•A novel algorithm is developed for accurately localizing faults on electrical transmission lines.•The Adomian Decomposition Method is used to spatially solve the sampled-time line model.•The obtained solution provides the sampled-time phase voltages and currents profiles as a function of line length.•The obtained results via different simulations demonstrate that the developed technique is efficient and accurate. The present paper describes a new algorithm for reliably locating the faults that frequently take place on electrical transmission lines. The proposed fault location technique considers a distributed-parameter line model that is given in the form of Partial Differential Equations (PDEs) whose boundary conditions are taken as synchronized time-domain data recorded from both sending and receiving terminals. The Adomian Decomposition Method is employed to spatially solve the sampled-time line model. The obtained solution provides phase voltages and currents profiles at each sample time as a function of line length. This function is expressed as a polynomial whose coefficients are simply determined by an easily-applied recursive procedure. One of the main interesting features of the developed scheme is that it can handle the case of unsymmetrical transmission lines without the need of modal decomposition that decouples the original three-phase system to an equivalent three independent single-phase systems. Simulations and calculations are all proceeded with MATLAB. The obtained results through different simulations show that the new methodology is operational, applicable, and accurate.