Detection of Leak Site in Sloped Transmission Lines

In this paper a method is presented to estimate the leak site in sloped transmission lines using a closed solution of the transmission line equations and linear observer. First, the equations are solved for a constant input state, and then the initial estimation of the leak site is presented for variable input state and the leak and pressure coefficient in the leak site is determined with the help of equations obtained from the closed solution using the estimation of the leak site. Then, the nonlinear model is determined by discretizing the transmission line equations with respect to the site variable considering a floating point for the leak site in the observer, designing a linear observer using the initial estimation obtained from the closed solution, and linearizing the observers equations at the obtained point.