This software "LinearLoadEstimation_v1" is the first version of an algorithm for parameter estimation using trajectory sensitivity method. The model is linearized to use perturbance measurements provoked by a under load tap changer of transformer (ULTC).All files are written in Python 2. The main routine is written on the 'LinearLoadEstimation_v1.py' file. In this code, the user will find the set of parameters that represent the real behaviour of the load used for the study, the set of initial guesses for the parameters and some method settings, such as tolerance, time step and parameters' variation. The equations describing the model's output behaviour can be found on the 'Matrix.py' file. The file was separated from the main routine to allow the use of the algorithm to identify parameters of different models, not only load models. The output behaviour is simulated using 'rk4.py', where the Runge-Kutta Method is implemented. 'Classification.py' ranks the set of parameters from ill to well-conditioned. This rank will be later used to identify the parameters in two steps, first the ill-conditioned and later the whole set. The function responsible to calculate the error between the real and modelled outputs via the Least-Square Method, is written on 'Error.py'. The code was written separately for the same as reason as 'Matrix.py', allowing the user to choose the error function. 'Gamma.py' gives us the error sensibility and the Hessian Matrix and calculates the parameters increment to minimize the error. In order to estimate the set of parameters of a different model all the user must do is change the set of parameters, the initial guesses and the settings on the 'LinearLoadEstimation_v1.py' and the matrices on 'Matrix.py'.