Comparison of damping techniques in non-linear spring-mass systems for power transformers under short-circuit condition

Purpose The simplified modeling of many physical processes results in a second-order ordinary differential equation (ODE) system. Often the damping of these resonating systems cannot be defined in the same simplified way as the other parameters due to the complexity of the physical effects. The purpose of this paper is to develop a mathematically stable approach for damping resonances in nonlinear ODE systems. Design/methodology/approach Modifying the original ODE using the eigenvalues and eigenvectors of a linearized state leads to satisfying results. Findings An iterative approach is presented, how to modify the original ODE, to achieve a well-damped solution. Practical implications The method can be applied for every physical resonating system, where the model complexity prevents the determination of the damping. Originality/value The iterative algorithm to modify the original ODE is novel. It can be used on different fields of the physics, where a second-order ODE is describing the problem, which has only measured or empirical damping.