Condition monitoring for three-phase inverters with the Derivative-free nonlinear Kalman Filter

A novel method for early fault detection and incipient fault diagnosis is developed, using as application example the model of a three-phase voltage inverter. To accomplish solution of the inverters' condition monitoring problem, a differential flatness theory-based filtering method under the name of Derivative-free nonlinear Kalman Filter is employed. The filter emulates the functioning of the inverter in the fault-free case. It makes use of state-variable transformations (diffeomorphisms) which depend on differential flatness theory. These transformations allow to express the dynamics of the system into the canonical (Bruunovsky) form. For the latter description, the associated filtering problem is solved after using the typical Kalman Filter's recursion. Next, a residuals' sequence is generated by comparing the output of the filter to the output of the voltage inverter. It is proven that the sum of the square of the residuals when multiplied by a weight matrix, results into a stochastic variable (statistical test) that follows the $\chi^{2}$ distribution. Moreover, by using the confidence intervals of the $\chi^{2}$ distribution one can define ranges about the normal functioning of the inverter.