Nonlinear Control of the Three-Phase Inverter using the Derivative-Free Nonlinear Kalman Filter

Abstract

The use of three-phase voltage inverters (DC to AC converters) is frequently met in the electric power system, such as in the connection of photovoltaics with the rest of the grid. The paper proposes a nonlinear feedback control method for three-phase inverters, which is based on differential flatness theory and a new nonlinear filtering method under the name Derivative-free nonlinear Kalman Filter. First, it is shown that the inverter's dynamic model is a differentially flat one. This means that all its state variables and the control inputs can be written as functions of a single algebraic variable which is the flat output. By exploiting differential flatness properties it is shown that the inverter's model can be transformed to the linear canonical (Brunovsky's) form. For the latter description, the design of a state feedback controller becomes possible, e.g. using pole placement methods. Moreover, to estimate the nonmeasurable state variables of the linearized equivalent model of the inverter, the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized inverter's model and of an inverse transformation that is based on differential flatness theory, which enables to compute estimates of the state variables of the initial nonlinear system. Furthermore, by redesigning the aforementioned filter as a disturbance observer it becomes also possible to estimate disturbance terms that affect the inverter and subsequently to compensate for them. The performance and disturbance rejection capability of the proposed nonlinear feedback control scheme is evaluated through simulation experiments.