Nonlinear Feedback Control of Three-Phase Inverter Systems Using the Derivative-Free Nonlinear Kalman Filter

摘要

The use of three-phase voltage inverters (DC to\udAC converters) is frequently met in the electric power system,\udsuch as in the connection of photovoltaics with the rest\udof the grid. The paper proposes a nonlinear feedback control\udmethod for three-phase inverters, which is based on differential\udflatness theory and a newnonlinear filtering method under\udthe name Derivative-free nonlinear Kalman Filter. First, it is\udshown that the inverter’s dynamic model is a differentially\udflat one. This means that all its state variables and the control\udinputs can be written as functions of a single algebraic\udvariable which is the flat output. By exploiting differential\udflatness properties it is shown that the inverter’s model can\udbe transformed to the linear canonical (Brunovsky’s) form.\udFor the latter description the design of a state feedback controller\udbecomes possible, e.g. using pole placement methods.\udMoreover, to estimate the non-measurable state variables of\udthe linearized equivalent of the inverter, the Derivative-free\udnonlinear Kalman Filter is used. This consists of the Kalman\udFilter recursion applied on the linearized inverter’s model\udand of an inverse transformation that is based on differential flatness theory, which enables to compute estimates of the\udstate variables of the initial nonlinear system. Furthermore,\udby redesigning the aforementioned filter as a disturbance\udobserver it becomes also possible to estimate disturbance\udterms that affect the inverter and subsequently to compensate\udfor them. The performance and disturbance rejection capability\udof the proposed nonlinear feedback control scheme is\udevaluated through simulation experiments.