Controle robusto baseado em desigualdades matriciais lineares aplicado a inversores conectados à rede elétrica

Abstract

This work provides as a main contribution a procedure to design robust state feedback current controllers applied to inverters connected to the grid by means of LCL filters, providing results which comply with performance requirements from the IEEE Standard 1547. First, the plant is modeled in the state space and discretized including a delay of one sample from the control signal implementation, and including in the augmented system a set of resonant controllers of arbitrary dimension. The uncertainty on the grid inductance is modeled, leading to a polytopic description of the augmented system. A state feedback controller is then used. The gains of this controller are determined by means of conditions based on linear matrix inequalities, which ensure the location of the eigenvalues in circular region inside the unit circle for the closed-loop system. The simulation results with this controller in the time domain and also in the frequency domain indicate good transient and steady state performances, tracking of sinusoidal reference and rejection of harmonics from the grid. The simulation results are corroborated experimentally, using a digital signal processor for the implementation of the control law. An example of design of a non robust controller, designed for a nominal value of the grid inductance, is presented, showing that this controller leads to instability for values of grid inductance different from the nominal, which emphasizes the importance of the use of robust controllers for this application. Also is presented a performance analysis based on the H1 norm that illustrates the effect of parametric uncertainties on the closed-loop disturbance rejection capacity. An extension for the control of three-phase inverters are presented. The three-phase robust controller is validated by means of simulations and experimental results similar with the results obtained for the single-phase case.