In this work, a new discrete-time direct robust adaptive PI controller is developed and applied on grid-side currents control of a three-phase full-bridge static converter connected to the electrical grid by LCL filter. The control structure is based on Robust Model Reference Adaptive Control (RMRAC) to adjust gains online, designed from a reduced-order model of LCL filter. The highlights of this controller are its intuitive design that requires a reduced set of design parameters if compared with others robust adaptive controllers for gridtied power systems, which implies an easier implementation and less computational burden. In addition, identifier robustness and control stability are discussed in discrete-time, considering the overall plant. Experimental results are presented to corroborate the proposed control strategy and discuss its performance for grid-side currents loop control, exogenous disturbance rejection, and robustness to parametric variation of grid impedance.
K E Y W O R D Sautomatic controller, discrete-time controller, grid-tied power converters, LCL filter, robust adaptive PI controllerNowadays, energy crises is a worldwide concern due to the energy generation limitation, fossil fuel depletion, and global warming. 1 A way to manage it is by integrating renewable energy sources in the power generation through List of Symbols and Abbreviations: A,B, system matrices; C, capacitance of the LCL filter; e 1 , tracking error; G, complete transfer function; G 0 , nominal part of the plant; I, disturbance amplitude; i c , converter-side currents; i g , grid-side currents; K i , integral gain; k m , high frequency gain of reference model; K p , proportional gain; k P , high frequency gain; L c , converter inductance; L g , total grid-side inductance; L g1 , grid-side inductance on LCL filter; L g2 , grid inductance; n à , relative degree; m 2 , majorant signal; M 0 , upper limit of θ à norm; N, amount of samples in one period; p, pole; p 0 , upper bound; q 6 , constant; q 7 , constant; r, limited reference signal; R c , converter resistance; R g , total grid-side resistance; R g1 , grid-side resistance on LCL filter; R g2 , grid parasitic resistance; ω, parameters vector; ω d , disturbance frequency; ϕ, parametric error vector; Ψ, residual set; σ, σ-modification; R m , monic Schur polynomial; R 0 , monic polynomial with degree n; T αβ0 , Clarke Transformation matrix; T s , sampling time; U, input signal; u, voltage synthesised by converter (control action); V , Lyapunov candidate function; v ab and v bc , are the measured voltages on PCC; V cc , DC link voltage; v c , capacitor voltage; V c , quadrature component of exogenous disturbance; v d , electrical grid; V s , phase component of exogenous disturbance; W m , reference model; y, plant output; y m , reference model output; Z m , monic Schur polynomial; Z 0 , monic polynomial with degree m; δ 0 , δ 1 and δ 2 , positive parameters; ϵ, augmented error; ϵ 0 , small arbitrary number; γ, constant; Γ, positive symmetric matrix gain; λ, eigenvalues; κ, posi...