A new discrete‐time PI‐RMRAC for grid‐side currents control of grid‐tied three‐phase power converter

Abstract

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...

Optimized parametrization of adaptive controllers for enhanced current regulation in grid‐tied converters

“…The plant modeling is well known in the literature 25‐27 . Hence, this paper provides a brief discussion on this topic.…”

“…The plant modeling is well known in the literature. [25][26][27] Hence, this paper provides a brief discussion on this topic. The three-phase LCL filter can be effectively modeled as a single-phase circuit.…”

“…However, this simplification is only feasible if the controller can robustly manage these neglected dynamics and grid uncertainties. The method was described and successfully implemented in References 25‐27. Given that the adaptive OSAP structure was demonstrated to be robust against both matched and unmatched dynamics in Reference 27, this procedure is viable, as long as the constraints from the Lyapunov stability analysis are addressed.…”

“…Thus, it cannot be ignored in practice. Therefore, the adaptive control structure is designed considering the grid dynamics as an exogenous and periodic disturbance, as described in References 21,25‐27.…”

“…Regarding DC‐AC converters, there are several methods for grid‐injected current control in the literature. In special, it is highlighted the emerging techniques coming from robust model reference adaptive controllers (RMRAC)‐based structures, such as References 25‐29, which presented high robustness to the plant uncertainties (parametric variations, grid disturbances, weak grids, faults, etc). The main characteristic of these controllers is the ability to rapidly change their gains to deal with grid condition changes, maintaining the system stable in the most different scenarios, as well as keeping the quality of grid‐injected currents with low total harmonic distortion (THD).…”