This paper provides robust H _∞ state feedback controllers suitable for implementation in three-phase grid-connected converters. This control strategy is known to provide optimal rejection of disturbances, but usually leads to high control gains, that may be difficult to be implemented in practice. To mitigate this problem, a linear matrix inequality condition based on slack variables is proposed, which allows to impose bounds on the control gains in a less conservative way than conventional quadratic stability. The performance is proven to be superior to similar H _∞ state feedback controllers in the literature, providing an upper bound for the converter output admittance and experimental grid currents complying with the IEEE Standard 1547.

This paper provides as contribution a systematic design procedure for robust current control of grid-tied inverters with LCL filters affected by inductor magnetic soft-saturation and also by uncertain grid impedances. The proposed design is based on: i) a polytopic time-varying model to describe the effect of the inductances variations; ii) a set of linear matrix inequalities to design fixed (robust) state feedback gains, ensuring bounded settling times for the closed-loop transient responses. A less conservative set of linear matrix inequalities is used to certify the procedure. Experimental results from real-time simulations and from a real prototype with commercial powder core inductors show that the proposed procedure can provide superior results than conventional controllers designed not taking into account the soft-saturation. The results with the proposed controller comply with the IEEE 1547 Standard, leading to grid currents with low harmonic content, respecting limits prescribed by this standard even under distorted grid voltages.

This paper proposes a modulated model predictive strategy suitable for current control of grid-connected converters with LCL filters, allowing fast dynamic responses with a fixed switching frequency, for both strong and weak grid conditions. The duty cycles are optimized within each switching period based on the minimization of a quadratic cost function with linear constraints from the space vector modulation. Full and reduced-order models are considered for the control design, and closed-form analytical solutions for the optimization problem are derived based on the Karush-Kuhn-Tucker conditions. The closed-form expressions for the optimal solution make it possible to implement the algorithm in real time using off-the-shelf microcontrollers. Extensive evaluation illustrates good transient and steady state performances for different grid conditions. In addition, the proposed MPC takes into account the voltage synthesis capability of the inverter and copes with overmodulation in an orderly fashion even in large transients.

Proportional-resonant controllers are largely used for grid-connected converters with LCL filters to ensure sinusoidal reference tracking and harmonic disturbance rejection. However, the design of such controllers becomes more difficult when it is necessary to ensure stability and suitable performance for converters operating under uncertain grid conditions, from stiff to weaker, and also when the number of resonants increases. In this more challenging scenario, available design procedures may lead to a poor tradeoff between transient and steady-state performances. To overcome this problem, this paper proposes an off-line automated control design procedure to obtain multiple robust optimized proportional-resonant controllers. The proposed procedure consists of two steps, where a particle swarm algorithm is used to obtain: i) the gains of an inner loop ensuring optimal active damping for the LCL filter resonance; ii) the gains of multiple proportional-resonant controllers by minimizing a tracking error index, taking into account uncertain grid impedance and control signal limits. The robust stability of the closed-loop system with the control gains tuned by the metaheuristics is certificated through a parameter-dependent Lyapunov function, constructed based on linear matrix inequalities. Several results from control Hardware-in-the-loop are presented for a case study, revealing that the proposal provides better performance in terms of reference tracking and disturbance rejection, when compared to similar control strategies from the literature. Experimental results from a prototype connected to the utility grid attest the practical feasibility of the proposed procedure.