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A Complex-Valued Feedback Linearization-Based Controller for a Voltage Source Inverter Tied to the Grid via a Second-Order Filter

Gerardo Tapia-Otaegui, Jorge A. Solsona, Sebastian Gomez Jorge, Ana Susperregui, Claudio A. Busada, M. Itsaso Martínez

TL;DR

This work addresses robust, high-dynamic-performance control of a grid-tied voltage-source inverter connected to a grid through a second-order LC filter under weak-grid conditions. It develops a complex-valued, energy-based flat output and performs full input-output linearization, followed by state-feedback with integral action and pole placement to achieve accurate reference tracking without inducing internal zero dynamics. The main contributions include the definition of an energy-based flat output $\vec{\xi}_1 = \tfrac{1}{2}(C_1 v_{C_1}^2 + L|\vec{i}_L|^2 + C_2|\vec{v}_{C_2}|^2) - j\int q dt$, the resulting linearizable dynamics, and a practical control law that estimates or measures required signals under an unknown grid Thévenin. Simulation on a very weak grid with SCR=0.5 demonstrates fast transient response, small tracking errors in the flat-output coordinates, and sustained operation without modulation saturation, illustrating the method's potential for improving grid-tied inverter performance in challenging grid conditions.

Abstract

In this document, a nonlinear control law for a grid-tied converter is introduced. The converter topology consists of a voltage source inverter (VSI) linked to the grid through an inductive-capacitive second-order filter, its input being connected to a capacitive DC-link supplied by a renewable energy-based input power source. In order to achieve good performance in presence of large state excursions caused mainly by substantial set-point modifications and/or considerable disturbances, a nonlinear control law based on a complex-valued feedback linearization strategy is designed. Specifically, a flat output is adopted, which is given by the summation of the energy stored in the DC-link capacitor and in the output filter's inductor and capacitor, as well as by the reactive energy at the output. After linearizing the system through a pertinent coordinate transformation and a nonlinear feedback, a linear trajectory tracking control law is implemented. The performance of the system controlled by applying the proposed strategy is tested via simulation for a very weak grid of unity X/R ratio, yielding satisfactory results.

A Complex-Valued Feedback Linearization-Based Controller for a Voltage Source Inverter Tied to the Grid via a Second-Order Filter

TL;DR

This work addresses robust, high-dynamic-performance control of a grid-tied voltage-source inverter connected to a grid through a second-order LC filter under weak-grid conditions. It develops a complex-valued, energy-based flat output and performs full input-output linearization, followed by state-feedback with integral action and pole placement to achieve accurate reference tracking without inducing internal zero dynamics. The main contributions include the definition of an energy-based flat output , the resulting linearizable dynamics, and a practical control law that estimates or measures required signals under an unknown grid Thévenin. Simulation on a very weak grid with SCR=0.5 demonstrates fast transient response, small tracking errors in the flat-output coordinates, and sustained operation without modulation saturation, illustrating the method's potential for improving grid-tied inverter performance in challenging grid conditions.

Abstract

In this document, a nonlinear control law for a grid-tied converter is introduced. The converter topology consists of a voltage source inverter (VSI) linked to the grid through an inductive-capacitive second-order filter, its input being connected to a capacitive DC-link supplied by a renewable energy-based input power source. In order to achieve good performance in presence of large state excursions caused mainly by substantial set-point modifications and/or considerable disturbances, a nonlinear control law based on a complex-valued feedback linearization strategy is designed. Specifically, a flat output is adopted, which is given by the summation of the energy stored in the DC-link capacitor and in the output filter's inductor and capacitor, as well as by the reactive energy at the output. After linearizing the system through a pertinent coordinate transformation and a nonlinear feedback, a linear trajectory tracking control law is implemented. The performance of the system controlled by applying the proposed strategy is tested via simulation for a very weak grid of unity X/R ratio, yielding satisfactory results.

Paper Structure

This paper contains 8 sections, 20 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Complex-Valued Model of the Converter
  3. Nonlinear Controller Design
  4. Feedback Linearization
  5. State Feedback with Integral Action for Reference Tracking
  6. Tuning of State-Feedback Gains
  7. Simulation Results
  8. Conclusions

Figures (3)

  • Figure 1: Schematic three-phase circuit of an inverter interfacing a RES with the grid through an LC filter.
  • Figure 2: Simulation Results. (a) Reference and actual values of the DC-link voltage. (b) Three-phase current in the grid filter's inductor. (c) Three-phase voltage of the grid filter's capacitor. (d) Three-phase grid current. (e) Three-phase grid voltage.
  • Figure 3: Simulation Results. (a) Three-phase modulation index. (b) Input power, and active and reactive powers injected into the PCC. (c) Real and imaginary parts of tracking error $\vec{e}_{\xi_1}$. (d) Real and imaginary parts of tracking error $\vec{e}_{\xi_2}$. (e) Real and imaginary parts of tracking error $\vec{e}_{\xi_3}$.