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Power Control of Converters Connected via an L Filter to a Weak Grid. A Flatness-Based Approach

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

TL;DR

The paper addresses robust control of grid-feeding inverters injecting instantaneous complex power into weak grids with unknown impedance. It extends a flatness-based nonlinear controller by incorporating a notch-filter to estimate the PCC voltage, replacing the measured voltage in the control law to avoid instability from rapid PCC voltage changes. It derives steady-state stability limits for inductive and resistive grids, analyzes transient stability with a filtered PCC voltage, and proposes a notch-filter design with conservative stability conditions, followed by simulation validation. Simulations demonstrate robust tracking and avoidance of inverter saturation under weak-grid operation, confirming practical guidance for safe operation of grid-tied converters in networks with uncertain impedance.

Abstract

In this article, a nonlinear strategy based on a flatness approach is used for controlling the instantaneous complex power supplied from the Point of Common Coupling (PCC) to a weak grid. To this end, the strategy introduced by the authors in [1] considering a strong grid is robustified for avoiding system instability when the converter is connected to an unknown grid. The robustification method consists of including a notch filter that estimates the PCC voltage and using it to build the controller (i.e. the measured PCC voltage used to design the control strategy for a strong grid is replaced by the PCC voltage estimated with the notch filter). In addition, before designing the controller, the steady-state stability and safe operation limits when injecting complex instantaneous power to a grid of unknown impedance are analyzed. This analysis is independent of the control strategy, and applies to all power injection schemes. Simulations are presented for showing the performance of the proposed controller in presence of a weak grid.

Power Control of Converters Connected via an L Filter to a Weak Grid. A Flatness-Based Approach

TL;DR

The paper addresses robust control of grid-feeding inverters injecting instantaneous complex power into weak grids with unknown impedance. It extends a flatness-based nonlinear controller by incorporating a notch-filter to estimate the PCC voltage, replacing the measured voltage in the control law to avoid instability from rapid PCC voltage changes. It derives steady-state stability limits for inductive and resistive grids, analyzes transient stability with a filtered PCC voltage, and proposes a notch-filter design with conservative stability conditions, followed by simulation validation. Simulations demonstrate robust tracking and avoidance of inverter saturation under weak-grid operation, confirming practical guidance for safe operation of grid-tied converters in networks with uncertain impedance.

Abstract

In this article, a nonlinear strategy based on a flatness approach is used for controlling the instantaneous complex power supplied from the Point of Common Coupling (PCC) to a weak grid. To this end, the strategy introduced by the authors in [1] considering a strong grid is robustified for avoiding system instability when the converter is connected to an unknown grid. The robustification method consists of including a notch filter that estimates the PCC voltage and using it to build the controller (i.e. the measured PCC voltage used to design the control strategy for a strong grid is replaced by the PCC voltage estimated with the notch filter). In addition, before designing the controller, the steady-state stability and safe operation limits when injecting complex instantaneous power to a grid of unknown impedance are analyzed. This analysis is independent of the control strategy, and applies to all power injection schemes. Simulations are presented for showing the performance of the proposed controller in presence of a weak grid.
Paper Structure (12 sections, 38 equations, 5 figures)

This paper contains 12 sections, 38 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System's Model
  3. Steady-State Stability for Weak Grids
  4. Inductive Grids
  5. Resistive Grids
  6. Control Based on a Flatness Approach
  7. Controller Design
  8. References
  9. Transient Stability Measuring $v_p$
  10. Transient Stability Filtering $v_p$
  11. Simulation Results
  12. Conclusions

Figures (5)

  • Figure 1: System's model using complex space vectors.
  • Figure 2: Reactive power limits for $|i|\leq1$, zone of stable operation and control action limit in SS for inductive grids.
  • Figure 3: Active power limits for $|i|\leq1$, zone of stable operation and control action limit in SS for resistive grids.
  • Figure 4: Strong grid simulation. (a) PCC voltage and filtered PCC voltage. (b) Injected current. (c) Reference power and injected power. (d) Scaled DC-link voltage and magnitude of PCC voltage.
  • Figure 5: Weak inductive grid simulation. (a) PCC voltage and filtered PCC voltage. (b) Injected current. (c) Reference power and injected power. (d) Scaled DC-link voltage and magnitude of PCC voltage.