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Cross-Forming Control and Fault Current Limiting for Grid-Forming Inverters

Xiuqiang He, Maitraya Avadhut Desai, Linbin Huang, Florian Dörfler

Abstract

This article proposes a "cross-forming" control concept for grid-forming inverters operating against grid faults. Cross-forming refers to voltage angle forming and current magnitude forming. It differs from classical grid-forming and grid-following paradigms that feature voltage magnitude-and-angle forming and voltage magnitude-and-angle following (or current magnitude-and-angle forming), respectively. The cross-forming concept addresses the need for inverters to remain grid-forming (particularly voltage angle forming, as required by grid codes) while managing fault current limitation. Simple and feasible cross-forming control implementations are proposed, enabling inverters to quickly limit fault currents to a prescribed level while preserving voltage angle forming for grid-forming synchronization and providing dynamic ancillary services, during symmetrical or asymmetrical fault ride-through. Moreover, the cross-forming control yields an equivalent system featuring a constant virtual impedance and a "normal form" representation, allowing for the extension of previously established transient stability results to include scenarios involving current saturation. Simulations and experiments validate the efficacy of the proposed cross-forming control implementations.

Cross-Forming Control and Fault Current Limiting for Grid-Forming Inverters

Abstract

This article proposes a "cross-forming" control concept for grid-forming inverters operating against grid faults. Cross-forming refers to voltage angle forming and current magnitude forming. It differs from classical grid-forming and grid-following paradigms that feature voltage magnitude-and-angle forming and voltage magnitude-and-angle following (or current magnitude-and-angle forming), respectively. The cross-forming concept addresses the need for inverters to remain grid-forming (particularly voltage angle forming, as required by grid codes) while managing fault current limitation. Simple and feasible cross-forming control implementations are proposed, enabling inverters to quickly limit fault currents to a prescribed level while preserving voltage angle forming for grid-forming synchronization and providing dynamic ancillary services, during symmetrical or asymmetrical fault ride-through. Moreover, the cross-forming control yields an equivalent system featuring a constant virtual impedance and a "normal form" representation, allowing for the extension of previously established transient stability results to include scenarios involving current saturation. Simulations and experiments validate the efficacy of the proposed cross-forming control implementations.
Paper Structure (56 sections, 4 theorems, 53 equations, 25 figures, 3 tables)

This paper contains 56 sections, 4 theorems, 53 equations, 25 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Motivations
  4. Contributions
  5. Organization and Notation
  6. Grid-Forming Control Objectives, Operation Modes, and FRT Services Provision
  7. Grid-Forming Control Objectives Under Grid Faults
  8. Current Limiting
  9. Grid-Forming Synchronization
  10. Positive-Sequence FRT Services Provision
  11. Negative-Sequence FRT Services Provision
  12. Multiple Forming Control Modes
  13. Capabilities to Serve Grid Code Requirements
  14. Cross-Forming Control
  15. Desired Equivalent Circuit of Cross-Forming Mode
  16. ...and 41 more sections

Key Result

Proposition 1

Voltage Magnitude Following Under Current Saturation: Consider the three-phase balancedProposition prop:voltage-following can be extended to unbalanced cases, where the Thevenin equivalent grid in Fig. fig:voltage-following-proof(a) models a positive-sequence aggregated circuit. circuit system in Fi

Figures (25)

  • Figure 1: Illustrations of (a) grid-forming (voltage-forming current-following), (b) grid-following (voltage-following current-forming), and (c) cross-forming modes.
  • Figure 2: (a) Phase-domain and (b) sequence-domain generic equivalent circuits for grid-forming inverters under grid short-circuit faults, where the grid-forming operation is maintained in the positive sequence while the negative sequence admits different options among negative-sequence grid-forming awal2023double, current injection zheng2018flexible, or impedance emulation nasr2023controlling.
  • Figure 3: (a) A generic circuit representing a current-saturated inverter ($\abs{\underline{i}} = I_{\lim}$) connected to a grid. In both (b) and (c), where $\angle{\underline{i}}$ and $\angle{\underline{v}}$ are specified, respectively, the voltage magnitude $\abs{\underline{v}}$ passively follows the circuit law.
  • Figure 4: Provisions of fault reactive current $i_Q$ and phase jump active current $i_P$ at the moment of a grid voltage dip and phase jump, respectively, resulting from the circuit equation of $\underline{v} = \underline{v}_{\mathrm{g}} + \underline{i}\,\underline{z}$. (a) Voltage-forming mode ($\underline{v}$ fixed), (b) Current-forming mode ($\underline{i}$ fixed), and (c) Cross-forming mode ($\angle \underline{v}$ fixed and $\lvert \underline{i} \rvert$ limited to $I_{\mathrm{lim}}$).
  • Figure 5: (a) Cross-forming control architecture, (b) desired equivalent circuit, and (c) cross-forming signal causality for inverters to perform voltage angle forming and current magnitude forming behaviors under current saturation.
  • ...and 20 more figures

Theorems & Definitions (15)

  • Definition 1
  • Definition 2
  • Definition 3
  • Proposition 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Lemma 1
  • ...and 5 more