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Grid-Forming Control with Assignable Voltage Regulation Guarantees and Safety-Critical Current Limiting

Bhathiya Rathnayake, Sijia Geng

Abstract

This paper develops a nonlinear grid-forming (GFM) controller with provable voltage-formation guarantees, with over-current limiting enforced via a control-barrier-function (CBF)-based safety filter. The nominal controller follows a droop-based inner-outer architecture, in which voltage references and frequency are generated by droop laws, an outer-loop voltage controller produces current references using backstepping (BS), and an inner-loop current controller synthesizes the terminal voltage. The grid voltage is treated as an unknown bounded disturbance, without requiring knowledge of its bound, and the controller design does not rely on any network parameters beyond the point of common coupling (PCC). To robustify voltage formation against the grid voltage, a deadzone-adapted disturbance suppression (DADS) framework is incorporated, yielding practical voltage regulation characterized by asymptotic convergence of the PCC voltage errors to an assignably small and known residual set. Furthermore, the closed-loop system is proven to be globally well posed, with all physical and adaptive states bounded and voltage error transients (due to initial conditions) decaying exponentially at an assignable rate. On top of the nominal controller, hard over-current protection is achieved through a minimally invasive CBF-based safety filter that enforces strict current limits via a single-constraint quadratic program. The safety filter is compatible with any locally Lipschitz nominal controller. Rigorous analysis establishes forward invariance of the safe-current set and boundedness of all states under current limiting. Numerical results demonstrate improved transient performance and faster recovery during current-limiting events when the proposed DADS-BS controller is used as the nominal control law, compared with conventional PI-based GFM control.

Grid-Forming Control with Assignable Voltage Regulation Guarantees and Safety-Critical Current Limiting

Abstract

This paper develops a nonlinear grid-forming (GFM) controller with provable voltage-formation guarantees, with over-current limiting enforced via a control-barrier-function (CBF)-based safety filter. The nominal controller follows a droop-based inner-outer architecture, in which voltage references and frequency are generated by droop laws, an outer-loop voltage controller produces current references using backstepping (BS), and an inner-loop current controller synthesizes the terminal voltage. The grid voltage is treated as an unknown bounded disturbance, without requiring knowledge of its bound, and the controller design does not rely on any network parameters beyond the point of common coupling (PCC). To robustify voltage formation against the grid voltage, a deadzone-adapted disturbance suppression (DADS) framework is incorporated, yielding practical voltage regulation characterized by asymptotic convergence of the PCC voltage errors to an assignably small and known residual set. Furthermore, the closed-loop system is proven to be globally well posed, with all physical and adaptive states bounded and voltage error transients (due to initial conditions) decaying exponentially at an assignable rate. On top of the nominal controller, hard over-current protection is achieved through a minimally invasive CBF-based safety filter that enforces strict current limits via a single-constraint quadratic program. The safety filter is compatible with any locally Lipschitz nominal controller. Rigorous analysis establishes forward invariance of the safe-current set and boundedness of all states under current limiting. Numerical results demonstrate improved transient performance and faster recovery during current-limiting events when the proposed DADS-BS controller is used as the nominal control law, compared with conventional PI-based GFM control.
Paper Structure (20 sections, 8 theorems, 160 equations, 11 figures)

This paper contains 20 sections, 8 theorems, 160 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Modeling of Grid-Connected IBRs
  3. Reference Frames and Coordinate Transformations
  4. Circuit Dynamics
  5. Grid-Forming Inverter Control
  6. Droop Relationships
  7. DADS-BS Control Laws
  8. Boundedness of States and Performance Guarantees
  9. Over-current Limiting with Control Barrier Functions
  10. Safety-critical control with locally Lipschitz nominal controllers
  11. Safe DADS-BS GFM control
  12. Numerical Results
  13. Proofs
  14. Auxiliary Lemmas
  15. Proof of Theorem \ref{['thm1']}
  16. ...and 5 more sections

Key Result

Theorem 1

Consider the droop-based GFM inverter described by inv1-xstte. Fix design parameters $K_{\rm VC},K_{\rm CC},\mu_{\rm d},\mu_{\rm q},\Gamma_{\rm d},\Gamma_{\rm q},\varepsilon,\omega_{\rm pc},\omega_{\rm qc},\overline{Q}>0,\overline P \in (0,+\infty]$, and $\xi_{\rm p},\xi_{\rm q}>1$. Let the setpoint and where $\ell\in \{\rm d, \rm q\}$.

Figures (11)

  • Figure 1: An IBR connected to the grid. In GFL operation, the objective is to inject prescribed active and reactive power at the PCC; in GFM operation, the objective is to establish the voltage waveform at the PCC.
  • Figure 2: PCC voltage in the $\rm dq$ and $\rm DQ$ frames.
  • Figure 3: Droop-based GFM control architecture with DADS-BS or PI lower-level control loops.
  • Figure 4: CBF-based safety filtering of the current controller. The CBF correction is activated when $\eta(\boldsymbol{x},\boldsymbol{v}_{\rm t}^{\rm n})<0$; see \ref{['sfty_ip1']}.
  • Figure 5: Grid voltage. A three-phase-to-ground fault occurs from $t = 2\,\rm{s}$ to $t = 4\,\rm{s}$. (a) Three-phase voltages. (b) Global $\rm{DQ}$ and local $\rm{dq}$ components.
  • ...and 6 more figures

Theorems & Definitions (16)

  • Remark 1
  • Remark 2
  • Theorem 1: Boundedness of states
  • Theorem 2: Performance guarantees
  • Remark 3
  • Definition 1: Extended class $\mathcal{K}$ functions
  • Definition 2: Forward invariant set
  • Definition 3: Control barrier function ames2016control
  • Theorem 3: ames2016control
  • Theorem 4: Safety with locally Lipschitz nominal controllers
  • ...and 6 more