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Safe Trajectory Gradient Flow Control of a Grid-Interfacing Inverter

Trager Joswig-Jones, Baosen Zhang

Abstract

Grid-interfacing inverters serve as the interface between renewable energy resources and the electric power grid, offering fast, programmable control capabilities. However, their operation is constrained by hardware limitations, such as bounds on the current magnitude. Existing control methods for these systems often neglect these constraints during controller design and instead rely on ad hoc limiters, which can introduce instability or degrade performance. In this work, we present a control framework that directly incorporates constraints into the control of a voltage-source inverter. We propose a safe trajectory gradient flow controller, which applies the safe gradient flow method to a rolling horizon trajectory optimization problem to ensure that the states remain within a safe set defined by the constraints while directing the trajectory towards an optimal equilibrium point of a nonlinear program. Simulation results demonstrate that our approach can drive the outputs of a simulated inverter system to optimal values and maintain state constraints, even when using a limited number of optimization steps per control cycle.

Safe Trajectory Gradient Flow Control of a Grid-Interfacing Inverter

Abstract

Grid-interfacing inverters serve as the interface between renewable energy resources and the electric power grid, offering fast, programmable control capabilities. However, their operation is constrained by hardware limitations, such as bounds on the current magnitude. Existing control methods for these systems often neglect these constraints during controller design and instead rely on ad hoc limiters, which can introduce instability or degrade performance. In this work, we present a control framework that directly incorporates constraints into the control of a voltage-source inverter. We propose a safe trajectory gradient flow controller, which applies the safe gradient flow method to a rolling horizon trajectory optimization problem to ensure that the states remain within a safe set defined by the constraints while directing the trajectory towards an optimal equilibrium point of a nonlinear program. Simulation results demonstrate that our approach can drive the outputs of a simulated inverter system to optimal values and maintain state constraints, even when using a limited number of optimization steps per control cycle.
Paper Structure (11 sections, 12 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 12 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation and Definitions
  4. Control barrier functions
  5. Safe gradient flow
  6. System Model
  7. Safe Gradient Flow for Dynamical Systems
  8. Simulation Results
  9. Trajectory Performance & Steady-State Optimality
  10. Controller Computational Burden & Solve-time
  11. Conclusion

Figures (4)

  • Figure 1: The dq reference frame model of an inverter connected to an infinite bus via an RL branch, with the inverter modeled as a controllable voltage source. The reference frame is taken with respect to the inverter voltage angle.
  • Figure 2: The states and current magnitude from the inverter system controlled with different control methods. While the MPC and droop controllers act are more aggressive, the STGF control drives the states smoothly to their new equilibria.
  • Figure 3: The outputs of the system included in the cost function for each control method. With STGF or MPC control the outputs converge to optimal values 'near' the given reference values. The droop control converges to values away from the optimal values.
  • Figure 4: Single-step run-times for solving controller optimization problems. An inset enlarged view of STGF run-times shows that they are significantly shorter than most MPC run-times.