Inverter Control with Time-Varying and Nonconvex State and Input Constraints

TL;DR

This work addresses power-tracking for grid-connected inverter-based resources (IBRs) under time-varying voltage and nonconvex input constraints, including a state PF bound and a voltage-related input limit. It introduces a static state-feedback controller with gain $\mathbf{K}$ and a parameterization framework that uses Lyapunov theory and the S-lemma to certify constraint satisfaction and stability, while precomputing a finite set of gains offline. Achievability is formalized, and an achievable set is maximized through SDP/BMI formulations and a Monte Carlo approach, with a convex-hull extension to yield continuous regions. Case studies on a two-bus system show the ability to maximize the achievable region, perform ride-through tests, and compare favorably against LQR and MPC in terms of constraint satisfaction and online computational efficiency, enabling safe, real-time operation of IBRs under dynamic grid conditions.

Abstract

The growing integration of inverter-based resources (IBRs) into modern power systems poses significant challenges for maintaining reliable operation under dynamic and constrained conditions. This paper focuses on the power tracking problem for grid-connected IBRs, addressing the complexities introduced by voltage and power factor constraints. Voltage constraints, being time-varying and nonlinear input constraints, often conflict with power factor constraints, which are state constraints. These conflicts, coupled with stability requirements, add substantial complexity to control design. To overcome these challenges, we propose a computationally efficient static state-feedback controller that guarantees stability and satisfies operational constraints. The concept of achievability is introduced to evaluate whether power setpoints can be accurately tracked while adhering to all constraints. Using a parameterization framework and the S-lemma, we develop criteria to assess and maximize the continuous achievable region for IBR operation. This framework allows system operators to ensure safety and stability by precomputing a finite set of control gains, significantly reducing online computational requirements. The proposed approach is validated through simulations, demonstrating its effectiveness in handling time-varying grid disturbances and achieving reliable control performance.

Figures (14)

• Figure 1: Overview of the proposed power control scheme for a grid-connected IBR with state, input, and stability constraints. The online safety-critical power controller is implemented as a static state-feedback controller to ensure computational efficiency. The control gain and achievable power setpoints are determined through an offline constrained optimization process, effectively shifting the computational burden from the online stage to the offline stage.
• Figure 2: The blue region denotes the state constraint on the power factor. The slope of the sector can be calculated from (\ref{['stateconstraint']}).
• Figure 3: The circle regions represent the nonconvex input constraints. The achievable control signal depends on the time-varying value of $V_{\rm G}$.
• Figure 4: Flowchart illustrating the Monte Carlo simulation for maximizing the achievable set by optimizing over the control gain $\mathbf{K}$. Here, $i_{\rm max}$ and $j_{\rm max}$ represent the total samples of $\mathbf{x}_{\rm ref}$ and $\mathbf{K}$, respectively.
• Figure 5: Illustration of applying Lemma 3 to identify continuous achievable regions. The achievability of a finite number of setpoint samples is verified by checking whether the constraints (\ref{['theorem1_lmi']}), (\ref{['stability_constraints1']}), (\ref{['stability_constraints2']}), and (\ref{['theorem2_lmi']}) are satisfied for a specific set of $\mathbf{K}$, $\mathbf{P}$, and $\mathbf{\Lambda}$. Setpoints not explicitly simulated but located within the triangular area (depicted by the colored triangles) are also deemed achievable. This approach leverages a discrete simulation method to derive a continuous achievable region.