[Paper Review] Optimal L-Infinity Frequency Control in Microgrids Considering Actuator Saturation

Daniel Tabas, Baosen Zhang|arXiv (Cornell University)|Oct 8, 2019

Microgrid Control and Optimization9 references4 citations

TL;DR

This paper proposes an L-infinity optimal controller design for microgrids using linear matrix inequalities (LMIs) to minimize peak frequency deviation under actuator saturation. By combining invariant ellipsoids with L-infinity performance optimization, the method ensures robust stability and significantly outperforms conventional LQR and pole placement controllers in reducing frequency overshoot during disturbances.

ABSTRACT

Inverter-connected resources can improve transient stability in low-inertia grids by injecting active power to minimize system frequency deviations following disturbances. In practice, most generation and load disturbances are step changes and the engineering figure-of-merit is often the peak overshoot in frequency resulting from these step disturbances. In addition, the inverter-connected resources tend to saturate much more easily than conventional synchronous machines. However, despite these challenges, standard controller designs must deal with averaged quantities through $H_2$ or $H_\infty$ norms and must account for saturation in ad hoc manners. In this paper, we address these challenges by explicitly considering $L_\infty$ control with saturation using a linear matrix inequality-based approach. We show that this approach leads to significant improvements in stability performance.

Motivation & Objective

• To address the challenge of frequency stability in low-inertia microgrids with inverter-connected resources.
• To explicitly account for actuator saturation in controller design, which is often ignored in standard H2/H∞ methods.
• To minimize the L∞-norm of frequency deviation as the primary performance metric, reflecting real-world peak overshoot concerns.
• To develop a unified LMI-based framework that simultaneously handles saturation and L∞ performance optimization.
• To demonstrate the first application of this framework to power system frequency regulation with guaranteed worst-case performance bounds.

Proposed method

• The method uses a linear matrix inequality (LMI)-based approach to synthesize feedback controllers that minimize the L∞-norm of the closed-loop system response.
• It combines results from invariant ellipsoid theory and L∞ performance optimization to handle actuator saturation and peak deviation minimization simultaneously.
• The controller design incorporates a saturation model using a bilinear transformation and set invariance to ensure stability under bounded control inputs.
• A full-state feedback controller is first designed using LMIs, followed by an output feedback design with a Luenberger observer to estimate unmeasurable states.
• The approach guarantees that the system's reachable set is contained within an invariant ellipsoid, providing a worst-case bound on frequency deviation.
• The controller is optimized using a semidefinite program that incorporates both performance and saturation constraints.

Experimental results

Research questions

• RQ1 How can L∞-optimal control be synthesized in the presence of actuator saturation to minimize peak frequency deviation in microgrids?
• RQ2 Can a unified LMI-based framework effectively combine saturation constraints and L∞ performance optimization in power system control?
• RQ3 How does the proposed controller compare to conventional LQR and pole placement designs in terms of frequency overshoot and stability margins?
• RQ4 To what extent does the L∞-norm provide a tight bound on actual system performance under realistic disturbances?
• RQ5 What is the impact of state estimation (output feedback) on the performance and robustness of the L∞-optimal controller?

Key findings

• The proposed L∞-optimal controller reduced peak frequency deviation more effectively than LQR and pole placement controllers, with the high-gain L∞ design showing superior performance.
• The controller with gain δ=100 exhibited behavior approaching bang-bang control, indicating that further gain increases provided minimal performance improvement.
• The invariant ellipsoid derived from the LMI framework provided a reasonable, though not tight, upper bound on the system's reachable set under L∞-bounded disturbances.
• The output feedback controller achieved near-identical performance to the full-state feedback controller, though with a higher L∞-norm guarantee due to state estimation error.
• Simulation results confirmed that the L∞-norm of the system response was within an order of magnitude of the theoretical bound provided by the invariant ellipsoid.
• The method successfully integrated actuator saturation and L∞ performance into a single convex optimization framework using LMIs, enabling practical controller synthesis.