Smooth Rate Limiter Model for Power System Stability Analysis and Control

TL;DR

The paper addresses the difficulty of incorporating rate limiters into small-signal stability analysis due to their non-smooth nature. It introduces a smooth, second-order rate limiter with state variables $\dot y = x$ and $\dot x = (\dot y_{\max} - x)(x - \dot y_{\min})[ k_{1}(u - y) - k_{2}x] - k_{3}x$, and proves that the derivative $\dot y$ remains bounded within $[\dot y_{\min}, \dot y_{\max}]$ while enabling linearization about equilibria via $\Delta \dot y = \Delta x$, $\Delta \dot x = - (k_{2}c + k_{3})\Delta x - k_{1}c\Delta y + k_{1}c\Delta u$ with $c = -\dot y_{\max}\dot y_{\min}$. This facilitates eigenvalue-based stability analysis and allows tuning of $k_{1},k_{2},k_{3}$ to enhance transient performance. The approach is demonstrated through case studies on a GFL VSI, a VSI current regulator, and the NY-NE 68-bus system, showing accurate replication of rate-limiter effects, improved control behavior, and observable shifts in linearized poles, while incurring minimal computational overhead. Overall, the smooth RL provides a practical tool for incorporating rate-limit dynamics into stability analysis and control design in power systems.

Abstract

The letter proposes a smooth Rate Limiter (RL) model for power system stability analysis and control. The proposed model enables the effects of derivative bounds to be incorporated into system eigenvalue analysis, while replicating the behavior of conventional non-smooth RLs with high fidelity. In addition, it can be duly modified to enhance the system's dynamic control performance. The behavior of the proposed model is demonstrated through illustrative examples as well as through a simulation of the New York/New England 16-machine 68-bus system.

Figures (4)

• Figure 1: Response of conventional rl and the proposed.
• Figure 2: gfl vsi response.
• Figure 3: vsi current regulated by rate-limited controller.
• Figure 4: Multi-machine power system response.