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Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove…
DC microgrids have promising applications in renewable integration due to their better energy efficiency when connecting DC components. However, they might be unstable since many loads in a DC microgrid are regulated as constant power loads…
Multiple types of Nyquist-like impedance-based criteria are utilized for the small-signal stability analysis of converter-based AC systems. It is usually considered that the determinant-based criterion can determine the overall stability of…
This paper presents a novel approach to stability analysis for grid-connected converters utilizing Scaled Relative Graphs (SRG). Our method effectively decouples grid and converter dynamics, thereby establishing a comprehensive and…
For many nonlinear control systems, the chosen equilibrium determines both the steady-state efficiency and the dynamic performance. This paper addresses the issue of obtaining an optimal equilibrium in terms of some steady-state operation…
This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal…
The output impedance matrix of a grid-connected converter plays an important role in analyzing system stability. Due to the dynamics of the DC-link control and the phase locked loop (PLL), the output impedance matrices of the converter and…
This paper studies stability analysis of DC microgrids with uncertain constant power loads (CPLs). It is well known that CPLs have negative impedance effects, which may cause instability in a DC microgrid. Existing works often study the…
Proportional-Integral-Derivative (PID) control has been the workhorse of control technology for about a century. Yet to this day, designing and tuning PID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on classical…
As the integration of renewable energy generation increases and as conventional generation is phased out, there is a gradual decline in the grid's strength and resilience at the connection point of wind turbines (WTs). Previous studies have…
Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and…
A network-level small-signal model is developed for lossy microgrids, which considers coupled angle and voltage dynamics of inverter-based microgrids and uses a more general framework of droop controls in the inverter. It is shown that when…
This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the…
DC microgrids are getting more and more applications due to simple converters, only voltage control and higher efficiencies compared to conventional AC grids. Droop control is a well know decentralized control strategy for power sharing…
Renewable-driven microgrids dominated by grid-forming (GFM) converters are subject to persistent power fluctuations, making equilibrium-known stability assessments restrictive. This paper develops an equilibrium-free contraction stability…
We consider the problem of quantifying and assessing the steady-state voltage stability in radial distribution networks. Our approach to the voltage stability problem is based on a local, approximate, and yet highly accurate…
Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. The upper bound on the error of oscillators from the center of the neighborhood is derived. Then the performance of an adaptive…
We consider the problem of computing equilibria (steady-states) for droop-controlled, islanded, AC microgrids that are both economic-optimal and dynamically stable. This work is motivated by the observation that classical optimal power flow…
This paper investigates the theory of resilience and stability in multi-microgrid networks. We derive new sufficient conditions to guarantee small-signal stability of multi-microgrids in both lossless and lossy networks. The new stability…
The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulation-based…