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We consider the problem of stability analysis for distribution grids with droop-controlled inverters and dynamic distribution power lines. The inverters are modeled as voltage sources with controllable frequency and amplitude. This problem…
The synchronization of power generators is an important condition for the proper functioning of a power system, in which the fluctuations in frequency and the phase angle differences between the generators are sufficiently small when…
Nowadays, power system inertia is changing as a consequence of replacing conventional units by renewable energy sources, mainly wind and PV power plants. This fact affects significantly the grid frequency response under power imbalances. As…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…
Today, electrical energy plays a significant and conspicuous role in contemporary economies; as a result, governments should place a high priority on maintaining the supply of electrical energy. In order to assess various topologies and…
The electrical power network is gradually migrating from a centralized generation approach to a decentralized generation with high shares of renewable energy sources (RES). However, power systems with low shares of synchronous generation…
Transient stability analysis (TSA) plays an important role in power system analysis to investigate the stability of power system. Traditionally, transient stability analysis methods have been developed using time domain simulation by means…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
Power grid outages cause huge economical and societal costs. Disruptions in the power distribution grid are responsible for a significant fraction of electric power unavailability to customers. The impact of extreme weather conditions,…
A key quality of any kind of system is its ability to deliver its respective service correctly. Often the unavailability of commercial systems may lead to lost revenue, which are minor compared to what may be at stake when critical…
Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…
This paper addresses the distributed frequency control problem in a multi-area power system taking into account of unknown time-varying power imbalance. Particularly, fast controllable loads are utilized to restore system frequency under…
The dynamic response of power grids to small transient events or persistent stochastic disturbances influences their stable operation. This paper studies the effect of topology on the linear time-invariant dynamics of power networks. For a…
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and…
A suite of input-to-state stability results are presented for a class of forced differential inclusions, so-called Lur'e inclusions. As a consequence, semi-global incremental input-to-state stability results for systems of forced Lur'e…
We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…
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…
With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to…
The energy transition towards high shares of renewable energy will affect the stability of electricity grids in many ways. Here, we aim to study its impact on propagation of disturbances by solving nonlinear swing equations describing…