Compositional transient stability analysis of power systems via the computation of reachable sets

Abstract

Abstract-The main challenge associated with the analysis of power systems via the computation of reachable sets is improving the algorithmic efficiency to scale towards industrially relevant problem sizes. In this paper, we present a compositional algorithm that can drastically reduce the computational effort required to assess the dynamical response of power systems during transients using reachability analysis. The main reason for the algorithmic efficiency is that we reformulate the transmission network into a set of subsystems, each consisting of a synchronous generator connected to a generator bus, whose algebraic constraints are unknown-but-bounded within some confidence intervals. This makes it possible to parallelize the computation of reachable sets for transient stability analysis and, more importantly, preserve the interaction and correlation between different machines connected to the grid. The applicability of the proposed compositional algorithm is illustrated on several benchmark examples and compared to other algorithms that compute the reachable set without employing any compositional techniques.

Review on set-theoretic methods for safety verification and control of power system

“…Although the centralised Lagrangian methods are powerful in evaluating system dynamics subject to disturbances, it is computationally impractical to apply these methods to a large‐scale non‐linear dynamic system due to the high dimensionality and operational flexibility [32 ]. A distributed formal analysis [27, 28 ] (or compositional formal analysis) is studied for efficient calculation and verification. Althoff [27 ] abstracts the dynamics of a large‐scale system to linear differential inclusions by using the full model and then compositionally computes the set of linearisation errors.…”

“…El‐Guindy et al . [28 ] split a large‐scale interconnected grid into subsystems for which the reachable sets are computed separately.…”

Estimating the region of attraction via forward reachable sets

“…Polynomial zonotopes allow one to select larger initial sets, thus reducing the size of the partitioned grid, which in return would substantially reduce the overall computational costs associated with our estimation algorithm. Finally, we intend to combine the proposed approach with a compositional reachability algorithm for transient stability analysis of power systems [36]. This allows one to compute provable stability margins, which are of great importance to transmission system operators to dynamically assess security of a transmission network [33].…”

Transient Stability Analysis of Power Grids with Admissible and Maximal Robust Positively Invariant Sets

“…Let G and L be the set of indices of all generator and load nodes, respectively, with |G| = p G , |L| = p L , and let p = p G + p L . For each generator, the dynamics is described by the swing equation, which is often used for transient stability analysis [8]- [12], [15], [18], [19], defined by…”