Assessing the Impact of Wind Variability on Power System Small-Signal Reachability

Abstract

We propose a method to assess the impact on power system dynamic performance of operational uncertainty caused by variability in the system supply side. Operational uncertainty is not new to power systems, e.g., demand variability. However, with the increased penetration of renewable-based generation, operational uncertainty will extend to a significant portion of the supply side, which may have an impact on system dynamic performance, e.g., frequency or voltage deviations beyond prescribed operational requirements. To address the problem, we propose the use of reachability analysis techniques, which will provide bounds on worst-case deviations of system variables that must remain within certain bounds. The method is illustrated with several examples.

Transient stability analysis by reachable set computation

“…The dynamic equations are described by a generator model [13]. For simplicity, we use the same model for all generators and synchronous condensers.…”

“…and analogously the overapproximations for the reachable set at points in time, where R d affine (τ k ) is taken from (13). Based on R d (τ k ), the algebraic reachable set R a (τ k ) is computed by evaluating the algebraic part of Prop.…”

“…One can prove transient stability without constructing a Lyapunov function by showing that the system returns to the set of initial states after a fault occurred. The main disadvantage of reachability analysis so far was the computational complexity for power system applications, so that only small systems have been verified [13], [19], [26]. In [19], transient stability analysis is performed using level-sets for a single-machine-infinite-bus system modeled by ODEs with only 2 state variables.…”

“…A slightly larger double-machineinfinite-bus system with 2 buses described by ODEs with 5 state variables is considered in [26]. In [13], an initial DAE model is simplified to ODEs and further to linear ODEs, without considering errors made during each conversion. A 3-bus system is considered in [13], and effects on wind variability rather than transient stability are investigated.…”

“…In [13], an initial DAE model is simplified to ODEs and further to linear ODEs, without considering errors made during each conversion. A 3-bus system is considered in [13], and effects on wind variability rather than transient stability are investigated.…”