Logic-based Resilience Computation of Power Systems Against Frequency Requirements
Negar Monir, Mahdieh S. Sadabadi, Sadegh Soudjani
TL;DR
This paper addresses resilience of power systems to disturbances under realistic frequency constraints by modeling grid dynamics as a Lur'e system and enforcing Signal Temporal Logic (STL) specifications to capture frequency response requirements. It formulates the problem as maximizing disturbance magnitude $\\mu$ such that all bounded disturbances $w_t$ keep the STL robustness $\\rho^{\\Psi}(y,t)$ above a threshold and the angular error $\\|z_t\\|$ within limits, then solves a robust nonconvex scenario optimization, encoded as a Mixed Integer Nonlinear Program (MINLP). The approach is demonstrated on a Single Machine Infinite Bus and the IEEE 9-bus system, yielding $\\mu^{*}=0.7746$ p.u. and $\\mu^{*}=1.6438$ p.u., respectively, under UK grid-code-inspired specifications and with probabilistic guarantees provided by the scenario framework. The method reduces conservatism relative to traditional frequency-bounded analyses and provides a practical path to quantify resilience under uncertainty in modern inverter-rich power grids.
Abstract
Incorporating renewable energy sources into modern power grids has significantly decreased system inertia, which has raised concerns about power system vulnerability to disturbances and frequency instability. The conventional methods for evaluating transient stability by bounding frequency deviations are often conservative and may not accurately reflect real-world conditions and operational constraints. To address this, we propose a framework for assessing the resilience of power systems against disturbances while adhering to realistic operational frequency constraints. Our approach leverages the Lure system representation of power system dynamics and Signal Temporal Logic (STL) to capture the essential frequency response requirements set by grid operators. This enables us to translate frequency constraints into formal robustness semantics. We then formulate an optimization problem to identify the maximum disturbance that the system can withstand without violating these constraints. The resulting optimization is translated into a scenario optimization while addressing the uncertainty in the obtained solution. The proposed methodology has been simulated on the Single Machine Infinite Bus case study and 9-Bus IEEE benchmark system, demonstrating its effectiveness in assessing resilience across various operating conditions and delivering promising results.