Fractional-Order Physics-Informed Neural Networks for Stability Analysis of Power System Models
Conventional integer-order models do not adequately represent intrinsic memory effects in the dynamics of modern power systems, which operate under increasingly nonlinear and uncertain conditions. This work proposes a Fractional-Order Physics-informed Neural Network (FOPINN) framework for power system stability analysis and forward dynamic modelling. The method allows for an accurate representation of memory-dependent dynamics by directly integrating fractional-order swing equations into the learning process. The framework is extended to a reduced Multi-Machine Infinite Bus (MMIB) system to examine inter-machine coupling and synchronisation dynamics, following with a validation on a Single Machine Infinite Bus (SMIB) system. A comparison with integer-order PINNs, Caputo-L1 fractional solvers, and classical RK4 shows that FOPINN achieves significantly improved prediction accuracy while maintaining physical consistency. The trained FOPINN further provides approximately $193\times $ faster inference than repeated Caputo–L1 numerical computation while demonstrating the expected influence of fractional order, damping, inertia, and network coupling on transient stability. The results show that transient behaviour is strongly influenced by fractional-order dynamics. Stronger memory effects alter the response as the fractional order decreases, causing long-lasting transient deviations and slower convergence before the system reaches steady state. It is demonstrated that memory effects propagate via machine coupling in the MMIB system, altering synchronisation characteristics and the stability margin as the disturbance level increases. Fractional-order analysis reveals oscillatory or unstable responses in high-loading regimes, whereas classical integer-order models predict stable behaviour. These results establish FOPINN as an effective, reusable and physics-consistent framework for capturing memory-driven dynamics in contemporary power grids and emphasise the significance of integrating fractional-order modeling for realistic power system analysis.