ded8498d-5d78-489b-b828-f4081d66263120251009064232060wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON POWER SYSTEMS2224-350X1790-506010.37394/232016http://wseas.org/wseas/cms.action?id=4057120202512020252010.37394/232016.2025.20https://wseas.com/journals/ps/2025.phpJavierBilbaoApplied Mathematics Department, University of the Basque Country (EHU), Bilbao School of Engineering, Pl. Ing. Torres Quevedo, 1, 48013 - Bilbao, SPAINThe power blackout that affected Spain on April 28, 2025, constitutes one of the most significant events in the recent history of the national electricity system. The sudden loss of approximately 15 GW of generation, in a context of high renewable energy penetration and low system inertia, caused an abrupt drop in frequency and the automatic disconnection of the Iberian system from the European electricity system. This study addresses the technical analysis of the event by applying two fundamental numerical methods in electrical engineering: the fourth-order Runge-Kutta method, oriented to the study of transient stability, and the Newton-Raphson method, used for the analysis of steady-state load flows. The combination of both approaches allows a comprehensive understanding of the dynamic and structural behaviour of the electrical grid during the blackout, revealing both the temporal evolution of critical variables and the redistribution of voltages and powers at the affected nodes. The analysis is based on real data, numerical simulations, and a rigorous technical interpretation of the results obtained. The Runge-Kutta method was used to simulate the evolution of system frequency following the loss of generation, considering parameters such as total system inertia, mechanical power, and instantaneous electrical power. The results showed a progressive drop in frequency in the first five seconds of the event, which triggered cascading automatic protections, including load shedding, the disconnection of nuclear power plants, and the separation of the Iberian system from the European one. This dynamic was key to understanding the rapidity with which the instability spread. Meanwhile, the Newton-Raphson method was applied to a ten-node network, allowing significant voltage imbalances to be identified at critical nodes such as N1, N2, and N3. Iterations of the method revealed efficient convergence, and the results showed voltage drops greater than 10% in areas with high renewable penetration and low response capacity. The combined interpretation of both methods showed how the system's low inertia, combined with an uneven distribution of generation and demand, contributed to the power collapse. Furthermore, correlations were observed between frequency drop times and protection activation, as well as between voltage profiles and disconnection points. Based on the results obtained, technical recommendations are made to improve the resilience of the Spanish electricity system. These include increasing inertia through energy storage technologies and synchronous generators, optimizing protection schemes to avoid uncoordinated automatic disconnections, and implementing predictive controllers to manage the high variability of renewable sources. Furthermore, periodic stability simulations are proposed with scenarios of high renewable penetration and critical demand, as well as reinforcing the transmission infrastructure in areas with high load density. Regional energy planning is also suggested, considering not only the balance between generation and demand, but also the structural robustness and operational flexibility of each area. This study demonstrates that the combined application of advanced numerical methods not only allows for the analysis of past events with technical rigor but also constitutes an essential tool for planning, preventing, and mitigating future blackouts in complex and highly interconnected electrical systems.1092025109202528929622https://wseas.com/journals/ps/2025/a445116-015(2025).pdf10.37394/232016.2025.20.22https://wseas.com/journals/ps/2025/a445116-015(2025).pdf10.1002/9781119689836Golpîra, Hêmin, Arturo Román-Messina, and Hassan Bevrani, Renewable integrated power system stability and control, John Wiley & Sons, 2021. 10.1016/j.renene.2005.04.008Lund, Henrik, Large-scale integration of optimal combinations of PV, wind and wave power into the electricity supply, Renewable energy, 31, no. 4, 2006, pp. 503-515. 10.1109/9780470544303Peterson, Andrew F., Scott L. Ray, Raj Mittra, and Institute of Electrical and Electronics Engineers. Computational methods for electromagnetics. Vol. 351. 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