Modelado de la confiabilidad de un sistema eléctrico de potencia nivel HL1 mediante redes de Petri

Abstract

The reliability assessment of electrical power systems at the HL1 hierarchical level is traditionally performed using a two-state (binary) model that represents generating units in normal operation or in a fault state. However, this simplification omits real-world situations involving degradations that reduce capacity operation due to subsystem unavailability, which can distort the power deficit risk estimate. This project develops a multi-state model implemented using Stochastic Petri Nets (SPNs), which can represent three operating states: normal, partial, and total fault. The proposed methodology is solved using sequential Monte Carlo simulation with a time step (Δt = 1 h) over a full year (8760 h). This allows us to construct chronological availability histories and thus estimate reliability indices. The multistate model parameters are adjusted using mean time to failure (MTTF) and mean time to repair (MTTR), which are converted into hourly probabilities and applied via random sampling within each simulation interval. Model consistency is verified by comparing theoretical and simulated forced unavailability (FOR), yielding relative errors of less than 1%, thus confirming the correct implementation of the transition logic. To validate the model's performance, a test case was designed based on the IEEE RTS-96 system and the Billington & Allan criterion for allocating capacity when auxiliary subsystems are degraded. Using N = 20,000 simulated years ensures the statistical stability of the estimators. The proposed multistate model reports LOLE = 25.3951 h/year and EENS = 2136.87 MWh/year; it also estimates 2.8499 events/year and an average duration of 8.91 h/year. Comparing these results with the traditional two-state model using the same system reveals that this model significantly overestimates the risk, yielding LOLE = 40.0887 h/year and EENS = 3281.68 MWh/year. Including the partial operation state reduces these estimates by approximately 36.65% for LOLE 4 and 34.89% for EENS, demonstrating that the classic two-state approach is overly conservative in assuming that any degradation is equivalent to a total failure. Taken together, the results show that implementing Stochastic Petri Nets with sequential Monte Carlo allows for a more representative quantification of deficit risk at the HL1 hierarchical level. By incorporating the partial operation state, the physical consistency of the states is maintained, and additional metrics (failure frequency and duration) are enabled, which are useful for reserve analysis and operational planning.