Quantifying Non-Linear Effects of Solar RES Penetration on Power System Reliability using Bayesian Generalized Additive Models

The integration of intermittent solar Renewable Energy Sources (RES) into power systems requires advanced methodologies for robust reliability assessment. Preliminary research using linear models indicated a non-significant relationship between solar penetration and reliability indices, potentially masking critical non-linear threshold effects. This study introduces Solaranalytica , an open-source R-based toolkit that rigorously compares the predictive performance of a Bayesian Linear Generalized Linear Model (GLM) against a flexible Bayesian Non-Linear Generalized Additive Model (GAM) using Hamiltonian Monte Carlo (HMC). Using real-world operational data from the CENPELCO San Carlos 20MVA substation, reliability indices (SAIDI, SAIFI, and EENS) were evaluated using WAIC and LOO-IC metrics. The results indicate that the grid is currently operating within a linear stability regime, with the Linear GLM showing slightly superior predictive density ( elpd value of -5316.23) compared to the GAM ( elpd value of -5316.52). However, the GAM's spline analysis successfully quantified latent non-linear structures, evidenced by non-zero smoothing parameters ( sds range: 0.49–0.68), particularly in the Expected Energy Not Supplied (EENS) index. These findings confirm that while average reliability remains stable, hidden "stress zones" exist where risks accelerate non-linearly. Consequently, this study suggests that future interconnection policies should mandate Reliability Sensitivity Analysis (RSA) — reporting not just average reliability indices but their sensitivity to solar variability — to ensure that the transition to high-renewable grids remains robust against non-linear tipping points. This research validates Solaranalytica as a critical decision-support tool, enabling grid operators to transition from reactive monitoring to a Dynamic Hosting Capacity (DHC) framework that identifies safe operational thresholds before instability occurs.