<p>The increasing integration of renewable energy sources (RES) into modern power systems introduces significant challenges related to numerical stability, disturbance propagation, and resilience of power flow solutions under uncertain operating conditions. Renewable intermittency, stochastic load variations, and stressed operating states may produce poorly conditioned susceptance matrices within the linearized DC power flow framework, thereby amplifying perturbations and reducing robustness of computed voltage angle solutions. This study investigates the application of L1 regularization for improving numerical conditioning and disturbance robustness in a renewable-integrated IEEE 16-bus test system. The proposed framework reformulates the DC power flow problem as a convex L1-regularized optimization problem solved using the iterative soft-thresholding algorithm (ISTA). Comparative analysis is performed against the unregularized formulation and classical L2 (Tikhonov) regularization using multiple numerical performance metrics, including voltage angle deviation, disturbance-energy metric, bus sensitivity, System Stress Index (SSI), and angle-based voltage stability indicator (VSI). A systematic regularization parameter analysis was conducted over the range (<i>λ </i>= 0.001 to 0.1), and (λ = 0.02) was identified as the most appropriate compromise between conditioning improvement, preservation of voltage angle structure, disturbance localization, and numerical robustness. Monte Carlo robustness analysis under stochastic perturbations in renewable generation, load injections, and line parameters further demonstrated substantial improvement in resilience characteristics through regularization. The results show that both L1 and L2 regularization significantly improve numerical stability relative to the unregularized system. However, L1 regularization exhibits stronger disturbance localization capability and better preservation of localized network response characteristics, whereas L<i>2</i> regularization provides stronger global conditioning improvement and smoother suppression of perturbation amplification. Although L1 regularization introduces moderately higher computational cost due to iterative optimization, the observed runtimes remain computationally feasible for practical applications. The findings demonstrate that L1 regularization provides an effective numerical stabilization framework for renewable-integrated DC power flow systems by improving conditioning, suppressing perturbation amplification, and enhancing robustness under stochastic operating uncertainty.</p>