STEEPEST DESCENT METHOD: LIMITATIONS ANALYSIS AND EVOLVING APPLICABILITY IN MODERN POWER SYSTEMS

• Date: 2026
• Main Authors: Korovushkin , V., Boichenko , S., Kuznietsov , M., Danilin , O.
• Format: Article
• Language: Ukrainian
• Published: Institute of Renewable Energy National Academy of Sciences of Ukraine 2026
• Subjects: Power System Optimization; AC Optimal Power Flow (AC-OPF); Steepest Descent Method; Stochastic Gradient Descent (SGD); Ill-conditioned problems; Convergence analysis.
• Online Access: https://ve.org.ua/index.php/journal/article/view/623
• Journal Title: Vidnovluvana energetika

The article provides a systematic critical analysis of the steepest descent (SD) method in the context of optimizing modern energy systems. Despite its historical significance as the archetype of iterative algorithms, SD has been proven to be significantly limited in solving large-scale problems such as economic load dispatch (ELD) and optimal power flow (AC-OPF). The paper investigates the mathematical reasons for this phenomenon in detail: it shows that the physical heterogeneity of power system components (different scales of line impedances and generation characteristics) leads to a poor condition of the objective function Hessian. A high condition number (κ) causes a “zigzag” convergence trajectory, which makes the method unsuitable for real-time operational control. Based on a comparative analysis with second-order methods (Newton's method) and quasi-Newton algorithms (L-BFGS), the transition to interior point methods as an industry standard for constrained problems is justified. The key novelty of the work lies in the study of the relevance of gradient methods in modern computational paradigms in the era of artificial intelligence. The authors demonstrate a paradigm shift: characteristics that were limiting factors in deterministic optimization (noisy trajectory and simplified gradient processing) have been transformed into decisive advantages of stochastic gradient descent (SGD). It has been proven that it is precisely this stochastic nature that allows neural networks to be effectively trained for the tasks of forecasting RES generation and demand management, transforming the traditional method into the foundation of modern data-driven solutions in the energy sector.