AI-Driven Logarithmic Base Optimization for Orthogonal Mode Decomposition in Power Systems Dynamics
Carlos E. Castañeda, P. Esquivel, Juan Cristobal Alcaraz Tapia, Héctor Vargas Rodriguez
Source abstract
Logarithmic Scaling and Normalization (LSN) of power system measurements has recently shown potential for improving modal representations and visualizing inter-area dynamic behavior. However, the logarithmic base used in LSN is commonly selected empirically, without a systematic criterion related to the modal structure of different measurement families. This work proposes an artificial-intelligence-driven framework for optimizing the logarithmic base by signal family to obtain an orthogonal modal representation of power system measurements. Particle Swarm Optimization (PSO), Bayesian Optimization (BO), and Genetic Algorithms (GA) are implemented to select family-specific bases for angular, voltage, and speed measurements from a two-area power system. The optimization is formulated using pre-projection modal quantities, including the raw dominant–residual angular deviation and the correction effort required by the Orthogonalized Residual Projection (ORP) stage. Then, the corrected 90∘ angle is interpreted as a post-projection validation result rather than as the only evidence of AI-based optimization. After applying LSN with the optimized bases and Orthogonalized Residual Projection, the corrected orthogonality angle remained within the target interval of 89∘ to 91∘ for the three signal families. Time-domain, decomposition, and polar representations confirmed the quadrature relationship between the dominant modal component and the orthogonalized residual component. Additionalrobustness tests under operating-point-like variations, additive noise, different sample counts, different time windows, modal superposition, and non-orthogonal mixing showed a post-ORP feasible rate of 100% in all tested cases. A comparison with grid search and golden-section search showed that one-dimensional optimizers are competitive for the scalar base-selection problem, while PSO, BO, and GA provide complementary evidence on consistency, repeatability, and computational effort. The proposed LSN–AI–Orthogonalized Residual Projection framework improves the interpretability of modal components for inter-area identification and provides an offline intelligent modal-preprocessing stage for power system dynamic analysis.
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