The optimal power flow (OPF) problem, characterized by its inherent complexity and strict constraints, has traditionally been approached using analytical techniques. OPF enhances power system sustainability by minimizing operational costs, reducing emissions, and facilitating the integration of renewable energy sources through optimized resource allocation and environmentally aligned constraints. However, the evolving nature of power grids, including the integration of distributed generation (DG), increasing uncertainties, changes in topology, and load variability, demands more frequent OPF solutions from grid operators. While conventional methods remain effective, their efficiency and accuracy degrade as computational demands increase. To address these limitations, there is growing interest in the use of data-driven surrogate models. This paper presents a critical review of such models, discussing their limitations and the solutions proposed in the literature. It introduces both Analytical Surrogate Models (ASMs) and learned surrogate models (LSMs) for OPF, providing a thorough analysis of how they can be applied to solve both DC and AC OPF problems. The review also evaluates the development of LSMs for OPF, from initial implementations addressing specific aspects of the problem to more advanced approaches capable of handling topology changes and contingencies. End-to-end and hybrid LSMs are compared based on their computational efficiency, generalization capabilities, and accuracy, and detailed insights are provided. This study includes an empirical comparison of two ASMs and LSMs applied to the IEEE standard six-bus system, demonstrating the key distinctions between these models for small-scale grids and discussing the scalability of LSMs for more complex systems. This comprehensive review aims to serve as a critical resource for OPF researchers and academics, facilitating progress in energy efficiency and providing guidance on the future direction of OPF solution methodologies.

Decaying DC (DDC) offset current mitigation is a vital challenge in phasor current estimation since it causes malfunctioning/maloperation of measurements and protection systems. Due to the inductive nature of electric power systems, the current during fault inception cannot change immediately and it contains a transient oscillation. The oscillatory component acts similar to an exponential DC signal and its characteristics depend on the X/R ratio of the system, fault location, and fault impedance. DDC attenuates accurate phasor estimation, which is pivotal in protection systems. Therefore, the DDC must be eliminated from the fault current (FC) signal. This paper presents an overview of DDC mitigation methods by considering different groups—before the discrete Fourier transform (pre-DFT), after the discrete Fourier transform (post-DFT), the least square-based (LS-based), and other methods. Through a comprehensive review of the existing schemes, the effects of noise, harmonics, multiple DDCs (MDDCs), and off-nominal frequency (ONF) on the accuracy of DDC estimation, were recognized. A detailed discussion (along with some simulation results) are presented to address the main advantages/disadvantages of the past studies. Finally, this paper presents a few suggestions for future researchers, for researchers to investigate more implementable solutions in this field.