This paper attempts to elucidate the transformative integration of computational techniques within power systems, underscoring their critical role in enhancing system modeling, control, and the efficient integration of renewable energy. It breaks down the two-sided nature of technological progress, highlighting both gains in operational efficiency and new challenges such as real-time processing, data management, and cybersecurity. Through meticulous analysis of query-based research patterns and mathematical frameworks, this study delves into the balancing act between specificity and breadth in scholarly inquiries while evaluating the impact and evolution of research trends through citation analysis. The convergence of interests and transient research trends is evident, particularly in Artificial Intelligence and optimization. This comprehensive narrative anticipates a sophisticated trajectory for power systems, advocating for continuous innovation and strategic research to foster sustainable, resilient, and intelligent energy networks.