Digital Twin (DT) technology has emerged as a valuable tool for researchers and engineers, enabling them to optimize performance and enhance system efficiency. This paper presents a comprehensive Systematic Literature Review (SLR) following the PRISMA framework to explore current applications of DT technology in the power generation sector while highlighting key advancements. A new framework is developed to categorize DTs in terms of time-scale horizons and applications, focusing on power plant types (emissive vs. non-emissive), operational behaviors (including condition monitoring, predictive maintenance, fault detection, power generation prediction, and optimization), and specific components (e.g., power transformers). The time-scale is subdivided into a six-level structure to precisely indicate the speed and time range at which it is used. More importantly, each category in the application is further subcategorized into a three-level framework: component-level (i.e., fundamental physical properties and operational characteristics), system-level (i.e., interaction of subsystems and optimization), and service-level (i.e., value-adding service outputs). This classification can be utilized by various parties, such as stakeholders, engineers, scientists, and policymakers, to gain both a general and detailed understanding of potential research and operational gaps. Addressing these gaps could improve asset longevity and reduce energy consumption and emissions.