Globally, the power system plays a pivotal role in the transformative journey towards carbon neutrality, and the widespread application of big data technology offers unprecedented opportunities to realize this objective. This study conducts a thorough examination of technological innovations and applications of big data in power systems, aiming to propel the achievement of carbon neutrality goals. Through an in-depth analysis of the latest empirical cases and technological trends worldwide, we intricately explore the cutting-edge applications of emerging technologies such as big data analytics, artificial intelligence, and the Internet of Things in power system optimization, load management, smart grid operations, and carbon emission monitoring. We further scrutinize how these technological innovations enhance system reliability, real-time capabilities, adaptability, and their role in facilitating the efficient integration of renewable energy sources. Additionally, we assess the impact of current policies on the introduction of these technologies, particularly considering privacy protection and data security considerations. Finally, we present future research challenges, including large-scale data processing and the development of intelligent decision support systems, to lead the power system towards a more intelligent, efficient, and carbon-neutral future.