The Internet of Energy (IoE) is changing how we manage energy by using digital technology to create smarter, more efficient, and sustainable energy systems. A key part of this change is Edge AI, which means running AI directly on devices like sensors and smart meters. This is different from using cloud-based AI because Edge AI processes data right where it is collected. This results in faster response times, better data privacy, and more efficient use of bandwidth. With Edge AI, energy systems can make real-time decisions and quickly adapt to changing conditions, which is especially useful for smart grids, integrating renewable energy, and predicting maintenance needs. This chapter delves into the comparative analysis of Edge AI and traditional cloud-based AI within the IoE framework, exploring their respective strengths and challenges. Edge AI excels in applications requiring instantaneous data processing and localized decision-making, creating it a model for situations like grid stability management and demand response. Additionally, by handling data at the source, Edge AI minimizes the need for extensive data transmission, thereby safeguarding sensitive information and reducing operational costs. However, challenges such as device management, standardization, and energy efficiency remain. This comprehensive examination highlights that Edge AI will be very important for energy management in the future. It could make energy systems around the world more efficient, reliable, and sustainable.