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As the modern electrical grid shifts towards distributed systems, there is an increasing need for rapid decision-making tools. Artificial Intelligence (AI) and Machine Learning (ML) technologies are now pivotal in enhancing the efficiency of power dispatch operations, effectively overcoming the constraints of traditional optimization solvers with long computation times. However, this increased efficiency comes at a high environmental cost, escalating energy consumption and carbon emissions from computationally intensive AI/ML models. Despite their potential to transform power systems management, the environmental impact of these technologies often remains an overlooked aspect. This paper introduces the first comparison of energy demands across centralized, distributed, and decentralized ML-driven power dispatch models. We provide a detailed analysis of the energy and carbon footprint required for continuous operations on an IEEE 33 bus system, highlighting the critical trade-offs between operational efficiency and environmental sustainability. This study aims to guide future AI implementations in energy systems, ensuring they enhance not only efficiency but also prioritize ecological integrity.