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With the rapid expansion of computational infrastructure, the electricity consumption of geographically dispersed Internet Data Centers (IDCs) has imposed a substantial influence on the power grid. Geographically distributed IDCs, which present a versatile electricity demand with significant operational flexibility, hold potential for mitigating cost issues and balancing regional supply and load demand. To exploit this flexibility, this paper has developed a dual-drive coordinated operational strategy, which integrates locational electricity prices and unit carbon emission costs based on the dynamic carbon emission intensity (DCEI) of various regions as interaction signals to improve coordination effectiveness. The upper-level determines the consumption behaviour of IDCs, the lower-level provides feedback on dual-drive signals factoring in IDCs' involvement in grid operation, whilst an iterative algorithm is suggested to solve the bi-level model. Case studies based on real-world datasets demonstrate that the proposed operation strategy can achieve arbitrage through multi-regional carbon-electricity markets, significantly reduce operating costs, and support the rapid development of IDCs. Additionally, this strategy facilitates optimal matching of power load in IDCs with renewable energy sources, thereby mitigating imbalances in regional renewable energy supply and demand. • Analysing the necessity of integrating IDCs into the carbon market. • Proposing a dual-drive coordination to activate spatiotemporal flexibility of IDCs. • An iterative algorithm for solving the bi-level model is designed. • Comparing impacts of carbon policies in IDC costs and renewable energy accommodation. [ABSTRACT FROM AUTHOR]