Abstract: A deep insight into the problem of energy cost optimization for cloud data center using green energy under constraints of satisfying SLA and long-term average carbon emissions. By formulating the problem into a constrained stochastic optimization problem, a carbon-aware energy cost optimal online algorithm based on Lyapunov optimization theory is proposed which can work without any future information. Furthermore, it is proved that this online algorithm can achieve the close-to-minimum solution compared to the offline optimal algorithm. Results of simulation based on real world data trace show that this algorithm has better performance than benchmark algorithm and can achieve offline optimal solution with tuning control parameters.