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The electricity cost of cooling systems can account for 30% of the total electricity bill of operating a data center. While many prior studies have tried to reduce the cooling energy in data centers, they cannot effectively utilize the time-varying power prices in the power market to cut the electricity bill for data center cooling. This is in contrast to the fact that various thermal and energy storage techniques available in today's data centers, such as ice or water-based thermal tanks and UPS batteries, can be utilized to store energy when the power price is relatively low. The stored energy can then be used to cool the data center when the power price is high. In this paper, we design and evaluate TEStore, a cooling strategy that exploits thermal and energy storage techniques to cut the electricity bill for data center cooling, without causing servers in a data center to overheat. The proposed TEStore system checks the low prices in the hour-ahead power market and precools the thermal masses in the data center, which can then absorb heat when the power price increases later. Meanwhile, TEStore also checks the energy level in UPS batteries and exploits it as a complementary method in shifting energy demand for data center cooling. On a longer time scale, TEStore is integrated with auxiliary thermal tanks, which are recently adopted by some data centers to store energy in the form of ice. We model the impacts of TEStore on server temperatures based on Computational Fluid Dynamics (CFD) to consider the realistic thermal dynamics in a data center with 1,120 servers. We then evaluate TEStore with workload traces from real-world data centers and power price traces from a real power market. Our results show that TEStore can achieve the desired cooling performance with a much lower electricity bill than the current practice.