Quantitative Evaluation of High-Performance Computing (HPC) Energy Consumption and Environmental Impact Using Mathematical Modeling

HPC is developing rapidly. In the context of the information age, computing power has become a key element in promoting technological innovation and economic development. This article aims to quantitatively evaluate the development prospects of HPC energy consumption and its impact on the environment through mathematical models. First, in order to derive the annual energy consumption model, this article collected HPC energy consumption data and determined the range of the annual energy consumption index. By interpolating the missing data in the Top500 list, weighted summation was used to calculate the total number of global HPC centers. Power consumption. Calculation results show that the maximum annual energy consumption of the Top500 HPC centers is approximately 9157 GWh, while the actual average annual energy consumption is approximately 4904 GWh. Based on the HPC energy consumption model, this paper established a carbon emission model and designed a simple carbon emission estimation model based on the energy structure of different regions. Combining the carbon emission factors of various energy sources and the energy structure of each HPC center location, we calculated the total carbon emissions of global HPC systems are 160,290 tons. Secondly, this paper establishes an ARIMA model for HPC scale growth and predicts changes in energy structure. After passing the ADF test, KPSS test and residual autocorrelation test, the parameters are fitted and predicted. At the same time, the energy structures of China and the United States are used as represents and predicts the changes in energy consumption structure in the next six years. The results show that the total power of global HPC will reach 1433412.3 kW in 2030, and the total energy consumption will be 22602.05 GWh, carbon emissions are 6436959.31 tons. Clean energy will account for more than 45%. Next, this paper establishes a Markov model to describe the energy structure shift to reflect mandatory policies or changes made by energy companies. In particular, it analyzes the challenges that may be faced in reaching the goal of 100% renewable energy. The results show that in with the intervention of policy and technological progress, the proportion of oil and coal consumption will decrease significantly, and natural gas, as a less polluting energy resource, can be used as a substitute in the transition period. Analyze the needs of the cooling system of the HPC center and the consumption of water resources. Through case studies, the cooling needs of the Frontier supercomputer are demonstrated, and the impact of seasons on coolant flow and temperature is analyzed. In order to reduce the impact of the HPC center on the environment, Plans such as developing green ICT, optimizing energy management, and carbon footprint tracking were proposed. In addition, in response to the problem of coolant waste, suggestions were made to locate HPC centers in high latitudes, recycle coolant, and participate in environmental protection projects. Finally, a model sensitivity analysis was conducted, which proved that even if there is uncertainty in the carbon emission factor data, its impact on the final carbon emissions is relatively limited, and the error does not exceed 15%.