In the global context of climate change mitigation and carbon emissions control, a carbon market risk analysis and control framework is in urgent need considering the seriousness of climate change problem, the solemnity of national political commitment or the urgency of sustainable development of energy industry. As the first part of a series of papers, this paper analyzes the relationship between climate constraints and the carbon market, discusses the mechanism of carbon market risk from a regulatory perspective, and reviews the carbon risk analysis and control practices in recent years. A multi-line risk defense framework of carbon market is proposed and designed by defining key features such as "disturbance occurrence", "parameter violation" and "market malfunction" and the coordinated control optimization method under this framework is discussed. Finally, the problem of carbon market risk prevention and control is mathematically formulated. Sand-table simulation and risk quantitative analysis technologies are suggested to be further improved to support carbon market risk analysis and control. The dynamic simulation platform for macro-energy systems (DSMES) developed by the authors' team can break through the barriers among different research paradigms, and effectively support the related research. Based on the defense framework proposed in this paper, simulation analysis and coordinated control results of the carbon market risk will be reported in the second part of the series papers.