The carbon market has become a major mechanism for global carbon emission reduction. However, the actual operation of the carbon market does not meet the expectation due to the drastic fluctuation of carbon prices. It is of great importance for regulators to fully understand the dynamic operation of the carbon market. This paper employs the carbon market dynamic assessment model to analyze key factors including emission reduction targets and power loads, which influence carbon prices under the European Union Emissions Trading System (EU ETS). The feasibility of the model is verified by simulating the carbon price crisis of the second stage of EU ETS. The simulation results specify that the total emissions are more susceptible to changes of power loads than emission reduction targets, which explains why the European Commission could do little to stabilize the carbon market when facing the disturbances of the global financial crisis and the European crisis. In addition, the threshold carbon price has a great important influence on emission reductions, which is of great importance for regulators to improve the market efficiency. Furthermore, according to the transfer rate from carbon prices to electricity prices, governmental subsidies could be needed to ensure the stability of the power grid.