With the launch of the national carbon market, electricity industry is expected to play an important role in the carbon market. However, the impact mechanism of carbon market on low-carbon scheduling in power systems remains underexplored and warrants further study. This paper investigates the impact of the annual clearing mechanism in the carbon market on the day-ahead dispatch of power systems. A non-parametric statistical model is developed to annual represent the carbon market price. Considering the uncertainty in carbon price, this paper proposes several low-carbon economic dispatch methods for power systems with different risk preferences, including conditional value at risk (CVaR) optimization, expected value optimization, and robust optimization. The impact of carbon price uncertainty on day-ahead dispatch is analyzed through a mathematical optimization framework. The results show that, compared with traditional economic dispatch models, the low-carbon economic dispatch model can reduce carbon emissions by 8.41%. Additionally, the more risk-averse the approach to carbon pricing, the lower the carbon emissions. The smaller carbon quota coefficient further promotes low-carbon dispatch through the carbon market. Finally, this paper identifies conditions under which carbon capture systems become profitable, specifically, when the carbon price in the market exceeds the product of the unit generation cost and the energy consumption coefficient of carbon capture.