The study of the risk spillover effects between the carbon market prices in different regions of China and the stock prices of listed power companies is essential for strengthening carbon market risk management and promoting energy conservation and emission reduction in power companies. This paper systematically investigates the static and time-varying spillover relationships between carbon prices and power company stock prices in both the time and frequency domains by constructing the spillover index. Further, it explores the main influencing factors of the risk spillover of the "carbon-power" system. The results show that: In the time domain, the carbon market price is a net risk recipient, and the total spillover index will increase significantly when the carbon market and the power market introduce relevant policies. However, the spillover effect has noticeable regional differences. Meanwhile, in the frequency domain, the risk spillover effects between the carbon prices and power company stock prices mainly occur in the short term (within 20 days), and the long-term impact of the carbon market in Shanghai and Hubei is slightly higher than that in Beijing and Guangdong. Finally, in terms of influencing factors, thermal power generation, national power supply coal consumption, renewable power generation, and the online trading of the national carbon market all positively impact the risk spillover effects between the carbon market prices and power company stock prices. In contrast, the positive development of the economy has an inhibiting impact on the risk spillover between the two.