The carbon-price mechanism has been proved to be an effective measure for promoting energy revolution and mitigating climate change. It is of vital importance to develop optimal energy development strategy for electric power-dependent regions by considering the complex interaction among carbon price, carbon emission control, and carbon-responsibility transfer. In order to fill the research gap on the optimal choice of carbon-price mechanism at the urban level, this study is the first attempt to express uncertainties embodied in the carbon price mechanism as interval values, probability distribution and downside risks. The developed risk-aversion-based interval two-stage stochastic programming (RITSP) model is effective in analyzing the effect of internal and electric-transmission related carbon-tax on power system structure. It is discovered that carbon compensation policy for imported electricity is more suitable for Tianjin's power system development. Tianjin would primarily purchase electricity from Inner-Mongolia. With the increase of carbon emission tax, Tianjin would import increasing proportion of electricity from Gansu. Due to the limited endowment of renewable energy in Tianjin, the impact of carbon emission limitations on the renewable energy power generation structure of is trivial, and it has a greater impact on stimulating the development of CCS technology. What's more, Tianjin's future power system planning is more inclined to develop CCS rather than renewable energy.