For electric power systems, although satisfying soaring power demand is critical for regions and countries, climate change mitigation by reducing carbon emissions is one of major challenges. Consequently, the primary obstacle for electric power system management is to tackle the trade-off between economic and environmental issues. Moreover, electric power systems exhibit a great number of complexities, associated with uncertainties and dynamics in system components, parameters and their interactions, such as future end-user demand, emission amounts and system violation. Therefore, efficient programming techniques are desired to deal with these uncertainties and complexities of the dual-objectives for maximizing economic profits and minimizing carbon emissions simultaneously. In this research, a set of multi-stage fractional programming approaches were proposed for electric power system management. The associated approaches included: (a) a multi-stage chance-constrained fractional programming (MCFP) approach for carbon-emission management; (b) a multi-stage joint-probabilistic left-hand-side chance-constrained fractional programming (MJCFP) approach for planning the electric power system in Saskatchewan, Canada; and (c) a stochastic risk-aversion dual-objective programming (SRDP) approach for electric power system management in Ontario, Canada. The proposed approaches can solve ratio-optimization problems with random information, reflect trade-offs between objectives and system reliability, and depict stochastic uncertainties and dynamics by introducing chance-constrained programming (CCP) technique into the fractional programming (FP) framework with a multi-layer scenario tree. To gain better insights on left-hand-side multi-randomness issues, especially when a joint-probabilistic requirement is imposed on multiple emission constraints, the MJCFP method was further developed to enhance the capabilities of MCFP approach. Furthermore, based on previous optimization approaches, the SRDP approach was improved by taking into consideration of financial risk management against extremely low profits conditions.