As energy demand grows and environmental pollution increases, low-carbon development has become a key focus in energy systems. To address the conflicting interests of the Source-Load-Storage System (SLSS), while also considering environmental benefits, this paper proposes an optimization model for the low-carbon economy of SLSS based on Stackelberg game theory and opportunity constraints. First, to ensure low carbon emissions and environmental protection, the carbon emissions of each entity in SLSS are constrained by a reward-penalty laddering carbon trading mechanism. Additionally, a demand response strategy is introduced on the user side, which accounts for both price and carbon compensation incentives. Next, considering the autonomy of the entities in SLSS, a decision-making model is developed based on the Stackelberg game. In this game-theoretic framework, the Power Management Operator acts as the leader, whereas the Power Generation Operator, Energy Storage Operator, and User serve as followers. This model also outlines the low-carbon interaction mechanisms among the various entities of SLSS. Finally, the model is solved using an improved particle swarm algorithm combined with the Gurobi optimization tool. Simulation results effectively validate the proposed model and method, showing that SLSS can rationally adjust its strategy within the low-carbon framework while balancing economic and environmental considerations.