With the steady enhancement of the green certificate trading system, maintaining the equilibrium between supply and demand in the green certificate trading market, alongside addressing peak shaving and valley filling challenges, has emerged as a pressing concern. To tackle this issue, inspired by the concept of real-time electricity pricing, a demand-based real-time green certificate pricing mechanism is put forth. A model aimed at maximizing system social welfare is formulated, employing the Lagrange duality and gradient projection methods to compute the Lagrange multiplier, commonly referred to as the shadow price, the optimal real-time pricing for green certificates is thus obtained. Secondly, taking into account the uncertainty associated with renewable energy output, both risk aversion and risk-seeking models are established through the incorporation of information gap decision theory (IGDT). Changes in social welfare under varying attitudes of renewable energy aggregators are investigated, providing valuable insights for maintaining the economic stability of the system. Finally, simulations are performed using Yalmip and Gurobi. The results demonstrate that the proposed model effectively balances green certificate supply and demand, enhances renewable energy utilization, and accomplishes the objective of low-carbon, economically stable system operation.