Operating virtual power plants (VPP) solely based on economic feasibility can cause stability problems, such as voltage violation and power congestion in the distribution system. A cooperation-based operation between the VPP and distribution system operator (DSO) is regarded one of the methodologies for solving stability problems. In the cooperation-based operation method, a VPP establishes an operation strategy considering the information provided beforehand by the DSO, such as the distribution system constraint (DSC). The DSC is uncertain because it is determined based on the forecasted grid situation. Therefore, operational strategies that rely only on the DSCs provided by DSOs may make the operation of the VPP passive and reduce profits depending on the accuracy of the announced DSCs. This study proposes an operating methodology and optimal operation model considering the uncertainty of the DSC to increase the profit of the VPP. In the proposed model, the VPP independently forecasts the DSC for profit maximization and establishes an operational plan considering penalties. Case studies were conducted to demonstrate the economic improvement of the VPP, considering the uncertainty of the DSC. The case study results demonstrated that the proposed model increased the profit of the VPP by 1.6 % compared with that of the conventional method.