Different from traditional distribution network, the controllable distributed generations assessed to Active Distribution Network (ADN) could participate in the economic operation of distribution network. The output allocation of controllable distributed generations is determined by the economic schedule strategy for ADN. In order to maximize Load Supplying Capability (LSC), controllable distributed generations usually work at rated state, which departs from the pursuit of economic operation. The contradiction has an impact on LSC. This paper highlights a bi-level optimization model for LSC of ADN based on chance-constrained programming. The upper-level model aims at calculating the LSC of ADN, and the lower-level model is to allocate the output of controllable distributed generations based on economic dispatch principle combining the characteristics of ADN effectively managing controllable distributed generations during the process of load growth. Finally, the modified IEEE 33-bus distribution system is taken as an example for verifying the proposed model. The results show that the LSC which meets the requirements of ADN economic operation is acquired. This work is supported by the Fundamental Research Funds for the Central Universities (No. DUT15QY50) and Science and Technology Project of State Grid Corporation of China (No. 2017YF-27).