Micro-grid is one of the important carriers for renewable energy integration. Optimizing the operation mode of micro-grid can improve economic benefits and reduce risks brought by uncertainties. To maximize the economic benefits of photovoltaic-storage-load micro-grid, a chance-constrained optimal operation model considering renewable and load uncertainties is proposed in this paper. Firstly, the photovoltaic (PV) power and load forecast error distribution function based on fitting method is obtained. Then, a probabilistic power balance constraint based on chance constrained theory is established to reflect risks brought by uncertainties. To protect the information privacy of different entities, the alternating direction multiplier method (ADMM) with self-adaptive parameters is used to the proposed optimal model in a distributed way. Case study demonstrates that the proposed model can achieve a profit and risk balance of micro-grid scheduling by setting different confidence levels, and the information privacy of micro-grid operator and users is well protected.