**5. Conclusions**

Currently, and in the future, increasing uncertainty brings challenges for power systems. The traditional SCOPF under strict N-1 criterion can barely meet the requirements of a secure operation. To obtain an operational state that is robust to uncertainties and to improve the overall operational reliability, a novel CC-PSCOPF was proposed in this paper. The probability distribution of the overall line flow is obtained and constrained within the limits with a high probability guarantee in the proposed optimization model. This type of constraint greatly reduces the number of constraints for the entire optimization problem, and additionally, the violation probability of each line can be flexibly adjusted as needed. In addition, the cumulant and Johnson systems are proposed to approximate the CDF curves, so the chance-constraint optimization model proposed in this paper is not limited to the Gaussian distribution assumption.

The proposed CC-PSCOPF can be used to improve the safety level of a system's operation, especially for a system with a high level of RES penetration. How to determine the optimal violation level and correlations between uncertainty sources will be investigated in subsequent studies.

**Author Contributions:** H.L. conceived and designed the study; this work was performed under the guidance of Z.Z., B.Z. and X.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors gratefully acknowledge the support of the National High Technology Research and Development Program of China (863 Program): No. 2015AA050201.

**Conflicts of Interest:** The authors declare no conflict of interest.
