**Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees**

#### **Hang Li \*, Zhe Zhang, Xianggen Yin and Buhan Zhang**

State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China; zz\_mail2002@163.com (Z.Z.); xgyin@mail.hust.edu.cn (X.Y.); zhangbuhan@hust.edu.cn (B.Z.) **\***Correspondence:leehang@outlook.com;Tel.:+86-1862-711-0403

Received: 17 March 2020; Accepted: 30 April 2020; Published: 8 May 2020

**Abstract:** The traditional security-constrained optimal power flow (SCOPF) model under the classical N-1 criterion is implemented in the power industry to ensure the secure operation of a power system. However, with increasing uncertainties from renewable energy sources (RES) and loads, the existing SCOPF model has difficulty meeting the practical requirements of the industry. This paper proposed a novel chance-constrained preventive SCOPF model that considers the uncertainty of power injections, including RES and load, and contingency probability. The chance constraint is used to constrain the overall line flow within the limits with high probabilistic guarantees and to significantly reduce the constraint scales. The cumulant and Johnson systems were combined to accurately approximate the cumulative distribution functions, which is important in solving chance-constrained optimization problems. The simulation results show that the model proposed in this paper can achieve better performance than traditional SCOPF.

**Keywords:** security-constrained optimal power flow; chance-constrained optimization; probability of contingency; renewable energy source
