*1.1. Literature Review*

Numerous studies have attempted to address the drawbacks of the traditional SCOPF model.

To the best of the authors' knowledge, there are currently two strategies to reduce the calculation burden of traditional SCOPF and make it easier to solve. One strategy uses a contingency filtering (CF) [8,9] technique to reduce the number of contingencies. Usually, an index that ranks the severity of a contingency is used to filter contingencies; thus, only the contingency that exceeds the severity threshold is included in the contingency set. However, choosing the severity threshold itself is a challenge, for example, a very severe contingency may have a very low probability of occurring, and controlling it through SCOPF may result in excessive costs. The second strategy is to use Benders decomposition (BD) [10–12] to decompose the original SCOPF problem into a master problem and several subproblems. In this way, parallel computing technology can be used to improve the computing efficiency; however, BD requires convexity of the feasible region, which is not guaranteed in an SCOPF problem [12].

The concept of risk-based SCOPF [13–15] has been proposed as a method that comprehensively considers the probability and severity of contingencies. The risk of a contingency is defined as the product of the probability and severity of a contingency. Risk-based SCOPF uses risk as constraints to achieve a tradeoff between economic and security. This method relaxes the constraints of a single contingency [14] but controls the total risk of a contingency set to a certain level. Although the security and economy of power system operations are enhanced by risk-based SCOPF, the uncertainty of RES and load are not taken into consideration because measuring system risk under uncertainty is a challenging task. Moreover, the optimization formulation of risk-based SCOPF is complicated, and the calculation time is 4–7 times that of traditional SCOPF [14], which makes it difficult to apply in a real-time dispatch.

Chance-constrained optimization (CCO) [16–26] is a promising method to handle the uncertainty in power systems and it has been successfully applied to many problems. Instead of rigid constraint, CCO ensures a certain level of probability that the constraint is satisfied. The work of Bienstock [19] provides a solid foundation for incorporating CCO with OPF. This model was further extended in [22] to incorporate corrective SCOPF. Li et al. [23] provided a novel transmission expansion planning approach based on CCO and BD. Liu et al. [24], proposed solutions based on CCO for peak power shaving and frequency regulation in microgrids. Based on CCO, a day-ahead scheduling approach is proposed in [25] and a volt/var control approach is provided in [26]. Although CCO has been successfully applied to a variety of problems, the probability distribution of the uncertainty source is usually assumed to follow a Gaussian distribution. Studies [27–29] have indicated that the distribution of wind power forecast error and photovoltaic power is very different from a Gaussian distribution; therefore, the existing models should be improved so that they are able to handle arbitrary distributions. Moreover, there are few CCO models that consider contingency probability.
