**1. Introduction**

The growth in renewable energy sources (RES) and charging loads in recent years, such as wind power, photovoltaics and electric vehicle, has brought considerable economic benefits; however, the uncertainty of power injections has increased, which leads to increased operational risks [1–3], especially for highly-loaded power systems. The increasing uncertainty of operation increases the need for new criteria, dispatch tools and control methods to better balance operational security and costs [4].

Optimal power flow (OPF) is the fundamental dispatch and planning tool that is used to minimize operational costs while ensuring the security of the normal state, and security-constrained optimal power flow (SCOPF) [4–7] is an extended form of OPF that considers the classical N-1 criterion. Unlike OPF, which only considers a single system topology (normal state), SCOPF typically ensures that the system state remains within the operational limits when unexpected component outages (contingency set) occur. However, with the emergence of uncertainties in the power system, several drawbacks of traditional SCOPF have become apparent and these need to be addressed. These include:

1. Traditional SCOPF does not consider the influence of the uncertainty of RES and loads, and it cannot provide a robust solution because increasing uncertainty makes the operational state more stochastic and may lead to frequent violations of the N-1 criterion.

2. Traditional SCOPF disregards the probability of a contingency occurring; in other words, it considers the occurrence probability to be 1 for every contingency in a contingency set [4]. Obviously, this does not match the actual situation because the probability of a contingency is usually very low.

3. The scale of the SCOPF problem is highly related to the scale of the power system and the number of contingencies. This means that for a large power system where a large number of contingencies are considered, the calculation burden is high, and directly solving a SCOPF problem in a short time is quite challenging.
