Due to the uncertainty of the nodal power caused by the varying renewable energies and the variety of loads, the line power of the distribution network (DN) is uncertainty also. In extreme scenarios, the line power may exceed the loading limits and incur overload violations. In this paper, a risk analysis specifically for overload violations based on the security region of the DN is established. This method takes the N-0 security of the DN as the reference to determine the bidirectional security region and violation distances. The calculation of the probability distribution of the overload violation in the distribution lines is established according to the distribution of node injections of the DN by using the semi-invariant algorithm. By referring to the security boundaries, the optimization model of the anti-violation strategy to minimize the cost of anti-violation is derived, by which the severity of violation risk events is obtained accordingly. Assessment of the risk cost is built with the CVaR index for violation events. Based on the above algorithms, the risk-tolerated scheduling model of the DN is arrived at with the objective of minimizing the comprehensive risk cost and operating cost. Finally, the validity of the proposed method is verified by a modified IEEE 33-node example.
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