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We would like to thank the discussers for their valuable discussions. They raised an important issue concerned with the treatment of extreme perturbations of low probable scenarios. Therefore, we would like to discuss how the system security is achieved against such uncertainties in real power system. Hereof, our policy of risk management is presented.We divide the uncertain events and disturbances into two categories according to their severity.Acceptable disturbances/events. Their impact to a system is less than a critical level so that the system can be recovered within assumed payable cost.Fatal disturbances/events. The impact is greater than the critical level and result in "fatal disaster." The losses exceed acceptable costs.We think that the former events should be treated in probabilistic manner, in which each risk is evaluated by its expected damage defined by the product of the expected cost and its probability. Note that probabilities of such events are not always reliable for events which rarely happen. Their probabilities tend to be close to zero and not suited for estimating their expected damage accurately. We think that such probabilistic approaches are still effective for the former events in reducing the expected annual cost of power system operation if the amount of cost is acceptable compared with annual cost. However, this may not be the case for the latter events since they are not accepted by the society. As we discussed in the IREP session, the cost is high beyond evaluation as well as its small probabilities. Therefore, their product as the expected cost in such cases is not meaningful in reality. Our underlying idea is that special treatments are required for the latter situations so that the fatal consequences are avoided. This policy is similar to the cases for national security against possible disasters and for risk management in finance against bankrupt. We think that, since the power system is very important infrastructure, a special type of risk management is necessary for the latter events. For this purpose, we have proposed a concept of "Robust N-1 Security," in which the system security is guaranteed in a deterministic way when the uncertain parameters of importance are within pre-specified confidence intervals. We suggest this deterministic treatment as a complement to the existing stochastic approaches. Figure 1, which was used in the presentation, describes the methodology of our paper in which a stochastic approach is used for less severe constraints of overloading.On the other hand, the robust security approach is adopted to guarantee important condition of demand and supply balance. This is an example of the proposed robust security approach for the application to Dynamic ELD problem. The main purpose of the robust security approach is to assess the system security quantitatively against the latter type of uncertain events as is demonstrated in the paper . Fig. 1 Robust Security Approach applied to DELDReference [2] in the discussion analyzes historical data of blackouts...

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