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Vol.6 No.3 2014

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Research paper : A proposal for setting electric power saving rate to avoid risk of electric power shortage occurrence (I. ARIZONO et al.)−146−Synthesiology - English edition Vol.6 No.3 (2013) Therefore, we have changed the quantity of the electricity supply of the conventional electric generating systems treated as a fixed value in the previous manuscript to a random variable in this revised manuscript.5 Characteristic and selection of the probability inequalityQuestion (Hiroshi Tateishi)Three probability inequalities are used without explanation. It is supposed that each probability inequality has an advantage and disadvantage. The authors should explain them. Furthermore, is there an inequality which seems to be usable other than these three inequities?Answer (Ikuo Arizono)The authors have represented the reasons for the three probability inequalities. The Bennett and Hoeffding probability inequalities require the range for each random variable that the one-sided Chebychev probability inequality does not need. In this case, this domain information is given based on the two-sigma method using expectation and variance only. The advantage and disadvantage of each probability inequality cannot be definitely shown. Note that the Hoeffding probability inequality, in particular, is recognized as a probability inequality with superior performance. The paper with the probability inequality by Hoeffding[8] was called a “celebrated paper” by Talagrand[12] and Bentkus.[13] From this fact, we consider that the combination of these three probability inequalities is valid. In addition, we are attempting various developments including the performance improvement of the Hoeffding probability inequality.6 Influence of simulation by the difference in stochastic distributionComment (Hiroshi Tateishi)In chapter 5, a simulation result using the log-normal distribution is shown. However, the simulation results under other stochastic distributions, e.g., the beta distribution and normal distribution should be presented for persuasiveness.Answer (Yasuhiko Takemoto)For reference, in Fig. 2, we have illustrated the simulation results in the case where all stochastic distributions for e0, e1 and e2 are assumed as the normal distributions, uniform distributions and beta distributions, respectively. In these simulations, the conditions in the expectation and variance of e0, e1 and e2 are corresponding to those in Fig. 1.For the beta distribution, the authors have taken the linear conversion because the range of beta distribution is usually from 0 to 1. Considering that the beta distribution greatly changes the shape of distribution by the setting of the parameters, the authors have utilized both situations where the peak of the density is on the left side and on the right side of the center.From comparisons with the results in Fig. 1, it is confirmed that the electricity shortage outbreak probabilities in Fig. 2 are definitely less than those evaluated based on the probability inequalities in Fig. 1. The authors have added the descriptions mentioned above.7 Interpretation of the power saving rateComment (Hiroshi Tateishi)The description in chapter 6 is somewhat incomprehensible. For example, when the quantity of the electricity supply decreased 15 %, is it correct to understand that the electric power saving rate is enough at 14.66 % in order not to increase the electricity shortage outbreak probability? If it is true, I think that the authors should show more extensive calculation results.Answer (Ikuo Arizono)That is not true and is a misunderstanding. As mentioned in the revised manuscript, when the electricity supply with the conventional electric generating systems decreased 15 %, 14.55 % of the total electricity supply was lost from the viewpoint of the average. It is found that, for the purpose of ensuring the value (5.462 %) of the electricity shortage outbreak probability in a stable condition, the electric power saving rate of 14.66 % exceeding the lost total electric power rate of 14.55 % is required. In other word, it is interpreted that the electric power saving from the viewpoint of expectation is not necessarily enough. At the same time, the proposed evaluation system shows that the excessive electric power saving is not required from the comparison of 14.66 % and 14.55 %. This is the effect of having considered the information of each variance in the electricity supply and demand. Based on this effect, the proposed evaluation system for the electricity shortage outbreak probability has the appropriate security-oriented property. Since the information disclosure of each electric power company is not enough, the numerical value of the analysis result is not necessarily important. However, it is meaningful to indicate the effect by having considered the information of each variance in the electricity supply and demand. Furthermore, through the existence of the proposed evaluation system, we can demand more information disclosure from the electricity companies and government. We think that this study is also meaningful in this aspect.

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