Vol.6 No.3 2014

Research paper : A proposal for setting electric power saving rate to avoid risk of electric power shortage occurrence (I. ARIZONO et al.)−139−Synthesiology - English edition Vol.6 No.3 (2013) mentioned above, in the present situation where there is no elbow room in electricity demand-supply balance.Under the assumption mentioned above, we simply define the relationship of e0+e1e2 as the situation that the electricity supply satisfies the electricity demand. Therefore, a system for evaluating the probability Pr{e0+e1+k}, where D is the random variable following an unknown distribution with expectation and variance 2, and k is a positive number. Then, we have the following inequality according to the one-sided Chebychev probability inequality:[6].We can make the relation of e2-(e0+e1)>0 equivalent to the relation of D>+k for the purpose of evaluating Pr{e2-(e0+e1)>0} by utilizing the one-sided Chebychev probability inequality. Then, the following equations are derived: =2-(0+1), (1) 2=02+12+22, (2) , (3)where it is obvious that k>0 because it is natural that the planned generation of electricity should be larger than the assumed demand of electricity. Therefore, the upper bound of the electricity shortage outbreak probability can be evaluated by utilizing the one-sided Chebychev probability inequality as follows:. (4) 3.2 Evaluation based on the Bennett probability inequalityLet us adopt the Bennett probability inequality[7] for a similar problem. In the case of utilizing the Bennett probability inequality, the lower limits a0 and a1 for e0 and e1, and the upper limit b2 for e2 are considered in addition to the expectation and variance for each ei. It is defined as follows:. (5)Actually, the values of a0, a1 and b2 might be given as the maximum values and the minimum values based on the past results.[10] However, in the case where those results cannot be obtained as exact values, we can evaluate these values based on the three-sigma method or the two-sigma method. Under the three-sigma method, the followings are obtained: a0=0-30, 1=1-31, b2=2+32.Similarly, we have the followings under the two-sigma method: a0=0-20, a1=1-21, b2=2+22.The upper bound of the electricity shortage outbreak probability can be evaluated by utilizing the Bennett probability inequality as follows: , (6)where and k are equivalent to equations (2) and (3), respectively, and the function h(u) is defined as h(u)=(1+u)ln(1+u)-u.3.3 Evaluation based on the Hoeffding probability inequalityWe can evaluate the electricity shortage outbreak probability by utilizing the Hoeffding probability inequality.[8] The Hoeffding probability inequality gives the evaluation of the upper bound for the electricity shortage outbreak probability as follows:, (7)


page 6