# Vol.6 No.3 2014 8/56

Research paper : A proposal for setting electric power saving rate to avoid risk of electric power shortage occurrence (I. ARIZONO et al.)−141−Synthesiology - English edition Vol.6 No.3 (2013) the simulation results in the case that all the 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 expectations and variables of e0, e1 and e2 are corresponding to the conditions in Fig. 1.As a matter of course, the difference of the assumed distribution of each random variable brings the difference in the electricity shortage outbreak probability. However, it is confirmed that the electricity shortage outbreak probabilities estimated under the assumed distributions are certainly less than the electricity shortage outbreak probabilities evaluated by the probability inequalities from the comparison with the results of Fig. 1. Accordingly, it is understood that the evaluation system based on the probability inequalities considered in this paper promises decision-making on the safe side.In Fig. 1, remark that the relationship among the evaluation values of the electricity shortage outbreak probability are varied by the situation. From this fact, we consider that the electricity shortage outbreak probability is evaluated as the minimum value among them based on the one-sided Chebycehv, Bennett and Hoeffding probability inequalities.In addition, notice that the electricity shortage outbreak probability based on the probability inequality is considerably larger than the value by simulation. Then, since the electricity shortage outbreak probability based on the probability inequality is given as a pessimistic value, the unnecessary confusion by this value should be avoided.For reference, the electricity shortage outbreak probability by simulation in Fig. 1 is estimated as 0.0717 % , in the case where the electricity supply based on renewable energy is given as 3 % as at present. In addition, it is estimated as 2.180 % in the case where the electricity supply is 10 % in 2020. This fact means that the risk in the electricity shortage increases only by replacing the electricity supply from the conventional electric generating systems with the electricity supply based on renewable energy.6 Relation between electricity shortage outbreak possibility and electric power saving rateIn the present situation where there is no elbow room in electricity demand-supply balance and it is difficult to increase the electricity supply, the reduction in electricity consumption might be required in order to avoid an electricity shortage outbreak, and the electricity demand-supply balance should be considered. However, excessive savings of electricity consumption without argument suppresses the economic activities and may threaten the social system. In the following section, we illustrate the role of the proposed evaluation system using the probability inequality.Suppose the stable condition for (e0, e1) as (0, 1)=(97.0, 3.0), V[e0]=02=(0.01×0)2 and V[e1]=12=(0.30×1)2, where this stable condition is interpreted as the condition in which the electricity demand-supply balance is in a stable state from the viewpoint of the electricity shortage outbreak probability. Thereafter, assume that the electricity supply by the conventional electric generating systems decreases 15 %. Then, we consider the required electric power saving rate under the condition of (0, 1)=(97.0×0.85, 3.0). In this case, from Fig. 1 it is found that the electricity shortage outbreak probability based on the probability inequality is evaluated greatly on the safe side. It is not suitable to decide on the electric power saving rate by setting the value requested in the real world against the electricity shortage outbreak probability evaluated by the probability inequality.In this paper, a stable condition mentioned above is interpreted as the condition that the electricity demand-supply balance is in a stable state from the viewpoint of the electricity shortage outbreak probability. We investigate the appropriate electric power saving rate in order to guarantee that the electricity shortage outbreak probability in a situation where the electricity supply with the conventional electric generating systems decreases 15 % is equal to that of a stable condition. The electricity shortage outbreak probability in the stable condition (0, 1)=(97.0, 3.0) is evaluated as 5.462 % based on the Hoeffding probability inequality.Under the condition that the electric power saving rate is achieved as , the expectation and variance of the electricity demand e2 can be described as ((1-)2, (1-)222). Then, we can evaluate the electricity shortage outbreak probability in the situation of (0, 1)=(97.0×0.85, 3.0) as the function of the electric power saving rate by the probability inequality. This probability is described as Pr{e0+e1 ※このページを正しく表示するにはFlashPlayer10.2以上が必要です