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Vol.6 No.3 2014

7/56
Research paper : A proposal for setting electric power saving rate to avoid risk of electric power shortage occurrence (I. ARIZONO et al.)−140−Synthesiology - English edition Vol.6 No.3 (2013) where , k and B are defined as equations (2), (3) and (5), respectively, and the value of “3” in the right hand of the equation (7) indicates the number of random variables e0, e1 and e2 in the considered system.4 Specification of range for each random variableThe expectation and variance of the random variable is commonly required in the one-sided Chebychev, Bennett and Hoeffding probability inequalities. The one-sided Chebychev probability inequality is defined only on the expectation and variance. On the other hand, the Bennett and Hoeffding probability inequalities require the range for each random variable in addition to the expectation and variance. Therefore, when we adopt the Bennett and Hoeffding probability inequalities, the range for each random variable needs to be specified.With the information about the electricity supply and demand, only the expectation and variance for each random variable is considered as mentioned above. It is thought that the lower limit and upper limit for each random variable are specified in conformity with the two-sigma or three-sigma methods. In this paper, the two-sigma method is employed for specified lower limit and upper limit for each random variable.5 Relation between electricity shortage outbreak possibility and electricity supplyIn this chapter, based on the one-sided Chebychev, Bennett and Hoeffding probability inequalities, the behavior of the upper bound of the electricity shortage outbreak probability for the changes of electricity supply is evaluated. Then, the influence on the electricity shortage outbreak probability by the ratio of the electricity supply based on renewable energy in the total electricity supply is examined.At first, the expectation of the electricity demand e2 is fixed as E[e2]=2=94.0. Furthermore, the variance of e2 is set as V[e2]=22=(0.015×2)2, because the fluctuation range of the electricity demand was illustrated as about ±3 % against the expectation of the electricity demand on the previously published website of the Kansai Electric Power Company. The total of the electricity supplies is fixed as E[e0+e1]=0+1=100. By changing 1 from 0.5 to 10, the fluctuation of the electricity shortage outbreak probability is examined. In this case, the variances for e0 and e1 are given as V[e0]=02=(0.01×0)2 and V[1]=12=(0.30×1)2.The combination of (0, 1)=(97.0, 3.0) is corresponding to the present situation where the electricity supply derived from renewable energy is approximately 3 %. On the other hand, the combination of (0, 1)=(90.0, 10.0) is corresponding to the target situation where the electricity supply derived from renewable energy will be approximately 10 % in 2020.The result based on three probability inequalities mentioned above is illustrated in Fig. 1. In Fig. 1, the electricity shortage outbreak probability evaluated by simulation is also shown. In this case, the simulation was carried out under the situation where the distributions of the electricity supplies and demand are assumed as the log-normal distributions, respectively. The iteration number was 1,000,000. From Fig. 1, it is found that the electricity shortage outbreak probability by simulation is less than the electricity shortage outbreak probabilities evaluated by the probability inequalities. This result indicates that the electricity shortage outbreak probability can be evaluated on the safe side. Similar results are also confirmed in the cases where the beta distribution, normal distribution and so on are assumed as the distributions of the random variables e0, e1 and e2. Therefore, it can be said that the electricity shortage outbreak probability evaluated in each probability inequality is evaluated on the safe side.For reference, in addition to the results in Fig. 1, Fig. 2 shows Fig. 1 Fluctuation of electricity shortage outbreak probability in the change of (0, 1)0 5 10 15 20 25 0.0 2.0 4.0 6.0 8.0 10.0 BennettChebychevHoeffdingSimulationRatio of electricity supply based on renewable energy in total electricity supply (%)Electricity shortage outbreak probability (%) 0.0 2.0 4.0 6.0 8.0 10.0 0.01.02.03.04.05.0Ratio of electricity supply based on renewable energy in total electricity supply (%)Electricity shortage outbreak probability (%)Log-normal distributionNormal distributionUniform distributionFig. 2 Results of simulation under assumed distributions

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