The accuracy of the proposed techniques is tested on a three-phase unbalanced IEEE 34-bus test system the results obtained applying the Monte Carlo simulation are assumed as reference. 2m+1 and 4m+1 schemes) are presented and tested. This paper applies the point estimate method to account for the uncertainties that affect the evaluation of the steady state operating condition of an unbalanced three-phase power system.Moreover, since the point estimate method requires that the input random variables are uncorrelated, a suitable adjustment to take into account the correlation is applied. It is shown that if $H_0$ and $H_1$ specify probability distributions of $X$ which are very close to each other, one may approximate $\rho$ by assuming that $X$ is normally distributed.
To obtain the above result, use is made of the fact that $P(S_n \leqq na)$ behaves roughly like $m^n$ where $m$ is the minimum value assumed by the moment generating function of $X - a$. For large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample of size $en$ with the second test. If $\rho_1$ and $\rho_2$ are the indices corresponding to two alternative tests $e = \log \rho_1/\log \rho_2$ measures the relative efficiency of these tests in the following sense. It is shown that with each test of the above form there is associated an index $\rho$. In particular the likelihood ratio test for fixed sample size can be reduced to this form. Specifically, it is desirable to compute efficiently and precisely the probability P = Pr X_j \leqq k,$ where $X_1, X_2, \cdots, X_n$ are $n$ independent observations of a chance variable $X$ whose distribution depends on the true hypothesis and where $k$ is some appropriate number. 1 General Theory In various fields of sciences and engineering, it is a frequent problem to compute distribution functions. The idea is to truncate the domain of summation or integration. In this paper, we propose a general approach for improving the efficiency of computing distribution functions.