Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

Novel Affine Power Flow Method for Improving Accuracy of Interval Power Flow Data in Cyber Physical Systems of Active Distribution Networks

A large number of load power and power output of distributed generation in an active distribution network(ADN)are uncertain,which causes the classical affine power flow method to encounter problems of interval expansion and low efficiency when applied to an AND.This then leads to errors of interval power flow data sources in the cyber physical system(CPS)of an ADN.In order to improve the accuracy of interval power flow data in the CPS of an ADN,an affine power flow method of an ADN for restraining interval expansion is proposed.Aiming at the expansion of interval results caused by the approximation error of non-affine operations in an affine power flow method,the approximation method of the new noise source coefficient is improved,and it is proved that the improved method is superior to the classical method in restraining interval expansion.To overcome the decrease of computational efficiency caused by new noise sources,a novel merging method of new noise sources in an iterative process is designed.Simulation tests are conducted on an IEEE 33-bus,PG&E 69-bus and an actual 1180-bus system,which proves the validity of the proposed affine power flow method and its advantages in terms of computational efficiency and restraining interval expansion.