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.