The high dimensional model representation (HDMR) has unique advantages in describing the relationship between output and multiple inputs in a certain system. And it so happened that this makes it suitable for the study of power flow state variables and multiple buses injections in the power network. Therefore

HDMR is applied to N-1 active power response steady-state security domain. The HDMR relationship between the power of the key branch and that of sources and loads is established by the typical representative samples. When there is a branch outage

to avoid large-scale rebuilding of HDMR models

the sensitivity and compensation methods are used to modify branch power flow with HDMR. Besides

as the DC power flow model has lower accuracy during the computing process in steady-state security domain

it is replaced by the HDMR model. The method proposed is capable of not only high speed analysis but also improved accuracy. In the case of known variation range of active power of part of the generators

a method is proposed for calculating the security domain of subset power variation of the buses of concern

which is helpful to monitoring if the system is still in the safe state after power variation. Numerical examples show that the HDMR model is able to successfully fit the power flow and be applied in the steady-state security domain.