The security region of power system can be shown with greater accuracy in multi-dimensional space since the distribution of power flow is complex in interconnected power grid and the factors that could have an influence on the maximum transfer power of a cross section are various

which shows the multi-dimensional character. On this basis

a rapid algorithm to determine the cross sectional thermal security region under the condition of the security N-1 criterion in multi-dimensional space is proposed. According to the calculation of power transfer distribution factor(PTDF)that reflects the influence of generator to transmission lines

the numerical relationship between generator and cross section limit of thermal stability with single constraint is analyzed. Furthermore

a rapid comprehensive algorithm of cross section thermal security region is proposed using the advantages of peak selection strategy

which is capable of seeking all the limit states of thermal stability in all parameter space as well as obtaining the piecewise linear approximation expression for the boundary of thermal security region by combining both advantages of numerical analysis and simulation and accurately calculating the operation boundary in control parameter space. So far

the proposed method has been applied in the operation mode analysis of a power grid in southern China.