A method is proposed for calculating and analyzing the section thermal limit under the condition of the security “N-1” criterion with the security region in multi-dimensional space taken into account. By calculating each generator’s power transfer distribution factor (PTDF) on section lines

the generators (groups) sensitive to the section thermal limit can be identified. With sensitive generators (groups) output as the axes of multi-dimensional space

the thermal limit points can be obtained under the condition of the security “N-1” criterion. Then the thermal stability security boundary can be formed when those thermal limit points are fitted in the multi-dimensional spaces. The thermal stability security boundary depicts the variation of section thermal limit with each sensitive factor output change and reflects the specific impact of sensitive factors on the section thermal limit. The further analysis shows that the thermal stability security boundary can be better fitted by one or more hyper planes

facilitating development of a fast algorithm for calculating the security region and discussing the application of security region in optimization control problems. The proposed method has been applied to the operation planning of a practical power grid in South China.