Abstract: The problem of distributed power constraint of lines to maintain the global voltage security and static power-angle stability of multiple voltage level (multi-level for short) power grid is difficult to analyze and lacks sufficient theoretical basis. The analysis found that the voltage amplitude of multi-level grid has a "sawtooth distribution" characteristic, and the key to maintaining the global grid voltage safety level is to limit the voltage differential of each line. The line load security domain obtained in the previous study plays a leading role in restraining the voltage difference of lines. Further research found that the allowable pressure difference of the line, the size of load safety domain, and the maximum power angle in the domain correspond to each other and approximately proportional. Regardless of the topology, in each level of power grid, the maximum power angle of the active path depends on the allowable voltage difference; but due to the lines load security domain constraint of maintaining the allowable voltage difference, the power angle of the active power path in the multi-level grid may exceed the limit, which does not meet the necessary and sufficient condition for static power-angle stability. Therefore, the correction methods for the safety zone of the line load were proposed. For example, considering the load power factor, using series impedance or distributing the line can limit the voltage difference to reduce the safety zone. Checking calculations show that the revised line load security domain can meet the static power-angle stability requirements of multi-level power grids while constraining the safety pressure difference. This local power constraint can be widely used in global optimization control, decentralized safety control, grid and reactive power planning, etc. It has great theoretical and practical significance.