A thermal security region（THSR）of power systems is defined in a decision making space，which is expressed by variables of active power injections and voltage magnitudes at all generator nodes，and variables of active power injections and reactive power injections at all load nodes.Fast calculation of the THSR in the decision making space is of vital importance to power system security monitoring，assessment and control.This paper further points out that practical THSR boundary can be approximately described by one or several hyperplanes in the actual interesting part for engineering practice in the decision making space.And expressions for calculating the coefficients of such hyperplanes are derived based on AC power flow equations.Test results on a practical large scale power system show that the computation speed and accuracy of the proposed approach can satisfy the demands of engineering online calculation.