This paper presents a New Total Energy Function (NTEF) based on Parallel Algorithms (PAs) and IEC 61850 for adaptive and reliable operation of smart grids. The NTEF presented in this paper is based on mathematical analysis without over/under estimation That leads to an accurate method for determining the actual Critical Clearing Time (CCT) for power system reliability and security. Then the calculated CCT for the system will be send to each associated protection relay using IEC 61850 Sample Value (SV) GOOSE messages to update the actual existing tripping delay times to guarantee that all tripping actions will be in the period of CCT. The SV GOOSE messages will be transferred specially to generator protection relays and distance protection relays and any other associated protection device. The NTEF is tested on IEEE 10-bus, 4-generating bus test system using Matlab Simulink files created by the authors to prove the validity of the NTEF for power system stability detection.