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Predicting the need for modeling and solutions is one of the largest difficulties in the electricity system. The static-constrained solution, which is not always powerful, is provided by the Gradient Method Power Flow (GMPF). Another benefit of using both dynamic and transient restrictions is that GMPF will increase transient stability against faults. The system is observed under contingency situations using the Dynamic Stability for Constrained Gradient Method Power Flow (DSCGMPF). The population optimization technique is the foundation of a recent algorithm called Training Learning Based Optimization (TLBO). The TLBO-based approach for obtaining DSCGMPF is implemented in this work. The total system losses and the cost of the individual generators have been optimized. Analysis of the stability limits under contingency conditions has been conducted as well. To illustrate the suggested approaches, a Standard 3 machine 5-bus system is simulated using the MATLAB 2022B platform. [ABSTRACT FROM AUTHOR]