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An electrical power system consists of many individual dynamic devices connected together to form a large and complex dynamic system. To analyze the behavior of such devices, its physical model needs to be transformed into mathematical model before it can be solved on a computer. In electric utility practices, the aspect of modeling and computational methods for power system dynamic devices such as generator, exciter and governor has not been given much attention by many engineers because such tasks could be solved using commercial software packages. The two most important requirements of such software packages are; i) the correct input data and assumptions; and ii) the output results that can be analyzed and understood. Hence, there was a lack of understanding of the modeling and computational methods and also the limitations of the individual dynamic devices. This paper presents the fundamental modeling and computation methods related to power system dynamics and performing the power system transient stability analysis by using Dynamic Computation for Power Systems (DCPS) software package. This C/C++ based software has been developed for research purposes and can be used to simulate load flow and transient stability analysis. The Improved Euler Method has been employed in this software to solve the mathematical model of power system dynamic devices namely synchronous generator, turbine-governor and exciter. The results showed that this software has been successfully developed to perform the transient stability analysis. The effect of varying load demand on the critical clearing time, tCCT has been tested on heavily loaded IEEE 9-bus test system when three phase fault is applied at bus 5. The simulation results showed that the critical clearing time decreases linearly with increasing load demand.