Mathematical description of electromechanical systems operation is powerful parameter to get high performance with practical implement of the systems. This paper describes a mathematical presentation for the behavior excitation system of synchronous generator based on the optimal values of the parameters. The study of the mathematical modeling for dynamics of excitation system required the knowledge for the effect of each parameter to get the typical values provided by the manufacturer implementing. The simulation of the final model which obtained was conducted on Matlab version 2019b. The final results of simulation for the mathematical model are satisfactory, and it proves the ability of independence this model as practical implement.

<span lang="EN-US">The power flow in power system can be controlled in an effective method by using FACTS devices through transmission lines. Distributed FACTS represent a new way to overcome these drawbacks. They are cost-effective, light weighted, higher performance and minimization of environmental impact. They are placed in a distribution method and in selected lines in the network according to line flow stability indices based on load flow calculations. In this paper, distributed static series compensator (DSSC) is used in order to attain the required power flow control by modifying the line reactance. They are installed directly on the present H.V transmission lines and as a result does not require H.V insulation. The load flow analysis has been carried using mat lab and the simulation for the purpose of stability by using Power World Simulator software. The results show an enhancement in stability performances of the system over the conventional controllers. </span>

In this paper, an intelligent digital low voltage power factor optimizer has been built. This power factor optimizer operates according to the measurement the value of phase shift angle between both of current and voltage, thus the power factor has been measured. It is simply that it will improve the power factor through connecting a set of shunt capacitors in order to reach to an optimal value of the power factor (close to unity). The proposed intelligent digital power factor optimizer for low voltage is built and simulated using the software which is called electronic work bench package (EWB) Multisim. Finally, this optimizer presents a good result when applied to different loads and variable currents. This optimizer is feasible, affordable and ready to be implemented especially in countries that suffer from higher prices of electrical power.