**CHAPTER ONE**

**GENERAL INTRODUCTION**

The transformation of a physical system to mathematical base is very important due to analysis of the systems behaviour. In this study an electric power system is considered, and this system is characterized with first-order differantial eqautions therefore stateequations which define behaviour of the system for any instant “t” are obtained. Exact solution and simulation of various engineering problems, “especially control engineering problems, depend on convenient mathematical models for elements and subsystems of the system considered. Process of the transformation of the system’s behaviour to mathematical basis is called “mathematical modelling”

When state-equation of the physical systems are determined, the methods which are known from Circuit Analysis Theory in Electrical Engineering may be successively used. Where, in order to obtain state-equations, lineer graph theory, very important technique is used . During analysis, it is assumed that the solution of a physical system given is possible. As general definition, in a proper system, voltage and current sources may not mesh and cut, respectively. Therefore, in the system graph for a proper system, a tree that graphelements of voltage sources and current sources correspond to branch and link, respectively may be chosen [9-12]. If possible, all capacitance-type elements are put in branches of the tree and a inductance-type elements are out of the tree. This tree used for writting the equations is called “proper tree”. State variables of the system are the voltages of capacitors in the branches and the currents of inductors out of the tree.Therefore, first-order differantial equations which consists of unknown voltages and

currents are written.

**AIMS & OBJECTIVES OF THE STUDY**

The study is to establish mathematical modeling on electric circuit.