Mathematical modeling of electric power flow and the minimization of power losses on transmission lines

摘要

The importance of electric power in today's world cannot be overemphasized, for it is the key energy source for industrial, commercial and domestic activities. Its availability in the right quantity is essential to advancement of civilization. Electrical energy produced at power stations is transmitted to load centres from where it is distributed to the consumers through the use of transmission lines run from one place to another. As a result of the physical properties of the transmission medium, some of the transmitted power are lost to the surroundings. The power losses could take off a sizeable portion of the transmitted power since the transmission lines usually span a long distance, sometimes several hundred kilometers. The overall effect of power losses on the system is a reduction in the quantity of power available to the consumers. As such, adequate measures must be put in place to reduce power losses to the barest minimum. Thus, in this paper, we developed a mathematical model for determining power losses over typical transmission lines, as the resultant effect of ohmic and corona power losses, taking into cognizance the flow of current and voltage along the lines. Application of the classical optimization technique aided the formulation of an optimal strategy for minimization of power losses on transmission lines. With the aid of the new models it is possible to determine current and voltage along the transmission lines. In addition, we note that the analytical method does not involve any design or construction and so is less expensive than other models reported in the literature. Hence, the goal of this paper is to address a very well-known engineering problem - reducing the power losses on transmission lines to the barest minimum.