TO DEVELOP MATHEMATICAL MODELS FOR POWER LOSSES ALONG TRANSMISSION LINES AND TO MINIMIZE THE LOSSES USING CLASSICAL OPTIMIZATION TECHNIQUES

Code No: 487641

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ABSTRACT

Availability of electric power has been the most powerful vehicle for facilitating economic, industrial and social developments of any nation. Electric power is transmitted by means of transmission lines which deliver bulk power from generating stations to load centres and consumers. For electric power to get to the final consumers in proper form and quality, losses along the lines must be reduced to the barest minimum. A lot of research has been carried out on analysis and computation of losses on transmission lines using reliability indices, but hardly any on the minimization of losses using analytical methods. In another vein, a large body of literature exists for the solution of optimal power flow problems using evolutionary methods, but none of them has employed the versatile tool of mathematical modelling.
Thus, the goal of this work is to use the classical optimization approach coupled with the mathematical modelling technique to minimize the transmission power losses. Specifically, the objectives of the study were to:
(i.) develop mathematical models for power flow and power losses along electric power transmission lines and solve the mathematical models for electric power flow along transmission lines using an analytical method; (ii.) develop empirical models of power losses as functions of distance; and (iii.) minimize the power losses using the classical optimization technique.
In the research, I employed Kirchoff â€™s circuit laws and a combination xiii of corona and ohmic losses in obtaining the mathematical models for the power flow and power losses respectively. Empirical models of the power losses were developed using regression analysis.
The findings of this study were:
(i.) the models for power flow along transmission lines evolved as homogeneous second-order partial differential equations which were solved analytically using the method of Laplace transform; (ii.) the model for power losses over the transmission lines was obtained as the sum of the ohmic and corona losses; (iii.) the empirical models developed are monotonic increasing functions of distance. Thus, establishing that power losses increases with distance; (iv.) power losses are minimized when the operating transmission voltage is equal to the critical disruptive voltage.
With the above results, a workable strategy can be formulated to reduce to the barest minimum electric power losses along transmission lines so as to ensure availability of electric power, in proper form and quality, to consumers.
Hence, this research work has addressed the problem of minimizing electric power losses during transmission.

CHAPTER 1

CHAPTER ONE
GENERAL INTRODUCTION
1.1 BACKGROUND TO THE STUDY
Energy is a basic necessity for the economic development of a nation. There are different forms of energy, but the most important form is the electrical energy, (Gupta, 2008) A modern and civilized society is so much dependent on the use of electrical energy. Activities relating to the generation, transmission and distribution of electrical energy have to be given the highest priority in the national planning process of any nation because of the importance of electrical energy to the economic and social development of the society. In fact, the greater the per capital consumption of electrical energy in a country, the higher the standard of living of its people. Therefore, the advancement of a country is measured in terms of its per capital consumption of electrical energy, (Gupta, 2008).
Power plantsâ€™ planning in a way to meet the power network load demand is one of the most important and essential issues in power systems. Since transmission lines connect generating plants and substations in power network, the analysis, computation and reduction of transmission losses in these power networks are of great concern to scientists and engineers.
A lot of research works have been carried out on the above listed aspects.(Zakariya, 2010) made a comparison between the corona power loss associated with HVDC transmission lines and the ohmic power loss. The corona power loss and ohmic power loss were measured and computed for different transmission line configurations and under fair weather and rainy conditions. It was pointed out in the work that the general trend of neglecting the corona power loss is not always valid. It was found from the comparison that, when the transmission line is moderately or lightly loaded, the percentage of corona power loss to ohmic power loss could reach up to one hundred percent especially if the transmission line is operating at a voltage well above the corona onset value. This percentage is also found to increase substantially under rainy conditions. Finally, it was also discovered that, the ratio of corona to ohmic power loss, decreases with increasing number of bundles. (Numphetch et al., 2011) worked on loss minimization using optimal power flow based on swarm intelligences.
(Thabendra et al., 2009) considered multi-objective optimization methods for power loss minimization and voltage stability while (Abdullah et al., 2010) looked at transmission loss minimization and power installation cost using evolutionary computation for improvement of voltage stability.(Bagriyanik et al., 2003) used a fuzzy multi-objective optimization and genetic algorithm-based method to find optimum power system operating conditions. In addition to active power losses, series reactive power losses of transmission system were also considered as one of the multiple objectives. (Onohaebi, 2010) considered the relationship between distance and loadings on power losses using the existing 330 KV Nigerian transmission network as a case study in his empirical modelling of power losses as a function of line loadings and lengths in the Nigeria 330 KV transmission lines while (Moghadam, 2010) developed a new method for calculating transmission power losses based on exact modelling of ohmic loss. (Ramesh et al., 2009) looked at minimization of power loss in distribution networks by using feeder restructuring, implementation of distributed generation and capacitor placement method. (Lo, 2006)considered feeder reconfiguration for losses reduction in distribution systems. Others who researched into power losses include(Rugthaicharoencheep, 2009),