الفهرس 
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Abstract
This thesis deals with the following main item:
1). In chapter(3), a complete study is given to two. equations representing the B-H curve. These are:
a- B = s ( 1 + bH - e-cH)
b- B = a.H + cH
ــــــــــــــ
b + H
To evaluate the unknown constants of each equation,
3 points situated on the magnetization curve are chosen.
Comparison between these two equations is made and we find that the second equation has better representation of the magnetization ourve than the first equation., Also, the errors of these equations may be decreased when the points which are used in solving
the equation constants are situated in the range
including the chosen 3 points.
2) Complete study of the non-linearity associated with power transformers due to operation initially in the saturated part of its magnetic circuit and supplell1entary by load increase is given in chapter(4).
3) Study of a power transmission network with two points of non-linearities namely two power transformers and comparing its performance when the load voltage is a pure sine wave and when it bas a trapezoidal form is made in chapters (6) and (7).
4) As a result of solving this network, we introduced new definitions of efficiency such as fundamental, first, third, fifth and overall efficiency. Also, we suggested new definitions of voltage regulation such as fundamental, third and fifth harmonic voltage regulation (see chapter(7))
5) Also, as a result of solving the power transmission network with a trapezoidal voltage at its load end, we give a new method for analyzing such networks having
non-linearities.
The method introduces what are called ”Harmonic network” each of them is identical in connection with the original network but having only parameters, voltages , currents and powers contributed only by the order of the harmonic.
concerned , So, we have en nth harmonic network having all quantities (auxiliary constants , voltages, currents, power, frequency) affected only by this nth frequency.
The solution of these harmonic networks will give finally, at any point of the network, the required value concerned including all its harmonic components at this
specified point of the network,
6) As a result of introducing these harmonic networks, similar harmonic auxiliary constants are obtained for each order of the harmonic investigated. The variation or
constancy of these auxiliary constants in the different harmonic networks are investigated and discussed in chapter (6) and (7)
7) The effect of harmonics is found to increase the losses and accordingly to decrease the overall efficiency by considerable values which may reach 13.3% at high loads. Also, the voltage regulation is increased by 11% due to these harmonics at also high loads.
8) It is shown that the effect of harmonic in such power networks Car.!l10G be neglected especially when the power transformers are operated with deep saturation at higher loads.