07-12-2012, 12:35 PM
On Electrical Machines and Drives
ELECTRIC DRIVES.pdf (Size: 2.34 MB / Downloads: 294)
Three Phase Circuits and Power
Chapter Objectives
In this chapter you will learn the following:
² The concepts of power, (real reactive and apparent) and power factor
² The operation of threephase
systems and the characteristics of balanced loads in Y and in ¢
² How to solve problems for threephase
systems
THREEPHASE
BALANCED SYSTEMS
Compared to single phase systems, threephase
systems offer definite advantages: for the same power
and voltage there is less copper in the windings, and the total power absorbed remains constant rather
than oscillate around its average value.
Magnetics
INTRODUCTION
Since a good part of electromechanical energy conversion uses magnetic fields it is important early
on to learn (or review) how to solve for the magnetic field quantities in simple geometries and under
certain assumptions. One such assumption is that the frequency of all the variables is low enough
to neglect all displacement currents. Another is that the media (usually air, aluminum, copper, steel
etc.) are homogeneous and isotropic. We’ll list a few more assumptions as we move along.
where ¹0 is the permeability of free space, 4¼10¡7Tm=A, and ¹r is the relative permeability of the
material, 1 for air or vacuum, and a few hundred thousand for magnetic steel.
There is a variety of ways to solve a magnetic circuit problem. The equations given above, along
with the conditions on the boundary of our geometry define a boundary value problem. Analytical
methods are available for relatively simple geometries, and numerical methods, like Finite Elements
Analysis, for more complex geometries.
Here we’ll limit ourselves to very simple geometries. We’ll use the equations above, but we’ll add
boundary conditions and some more simplifications. These stem from the assumption of existence
of an average flux path defined within the geometry.
SATURATION AND HYSTERESIS
Although for free space a equation 2.3 is linear, in most ferrous materials this relationship is nonlinear.
Neglecting for the moment hysteresis, the relationship between H and B can be described by a curve
of the form shown in figure 2.4. From this curve, for a given value of B or H we can find the other
one and calculate the permeability ¹ = B=H.