WIND ENERGY SYSTEMS - Cd3wd

Chapter 5—Electrical Network 5–4
The list in Table 5.1 illustrates one difficulty in designing a wind electric system in that
many options are available. Some components represent a very mature technology and well
defined prices. Others are still in an early stage of development with poorly defined prices. It
is conceivable that any of the eight systems could prove to be superior to the others with the
right development effort. An open mind and a willingness to examine new alternatives is an
important attribute here.
2 AC CIRCUITS
It is presumed that readers of this text have had at least one course in electrical theory,
including the topics of electrical circuits and electrical machines. Experience has shown,
however, that even students with excellent backgrounds need a review in the subject of ac
circuits. Those with a good background can read quickly through this section, while those
with a poorer background will hopefully find enough basic concepts to be able to cope with
the remaining material in this chapter and the next.
Except for dc machines, the person involved with wind electric generators will almost
always be dealing with sinusoidal voltages and currents. The frequency will usually be 60
Hz and operation will usually be in steady state rather than in a transient condition. The
analysis of electrical circuits for voltages, currents, and powers in the steady state mode is
very commonly required. In this analysis, time varying voltages and currents are typically
represented by equivalent complex numbers, called phasors, which do not vary with time.
This reduces the problem solving difficulty from that of solving differential equations to that
of solving algebraic equations. Such solutions are easier to obtain, but we need to remember
that they apply only in the steady state condition. Transients still need to be analyzed in
terms of the circuit differential equation.
A complex number z is represented in rectangular form as
z = x + jy (1)
where x is the real part of z, y is the imaginary part of z, andj = √ −1. We do not normally
give a complex number any special notation to distinguish it from a real number so the reader
will have to decide from the context which it is. The complex number can be represented by a
point on the complex plane, with x measured parallel to the real axis and y to the imaginary
axis, as shown in Fig. 1.
The complex number can also be represented in polar form as
where the magnitude of z is
z = |z|̸ θ (2)
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001