Electromagnetic Interference from Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 546

Analysis of Signals with Electromagnetic Interference

Interference in the Ambient Signal Field

A general mathematical model has been developed of the essential mechanism by
which a wind turbine can produce electromagnetic interference [ e.g. , Senior et al. 1977].
Referring to Figure 9-1, the total electric field strength of the ambient signal, E , surrounding
a receiving point, R , can be written as

E R (P, t ) = E R , D (P, t ) + E R , S (P,

w

t , B W t ) (9-1)

where

E R = field strength at the receiver of the total signal (mV/m)

E R,D = field strength at the receiver of the direct (transmitter) signal (mV/m)

E R,S = field strength at the receiver of the scattered (wind turbine) signal (mV/m)
Õ( r ,q,f) = relative positions of the transmitter, wind turbine, and receiver (m, rad, rad)
w = frequency of the transmitted signal (rad/s)

t = time (s)

B = number of blades
W = rotor speed of the turbine (rad/s)

Field strengths will be treated as scalar quantities with assumed time dependence exp ( j w t ),
which has been omitted from Equation (9-1) for simplicity. All of the quantities in this
equation are complex. The time dependence of the scattered signal (and, hence, of the total
signal) is caused by the blade rotation. Further insight into the interference mechanisms can
be obtained by considering the general nature of the total signal given by Equation (9-1).
We can separate out the time dependence in the scattered field by writing

E R , S (P, w t , B W t ) = | E R , S (P)| f m ( t ) exp[ j d s ( t )] (9-2)

where
| E R , S (Õ)|

= maximum amplitude of the scattered field during a rotor revolution (mV/m)

f m = time-varying modulation shape function; -1 £ f m £ 1

exp[ ] = exponential of [ ]

j = square root of -1
d S = time-varying radio-frequency (RF) phase of the scattered signal (rad)

If we also express the direct field as

E R , D (P, t ) = | E R , D (P)| exp( j d D ) (9-3)

where
| E R , D (Õ)| = amplitude of the direct field at the receiver (mV/m)

d D = RF phase of the direct signal (rad)