Digital Signal Processing Reference
In-Depth Information
Fig. 13.14 Optimization
process for the AVR assessed
with fitness function
Q according to Eq.
13.3
1300
1200
1100
1000
900
800
700
600
500
400
300
0
2
4
6
8
10
12
14
16
18
Generation No.
The quality of each individual is assessed with appropriately defined fitness
function. An optimal AVR unit should provide possibly fastest response to any
changes of generator's terminal voltage and minimal (or zero) for steady-state
regulation error. With such a specified optimization goal the fitness function may
be defined in various ways, taking into account specific parameters of the machine
output signal such as overshoot and time-to-steady-state. Here the fitness function
Q
e
was defined as
!
1
Q
¼
X
N
X
F
N
1
V
rms
ð
n
Þ
V
ref
Þ
2
ð
13
:
3
Þ
c
¼
1
n
¼
1
where F—number of considered EMTP-ATP simulation cases, N—number of
samples over which the AVR operation is assessed and n—time index (sample
number).
From the Eq.
13.3
it follows that the fitness function adopted is a digital version
of the integral of regulation error squared (ISE index), averaged for all considered
simulation cases.
The genetic optimization procedure stops when either the prescribed number of
iterations (generations) is reached or the best individual fitness value exceeds
certain threshold.
The convergence of the optimization process can be observed in Fig.
13.14
.Itis
seen that the genetic run ends up after\20 generations, when the preset fitness level
equal to 1,200 was reached. The most significant increase of the average fitness
function of the AVRs is visible within first eight generations. Further run of the
procedure does not change the optimal solution a lot, however, the population of
voltage controllers becomes slowly dominated by the final solution, i.e. the best AVR.
The quality index (fitness value) of the initial non-optimized AVR set as
mentioned above was equal Q = 203.36. The best individual AVR from the last
Search WWH ::
Custom Search