Environmental Engineering Reference
In-Depth Information
40
20
0
−20
−40
7.98
8.02
8.06
8.1
8.14
8.18
Time [s]
Figure 22.7
Input signal v when f g jumped from 40 Hz to 50 Hz
where n ( t ) is a uniform random noise with the amplitude of 2 2 V. The frequency f g =
ω g
2
π
of the signal, which varied from 40 Hz to 60 Hz periodically with the cycle of 8 s, is expressed
for the first period as
,
0
<
(0
t
2)
(2
<
t
3)
10 ( t
2)
,
(3
<
t
3
.
5)
10
,
=
+
sin ( 2
π
t )
+
(3
.
5
<
t
4)
f g ( t )
50
(22.9)
10
18 ( t
3
.
5)
,
(4
<
t
5)
1
( t
4)
,
(5
<
t
7)
5 ( t
5)
,
(7
<
t
8)
.
10
,
The signal when the frequency f g jumped from 40 Hz to 50 Hz is shown in Figure 22.7.
The SOGI-PLL shown in Figure 22.5(b) and the STA shown in Figure 22.6 were simulated
with the parameters given in Table 22.1, which were optimised to compromise the dynamic
performance and stability. The relevant signals from the simulations are shown in the left
column of Figure 22.8 for the SOGI-PLL and in the right column of Figure 22.8 for the
STA. It is worth mentioning that, although the amplitude of the fundamental component
does not change, the amplitude of
v h ( t ). However, the estimated
amplitude E should track that of the fundamental component, which is V m . Although the
phase of the reference signal was tracked well with both methods, the frequency variations
were noticeable. The result is compatible with the simulation results in (Ciobotaru et al . 2006;
Ziarani and Konrad 2004). The SOGI-PLL offered better performance than the STA in tracking
the frequency.
v
does change because of
Table 22.1 Parameters of SOGI-PLL and STA for
simulations and experiments
For the SOGI-PLL
Values
For the STA
Values
k
1
μ 1
200
K p
2 . 5
μ 2
500
K i
50
μ 3
0 . 01
 
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