Sinusoid-locked Loops - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 371

harmonics and noise contained in the signal, the amplitude, frequency and phase of the fun-
damental component were tracked very well by the SLL without any problem, even when
there was a large step change in the frequency from 40 Hz to 50 Hz at t 8s.The

amplitude of the generated voltage e is very close to the reference fundamental amplitude
v m of

=

v − v h . It was insensitive to the amplitude of harmonic components and tracked v m

very well.
For the purpose of comparison, the results of the SOGI-PLL shown in Figure 22.8 are
reproduced in the right column of Figure 23.3. Although the phase of the signal was tracked
well with the SOGI-PLL, the frequency variations were larger than those obtained with the
SLL; the ripples in the voltage amplitude were much bigger than those obtained with the SLL
and the THD of the recovered voltage was much higher as well.

23.7.2 With a Noisy Distorted Square Wave
In this simulation, the noisy distorted square wave used in Section 22.7.2, as shown in Figure
22.9, was adopted to test the SLL. The results are shown in the left column of Figure 23.4.
The results of the SOGI-PLL shown in Figure 22.10 are reproduced in the right column of
Figure 23.4 for comparison. The SLL demonstrated excellent performance and is superior to
the SOGI-PLL. The SOGI-PLL caused noticeable frequency variations but the SLL estimated
the frequency very well. The SOGI-PLL was not able to track the amplitude while the SLL
detected the amplitude very well. The recovered signal e from the SLL is clean and sinusoidal
with the THD as low as 0

. 8% at the fundamental frequency of 52 . 63 Hz, but the recovered

signal from the SOGI-PLL has a significant amount of harmonics.

23.8 Experimental Results
Various experiments were carried out on the same test rig used in the experiments presented
in Chapter 22, under the same conditions. The time constant of the SLL frequency loop
was chosen as five times of the sampling frequency and, hence, the frequency was expected
to settle down in about 15 20 sampling periods, that is less than one-tenth of the grid

period. In addition to the two experiments carried out with the voltage signals adopted in
the simulations, an experiment was carried out with the input signal directly taken from the
utility grid.

∼

23.8.1 With a Voltage Taken from the Grid
The grid voltage was scaled down with a single-phase transformer and then shifted and
conditioned by op-amps to form a signal that could be read by the ADC module. The same
experiment was carried out with the SLL and the SOGI-PLL with the results shown in the left
column and the right column of Figure 23.5, respectively. The phase was tracked well by both
methods. The SLL tracked the voltage almost immediately, producing accurate frequency,
amplitude and phase. Although the grid signal was not clean, the SLL did not have any
difficulty in tracking it. Because there is no phase delay, the SLL can also be used as a
filter. The SOGI-PLL took about one cycle to produce the correct amplitude and a half cycle to