Sinusoid-locked Loops - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 369

With comparison to the STA or EPLL shown in Figure 22.6, the SLL has the following
features:

1

1. The error signal v − e is passed through a low-pass filter

R , which reduces the impact Ls +

and also amplifies the difference to speed up the tracking process
because R and L are often chosen to be small.
2. The hold filter H ( s ) is applied to both channels, which removes the ripples in the signal
entering the integrators and reduces the variations in frequency

of the harmonics in v

˙

θ and amplitude E .

˙

θ

3. The frequency is forwarded into the voltage channel, which speeds up the tracking process

when the frequency changes.
4. M f i f is forwarded into the frequency channel, which speeds up the tracking process when
the voltage changes.
5. A local feedback loop consisting of D p and

K i
s

is added to the frequency loop, which is

s + D p K i s + 1 /τ fn 1

Js . Since

equivalent to cascading

J =

to τ fn τ f ,

s + D p K i + D p / s + 1 /τ fn + 1 /τ f

s + D p K i

is a lead compensator. It provides phase lead at all frequencies and

s + D p K i + D p / J

enhances the responsiveness and stability of the system.

23.7 Simulation Results
The same simulations carried out in MATLAB R

/Simulink R for the SOGI-PLL and the
STA presented in Chapter 22 were repeated to verify the SLL with the parameters given
in Table 23.1. The results of the SOGI-PLL are reproduced here for comparison.

23.7.1 With a Noisy Distorted Signal having a Variable Frequency
The distorted noisy voltage

v

used for simulations in Section 22.7.1, of which the frequency
varies in a wide range, was adopted to test the SLL. The results are shown in the left col-
umn of Figure 23.3. It is worth mentioning that, although the amplitude of the fundamental
component does not change, the amplitude of v h ( t ). As a result,

the estimated amplitude E is not a straight line. Although there was significant amount of

v does change because of

Table 23.1 Parameters of the SLL for simulations and

experiments

Parameters Values Parameters Values

f n 50 Hz J 2 . 0264 × 10 − 5

τ f 0.0005 s K 4809 . 6

τ fn 0.049 s K i 100

τ q 18.37 s L 0 . 3mH

D p 0 . 2026 R 0 . 01