This research paper focuses on the modeling and design of both conventional proportional-integral (PI) and a proposed intelligent fuzzy logic controller (FLC) applied to synchronous reference frame phase-locked loops (SRF-PLLs), commonly used as synchronization units for grid-connected inverters. Ensuring the optimal performance of this unit is crucial, especially during the injection of current into the grid. To achieve the best PLL performance, the proposed FLC-based SRF-PLL and conventional PI-based SRF-PLL were evaluated within the context of a 1-megawatt (MW) three phase grid-connected voltage source inverter (VSI) current controller predefined model. The simulation results in Matlab/Simulink revealed that the proposed FLC controller significantly improved the performance of the PLL within the system compared to the PI controller.
and [
There have been a lot of studies done in the past few the lack of essential components such as an LCL filter and
years on phase-locked loop (PLL) techniques, which play transformer in the simulation model makes the test
sysa critical role in grid-connected power converters to en- tem less practical and representative of real three-phase
able precise synchronization of the converter with the grid-connected inverter systems.
grid voltage. M. P. Thakre et al. [
0000-0002-6344-0789 (N. Mennai); 0000-0003-4073-6883 (A. Faleh) © 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
For balanced three phase grid voltages with a phase and peak value Vm shifted from one another by 120 degrees as described in Eq. (1), clark and park transformation in Eqs. (2) and (3) are used to convert the grid voltage Vabc to V
in stationary reference frame then to SRF
components Vdq [
= sin( − ⎩ = sin( + 23 )
23 ) = = − 1 2 √ 3 2 2 [︃1 is applied to Eq. (4), which leads to Eq. (5). The simplified model of the SRF-PLL becomes as seen in Fig. 3 and the closed-loop transfer function of it is in Eq. (6). ︂{ ≈ ≈ −
( − ′ )
Getting a faster response from the PI controller will lead
to instability problems. Also, PI controllers are highly
sensitive to varying parameters and sudden fluctuations,
for example, in frequency or voltage during grid faults.
Such controllers may not give the desired response. As
mentioned in [
In this section the PI controller of the dq-PLL is substituted by the Fuzzy logic controller (FLC) as shown in Fig. 4. The design of the proposed FLC must follow to the structure shown in Fig. 5. The primary steps of the FLC can be categorized into three main stages: fuzzification, inference rules, and defuzzification [9]. (5) (6) (7) (8)
The first input of this intelligent controller is the error (E(k)), representing the diference between the reference value of the quadrature component of grid voltage (Vq*) and its measured value (Vq), while the second input is the change in error (CE(k)) is the derivative of E(k), as defined by Eq. (9).
{︃() = (* − ) () = (() − (− 1))/ (9) The output of this controller is then multiplied by Ku before continuing its path in the loop to detect the phase angle.
With Tst is the sampling time and ke, kce, and ku are the scaling factors, these gains are very important in normalizing the input and output variables and for the performance and stability of the control system.
In fuzzy logic systems, fuzzyification is the
transformation of exact input values into fuzzy sets that represent
input variables as linguistic variables and membership
functions (MF) [
The Inference System is the fundamental component of FLC, since it is responsible for making decisions based on if-then fuzzy rules and fuzzy implication sub-blocks. The two most popular approaches used for this are Mamdani and Sugeno [10]. The fuzzy inference of this study is done with the Mamdani inference engine and the maxmin implication technique, where the "AND" operator is represented by the MIN operation and the "OR" operator by the MAX operation. The 25 fuzzy rules that determine the FLC’s output depending on its two inputs are indicated in Table 1. While Fig. 7 shows the control surface of the fuzzy rule base.
(a) (b) (c)
The fuzzy output result generated by the Mamdani inference engine in the form of MF is then transformed into a numerical value by employing defuzzification techniques such as the Center of Gravity (COG) and Mean of Maximum (MOM) methods [10]. In this research, COG is used during the defuzzification process. All previous design steps was implemented by Matlab fuzzy logic toolbox.
To test the designed PLLs, both of them were placed in the control block of a predefined model of a three-phase grid-connected 2-level voltage source inverter (2L-VSI) as shown in Fig. 9 in order to evaluate the performance of each in such a system. Simulation tests were conducted in the Matlab/Simulink environment during normal grid conditions to evaluate their transient and steady-state responses. All parameters used in the test system are outlined in Table 2. The model used in this simulation is shown in Fig. 8.
Inverter
LCL-Filter Transformers and transmission line
PI controller for SRF-PLL Vdc fg Vac fsw Prated Li Cf Lg
Rd step-up transformer
R’ X’
B’ step-down transformer
Kp-srfpll Ki-srfpll
(a) Phase voltage and phase angle (b) Direct voltage component (a) Phase voltage and phase angle
(b) Direct voltage component (c) Quadrature voltage component
Similarly to the previous simulation, PI based-PLL was replaced in the current controller of the 2L-VSI with the proposed FLC. The results are shown in Fig. 11.
Similar to the previous results, the FLC was able to efectively lock onto the grid phase. Notably, there is a
The plot in Fig. 10a demonstrate that the dq-PLL marked improvement in the plot of Vq and Vqref in Fig. successfully detected the grid voltage phase accurately. 11c compared to that of the PI controller. With the FLC, Furthermore, the PI controller efectively regulated the the quadrature voltage component was maintained at its quadrature component Vq to zero after a half cycle (0.01s), reference without a significant overshoot and in less than but with a noticeable overshoot as seen in Fig. 10c. On half a cycle. the other hand, as Vq is forced to zero, the direct compo- Additionally, in Fig. 11b Vd remains constant at 1 per nent of the grid voltage Vd becomes constant and close unit without any transient disturbances, indicating that to 1 per unit (pu) after a slight drop in the transient state, the FLC yields better results than the PI controller at this corresponding to the peak value of the grid voltage Vm, stage. as mentioned in Eq. (5). The frequency response for both PLLs was plotted in Fig. 12 to evaluate and compare their performance in this 4.2. Results for FLC based SRF-PLL system. Table 3. presents the performance characteristics for each PLL.
By analyzing the frequency responses and performance characteristics of both PLLs, it can be confirmed that the proposed FLC controller outperformed the conventional PI controller not only in tracking the grid voltage phase and frequency but also in terms of the PLL performance within the VSI controller. The FLC-based PLL exhibited a low overshoot of 0.3249% and a short settling time of 4.7 ms. These results suggest that the FLC-based PLL could be a promising alternative to the conventional phase-locked loop.
In this research, the modeling and design of conventional and intelligent fuzzy logic controllers for synchronous reference frame phase-locked loops are presented. These PLLs were tested inside a 1 MW grid-connected VSI current controller predefined model. The diferent simulation results during normal grid conditions showed the efectiveness of both controllers in terms of detecting phase angle of grid voltage and reference tracking, but in terms of performance, the FLC-based SRF-PLL provided a better response compared to the PI-based SRF-PLL, reaching a short settling time with very low overshoot. These ifndings suggest that the FLC-based PLL could be a potential replacement for the traditional phase-locked loop, and much future work can be considered for this purpose.
The authors received no financial support for this research. (SSD), IEEE, 2022, pp. 917–922. doi:https://doi. org/10.1109/SSD54932.2022.9955866. [9] N. Ikken, A. Bouknadel, H. El Omari, H. El Omari, Design and implementation of intelligent pifuzzy logic control for grid connected inverters, in: International Renewable and Sustainable Energy Conference (IRSEC), IEEE, 2016, pp. 1111–1117. doi:https://doi.org/10.1109/ IRSEC.2016.7984022. [10] A. Guidara, Policy decision modeling with Fuzzy Logic: Theoretical and computational aspects, volume 405, Springer Nature, 2020. doi:https://doi. org/10.1007/978-3-030-62628-0.