12355 FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 37, No 2, June 2024, pp. 369 - 389 https://doi.org/10.2298/FUEE2402369K © 2024 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper PERFORMANCE ANALYSIS OF PLL CONTROL STRATEGIES ON GRID CONNECTED PV SYSTEM UNDER DISTURBED GRID CONDITIONS Aakriti Khanna1, Anjali Garg1, Shradha Singh Parihar2 1The NorthCap University, Gurugram, India 2Greater Noida Institute of Technology, Greater Noida, India ORCID iDs: Aakriti Khanna https://orcid.org/0000-0003-2792-3473 Anjali Garg https://orcid.org/0000-0001-8157-0379 Shradha Singh Parihar https://orcid.org/0000-0001-8809-4504 Abstract. The rising demand for renewable energy, particularly solar power, stems from its immediate availability and the imperative to curb carbon emissions associated with fossil fuel consumption. Consequently, there has been a significant surge in the installation and development of grid-connected Photovoltaic (PV) systems. However, integrating PV sources with the grid presents various challenges related to power quality. This article aims to explore how grid-connected PV systems perform when faced with different disruptions within the grid. To address this, a novel Dual Sliding Fourier Transform (DSFT) Phase-Locked Loop (PLL) control strategy has been proposed. The methodology involves modeling a typical grid-connected PV system. The proposed and conventional control strategies to regulate the grid-connected inverter have been implemented under four distinct disturbed conditions: frequency disturbance, harmonic disturbance, phase jump disturbance, and DC offset disturbance. This approach is further compared with the traditional techniques, namely Dual Second Order Generalized Integrator (DSOGI PLL) and decoupled stationary reference frame (dαβ PLL). The evaluation criterion considers the time required to track frequency changes, mitigation of harmonics, and accuracy in phase error estimation. The findings reveal that the DSFT PLL control strategy outperforms the conventional techniques across all four disturbed conditions in the context of grid-connected PV systems. Key words: Disturbed condition, Grid connected PV system, control strategies, PLL, Inverter Received November 20, 2023; revised January 09, 2024; accepted January 14, 2024 Corresponding author: Aakriti Khanna The NorthCap University, Gurugram, India E-mail: aaki.0502@gmail.com https://orcid.org/0000-0003-2792-3473 https://orcid.org/0000-0001-8157-0379 https://orcid.org/0000-0001-8809-4504 370 A. KHANNA, A. GARG, S.S. PARIHAR 1. INTRODUCTION 1.1. Motivation In recent times, fossil fuels have been the main source of power generation. Due to extreme change in the environmental conditions and the incessant demand for energy, renewable energy sources are gaining unprecedented interest. Renewable energy sources play a pivotal role in the realm of energy generation, standing prominently as a key contributor to the global energy landscape. These sources, which harness naturally replenishing elements such as sunlight, wind, water, and geothermal heat, have become increasingly integral to addressing the growing demand for sustainable and environmentally friendly energy solutions [1, 2]. Solar energy, being an inexhaustible source of energy, is a good renewable energy source. Here, the solar energy by the use of PV cells converts the solar or the PV energy into electrical energy. The connection of PV with grid represents a pivotal advancement in renewable energy integration. However, the grid integration comes with various issues posing a number of problems related to power quality, equipment disruption, complete failure of the grid connected system. Hence, it is obligatory to overcome the disturbances for the safe working of grid connected systems. 1.2. Literature Survey The organization of PV cells into modules that are interconnected into various configurations for optimizing the tracking of maximum power for the generation of electrical energy has been discussed in [3-6]. For the effective utilization of PV power, PV systems are integrated with grid. Authors in [7-11] discussed about the need of PV arrays and inverters for the grid connection. Various consequences of power electronic converters have been presented in [12]. The increased usage of nonlinear loads which include compact fluorescent lamps (CFLs), power electronics interfaced converters, etc. deteriorates the power quality and increases the harmonic distortion of the grid connected PV system [13]. The synchronous reference frame phase-locked loop (SRF PLL) [14] is a commonly employed method for achieving grid synchronization in a grid-connected voltage source inverter (VSI). Its purpose is to precisely determine the parameters of voltage, frequency, and phase angle under conditions of balanced grid voltage as demonstrated in [15]. But, unfortunately, under unbalanced conditions, the results of SRF-PLL produce errors; hence, they will not be able to accurately track the parameters thereby affecting the stability of the grid connected PV system. To overcome the drawback of conventional SRF-PLL, many researchers have examined several types of modified SRF-PLL including double decoupled SRF-PLL (DDSRF-PLL) [16], second order generalized integrator PLL (SOGI-PLL) [17], double second order generalized integrator (DSOGI-PLL) which works well for strong grids, but may harm equipment with weak grids [18], mixed second and third order generalized integrator PLL (MSTOGI-PLL) [19]. The DDSRF-PLL extracts positive and negative components from grid voltages, thereby obtaining better results of PLL by using a decoupling network. However, the control algorithm of DDSRF-PLL is complex to implement. SOGI PLL is sensitive to variations (Sensitive to DC Offset and low order harmonics), thus leading to a very poor dynamic response. The MSTOGI- PLL method presented in [19], eliminates the dc offset of input signals in the SOGI. However, it affects filtering capability, requires high bandwidth for fast response and has poor dynamic performance. Sliding mode based control for the LCL grid inverters has been analyzed in [20] Performance Analysis of PLL Control Strategies on Grid Connected PV System… 371 providing satisfactory performance but with a drawback of higher overshoots in responses. Dαβ PLL works well in the presence of unbalanced grid voltages [21]. Various asynchronous techniques are also being researched and are compared with PLL based techniques in [22]. 1.3. Paper Contributions It has been seen from the existing literature survey, that most researchers consider only PID tuning to give a trade-off condition having a single disturbance in the grid for the analysis of the control technique. In this article, four different types of disturbances are considered for the evaluation of the presented novel control strategy. The major contributions of this research paper are mentioned below: 1) A new control strategy Dual Sliding Fourier Transform (DSFT) has been developed for the first time which takes Fourier transformation into consideration playing a crucial role in frequency tracking. Here, the Fourier transform identifies the grid frequency without compromising the power system’s overall stability and reliability. 2) The proposed control strategy has been tested for four disturbances: frequency disturbance, harmonic disturbance, phase jump disturbance and DC offset disturbance. 3) Simulink model of the proposed strategy (DSFT) has been implemented and compared with traditional control techniques (DSOGI PLL and dαβ PLL) to validate the effectiveness and are found to be beneficial for grids polluted with different types of disturbances. 4) The results attained in the research paper result in high immunity of the grid connected structure and elimination of complex PID controller tuning. 1.4. Paper Organization The article is organized as follows: In Section 2, description of the grid connected PV system is presented, Section 3 comprises the control strategies, the result analysis has been done in Section 4 and Section 5 summarizes the paper along with the future scope of the proposed control technique. 2. DESCRIPTION OF PV SYSTEM The block diagram depicting grid connected Photovoltaic system is shown in Fig. 1 which comprises of PV array, DC-DC Boost converter, DC-AC converter (inverter), control strategy for the pulses of the inverter, loads and grid. Fig. 1 Block Diagram of grid connected PV system 372 A. KHANNA, A. GARG, S.S. PARIHAR PV array converts daylight (irradiance) into electricity. The PV Array, shown in Fig.1, generates 33.4 KW of maximum power having 9 parallel strings; each string has 17 modules connected in series. The number of cells per module are 60 having an open circuit voltage (Voc) of 36.6V, short circuit current (Isc) of 7.97A, maximum power point voltage (Vmpp) of 29.3V and maximum power point current (Impp) of 7.47A. DC-DC converter used is the boost converter, required to boost the PV voltage to tone with DC link voltage. DC-AC converter used in the grid connection takes the DC input and converts it into AC. It molds the current into sinusoidal waveform in a way that it can be fed into the electric utility grid. Fig. 2 presents the structure of a 3-phase inverter used in Grid connected PV system. Here, the inverter performs the function of frequency synchronization and maintenance of DC-link voltage. The topology uses six insulated gate bi-polar transistor (IGBT) switches connected in bridge configuration (these switches are considered to be ideal, i.e., balanced voltages and constant dc link voltage). Inverters also add layer for the protection of devices from power outages, over-voltage and over current. Fig. 2 Three phase grid connected inverter [23] The grid under examination in this paper is regarded as a contaminated unit that has been intentionally subjected to various disturbances. All the disturbances like frequency variation, harmonic distortion, phase jump and DC offset disturbance have been introduced to analyze their impact on the grid's performance. 3. CONTROL STRATEGIES This paper deals with different control strategies, namely: 3.1. Traditional Control Strategies: 3.1.1. DSOGI PLL 3.1.2. dαβ PLL 3.2. Proposed Dual Sliding Fourier Transform (DSFT) PLL and its implementation 3.1. Traditional Control Strategies Traditional control strategies considered in this paper are DSOGI PLL and dαβ PLL for the reason that these have been widely used in the literature by the researchers. Performance Analysis of PLL Control Strategies on Grid Connected PV System… 373 3.1.1. DSOGI PLL Dual Second Order Generalized Integrator (DSOGI-PLL) [24] control strategy translates the three-phase voltage from the abc to αβ reference frame. A positive sequence calculator is used to extract the positive sequence voltage components of αβ frame as shown in Fig. 3.These are then translated to dq reference frame. Here, SRF PLL is employed to achieve phase locking by closed-loop control of the q-axis component of voltage. However, DSOGI PLL is not suitable for weak grids, has large convergence time, has high frequency overshoot and may harm grid connected equipments. Fig. 3 Structure of DSOGI PLL 3.1.2. dαβ PLL dαβ PLL [25] refers to decoupled stationary reference frame PLL which has evolved from the combination of decoupled double synchronous reference frame PLL (DDSRF PLL) and stationary reference frame PLL (αβ PLL) strategies. dαβ PLL uses decoupling of voltage sequence from DDSRF PLL and uses αβ PLL algorithm for estimation of phase angle. The structure of dαβ PLL is shown in Fig. 4 [25]. The benefit of dαβ PLL is that it works with distortions, which is the drawback of SRF PLL. However, it suffers from high overshoot of phase angle tracking error when a fault occurs and has non immunity to DC offset and harmonics. Fig. 4 Structure of dαβ PLL [25] 374 A. KHANNA, A. GARG, S.S. PARIHAR 3.2. Proposed Dual Sliding Fourier Transform PLL and its implementation In this paper, Dual Sliding Fourier Transform (DSFT) PLL control strategy has been proposed. DSFT PLL aims to overcome the drawbacks of Sliding Fourier Transform (SFT) technique [26], [27] involving long settling time, requirement of PID tuning, elimination of harmonics, etc. Here, two stages of SFT are connected in such a way that fast and accurate estimate of frequency variation is detected. For example, if there is a sudden change in the frequency of the grid, the controller is designed in such a way that the model tracks the change within the shortest time. The estimated frequency of the first stage of DSFT PLL defines the window size for the second stage of DSFT PLL. Mathematical analysis of SFT PLL which forms the base for DSFT PLL is presented using (1) to (25). A balanced set of three phase sinusoidal voltage Vg is considered as grid voltages for the three phases with E (volts), being the peak value and fg (Hz) being the frequency. Vg is given in (1). Vga = E sin(2πfgt + θ) Vgb = E sin(2πfgt − 2π 3 + θ) (1) Vgc = E sin(2πfgt + 2π 3 + θ) where, θ represents the initial phase shift (radians) of voltage Vga, fg is assumed constant for the analysis. The three-phase voltages undergo processing through sine and cosine filters employing the principle of orthogonal signal generation as outlined in [28-30]. The filtering is done based on the assumption that the filters are made using two orthogonal sets of balanced equations, which originally have same grid phase sequence, running at nominal (pre- known) frequency fn (Hz), having unity amplitude. The first set is called as direct set or the sine set, represented by Vcx, given by sine functions as shown in (2). Vcax = sin(2πfnt) Vcbx = sin(2πfnt − 2π 3 ) (2) Vccx = sin(2πfnt + 2π 3 ) The second set is called as quadratic set or the cosine set, represented by Vcy, given by cosine functions as shown in (3). Vcay = cos(2πfnt) Vcby = cos(2πfnt − 2π 3 ) (3) Vccy = cos(2πfnt + 2π 3 ) Fourier transform is applied on the (1) - (3) using the integrations given by (4) and (5), which are the compact versions for the three phases, here, i = a,b,c (three phases) and Tn is the time period, given by Tn = 1/fn. xi = 1 Tn ∫ vcix t+Tn t vgidt (4) yi = 1 Tn ∫ vciy t+Tn t vgidt (5) Performance Analysis of PLL Control Strategies on Grid Connected PV System… 375 For fn being any positive and a non-zero value, two cases will arise while solving the integrals: Case (i): when the value of two frequencies are not equal i.e. fg ǂ fn(off-nominal frequency case) Case (ii): arises when fg = fn (nominal frequency case). Case (i): The case of ‘off-nominal frequency’ For |fg-fn|< fn, xi and yi, the active component (direct) and reactive component (quadratic) are functions of frequencies and time as follows: For Phase A: xa(t) = k1 cos[wDt + θ + ∆θ1] − k2cos[wTt + θ + ∆θ2] (6) ya(t) = k1 sin[wDt + θ + ∆θ1] + k2sin[wTt + θ + ∆θ2] (7) For Phase B: xb(t) = k1 cos[wDt + θ + ∆θ1] − k2cos[wTt + θ + ∆θ2 + 2π 3 ] (8) yb(t) = k1 sin[wDt + θ + ∆θ1] + k2sin[wTt + θ + ∆θ2 + 2π 3 ] (9) For Phase C: xc(t) = k1 cos[wDt + θ + ∆θ1] − k2cos[wTt + θ + ∆θ2 − 2π 3 ] (10) yc(t) = k1 sin[wDt + θ + ∆θ1] + k2sin[wTt + θ + ∆θ2 − 2π 3 ] (11) where, wD = 2π(fg − fn) (12) wT = 2π(fg + fn) (13) ∆θ1 = wD 2fn (14) k1 = Esin(∆θ1) 2∆θ1 (15) ∆θ2 = wT 2fn (16) k2 = Esin(∆θ2) 2∆θ2 (17) Equations (6) to (11) represent the active and reactive components for the three phases comprising of two sinusoidal terms. It is observed from these set of equations that one of the sine term has higher magnitude (k1) and lower frequency (wD), while the second sine term has lower magnitude (k2) and higher frequency (wT). From (6), (8) and (10), it is evident that these are for balanced set of three phases in cosine terms which results in zero sum. Similarly, the second terms of (7), (9) and (11) show that these are for balanced set of three phases in sine terms which results in zero sum. Hence, the sum of the two components xi and yi(active and reactive) are calculated and given by (18) and (19), respectively. xi = ∑ 3k1cos[wDt + θ + ∆θ1]c i=a (18) yi = ∑ 3k1sin[wDt + θ + ∆θ1]c i=a (19) 376 A. KHANNA, A. GARG, S.S. PARIHAR Equation (20) is obtained by dividing (19) by (18). yi xi = tan[wDt + θ + ∆θ1] (20) Substituting (12) in (20), we get (21). 2π(fg − fn)t + θ + ∆θ1 = tan−1 yt xt (21) Rearranging (21) and using (1), the phase angle for the first phase θa can be obtained and given by (22). θa = 2πfgt + θ = tan−1 yt xt + 2πfnt − ∆θ1 (22) Equation (23) can be obtained by substituting (14) and (12) in (22). θa = tan−1 yt xt + 2πfnt − π(fg−fn) fn (23) As fg is a constant value, so ∆fg ∆t = 0 where Δθ1 and θ both are constants, so, their time derivatives will be zero. Therefore, the value of fg can be calculated by taking the time derivative of (22) and is given in (24): fg = 1 2π d dt (tan−1 yt xt ) + fn (24) As fg is estimated, θ can be estimated using (22) and Δθ1 can be estimated using (14). E, the peak value of the voltage, can then be estimated with the help of (15), (18) and (19) and is given in (25): E = 2 3 ∆θ1 sin (∆θ1) √xt 2 + yt 2 (25) where, ∆θ1 sin (∆θ1) is the magnitude correction factor and 2 3 √𝑥𝑡 2 + 𝑦𝑡 2 is the uncompensated magnitude. Case (ii): The case of ‘Nominal frequency’ For fg= fn, using (23), the phase angle θa of grid voltage Vga is expressed as (26) θa = 2πfgt + θ = tan−1 yt xt + 2πfnt (26) This makes case (ii) as a special case of the off-nominal case (i). 3.2.1. Implementation of the Proposed Dual Sliding Fourier Transform PLL In DSFT PLL, the second stage Fourier transform finds its filter frequency using the grid frequency determined from the first stage. Fig. 5 presents the generation of xi and yi using (4) and (5) wherein the value gets updated with every sample of grid voltage. To update the integrals, constant width delays are considered. The formulation of active and reactive components for the three phases using SFT is shown in Fig. 6. Performance Analysis of PLL Control Strategies on Grid Connected PV System… 377 Fig. 5 Schematic representation of integrals for SFT Fig. 6 Active and reactive components of three phase voltage using SFT Grid frequency is estimated using (24) in the stage 1 i.e. using the first SFT. The schematic representation of grid frequency is depicted in Fig. 7. Fig. 7 Estimation of grid frequency using SFT 378 A. KHANNA, A. GARG, S.S. PARIHAR Fig. 8 presents the proposed system of DSFT PLL. In this, stage 1 SFT has fixed window width i.e. the delay is fixed. This provides the estimate of actual frequency (fgi in Fig. 8) of grid voltage. This estimated frequency is then filtered using Filter 1 in order to attenuate the ripples of high frequency. The output of this filter (fgif in Fig. 8) is then passed to the stage 2 SFT where the size of the window is variable. The filter output of Filter 1 controls the duration of the delay needed. The filtered frequency is integrated in order to find the filter phase angle. This drives the sine/cosine filters of second stage SFT. The output frequency, fgii from stage 2 is also filtered using Filter 2 to get a smooth estimate of grid frequency. The output phase angle from second stage is added to the filter phase angle in order to estimate the required grid positive sequence phase angle. Fig. 8 Structure of proposed DSFT PLL 4. RESULTS The proposed control strategy has been simulated for grid connected PV system and is compared with dαβ PLL and DSOGI PLL in MATLAB Simulink. The simulink model of the proposed strategy implemented in MATLAB/Simulink is presented in Fig. 9. Fig. 9(a) shows the overall structure of proposed control strategy, whereas, Fig. 9 (b) depicts the detailed internal structure of DSFT block where the two stages of SFT and two filters have been used for the estimation of phase and frequency. The simulation parameters for the proposed strategy are tabulated in Table 1. Here, the simulations are carried out for four disturbed conditions: frequency disturbance, harmonic disturbance, phase jump disturbance and DC offset disturbance. Fig. 9(a) Simulink model of proposed control strategy Performance Analysis of PLL Control Strategies on Grid Connected PV System… 379 Fig. 9(b) Internal Structure of DSFT block Fig. 9 Implementation of proposed control strategy 380 A. KHANNA, A. GARG, S.S. PARIHAR Table 1 Simulation parameters for proposed strategy Parameter Value Frequency, fnom (Hz) 50 Sample time, Ts (sec) 0.00015625 pi 3.14 Step time (s) 2/fnom Gain, K 0.7071 where fnom is the nominal frequency (the frequency on which the control strategy has been built), Ts is the sample time of the control strategy, step time is the time given to the step generator for enabling the input and K is the gain involved in the estimation of theta. 4.1. Frequency Disturbance Frequency disturbance deals with shift in grid frequency from 50 Hz to a different value. Here, the frequency is disturbed for two conditions (a) long duration frequency distortion with a shift in frequency from 50 Hz to 50.34 Hz and (b) short duration frequency distortion with a shift in grid frequency from 50 Hz to 52 Hz. Fig. 10 and Fig. 11 shows the frequency comparison and phase error comparison respectively with frequency distortion as a grid disturbance. 4.1.1. Long duration frequency disturbance from 0.2 sec to 1.0 sec Here, frequency disturbance is given for a long duration of 0.8 seconds and has been analyzed for three different control strategies (proposed DUAL SFT (DSFT) PLL, DSOGI PLL and dαβ PLL). Fig. 10 and Fig. 11 illustrate the comparison of PLL techniques considering frequency disturbance in terms of frequency and phase error respectively. Fig. 10 infers that DSFT PLL control strategy took 0.02 seconds to track the frequency change; DSOGI PLL strategy took 0.1 seconds to track whereas dαβ PLL strategy took around 0.3 seconds to track the frequency change. From Fig.11, we see that DSFT PLL settles the phase error in 0.02 seconds; DSOGI PLL settles the phase error in 0.15 seconds while dαβ PLL is unable to settle the phase error. Fig. 10 Frequency comparison of PLL techniques with frequency disturbance Performance Analysis of PLL Control Strategies on Grid Connected PV System… 381 Fig. 11 Phase error comparison of PLL techniques with frequency disturbance 4.1.2. Short duration frequency disturbance from 1.4 sec to 1.6 sec Here, the frequency disturbance prevails for a short duration of 0.2 seconds. Fig. 10 and Fig. 11 demonstrate the frequency and phase error comparison respectively for the three control strategies (proposed DSFT PLL, DSOGI PLL and dαβ PLL). It has been observed that DSFT PLL took the least time to track the change in frequency which is around 0.02 seconds, DSOGI PLL tracks the frequency change in around 0.1 seconds while dαβ PLL was unable to track from Fig. 10. In terms of the phase error comparison, Fig. 11 shows that DSFT PLL settles to zero in 0.02 seconds while DSOGI PLL took 0.15 seconds to settle and dαβ PLL was unable to settle. Comparative results obtained for the frequency disturbance in terms of frequency tracking time and phase error settling time are tabulated in Table 2. Table 2 Comparison of control strategies for frequency disturbance 4.2. Harmonic Disturbance Harmonic disturbance, here, refers to the harmonic injections in the grid voltage [31- 33]. The disturbance is analyzed in two categories (a) Injection of 3rd and 5th harmonic component with fundamental component and (b) Injection of 3rd, 5th, 7th and 9th harmonic component with fundamental component. Fig. 12 (a) shows the grid voltage of phase A when 3rd and 5th harmonic component gets injected and Fig. 12 (b) shows the grid voltage of phase A when 3rd, 5th, 7th and 9th harmonic component gets injected as disturbance from 0.5 sec to 0.85 sec. Type of Disturbance Control Strategy Frequency tracking time (sec) Phase Error Settling time (Sec) Long duration frequency disturbance (0.8 seconds) Proposed DSFT PLL 0.02 0.02 DSOGI PLL 0.1 0.15 dαβ PLL 0.3 Unable to settle Short duration frequency disturbance (0.2 seconds) Proposed DSFT PLL 0.02 0.02 DSOGI PLL 0.1 0.15 dαβ PLL Unable to track Unable to track 382 A. KHANNA, A. GARG, S.S. PARIHAR Fig. 12(a) Grid voltage with 3rd and 5th harmonic component injection in phase A Fig. 12(b) Grid voltage with 3rd, 5th, 7th and 9th harmonic component injection in phase A Fig. 12 Grid Voltage with harmonic components The frequency comparison of the proposed DSFT PLL technique with the DSOGI PLL and dαβ PLL techniques for the disturbance period between 0.5 to 0.85 seconds is illustrated in Fig. 13. It clearly shows that for DSFT PLL, the frequency remains 50 Hz throughout the disturbance period while for the DSOGI PLL frequency varies in range of 49Hz-51Hz and for dαβ PLL, the range of variation of frequency is 44Hz-56Hz during the disturbance period. The effect of PLL control techniques on the grid voltage during harmonic disturbance period is depicted in Fig. 14. Fig. 14(a), Fig. 14(b) and Fig. 14(c) display the grid voltage of the proposed control strategy DSFT PLL, DSOGI PLL strategy and dαβ PLL strategy respectively. It shows that DSFT PLL reconstructs the voltage, which was harmed during the injection of harmonics, DSOGI PLL reduces the amplitude of the grid voltage and dαβ is inefficient in removing the harmonics from the system. The output of dαβ PLL is non- sinusoidal in nature. Performance Analysis of PLL Control Strategies on Grid Connected PV System… 383 Fig. 13 Frequency comparison of PLL techniques with harmonic disturbance Fig. 14(a) Grid voltage with harmonic disturbance using proposed DSFT PLL control technique Fig. 14(b) Grid voltage with harmonic disturbance using DSOGI PLL control technique 384 A. KHANNA, A. GARG, S.S. PARIHAR Fig. 14(c) Grid voltage with harmonic disturbance using dαβ PLL control technique Fig. 14 Effect of PLL control techniques on the grid voltage with harmonic disturbance The comparison results attained for the three control techniques i.e. DSFT PLL, DSOGI PLL and dαβ PLL on grid voltage with harmonic distortion has been tabulated in Table 3. It infers that the proposed DSFT strategy works better than DSOGI PLL and dαβ PLL techniques for the harmonic disturbance. Table 3 Comparison of grid voltage for different control strategies in the presence of harmonic disturbance Type of Disturbance Control Strategy Grid voltage during harmonic disturbance Harmonic component injection Proposed DSFT PLL 220 V DSOGI PLL 200 V dαβ PLL 250 V 4.3. Phase Jump Disturbance In this paper, a shift of +90 degrees at 1.1 seconds and -90 degrees at 1.5 seconds has been considered. During this disturbance, the grid voltage undergoes a phase shift. The grid voltage for phase A during the phase jump disturbance period is shown in Fig. 15. Fig. 15 Injection of Phase jump disturbance in grid voltage Performance Analysis of PLL Control Strategies on Grid Connected PV System… 385 Fig. 16 and Fig. 17 present the comparison of frequency and phase error for different PLL strategies considering phase jump disturbance, respectively. In Fig. 16, the DSFT PLL settles to 50 Hz frequency in 0.02 seconds, DSOGI PLL shows damped oscillations and, it hardly settles to the 50 Hz frequency, while dαβ PLL settles in 0.1 seconds to 50 Hz. Fig. 16 Frequency comparison of PLL techniques with phase jump disturbance Fig. 17 Phase error comparison of PLL techniques with phase jump disturbance The results obtained for proposed DSFT PLL, DSOGI PLL and dαβ PLL in terms of frequency tracking time and phase error settling time with phase jump disturbance is tabulated in Table 4. Table 4 Comparison table for phase jump disturbance for frequency tracking and phase error settling time Control Strategy Frequency tracking time (Sec) Phase Error Settling time (Sec) Proposed DSFT PLL 0.02 0.02 DSOGI PLL Damped oscillations Damped oscillations dαβ PLL 0.1 0.1 Table 4 clearly demonstrates that DSOGI PLL has damped oscillations, dαβ settles to zero error in 0.1 seconds while the proposed control technique DSFT PLL settles to zero phase error in only 0.02 seconds. 386 A. KHANNA, A. GARG, S.S. PARIHAR 4.4. DC Offset Disturbance In this type of disturbance, the DC offset value as presented in Fig. 18 gets added to the grid voltage. Here, the disturbance period ranges from 1.4 seconds to 1.65 seconds, during which 0.1*E (E is the peak of grid voltage) is added to phase A of grid voltage. Fig. 18 Injection of DC offset disturbance in phase A of grid voltage Fig. 19 illustrates the variation of frequencies in comparison with the original frequency kept at 50 Hz depicting that DSOGI PLL and dαβ PLL both results in oscillations. The oscillations of DSOGI PLL are much higher than dαβ PLL, whereas proposed DSFT PLL tracks 50 Hz frequency in 0.04 seconds. Fig. 19 Frequency comparison of PLL techniques with DC offset disturbance The comparison of PLL techniques in terms of phase error settling time for DC offset disturbance is given in Fig. 20. Fig. 20 Phase Error comparison of PLL techniques with DC offset disturbance Performance Analysis of PLL Control Strategies on Grid Connected PV System… 387 Table 5 presents the frequency tracking time and the phase error settling time of all the considered PLL techniques under the DC offset disturbance condition. It infers that DSOGI PLL and dαβ PLL both have oscillations. It also presents that DSFT PLL settles to zero phase error in 0.03 seconds and tracks 50Hz frequency in 0.04 seconds. Table 5 Comparison of control strategies on frequency tracking time and phase error settling time with DC offset disturbance 5. CONCLUSION This paper meticulously examines the performance of a grid-connected PV system in the presence of a disturbed grid connection, specifically addressing four types of disturbances: frequency disturbance, harmonic disturbance, phase jump disturbance, and DC offset disturbance. The evaluation is based on key performance parameters, namely frequency tracking time and phase error settling time. A novel proposed control strategy, Dual Sliding Fourier Transform (DSFT) Phase- Locked Loop (PLL), has been scrutinized under the influence of these disturbances and further compared against the conventional control strategies facing major drawbacks of large settling time, requirement of PID tuning, ineffectiveness in eliminating distortions, high frequency overshoots, namely, DSOGI PLL and dαβ PLL. The uniqueness of the proposed system is underscored by its superior performance, demonstrating that the DSFT PLL control strategy surpasses the efficacy of the other control strategies. The proposed DSFT PLL avoids sustained oscillations and has shorter settling time over DSOGI PLL and dαβ PLL. The DSFT PLL effectively mitigates harmonics induced by grid disturbances, contributing to a cleaner signal and provides high immunity of the grid connected structure. Also, the strategy eliminates the necessity of PID controllers involving complex computations for tuning purposes. These findings underscore the considerable potential of the proposed control strategy for enhancing the performance of grid-connected PV systems with grid disturbances implying a more reliable and resilient operation of solar power systems. The proposed strategy is versatile and can be extended to address multiple disturbances for real time applications such as faulty oscillations, low voltage ride-through and load fluctuations. This implies a broad applicability of the strategy. The economic feasibility of the proposed strategy can also be worked upon in future. The demonstrated novelty of the technique positions it as a valuable contribution to the field of grid-connected PV systems. DECLARATIONS On behalf of all authors, the corresponding author states that there is no conflict of interest. No funds, grants, or other support was received. 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