https://orcid.org/0000-0002-2478-7704
Figures
Abstract
The sustainable growth of renewable energy sources, especially photovoltaic (PV) driven electricity generation, is expected to grow exponentially over the next few years. The extraction of grid parameters such as the line voltage’s magnitude, phase angle, and phase sequence, are crucial for the effective control of PV-grid synchronization. The existing grid synchronization technique such as a conventional phase-locked loop (PLL) is unable to provide an accurate fundamental frequency positive sequence under various types of grid fault conditions. Therefore, the main purpose of this article is to model and analyze the introduction of cascaded delay signal cancelation (CDSC) for a 100 kW two-stage three-phase grid-connected PV generation system under absurd atmospheric and various grid disturbances. The performance of the CDSC is benchmarked with a conventional structure of PLL as well as a double second-order generalized integrator (DSOGI). The modeling and analyses of these selected grid synchronizers were performed in a Matlab-Simulink (R2020b) environment.
Citation: Mohamed Hariri MH, Salem M, Mohd Jamil MK, Abdullah MN, Mat Desa MK (2025) Modeling and analysis of 100 kW two-stage three-phase grid-connected PV generation system under absurd atmospheric and grid disturbances. PLoS One 20(6): e0323269. https://doi.org/10.1371/journal.pone.0323269
Editor: Shady H.E. Abdel Aleem, Institute of Aviation Engineering and Technology, EGYPT
Received: March 19, 2024; Accepted: April 5, 2025; Published: June 20, 2025
Copyright: © 2025 Hariri et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All data are in the manuscript.
Funding: This research work was supported by a Universiti Sains Malaysia, Short-Term Grant with Project No: 304/PELECT/6315776. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
1. Introduction
Renewable energy (RE) is defined as clean energy that comes from natural renewable resources, such as wind, hydro, biomass, geothermal, tidal, and solar (photovoltaic). The future energy pathways based on existing analysis show that better access to energy, clean air, and preserved energy security can be simultaneously achieved while mitigating harmful climate changes [1]. Amongst the mentioned RE, hydro and photovoltaic (PV) are among the most prominent ones due to the huge potential they offer [2,3]. The sustainable future of PV is elaborated in detail in [4,5]. Stand-alone and grid-connected PV (GPV) generation systems are the two primary categories of solar energy systems. Both systems’ implementations and objectives share a number of similarities and distinctions. A GPV system is a separate, decentralized power system that is linked to a transmission and distribution network for electricity. The integration of GPV systems to the utility grid keeps growing over the years. It requires a proper grid synchronization mechanism with a fast transient response and poses a high resilience against various grid disturbances to further improve the reliability and the quality of power transfer from the PV system to the utility grid [6,7].
There are two main circuit configurations of GPV systems, namely single-stage and two-stage systems. Both systems share similarities in their purposes and implementations but differ significantly. Based on the literature, single-stage three-phase GPV generation systems suffer from several drawbacks such as excessive installation costs, high complexity, and a greater input current stress on the series inductors [8]. In addition, the performance of the MPPT of the GPV system particularly on the tracking efficiency under various weather conditions is still being debated. For instance, the operating point of PV using the famous P&O techniques creates oscillations in the region of the maximum power point (MPP), giving rise to the waste of energy [9,10]. Furthermore, several technical problems regarding stability, safety, and power quality issues such as harmonics, frequency fluctuations, and others have cropped up owing to the increased penetration of GPV systems [11,12]. Several problems have arisen with regard to this issue due to the integration of large amounts of GPV systems at different locations (randomly installed) and possessing different voltage profiles which leads to voltage imbalance along the feeders [13–15]. At the moment, the voltage rise should not exceed the 2% limit as stated by the grid code standards [16,17]. In some cases, there are faulty conditions on the transmission line that cause the grid variables (voltage amplitude, phase angle, and frequency) to reach and exceed threshold limits, consequently causing the controllers to malfunction [18–20]. Moreover, the GPV systems which comprise a portion of power electronics devices could transfer the generated PV power without proper guidelines, causing a huge influx of total harmonic distortion (THD) at the point of common coupling (PCC) [21]. The effect of harmonic content on transmission lines is enormous as discussed in [22]. In a GPV system, the synchronization process should be fast, effective, and robust even with the presence of miscellaneous types of sources and load profiles along the feeder. Up-to-date, there are numerous synchronization methods proposed in the literature to synthesize grid information. Among these, the zero-crossing strategy (ZC) remains the simplest strategy even though it is not the most accurate strategy under non-ideal conditions [23]. During voltage variation or the presence of harmonics, the ZC point is detectable only every half period of the grid voltage or frequency. Consequently, due to insufficient detections, the dynamic performance of the controller will degrade [24]. Moreover, the existing PLL synchronization mechanisms of the GPV system face difficulties in providing the accurate value of grid information during fault conditions [25]. A combination of suitable and latest controllers combined with a two-stage three-phase inverter structure configuration could improve the efficiency and the reliability of the proposed system in the event of absurd atmospheric and various grid fault conditions. A comprehensive comparative analysis that highlights how this proposed research work differs from prior studies is summarized in Table 1.
Hence, a proposed 100 kW two-stage three-phase GPV generation system is presented in this article. The overall system response towards the transient conditions due to the presence of absurd atmospheric profiles and different types of faults such as voltage unbalance, voltage dip, total harmonic distortions, and line faults in grid power line becomes the main concern in this research in assessing the ability of the proposed system, as well as the overall performance of the designated local controllers to compensate the changes. The overall results show that the proposed two-stage three-phase GPV generation system comprises controllers of the Cuckoo Search (CS) MPPT technique; the SVPWM switching topology in combination with the CDSC synchronization mechanism is the most effective PV-grid system configuration as it proved to have better MPPT tracking efficiency of
and requires only
to reach steady-state in the course of transient,
level of
, and the most important is the proposed system works efficiently even in the case of grid fault conditions.
This article is structured as follows: Section 2 reveals the mathematical modeling of PV; Section 3 presents the MPPT; Section 4 describes the technical specifications of DC-DC boost converter; Section 5 covers three-phase VSI; Section 6 outlines the details of SVPWM; Section 7 presents the design parameters of interfacing line filters; Section 8 overviews grid synchronization mechanisms; Section 9 explains the CDSC technique; Section 10 summaries the system’s specifications; Section 11 covers results; Section 12 concludes the overall system performances.
2. Mathematical modeling of photovoltaic
The PV cell circuit is generally depicted as a single-diode model that is made up of four major components – a photocurrent source , a series resistor,
a diode that is parallel to the sources, and a shunt resistor,
(see Fig 1).
The current flow through a diode is defined as ,
is shunt current, the series resistance,
is the internal resistance of the PV cell. Leakages at the junction lead to shunt resistance,
and
is the cell voltage of the PV. The
features of a PV cell are determined as follows:
Here, stands for photo-current,
is the solar irradiation in
,
stands for the operating temperature of the PV cell,
is short-circuit current of cells at
and
.
Here, is the diode saturation current,
is electron charge with the value of
, and
is Boltzmann constant
Here, stands for reserve saturation current,
is the nominal temperature of
is the bandgap energy of a semiconductor
,
and
constants are ideality factors of the diode that vary between
and
,
is an open-circuit voltage of the PV cell.
The operating voltage of PV cells can be improved by connecting them in series while the current capacity can be enhanced by connecting them in parallel. Hence, the calculation of the total current in the PV module is done as follows:
where represent the number of serially connected PV cells and
are the number of PV cells connected in parallel. The simulation process in this work is done using the BP275F solar module as the reference PV model.
3. Maximum power point tracking
Two categories of MPPT techniques are implemented in this research work. A conventional approach is represented by perturbation and observation (P&O) and incremental conductance (INC) whereas the advanced computing methodology is represented by Cuckoo Search (CS). The P&O algorithm flowchart is illustrated in Fig 2(a). Meanwhile, the INC MPPT technique is founded on the notion that, at the MPP, the PV module power-voltage curve has a slope value of zero, a negative slope on the right of the MPP, and a positive slope value on the left of the MPP. The INC method is depicted in the flowchart diagram in Fig 2(b).
On the other hand, CS algorithm as illustrated in Fig 3 can be classified as one of the metaheuristic algorithms in which its working principle is based on the nature-inspired brood parasitism of some cuckoo bird species along with Levy flights random walks [29].
4. Technical specification of DC-DC boost converter
The DC-DC boost converter is a preferable DC-DC converter topology as it provides a higher voltage level on the output side which is later been projected as a DC input to the three-phase VSI inverter. The typical circuit diagram of the DC-DC boost converter is illustrated in Fig 4.
The mathematical expression of output voltage, in terms of input voltage,
is as follows:
The notation represents the duty cycle. For the inductor current,
and capacitor voltage,
to work in CCM, several conditions must be fulfilled. The design of the DC-DC boost converter’s specifications starts with the selection of the inductor capacity
as given by Eq. (9).
The mathematical expression of the inductor ripple current is given as follows:
Meanwhile, the minimum value of the output capacitor is expressed as follows:
The notation of ,
,
and
stands for DC-DC Boost converter’s frequency switching, maximum output current, output voltage ripple, and the amount of allowable output capacitor equivalent series resistance, respectively.
5. Three-phase voltage source inverter
The conversion of an input DC voltage from a DC-DC boost converter into a symmetrical 3-phase sinusoidal AC waveform of the expected operating line frequency and voltage magnitude was achieved in this study using the 3-phase voltage source inverter (VSI) shown in Fig 5.
Two types of conduction modes can be applied to the three-phase VSI switches, these are the and
conduction. The preferred method in this work is the
conduction mode because of its better switch utilization. For the three-phase VSI, the RMS line voltage
that corresponds to the DC-DC boost converter’s input DC voltage,
is given by Eq. (13) [31].
where the modulation index is given as . The expression of the instantaneous line-to-line voltage
in a Fourier series is given as:
where the phase angle is given as in radian while
represent the number of harmonics. Meanwhile, both
and
can be found in Eq. (14) by phase shifting
by 120o and 240o, respectively. Therefore,
Furthermore, the instantaneous phase voltages for a -connected load are given in Fourier series expressions as follows;
Meanwhile, Eq. is the formula for both either voltage or current total harmonic distortion (THD) and is expressed as follows;
where is the RMS value of the harmonic component of
of the quantity
(voltage or current). On the other hand, the efficiency,
of the system can be calculated by using the following equation,
As mentioned previously, since the three-phase VSI is selected as the main inverter topology in this research, the most commonly coupled switching control technique is pulse-width modulation (PWM).
6. Space-vector pulse-width modulation
In SVPWM, three-phase quantities are represented as vectors in two-dimensional
reference frame as seen in Fig 6(a) and 6(b), respectively [32,33].
Adjacent vectors are used to calculate the reference voltage vector, as seen in Fig 6(b). The calculation of the stationary
reference frame is done using Eq. (22) [34].
The value of is used to determine the magnitude of the reference voltage vector
as given in Eq. (23).
Eq. (24) is used to calculate the angle between these two adjacent vectors.
The required switching period at sector 1 is expressed thus:
Hence, the switching time of SVPWM at any sector can be estimated using Eqs. (26)–(28).
7. Interfacing line filters parameters design
In the GPV generation system, the presence of power electronic components such as power Mosfet or IGBT which are modulated by the high-frequency PWM. These high-frequency PWM modulations resulted in a high-rate change of voltage and current over time. The voltage and current generated from the inverter especially consist of high harmonic order and if it flows into the power grid, will create harmonic pollution. For this reason, line filters need to be installed. According to various research works as discussed in [35–37], among several passive filter configurations, LCL filters have the best high-frequency attenuation characteristics as compared to L and LC filters. Therefore, the LCL filter configuration is applied to the proposed two-stage three-phase GPV generation system. The design of three-phase LCL power filters begin with the mathematical derivation to obtain the transfer function of filters. The three-phase LCL filter configuration is re-drawn in -domain circuitry as illustrated in Fig 7.
Here, denoted as the inverter voltage,
represents inductor value on the inverter side,
represents the inductor value on the grid side,
is the total capacitance, and
is symbolized as the grid voltage. By applying Kirchhoff’s current law at point
, the mathematical expression is given as follows:
The voltage expression at junction in terms of grid current,
is given by the following equation;
Solving both Eqs. (29) and (30) simultaneously will result in the arrangement of the transfer functions equation as follows:
Lets,
and
Again, solving Eq. (31) until Eq. (33) respectively brings out the new mathematical expression as shown in Eq. (34).
The mathematical expression of the resonant frequency is given as follows:
The selection of the switching frequency, is based on several factors, such as component constraints, size, cost of the components, and thermal considerations [38]. The switching frequency for the three-phase VSI was selected as
. As a rule of thumb, the resonant frequency,
is defined as follows:
Therefore,
Based on the IEEE grid code standards which state that the total reactive power, should be less than
of the system’s rated power,
, therefore:
The designing of the LCL filter is continued by determining the value of line filter inductance, . Referring to Eq. (34) and given that the notation
,
By mathematical definition, and by taking the magnitude, Eq. (38) becomes:
Rearranging Eq. (39) gives the magnitude of inductance, as follows:
By considering all the requirements set by the established grid code standards in the whole calculation design for line LCL passive filters, therefore, the single conductor value, is fixed at
and the value for single capacitance,
is set at
. These values will be used for the interfacing passive power filters in this research work.
8. Grid synchronization
Two control loops—an exterior voltage control loop and an internal current control loop—are used in the design of the three-phase GPV generation system’s control mechanism. The regulation of the injected current from the inverter to the grid is performed by the current control loop; this loop also keeps the injected current in phase with the grid voltage to ensure the achievement of the unity power factor. The voltage control loop is used to regulate the output power from PV modules to the grid; it also balances the power flow. A crucial part of grid synchronization is the phase-locked loop (PLL) control mechanism, which is used in the synchronous reference frame (SRF). The main advantages of SRF are that the fundamental components of three-phase waveform signals are converted into DC signals
, consequently reducing the computational difficulty. The phase angle,
and rotation frequency,
are the two critical pieces of information extracted from the grid voltages by using the SRF-PLL method. This three-phase
natural frame is converted into three constant DC components by using a
transformation which is also known as synchronous reference frame or SRF in short form. The three DC components in the SRF plane are denoted as direct
, quadrature
and zero
, respectively. The relationship between these two frames in terms of voltages and currents is given by the following expression:
The matrix is sometimes called Park Transformation. The active,
and reactive powers,
injected by the three-phase VSI inverter can be calculated in
frame by using the following expression:
In SRF, by using a PLL technique, the grid frequency is locked in such a way that the quadrature component, is set to zero, i.e.,
. Therefore, the real and reactive power expressions can be simplified to:
From the above expression, since is kept constant, the real power,
injection into the grid can be accomplished by regulating the value of DC-Link voltage through the control of direct axis current
. On the other hand, the reactive power,
depends on the value of
. Based on the principle of power balance between input and output power, the voltage dynamics of DC-Link capacitor is given by:
The reference direct axis current is extracted from the error difference between
and
using a proportional-integral (PI) controller Integrating Eq. (48) with respect to time gives the new mathematical expression depicted as:
where is designated as. The voltage expressions in
can be translated as follows;
where ,
,
and
are grid voltage and grid current’s DC components, respectively;
,
,
and
are the inverter output waveforms’ DC components for achieving unity power factor; it is required that the
-axis quadrature current component is equal to zero consequently the reference command reactive current
is set to zero
[39].
9. Cascaded delay signal cancellation
The introduction of cascaded delay signal cancellation or CDSC is based on the statement that the PLL is unable to perform accurately during the conditions where the line grid voltage is highly distorted [40]. The CDSC operator in reference frame introduces the time delay expression into the SRF-PLL configurations’ control loop. The PLL dynamic performance is adversely affected by the introduction of this in-loop delay. Therefore, the stability of SRF-PLL is ensured by relocating the equivalent of CDSC operators into
reference frames using these equations [41];
where and
are the fundamental angular frequency and the harmonic order respectively;
is the positive sequence component of the harmonic frequency that the CDSC operator needs to extract; ‘
‘
represent positive and negative sequence signals respectively, and
. The equations are then translated into the block diagram configuration as shown in Fig 8.
10. Specifications of the proposed three-phase GPV generation system
As mentioned earlier, the key objective of the research work is to design and model a two-stage three-phase GPV generation system that can deliver the real power of from the PV system to the utility grid under various atmospherics and grid fault conditions. The overall block diagram of the proposed GPV generation system is illustrated in Fig 9.
The generated output voltage and injected current waveforms from the PV system need to comply with the grid code standards and regulations. The list of design parameters for the proposed two-stage three-phase GPV generation system was tabulated in Table 2.
11. Results and discussion
The PV module from 1Soltech (1STH-215-P) is selected as the reference PV model in this research. Based on the datasheet, the voltage value at the maximum power point of a 1Soltech (1STH-215-P) PV module, is
. Meanwhile, the PV module current at the maximum power point,
is rated at
. Therefore, the maximum power rating,
for this single PV module is
In this research, the surface temperature,
is set at a constant value of
since it does not have much effect on the generation of PV current, and its analyses are not covered in this research work. The designated PV modules are poised to generate
of real power,
. Therefore, it requires PV modules to be connected in 47 parallel strings and 10 pieces of PV modules in series connections to form PV arrays. The PV arrays are tested at three different levels of irradiation,
which are fixed at 1000
, 600
and 200
respectively. Fig 10 shows the relationship between
and
characteristics of PV arrays according to the selected value of irradiation level.
The overall system performance during abrupt atmospheric changes is presented in Fig 11. The most upper waveform in red color indicates the irradiation value and its corresponding output PV power generated. The next row (green color) indicates the motion from the duty cycle, response due to the changes in input parameters produced by the maximum power point tracking technique (MPPT) algorithm. The following rows indicate the equivalent voltage and the injected current waveforms of the proposed GPV system. The subsequent row displays the phase R voltage and the component of the injected current waveform is in-phase even though in case of irradiation changing. The last row presents the value of the power factor,
The
is kept constant at a value of
except during irradiation drops occurred at
until
as it is unable to provide good
reading due to the very low generation and distorted current waveform.
Detailed performance comparison of the tracking response and the magnitude of PV power oscillation of all the selected MPPT methods are further analysed as illustrated in Fig 12. Based on the result provided, the highest magnitude of PV power oscillation that occurred in generated output PV power is produced by the PO MPPT method. The difference between the two points of power oscillation is almost which is a huge loss in terms of power efficiency. As compared to both of its counterparts, the CS MPPT technique offers huge advantages for PV maximum power point extraction, especially with the high degree of tracking efficiency and almost unnoticeable effect on duty cycle variation in the event of sudden changes of irradiation that took place between the period of
until
. Furthermore, during the transient atmospheric condition (sudden drops of irradiation level), the CS MPPT method is the fastest in terms of speed to reach the steady-state form
which is one of the important features of improving the maximum PV power tracking efficiency. In addition, the CS produces very small (approximate
PV power oscillation that consequently resulted in improved overall system efficiency. Moreover, the CS created less if not zero amplitude variation of
even in the event of absurd atmospheric situations and was able to reduce the electrical stress on the power switches. Therefore, the CS algorithm MPPT technique produces the best result in terms of power oscillation, tracking efficiency, and ability to track MPP even under the most absurd atmospheric conditions.
The DC-link voltage, should be constant in case of any input fluctuations. As illustrated in Fig 13(a), in the beginning, the level of solar irradiation is poised at a steady level and starts to gradually decrease at
and reached an irradiation level of
at
. In the event of absurd atmospheric conditions which occurred at
until
, the
waveform was still able to be kept at a constant value of
even though a noticeable fluctuation occurred due to the controller action which required a certain time to achieve a steady-state voltage level. In contrast, there is no current oscillation that would be noticed during gradual changes of irradiation that took place at
until
as demonstrated in Fig 13(b). However, at the time,
until
certain transient was been identified for the direct current component,
; it occurred during sudden changes in irradiations. On the other hand, the value of the quadrature current component,
is kept at nearly zero values.
Moreover, as displayed in Fig 14, the maximum amplitude of the grid voltage is whereas the maximum amplitude of the injected current waveform showed a reading of
. Furthermore, it can be observed that the waveform of the injected current (phase R) is in phase with the waveform of grid voltage,
and as a consequence, it kept the power factor
near unity or
. Furthermore, the reactive power,
can also be delivered
to the grid by controlling the value of the quadrature current,
. It can be noticed that there is a drop in the power factor value
after time
.
The THD level for the injected current waveform using SVPWM switching as displayed in Fig 15, is around ; this value is below the grid code limit of
. The recorded amplitude of the current waveform at the fundamental frequency is
.
The effectiveness of the grid synchronization mechanism during fault conditions is vital. The grid fault is defined as the grid in a faulty state when the peaks of voltage or line frequency are in severe states and exceed the maximum margins mentioned in the standards. The grid fault or grid disturbance can be categorized into several types of faults such as the grid fault due to the voltage unbalance, voltage surge, voltage dip, frequency jump, phase angle jump, harmonic distortions, and grid-lines faults as illustrated in Figs 16–18, respectively.
(a1) Voltage unbalance, (b1) Voltage surge, and (c1) Voltage dip with their corresponding outcomes shown in (a2), (b2), and (c2) respectively.
(a1) Frequency jump, (b1) Phase angle jump, and (c1) Harmonic distortion with their corresponding outcomes shown in (a2), (b2), and (c2) respectively.
(a1) Line-to-line fault, (b1) Line-to-line-to-ground fault, and (c1) Line-to-line-to-line fault with their corresponding outcomes shown in (a2), (b2), and (c2) respectively.
The performances of all the studied MPPT algorithms are analyzed in terms of generation. In Fig 19, it is proved that the CS is able to improve the
and reach the recommended level at the irradiation level of
.
Moreover, as shown in Fig 20, the SVPWM switching topology reached the acceptable limit of less than
of the rated inverter input current at the irradiation level of
as compared to the SPWM which touched the
limit at the irradiation level of
. Hence, with the utilization of the SVPWM, the proposed GPV generation system is able to deliver an additional good quality of power from the PV system to the utility grid even at a low irradiation level. On top of that, the SVPWM proved to be more superior and produced a low value of
at every irradiation level as compared to the SPWM switching technique.
A detailed comparison of the individual performance between the proposed GPV generation system and similar research works is tabulated in Table 3. The proposed two-stage three-phase GPV generation system comprises controllers of the Cuckoo Search (CS) MPPT technique; the SVPWM switching topology in combination with the CDSC synchronization mechanism is the most effective PV-grid system configuration as it proved to have better MPPT tracking efficiency of
and requires only
to reach steady-state in the course of transient,
level of
and the proposed system is able to work efficiently even in the case of grid fault conditions.
12. Conclusion
The two-stage three-phase GPV generation system with a power rating of has been successfully designed, modeled, and analyzed in this research work. To attain the maximum
active power delivery from the PV arrays into the utility grid, the proposed GPV generation system is constructed based on the two-stage power circuitry topology. The two-stage power circuitry topology is interpreted as having a stage-by-stage power conversion from DC to AC forms. Based on the results, the designated two-stage three-phase GPV generation system was able to deliver a total of
from the PV system to the utility grid at the irradiation level of
. Furthermore, this circuitry configuration reduced the controller complexity where each of the individual local controllers (MPPT, DC-DC Boost, Inverter, Grid synchronization) was able to perform the designated operation effectively. As a consequence, it optimized the overall reliability of the proposed GPV generation system. Moreover, with the suitable controller parameters, the
for the injected current waveforms at the irradiation level of
is measured with an average value of around
of allowable
, thus complied with the grid code standards. Furthermore, it is proved that a designated
two-stage three-phase GPV generation system is combined with improved local controllers which are made up of an advanced CS MPPT, SVPWM as well as the CDSC grid synchronization mechanism is the most effective control mechanism against the absurd atmospherics and various grid fault conditions.
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