Abstract
In a grid-integrated photovoltaic system (GIPVS), there exist issues such as surplus active power and inadequate performance of maximum power point tracking (MPPT). A surplus active power causes the overvoltage problem at the point of common coupling in low- or medium-voltage grid during the peak hours of power generation. Additionally, the inadequate performance of the MPPT algorithm results in power loss due to high settling time during the sudden change of irradiance. Therefore, to solve the surplus power problem, the curtailment of active power is suggested with improved MPPT algorithm under variable irradiance conditions. In this paper, a derated power generation mode (DPGM) control strategy is presented for the curtailment of active power. Additionally, a drift-free (named as modified) perturb and observe (P&O) technique is also proposed to improve the performance of the MPPT algorithm. Consequently, the DPGM control scheme with the intermediate boost converter shaves the surplus active power during the peak hours of power generation. Furthermore, the modified MPPT algorithm deals with the fluctuation of irradiance during non-peak hours. Thus, the proposed control scheme delivers in a more efficient system during the peak hours of power generation. In addition, it reduces the power loss and settling time during the change of irradiance for non-peak hours. Based on the proposed control scheme, a 30 kW system has been simulated in MATLAB/Simulink using Simpower tools under different environmental conditions.
NOWADAYS, the integration of renewable energy sources (RESs) is increasing in power generation due to the shortcoming of fossil fuels. RESs include wind energy, solar energy, hydro energy, fuel cell and tidal energy. Among these RESs, the installation of photovoltaic (PV) solar system is advantageous due to low-cost maintenance. Therefore, the integration of the PV systems is booming in the renewable energy market. However, the PV power generation depends upon the irradiance, which affects the power generation but can be improved by power forecasting [
Many researchers have contributed to solving the problems such as overvoltage and inadequate performance of MPPT in GIPVS. Reference [
Reference [
Therefore, to derate the PV power during peak hours of power generation, the applied control schemes in the aforementioned literature have the following limitations:
1) Most of the existing technologies are based on conventional MPPT (P&O and incremental conductance) techniques.
2) Implemented systems are mostly single-phase GIPVSs.
3) A proper tracking strategy has not been proposed, which can reduce the power loss during the search of maximum power point (MPP).
The aforementioned limitations can be resolved through a proposed derated power generation control scheme with a modified MPPT. The proposed scheme will perform in both peak and non-peak hours of power generation, and improve the tracking capability of the MPPT algorithm. It will resolve the problems such as overvoltage, drifting, oscillation near the MPP, and tracking speed. As a result, the power loss during the search of operation point will be reduced at variable irradiance level. Hence, a suitable MPPT algorithm is required.
Many researchers have classified various MPPT techniques on the basis of the properties such as tracking speed [
The issue of excess power generation during peak hours affects the distribution network. Therefore, it is required to limit the power transfer during peak hours. The power transfer is limited by introducing the tap-changing transformer and voltage regulator, increasing the conductor size, and using storage and curtailment approaches [
The significant contributions of this paper are summarized as follows.
1) A derated-mode GIPVS has been proposed to limit the power transfer and resolve the overvoltage problem at PCC during peak power generation.
2) The proposed scheme introduces a modified MPPT, which limits the power transfer.
3) This MPPT algorithm results in improved tracking speed and efficiency, which reduces the power loss under variable irradiance condition.
The remainder of the paper is organized as follows. Section II presents the system framework and its working strategy. Section III elaborates the proposed control strategy of GIPVS. Further, the simulation results are presented in Section IV to support the proposed control strategy. Finally, the conclusion is presented in Section V.
This section briefs the system structure and proposed control strategy of GIPVS. The proposed system consists of two stages as shown in

Fig. 1 Block diagram of proposed two-stage three-phase GIPVS.
Stage 1 includes a PV array, input capacitor , boost converter, and the MPPT control. In the proposed system, a modified MPPT algorithm has been implemented which works in DPGM and modified MPPT mode. The DPGM gets activated when the generation exceeds the pre-defined power limit ; otherwise, it works in the modified MPPT mode [
In this section, the control approach of each converter used for the first and second stage of the system has been presented. In the first stage, the functionality of MPPT with the boost converter is illustrated in the upcoming subsections.
In the MPPT technique, the extracted voltage and current from the PV source are provided to the boost converter as shown in

Fig. 2 Circuit diagram of DC-DC boost converter with MPPT control.
This controller reaches the operation point using direct duty ratio three-step strategy on the power-voltage (P-V) characteristic curve as shown in

Fig. 3 Searching strategy of conventional P&O MPPT algorithm.
(1) |
The corresponding increment and decrement in the duty ratio are due to the change of input power with respect to voltage. Consequently, the impact of the change in duty ratio on output voltage and current of boost converter can be illustrated as:
(2) |
(3) |
The ratio of and is the output impedance of the boost converter which is calculated as:
(4) |
At constant , the value of is inversely proportional to the duty ratio. Therefore, to achieve the maximum power, voltage and current at a particular duty ratio, the value of is depicted as:
(5) |
Moreover, the performance of P&O depends upon the increment or decrement in step size of the duty ratio [
The proposed modified algorithm reduces the power loss and reduces the search time of MPP. It also keeps the system drift-free under variable irradiance condition. In addition, the proposed MPPT limits the excess power generation during peak hours. The proposed algorithm operates in two modes, i.e., modified MPPT mode and DPGM, which are illustrated in

Fig. 4 Flow chart of modified P&O MPPT algorithm.
Whenever the generated PV power is within the power transfer limit, the system works in modified MPPT mode. Otherwise, the system works in DPGM as depicted below.
(6) |
The modified MPPT mode of the proposed algorithm follows the direct duty ratio in a three-step strategy as mentioned in Section III-A. In the strategy, a large value of is considered for shorter response time. However, the large value of creates the problem of drift during irradiance change. As discussed in [
(7) |
The MPP value of the PV array delivered at particular is depicted as:
(8) |
By using Taylor’s expansion on (8) till the first order and substituting (4) and (5), (8) can be rewritten as:
(9) |
(10) |
By substituting (7) into (9) and (10), and can be expressed as:
(11) |
(12) |
Therefore, the maximum value of and with respect to is expressed as:
(13) |
(14) |
Since is increasing, , , , , , , and are constants at STC, and , , and are positive. Simultaneously, the temperature also increases with irradiance. Therefore, in (13) and (14), all terms are positive as the irradiance increases, which means that the voltage and current are positive with respect to irradiance, i.e., and . Similarly, , and .
Thus, based on current, voltage and power information, the drift problem can be avoided and analyzed as follows.
When the irradiance is increasing, point b shifts to point c and then to point d on a new P-V curve, as shown in

Fig. 5 Drift analysis of operation point during variable irradiance condition.
On this curve, the differences between points b and d for , , and are positive. It can be observed that the and are positive only when the irradiance is increasing. This shows that the current information during MPPT is essential. Further, based on these observations, and are positive, which leads to the reduction in the duty ratio. Consequently, the corresponding voltage decreases compared with the conventional P&O, where the voltage increases. This means that the operation point which is used to move away from the MPP starts moving towards the MPP because of the current information. It means that the operation point is not deviating from the MPP during variable irradiance condition, or, in other words, not drifting away from the MPP.
In DPGM, the modified P&O MPPT algorithm gets activated during available surplus power. As we know, the peak power rating of the installed PV array is always more than the average power generated in the whole day. Thus, the PV array generates surplus power during peak hours. Therefore, to remove the surplus power, a power limit is required so that the power can be transferred without affecting the distribution network equipment. In this paper, a power limit has been considered which is the average of power generated during 9 to 16 hours and is presented as:
(15) |
When the generated power exceeds , the DPGM turns on and shaves the surplus power. In

Fig. 6 Day-time power profile of a PV array.
Based on the above discussion in Sections III-A and III-B, the conventional and proposed MPPT algorithms with boost converter generate the DC power in the first stage. Furthermore, in the second stage, the generated DC power is provided to the VSI for power conversion with inverter control which has been discussed in the previous subsection.
The generated DC power is converted into AC power using VSI. The obtained AC power is further injected into the power grid with the help of inverter control as shown in

Fig. 7 Circuit diagram of grid-integrated VSI.

Fig. 8 Voltage regulation/outer loop of inverter control.

Fig. 9 Current control/inner loop of inverter control.
(16) |
The mathematical expressions of the system are of a higher degree in the natural reference frame (). Therefore, to use a simple controller (i.e., PI) and realize less mathematical complexity, the present reference frame is transformed into rotating reference frame using Park’s transform [
(17) |
Or:
(18) |
(19) |
As mentioned in [
(20) |
By substituting (20) into (19), the modulating signals are:
(21) |
These modulating signals and have been transformed from to to provide the gate signals (-) to the VSI, which generates voltage and current. Since the power has to be transferred in the grid, the generated voltage and current should be in phase. Thus, a phase-locked loop technique has been added in the system, which synchronizes the generated voltage of VSI and the current with the power grid.
Finally, in the next section, the performance of the control approaches will be evaluated and verified in MATLAB/ Simulink environment.
A 30 kW two-stage three-phase GIPVS using modified P&O MPPT algorithm is simulated in MATLAB/Simulink environment with Simpower tools. The modified MPPT performs derated power generation which restricts the power generation when it exceeds . Simultaneously, the conventional P&O algorithm is also examined to select a suitable for the modified P&O algorithm under variable irradiance condition. Thereafter, the performance of the conventional and modified P&O algorithm are analysed in terms of PV power, PV voltage, duty ratio, DC-link and output power as follows.
For the evaluation of input voltage deviation and response time, the conventional P&O algorithm is tested for different values of . Simultaneously, to test the robustness of the system, the algorithm is evaluated under variable irradiance condition. For the sake of evaluation, a small step size and a big step size are considered. From

Fig. 10 Steady state performance of conventional P&O algorithm. (a) At . (b) At .
The performance of the modified P&O algorithm is evaluated in two modes. One is the modified MPPT mode and the other is the DPGM.
In this mode, the modified MPPT works like the conventional P&O until the power generation does not reach the power limit. Besides, the modified algorithm provides the right direction and less variation in voltage of the operation point towards MPP.

Fig. 11 Dynamic performance of modified P&O algorithm in modified MPPT mode. (a) PV source output performance. (b) DC-link and inverter output performance.
Thus, does not deviate and reaches the operation point. In addition, the effect of irradiance change in DC-link voltage, phase voltage , and current is shown in
The system enters into the DPGM when the net power generation exceeds the power limit. In this mode, the modified P&O MPPT algorithm curtails the excess power. A power profile is presented in

Fig. 12 Dynamic performance of modified P&O algorithm in DPGM. (a) PV source output performance. (b) DC-link and inverter output performance.
Further, to analyze the performance of proposed modified and conventional P&O MPPT algorithms, a statical analysis has been presented in
A two-stage three-phase GIPVS works in the DPGM to curtail the extra feed-in power during peak hours. In addition, it avoids the drift phenomena which exists in traditional P&O algorithm. Furthermore, the proposed algorithm works in a modified MPPT mode during non-peak hours. In this mode, the MPPT holds the information of current to distinguish irradiance change. Thus, it can estimate the search direction towards MPP during irradiance change. Thereby, the operation point does not diverge from the shortest path of MPPT. Moreover, to enhance the tracking capability of the modified MPPT, it is examined on different step sizes . In this paper, a large step size has been chosen which increases the response time and reduces the oscillation using the proposed algorithm. The system is implemented for a 30 kW two-stage three-phase GIPVS and simulated in MATLAB/Simulink environment using Simpower tools. The performance of the system presents that the proposed algorithm actively participates in power curtailment during peak hours of power generation. Additionally, the performance shows that the modified algorithm gives a faster response than the traditional P&O algorithm under variable irradiance condition.
NOMENCLATURE
Symbol | —— | Definition |
---|---|---|
—— | Step size of duty ratio | |
—— | Change in photovoltaic (PV) power | |
—— | Temperature difference between actual and standard test condition (STC) | |
—— | Change in PV voltage | |
—— | Angular frequency of grid voltage | |
—— | Input capacitor | |
—— | Direct current (DC)-link capacitor | |
—— | Duty ratio for boost converter | |
—— | Operating solar irradiance | |
—— | Reference solar irradiance | |
—— | -axis and -axis reference currents of inverter | |
—— | -axis and -axis currents of inverter | |
—— | Reverse saturation current of diode | |
—— | Grid-side three-phase currents of grid-intigrated PV system | |
—— | Output current of boost converter | |
—— | Current at maximum power point | |
—— | Current of PV array | |
—— | Short-circuit current of PV array at STC | |
—— | Short-circuit current of PV array | |
—— | Temperature coefficient | |
—— | Interfacing inductor at output of inverter | |
—— | -axis and -axis modulation indexes for inverter | |
—— | Number of PV modules in parallel | |
—— | Number of PV modules in series | |
- | —— | Power generated from PV source in particular hours of day |
—— | Output power of boost converter | |
—— | Power transfer limit | |
PMPP | —— | Power at maximum power point (MPP) |
Ppeak | —— | Maximum generated power |
—— | Power of PV array | |
—— | Resistance of each phase | |
—— | Input impedance of boost converter | |
—— | Output impedance of boost converter | |
- | —— | Gate signals for inverter |
- | —— | Particular hours of day |
—— | Settling time to meet | |
-link | —— | Settling time to meet -link |
—— | -axis and -axis reference voltages of inverter | |
-link | —— | Reference DC-link voltage for inverter |
—— | -axis and -axis voltages of inverter | |
—— | Thermal voltage of diode | |
DC-link | —— | Measured DC-link voltage of inverter |
—— | Output voltage of boost converter | |
—— | Voltage at MPP | |
VPV | —— | Voltage of PV array |
—— | Grid-side voltages of grid-integrated PV system | |
—— | -axis and -axis voltages of power grid | |
—— | Terminal voltages of inverter |
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