Introduction

To match the ever-increasing need of power, the concept of renewable-based power generation is being implemented and a lot of research is being carried out on the same [1, 2]. With a new NHS MPPT technique, a single-phase two-stage system with storage connected to the grid is implemented in [3]. Here, the VSC is controlled using a new PNKLMS technique which also maintains the power quality. Further, any sensor for DC-link voltage measurement is not required [3]. Fuzzy logic-based MPPT technique for PV-based UAV is proposed in [4] which has a quick response in tracking the MPP with reduced oscillations and increased efficiency. An MPPT controller based on RBFN for both solar and wind generation systems is examined, and its performance is compared with the conventional MPPT algorithms. The scheme has an interesting advantage of decreasing the components in the hardware MPPT controller design [5]. An innovative CPHO regulated MPPT algorithm which includes an optimum duty cycle through a PI controller for boost converter is introduced in [6]. It works on the rule height convergence, and its performance is compared with conventional P&O technique. For partial shading condition (PSC), there will be multiple maximum power points, so a new overall distribution (OD) MPPT algorithm to rapidly search MPP and after being integrated with PSO algorithm to enhance accuracy is proposed in [7]. A grid-connected SPEGS is implemented in [8] which provides multi-functional deals with active power filtration and supports active power demand. Also, a new multi-purpose DS controller is used to get reference grid currents and to improve performance. SECS is mostly preferred due to its numerous advantages over other types of renewable-based energy conversion systems [9]. Major advantages are low maintenance cost, static generation, and being abundant in almost all over the world. Simultaneously, a lot of research is being carried out in the area of SECS [10,11,12]. The output of SECS depends on the irradiance and temperature. If the irradiance increases, the output will also increase and vice versa, while if temperature increases, the output decreases and vice versa. The I–V characteristics can be used to determine the exact variations in the solar output with the change in irradiance and temperature [13]. A technique called MPPT is used to extract maximum power under variable irradiance and temperature. There is a lot of literature available on MPPT for SECS. There are several existing techniques for MPPT, e.g., P&O [14], incremental conductance [15], constant voltage [16], current sweep [17], temperature measurement [18] methods, etc. The most used method is P&O due to its simplicity [19]. Other methods also have their benefits and limitations. For instance, the control logic of the incremental conductance method is complex for hardware implementation, the temperature measurement method does not include the effect of irradiance change, and so on. Therefore, there is still some scope for improvements in MPPT. Moreover, the basics of the SECS still need to be discussed in detail for a better understanding of the readers. A literature survey states that compared to buck and buck–boost converters, boost converter works at high efficiency and is good at tracking MPPT [20], [21].

This article presents a detailed study of the basics of stand-alone as well as grid-connected SECS with MPPT using a boost converter and also proposes a new MPPT technique. Furthermore, the newly proposed technique is compared with the conventional P&O technique. From the comparative analysis, it is found that the proposed method gives lesser oscillatory output than that of the P&O technique in stand-alone mode while providing better performance in grid-connected mode.

Solar Energy Conversion Technique The equivalent circuit of a solar cell—excluding the lossy components as they have a minor impact on the characteristics—is shown in Fig. 1a. The output current equation of the solar cell can be obtained using (1) and (2) and is given in (3).

Fig. 1
figure 1

a Equivalent circuit of a PV cell; b I–V characteristic of solar cell and different areas; c plot of impedance of the PV array v/s voltage d; plot of impedance offered by boost converter v/s duty cycle; e power v/s voltage curves for irradiances 800 and 700 W/m2 and their respective MPPs

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$$I_{pv} = I_{D} + I$$
(1)
$$I_{pv} = I_{o} \left[ {e^{{\frac{V}{{\eta V_{T} }}}} - 1} \right] + I$$
(2)

Since \(I_{D} = I_{o} \left[ {e^{{\frac{V}{{\eta V_{T} }}}} - 1} \right]\)

$$I = I_{pv} - I_{o} \left[ {e^{{\frac{V}{{\eta V_{T} }}}} - 1} \right]$$
(3)

The current Ipv depends upon the irradiance and temperature, while the diode current ID depends on various other parameters including voltage and temperature. Moreover, for a constant irradiance and temperature, if the load RL is varied, the solar cell-voltage and current will vary in the manner as depicted in Fig. 1b—also known as the I–V characteristic of a solar cell. It can also be seen that there are two hatched areas: one due to maximum power point and another due to open-circuit voltage Voc and short circuit current Isc. The ratio of these two areas is nothing but the fill factor (FF) of the solar cell and is given in (4). The typical value of the fill factor is greater than 0.8 for V/VT to be 20 [22]. In Fig. 1e, power output v/s voltage curves of the considered solar panel are shown with their respective MPPs for each irradiance.

$$FF = \frac{{V_{mp} I_{mp} }}{{V_{oc} I_{sc} }}$$
(4)

The value of the fill factor defines the power conversion efficiency of a solar cell [13]. This efficiency may reduce if the maximum power point has not been achieved. The MPPT can be achieved by controlling the effective value of load resistance RL. A DC-to-DC converter can help to vary the effective value of load impedance offered to the solar cell or PV module. The selection of the type of converter depends upon the impedance corresponding to maximum power and actual load impedance. For example, if the load impedance is, say, 20 Ω and impedance corresponding to a maximum power point (MPP) is 1.25 Ω, the boost converter should be used. On the contrary, if the load impedance is 12.5 Ω and impedance corresponding to MPP is 20 Ω, the buck converter should be used. The buck–boost converter has the capability of both. However, in most of the cases when irradiance is more, the impedance corresponding to MPP is less than the load impedance [23]. Therefore, either boost or buck–boost converter can be used. But since boost converter has higher efficiency and greater control over the range than buck–boost converter [20] and good tracking performance than buck converter [21], it is used in this study for maximum power-point tracking. According to the I–V curve of the PV array, the impedance seen by the photovoltaic (PV) array Zseen is calculated using (5).

$$Z_{seen} = \frac{V}{I}$$
(5)

In the I–V curve, when the PV output voltage is increasing, the PV output current decreases gradually up to the MPP. After the MPP, current decreases drastically. Therefore, the \(Z_{seen}\) v/s PV output voltage plot, as shown in Fig. 1c, is nearly linear up to MPP, but after that, the impedance increases drastically because the PV voltage increases and the PV current decreases rapidly. Further, the impedance offered by the boost converter, i.e., Zoffered, with the change in duty cycle D is given in (6) and plotted in Fig. 1d. By observing Fig. 1d, it can be said that the variable impedance offered by the boost converter Zoffered will be less than the load impedance as given in (7).

$$Z_{offered} = Z_{L} (1 - D)^{2}$$
(6)
$$Z_{offered} \le Z_{L}$$
(7)

Now, using the I–V characteristic, Z–V characteristic can be obtained since impedance Zseen is nothing but the ratio of voltage V and current I. Normally, to obtain the MPP, the search is done by varying impedance using the duty cycle of the converter. Figure 1c, d depict the impedance obtained from the I–V characteristic Zseen and impedance offered by the boost converter Zoffered for a representative case. The relation between Zoffered and D is approximately inverse and the maximum impedance that the converter can offer to the solar panel is equal to the load impedance as D can be varied from 0 to 1—refer (6). Therefore, to increase the impedance offered by the converter, the duty cycle of the converter must be decreased. Now, suppose the operating point of the PV module is at O1 as shown in Fig. 1c. At this operating point, the impedance offered by the converter is Z1 corresponding to duty cycle D1 and the PV module voltage is V1. To get the operating point shifted to O2—for the extraction of maximum power, the PV voltage should be shifted to V2. That can be done by changing Zoffered to Z2 with the help of changing the duty cycle to D2. Figure 2 includes the block diagram of a typical SECS. The PV array converts the sunlight into an electrical signal (DC). This DC output of the PV array is given to the boost converter to implement the MPPT. The MPPT controller measures the voltage and current of the PV array and generates the duty cycle for the boost converter. An inverter is usually connected after the boost converter to convert DC into AC. A capacitor is placed at DC bus to avoid the effect of fluctuations due to switching events. The inverter controller usually controls the output power to keep the capacitor voltage constant. In this study, both stand-alone mode and grid-connected mode are implemented separately. The circuit breaker is represented by switch S1 which can be used to connect/disconnect the grid.

Fig. 2
figure 2

Block diagram of SECS

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Proposed MPPT Technique

First, the P–V curve of the solar panel is categorized into three regions based on the calculation of slope (dP/dV). The three regions are:

  1. 1.

    Low-slope region;

  2. 2.

    Medium-slope region;

  3. 3.

    High-slope region.

By observing the three regions shown in Fig. 3a, the MPP lies in the low-slope region. MPP is the intersection point of the +ve slope and −ve slope portions of the P–V curve. P–V curve varies with the variations in irradiance and temperature—accordingly, MPP gets shifted as represented earlier in Fig. 1e. Hence, the adopted MPPT technique must recognize the change in irradiance and temperature and consequently track the MPP on the P–V curves. The flowchart illustrates the proposed MPPT technique is shown in Fig. 3b. The objective is to obtain Imp and Vmp of PV array—corresponding to maximum power for particular irradiance and temperature. Since the proposed MPPT technique works on the division of the P–V curve into different regions, the algorithm starts by calculating the change in voltage dV, change in power dP and slope dP/dV. Then, if either the change in voltage or the change in power is zero, it indicates that MPP is reached, and if it is not zero, the voltage must be increased or decreased using the duty cycle D of the converter. Equation (8) represents the updated duty cycle D where D1 is the old duty cycle and dD is the change in duty cycle. The term dD is calculated by \({\text{d}}D = K*\left( {\frac{{{\text{d}}P}}{{{\text{d}}V}}} \right)\), where K is the factor multiplied to slope value according to the regions that are illustrated in Fig. 3a. The regions are divided based on the calculation of slope dP/dV. For the low-slope region, the slope value is less than LS, and for medium-slope region, it is between LS and HS. For the high-slope region, the slope value will be greater than HS. For every iteration, the absolute value of calculated slope dP/dV is compared with the predefined LS or HS. When the operating point is close to MPP (i.e., low-slope region), the changes in duty cycle dD should be small, and when it is away from MPP (i.e., medium-slope region), dD should be larger. A small change in duty cycle dD at a high-slope region leads to a huge change in power, and therefore, dD should be smaller in this region. Therefore, the value of K will be different for each region and is given in the flow diagram, i.e., for low and high-slope regions, it is − 1 × 10−6 and for medium-slope region, it is − 1 × 10−4. Now, the changes in duty cycle dD are added to the previous duty cycle D in every iteration and the change in power dP is also monitored continuously.

Fig. 3
figure 3

a Different regions of the P–V curve; b flowchart of the proposed MPPT technique

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$$D = D1 + {\text{d}}D$$
(8)

DC Bus Voltage and Active Power Flow Control

The voltage across the DC bus capacitor will be controlled by controlling the power injected to the AC system by the inverter. This can be done on the principle that the current drawn from the boost converter Iin should be equal to the current delivered to the AC grid side through VSI i.e., Iout. Then, the voltage across the capacitor can be maintained at the desired level. The control scheme can be explained with the help of Fig. 4a, b. The DC bus voltage VDC can be controlled by using a PI controller which generates the reference current magnitude—to be injected into the AC system.

Fig. 4
figure 4

a DC bus capacitor; b DC bus voltage control using PI controller

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The voltage VDC depends upon the difference between Iin and Iout as follows:

If Iin < Iout, then → VDC < V* DC  → Iref should decrease.

If Iin > Iout, then → VDC > V* DC  → Iref should increase.

If Iin = Iout, then → VDC = V* DC  → Iref should remain constant.

Here, V* DC is the reference DC bus voltage and Iref is the current reference generated by the PI controller and it is to be tracked by the VSC to control the active power injected to the AC system. By using hysteresis current control (HCC) scheme [24], Iref can be tracked to regulate the active power flow so that the voltage across DC bus capacitor can be maintained at desired magnitude. Using dqo to abc reference frame theory, the three-phase reference currents are generated from Iref [24]. PLL is used to get the exact phases in which the three-phase reference currents should be generated. The firing pulses are generated using actual and reference currents [24].

Results and Discussion

The performance of the proposed scheme has been compared with the existing P&O method in two different modes, namely stand-alone mode and grid-connected mode.

  1. (1)

    Stand-alone Mode of SECS.

To investigate the functioning of the new MPPT technique and to compare it with that of the P&O method, MATLAB/Simulink simulation study is carried out. An array consisting 10 series modules and 40 parallel strings of photovoltaic model TDB156x156-60-P 225 W was simulated. The complete rating of the considered PV array used in this study is as follows. Sun Earth Solar Power PV array model is considered for the implementation in MATLAB/Simulink. The ratings of the considered PV array are 10 × 40 modules of each 225 W, total PV array voltage of 370 V, a peak power of 90 kW at 1000 W/m2 irradiance.

In this mode, the DC power is utilized after tracking the MPP using boost converter and the load is having a fixed impedance of 20 Ω and therefore, conversion of DC into AC is not required. The converter switching frequency is kept 5 kHz, converter inductor is 50 mH, and the capacitor is 4 mF. Next are the two cases considered for the verification of the proposed MPPT scheme in stand-alone mode.

Change in irradiance To show the impact of change in irradiance, a step change in the value of irradiance is made from 700 to 800 W/m2 at t = 0.2 s as depicted in Fig. 5a. The temperature is kept constant at 25 °C. Figure 5b, c show the comparison of voltages and powers between conventional P&O and proposed MPPT techniques, respectively, for changed irradiance and at a constant temperature. It is found that the rise time and settling time of voltage and power of both the techniques are nearly equal and the steady-state values of voltages and powers for both the techniques are the same. However, both the plots for the proposed technique give lesser oscillations.

Fig. 5
figure 5

Comparison of P&O and proposed MPPT techniques for stand-alone mode with change in irradiance a irradiance, b converter output voltage, c power

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Change in temperature To show the impact of change in temperature, a step change in the value of temperature is made from 40 to 25 °C at t = 0.3 s as depicted in Fig. 6a. The irradiance is kept constant at 800 W/m2. Figure 6b, c show the comparison of voltages and powers between conventional P&O and proposed MPPT techniques, respectively, for change in temperature and at a constant irradiance. It is, again, found that the rise time and settling time of voltage and power of both the techniques are nearly equal and the steady-state values of voltages and powers for both the techniques are the same. Though the proposed scheme gives lesser oscillations, the overshoot is slightly more.

Fig. 6
figure 6

Comparison of P&O and proposed MPPT techniques for stand-alone mode with change in temperature a temperature, b converter output voltage, c power

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For better understanding and comparison in stand-alone mode, the outcome of both the techniques is given in Table 1.

Table 1 Comparison in stand-alone mode
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  1. (2)

    AC grid-connected mode of SECS.

In this mode, the circuit is simulated as per the block diagram shown in Fig. 2. The AC load is considered to be parallel RLC load having R = 10Ω, L = 15 mH, and C = 470 μF with 0.84 pf lagging. The DC bus capacitor is initially charged to 1400 V to avoid high transient currents. The grid rms voltage is 400 V L–L. The grid interfacing inductance is 0.1 mH. The steady-state value of the DC bus voltage is 1440 V.

The performance is investigated by changing the irradiance from 700 to 800 W/m2 at time 0.2 s—similar to that of stand-alone mode. The inverter is operated in active power injection mode with the help of a hysteresis current controller [24]. From Fig. 7, we can observe that the SECS takes more time in achieving the steady state as compared to that of stand-alone mode. When the irradiance is changed from 700 to 800 W/m2 at t = 0.2 s, the SECS was not able to achieve steady state for irradiance of 700 W/m2 due to transient period, but it achieved the same for 800 W/m2 in about 0.6 s. Figure 7a illustrates the irradiance, Fig. 7b shows the DC bus voltage, and Fig. 7c represents the power extracted from SECS which is supplied to the AC system. It is also evident that the maximum power can be extracted from the solar panel at a given irradiance, i.e., at an irradiance of 800 W/m2 the maximum power of 72 kW is extracted, and it is shown in Fig. 7c. Now, for comparison purposes, Table 2 includes different parameters for both the schemes.

Fig. 7
figure 7

Comparison of P&O and proposed MPPT techniques for grid-connected mode with change in irradiance a irradiance, b converter output voltage, c power

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Table 2 Comparison in grid-connected mode
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Conclusion

According to the change in irradiance and temperature, there will be a change in the I–V curve, P–V curve, and maximum power point. Therefore, the operating voltage of the PV array needs to be modified to extract the maximum power. In other words, the impedance offered by the converter should be varied in accordance with that of the PV array. To change this offered impedance, the duty cycle of the converter needs to be varied accordingly. Different aspects of the solar energy conversion system have been discussed in detail, and a new MPPT technique has been proposed. In stand-alone mode, the new technique successfully tracks the MPP down and gives comparable results to that of the P&O technique and the oscillations in the proposed technique are lesser than that of the P&O scheme. In grid-connected mode, the proposed scheme gives improved results and provides lesser oscillations in output and has improved rise time and settling time. Overall, the detailed study of the solar energy conversion system and the proposed scheme will surely be interesting and helpful to the readers.