1. Introduction

In renewable energy, the development of photovoltaic (PV) systems is a significant source of power owing to benefits from cleanliness, environmental conservation, and little noise. The output power of PV arrays varies over time in terms of solar irradiance and atmospheric temperature. In a PV system, maximum power point tracking (MPPT) is an important parameter needed to obtain maximum PV array power ^[1,2]. The PV power voltage curve characteristics have only one operating point. If atmospheric conditions change, MPPT determines the maximum power and maintains it to supply the system ^[3]. To obtain constant maximum power, MPPT and various other algorithms are used ^[4,5]. Fuzzy logic theory is used to achieve a high-power PV output, which is an efficient method ^[6].

To reduce costs and improve the system, distributed systems based on renewable energy have been designed ^[7]. These modular DC-to-AC structures reduce the number of passive components in the inverter and reduce its size ^[8]. For DC-to-AC conversion, the voltage source inverter (VSI) is better than the conventional topology ^[9]. Thus, the VSI’s instantaneous average output voltage is always less than the DC voltage input, so a DC-to-DC boost converter is used. When this is used, the required output AC voltage is higher than the input DC voltage ^[10]. Thus, use of an additional DC-to-DC boost converter increases loss, weight, and cost, and decreases reliability ^[11].

In much of the literature, the main task is the DC-to-DC converter design and is a power interface between the PV panel and the load ^[12,13]. Compared to the input voltage of the buck boost converter and the Cuk converter, the output voltage is higher or lower than the input voltage. But there are some drawbacks in a buck boost converter ^[14,15]. The current of the buck boost converter input is discontinuous, the power component current is at a peak level, efficiency is lower, and the response of the transient is poor ^[16,17]. Therefore, compared to the buck boost converter characteristics, the Cuk converter has better input and output current characteristics ^[18,19]. Also, the configuration of the switching power supply unites the switching technology advantages, and current ripple switching is eliminated ^[20]. In the literature, using a Cuk converter reduces power dissipation and avoids interrupted conduction modes ^[21,22]. Therefore, compared to other topologies, a Cuk converter is the best power source to connect the PV panel to the load ^[23,24].

As a result, metaheuristic algorithms are developed and used to solve many problems, with alternative solutions competing based on ease of implementation ^[25,26]. Sivakumar and Kanagasabapathy ^[27] presented an optimization technique inspired by nature to compete with additional optimizers. The main ideas of the proposed optimization are inspired by the Harris hawk, which exhibits intelligent cooperative behavior when capturing food (rabbits in particular) while flying. A mathematical model for this is used in this work ^[25].

In this paper, we design and implement a quasi-resonant Cuk converter (QRCC) for photovoltaic applications. The proposed Cuk converter reduces switching losses and is a significant improvement over other converter topologies, so system performance is improved. The proposed system is detailed in Section 2. In Section 3, the optimization problem is formed. Section 4 discusses the simulation results, and Section 5 is the conclusion.

2. Proposed System Description

The proposed system consists of a photovoltaic system, a quasi-resonant Cuk converter, a voltage source inverter, a transmission line, and the grid. The PV output is linked to the QRCC. The output voltage of the QRCC is greater than the input voltage. A switching technique is applied to the quasi-resonant Cuk converter switches. The switching techniques are zero voltage transition (ZVT) and zero current transition (ZCT). Owing to this ZCT-ZVT switching, low-value resonant components are used, and this results in the switching frequency being increased. The resonant components are placed across the switch of the Cuk converter ^[26]. This ZCT-ZVT switching technique abates the switching, and conduction losses are reduced. The QRCC is linked to a three-phase VSI. Here, the inverter switches are controlled by using proportional and integral (PI) controller-based optimization techniques. Harris hawks optimization (HHO) is used to improve system performance and reduce the harmonics. The proposed system’s blocks are described as follows.

2.1 The PV Electrical Model

The PV equivalent electrical circuit model, shown in Fig. 2, consists of photoelectric current I$_{\mathrm{ph}}$, diode current I, plus series resistance and parallel resistance (Rs and Rp, respectively).

The V-I characteristics of the PV-cell-based equation are expressed as follows:

(1)

I = I$_{\mathrm{ph}}$ - I$_{\mathrm{s}}$[exp ($q\frac{\left(V+RseL\right)}{kTcA}$) - 1] - $\frac{V+IRs}{R_{sh}}$

Here, photoelectric current I$_{\mathrm{ph}}$ depends mainly on the temperature and irradiance of the PV cell and is expressed as follows:

(2)

I$_{\mathrm{ph}}$ = [I$_{\mathrm{sc}}$ + K$_{I}$(T$_{\mathrm{C}}$ ${-}$T$_{\mathrm{Ref}}$) ]${\Lambda}$

The PV array’s final expression with voltage V and current I is

(3)

I = N$_{\mathrm{p}}$ I$_{\mathrm{ph}}$ ${-}$ N$_{\mathrm{P}}$I$_{\mathrm{s}}$[exp(q(V / N$_{\mathrm{S}}$ + IR$_{\mathrm{s}}$ / N$_{\mathrm{P}}$) / kT$_{\mathrm{C}}$A)${-}$1]${-}$(N$_{\mathrm{P}}$V / N$_{\mathrm{S}}$ + IR$_{\mathrm{s}}$ )/R$_{\mathrm{sh}}$

Rs is evidently significant, and R$_{sh}$ (shunt resistance) becomes infinite. Solar modules are subsequently organized in a series of parallel arrangements to attain the preferred output energy.

The arithmetical formula of a comprehensive structure can be expressed as follows:

(4)

I = N$_{\mathrm{P}}$ I$_{\mathrm{ph}}$ ${-}$ N$_{\mathrm{P}}$ I$_{\mathrm{s}}$[exp (q (V / N$_{\mathrm{S}}$ + IR$_{\mathrm{s}}$ / N$_{\mathrm{P}}$) / kT$_{\mathrm{C}}$A)${-}$1]

The corresponding model is in formula (5):

(5)

I = N$_{\mathrm{P}}$ I $_{\mathrm{ph}}$ ${-}$ N$_{\mathrm{P}}$ I$_{\mathrm{s}}$ [exp (qV/N$_{\mathrm{S}}$kT$_{\mathrm{C}}$A) - 1]

where N$_{\mathrm{P}}$ and N$_{\mathrm{s}}$ are the parallel-connected PV array and the series-connected PV array, respectively.

Fig. 1. The quasi-resonant Cuk converter block diagram.

Fig. 2. The PV cell’s equivalent electrical circuit.

2.2 The Quasi-resonant Cuk Converter

The components in the quasi-resonant Cuk converter’s MOSFET are shown in Fig. 3; capacitors are denoted C$_{1}$ and C$_{2}$, inductors are denoted L2, resonant components are Lr1 and Cr1, the diode is D and the load is R. In the Cuk converter circuit, the input is from the PV array, and the Cuk converter input voltage is fed into the circuit through resonant inductor Lr1. When the switch is ON, the ZVT is applied, and the switch is OFF when the ZCT is working ^[5]. During the ON state, the diode is reverse-biased and dissipates the energy from capacitor C$_{2}$. During the OFF state, the resonant current flows to inductor Lr1. It provides energy through the resonant capacitor to the load. In the steady state, the inductor current must be zero. But a small resonant current flows to resonant inductor Lr1. This reduces switching losses and conduction losses and improves the switching frequency.

(6)

$ \frac{V_{0}}{V_{d}}=\frac{d}{1-d} $

In (6), d denotes the duty cycle. Here, the MPPT algorithm is used to provide the duty cycle of the Cuk converter. MPPT input is the voltage and current of the PV system. In the quasi-resonant Cuk converter, output voltage V0 is either lower than or higher than input voltage Vd. By using MPPT, the disturbance in the circuits is reduced significantly.

Fig. 3. The quasi-resonant Cuk converter circuit.

2.3 Voltage Source Inverter

The three-phase voltage source inverter components consist of six switches and a filter. The input from the voltage source inverter is from the quasi-resonant Cuk converter. The six switches are denoted Q1 to Q6 and are triggered by using pulses generated by the PI controller. The gain parameters of the PI controller are tuned using HHO, and the output of the VSI voltage is adjusted. The PI-tuned optimization control technique is used for the evaluation. The Harris hawks optimization method is used for analysis. The proposed QRCC method is compared with the quasi-resonant single-ended primary inductance converter (QRSEPIC). The VSI to the grid is shown in Fig. 4.

Fig. 4. A VSI connected to the grid.

3. Optimization Problem Formulation

The choice of a best practice depends on the optimization problem type. Recently, numerous progressive techniques for optimization have been used to reduce the THD of a voltage source inverter. Use of the open loop and the closed loop was designed in Simulink. In a closed loop PI, the controller is used for VSI switching. The PI tuned optimization control technique and Harris hawks optimization were used for comparison. The proposed converter operation was compared to the single-ended primary inductance converter.

Harris Hawks Optimization Design

The Harris hawk’s main tactic for capturing prey is the sneak attack, also known as the seven kills strategy. Attacks can be completed quickly, catching surprised prey within seconds, but sometimes, depending on the mode of escape and behavior of the prey, the seven kills strategy may involve repeated, brief, rapid dives near the prey for several minutes ^[25]. Simple illustrations of rabbit dives are shown in Figs. 5 and 6. Fig. 5 shows the 2D process. Fig. 6 shows the 3D process.

Using the equation $X\left(t+1\right)=\left\{Y\,\,if\,F\left(Y\right)<\right.$ $\left.F\left(X\left(t\right)\right)\,\,Z\,\,if\,F\left(Z\right)<F(X\left(t\right)\right)$, the location vector is updated.

The constraints of the PI controller parameters are

0.5 < Ki < 1

1 < Kp < 3

In HHO therefore, the optimal gain parameters for the PI controllers are obtained. Then, optimal control pulses are generated based on the optimized gain parameters.

Fig. 5. The HHO 2D process.

Fig. 6. The HHO 3D process.

4. Simulation Results and Discussion

In this section, Simulink is used to design the quasi-resonant Cuk converter based on a voltage source inverter. Using the MATLAB/Simulink platform, the proposed system was designed on an Intel Core i5 processor with 8GB of RAM running Linux Release 2016a. Fig. 7 shows the Simulink model implementation.

The Simulink PV implementation consists of the QRCC, the VSI, and the grid. Fig. 8 shows the Simulink representation of the PV for the quasi-resonant Cuk converter. Simulink is shown in Fig. 9. Fig. 10 shows the Simulink VSI representation.

The electrical feature model, the PV is designed in Simulink. The input of the PV is the temperature and the irradiance, both constant.

The Quasi-resonant components include two capacitors, two inductors, switches, and a diode. The QRCC PV input is DC, and the output voltage is greater than the QRCC input voltage.

To obtain the desired DC output voltage, the novel quasi-resonant Cuk converter is linked to the PV system. Reduction of the harmonics is obtained using PI control of the VSI. The gain parameters of the PI controller were tuned using the HHO algorithm. The proposed optimization techniques are used to compensate for the grid voltage.

The proposed system’s improved results are shown below, and these results are compared to existing converters. The existing techniques are open loop operation, closed loop operation using the PI controller, and the PI-tuned Harris hawks optimization technique. The proposed converter parameters are shown in Table 1.

Fig. 7. Simulink representation of the grid-connected PV-based QRCC.

Fig. 8. Simulink’s schematic of the PV system.

Fig. 9. Schematic of the proposed QRCC.

Fig. 10. Simulink representation of the VSI.

4.1 Photovoltaic System

The photovoltaic system produces output at 300V DC, and the produced current is 50A. Fig. 11 shows the PV voltage waveform and the current. If irradiance and temperature are constant, the irradiance is 1000W/m$^{2}$ and the temperature is 25$^{0}$C.

Fig. 11. PV Voltage and Current.

4.3 Converter Operation

The MPPT algorithm is used to control the quasi-resonant Cuk converter switches. The QRCC pulse is generated using the MPPT technique. The generated pulse controls the proposed QRCC’s switches. The output of the converter is fed into the grid through the VSI. With proper control of VSI switching, the grid-side harmonics are reduced. Therefore, the optimization technique based on PI control is applied to the VSI.

We compared the proposed converter switching without MPPT, with MPPT, and by using MPPT with incremental conductance and an integral regulator (MPPT-INCIR). Fig. 12 shows ZVT switching, and Fig. 13 shows ZCT switching. When using the pulse generator, switching loss is 38%, but using the MPPT technique, switching loss is 5%, and with the proposed MPPT-INCIR, switching loss is only 2%.

During quasi-resonant Cuk converter operation, the obtained voltage is 450V and the current is 76.7A. Fig. 14 shows the QRCC’s voltage waveform, and Fig. 15 shows the current waveform. By using the pulse generator, output voltage is not settled. In this, the overshot is high, so we go to closed loop operation. In closed loop operation, the output voltage oscillates, so we reduce oscillations with the MPPT controller. Overshoot, settling time, and rise time are low by using the MPPT-INCIR controller.

The grid-side voltage is compensated for by using proper control of the VSI. Grid-side control switching is completed using the PI controller with gain parameters tuned by using the HHO algorithm. The transmission line values are three-phase, the frequency is 50Hz, and the transmission line voltage is 415V AC. To compensate for voltage sag, the proposed HHO technique is used. Figs. 16 and 17 show grid voltage and grid current, respectively, of the proposed QRCC.

The THD is noted using the grid voltage waveform. The time period was 0.08sec to 0.15sec, and the voltage was maintained at the sag level. So, to rectify it by using optimization techniques, the obtained THD is noted in Table 2. Under open loop operation using the pulse width modulation technique, the obtained THD was 40.68%; using the PI-controller-based PWM techniques, the obtained THD was 29.83%, and from the proposed PI-controller-tuned HHO algorithm, the obtained THD was 0.678%.

Comparative analysis

The following figures show the existing SEPIC converter compared with the proposed Cuk converter. For the same input voltage, both converters produced the output voltages shown in Fig. 18. Grid voltage compensation from both converters is shown in Fig. 19. Table 3 shows the proposed algorithm parameters

A comparison of the proposed Cuk converter and the existing SEPIC converter is shown in Fig. 18. From the comparison, the proposed converter’s settling and rise time were better than in the QRSEPIC. The QRCC output voltage was 450V and the SEPIC voltage was 400V. Both PV converters’ input voltages were 300V. Fig. 19 shows the grid voltage THD comparison. Using the QRCC, the THD was minimized at 0.678%, and the QRSEPIC was 0.832%. From the figures, we clearly see that the QRCC is better than the QRSEPIC.

Fig. 12. ZVT soft switching.

Fig. 13. ZCT soft switching.

Fig. 14. Output Voltage of the QRCC.

Fig. 15. Output Current of the QRCC.

Fig. 16. Grid Voltage.

Fig. 17. Grid Current.

Fig. 18. Converter Voltages.

Fig. 19. Grid Voltages.

Table 2. THD and Efficiency Comparison.

Control technique	Kp	Ki	THD (%)	Efficiency (%)
Without PI controller	-	-	40.68	79
With PI controller	2	0.76	29.83	89
HHO	1	0.65	0.678	99.30

Table 3. Parameter values for the algorithm.

HHO parameters
Parameter	Value
Number of rabbits	30
Number of iterations	500

Table 4. Techniques for switching THD [28-31].

No.	Technique	THD (%)
1	PSO-based SHE-PWM	4.46
2	Parallel algorithm	4.71
3	MGWO-PI-PWM	6.51
4	PI-HHO (SEPIC converter)	0.812
5	HHO- PI	0.678

5. Conclusion

This paper presented a quasi-resonant Cuk converter based on a voltage source inverter control. Switching losses in this converter are reduced by adopting soft switching techniques. The proposed VSI is based on applying an optimization technique to minimize the objective function. As a result, the objective function that needs to be minimized is associated with THD. Simulation studies were carried out with MATLAB/Simulink for photovoltaic systems, and the inverter based HHO gave better results than other optimization techniques. The proposed method achieved 99.30% efficiency and reduced THD to 0.678%, compared to PI-controller and HHO techniques. Therefore, switching losses are reduced, and compared to existing work, efficiency and system performance are improved as well.

Future work: In future, this work will be extended to compare ZETA converters.