## 1. Introduction

The use of renewable energies, especially solar energy, is increasing due to environmental problems caused by fossil fuels. For commercial use of solar energy, reducing cost and system size and also improving output power efficiency are among the significant challenges [

1,

2]. Photovoltaic systems are used in both standalone and grid-connected applications [

3,

4,

5]. Two main structures of the grid-connected photovoltaic strings are shown in

Figure 1 and

Figure 2 [

6,

7]. In a centralized structure, multiple photovoltaic (PV) strings are connected in parallel to make an array, and then, the PV array is connected through a DC/DC converter and an inverter as a power conditioning system (PCS) to the grid [

8,

9,

10]. In

Figure 2, each string with associated PCS makes one AC module, and then AC modules work together in parallel. The parallel structure in

Figure 2 has the following advantages compared to the centralized one of

Figure 1 [

11,

12]:

- (1)
Less time and cost are needed for developing the high-power PV system; also, it is more flexible.

- (2)
It is more reliable because if the DC/AC converter is interrupted in the centralized structure, the whole system will interrupt.

PCS unit must firstly harvest the maximum power of the PV string, which can be extracted under specific temperature and weather conditions and, secondly, inject power to the grid and control the grid current to be sinusoidal [

13]. Nonlinear characteristic of PV modules, unpredictable weather conditions, and changing the grid working modes and parameters affect the PCS performance [

3,

8].

Two-stage PCS structures, including a DC/DC converter and an inverter, are widely used in the PV industry [

9]. The DC/DC converter is usually a step-up voltage converter that must track the maximum power point (MPP) of the PV array. The inverter is used for injecting the power to the grid. Currently, leading companies in the PV industry such as ABB and Schneider introduce an integrated PCS system with several inputs for PV strings wherein DC/DC converters are working in parallel, and then, one inverter is responsible for injecting power to the grid [

14,

15]. Industrial solar string inverters show acceptable performance in real projects in terms of tracking MPP tracking (MPPT) and meeting the grid codes in the AC side. However, their reliabilities are low, since the operation of the whole PCS depends on the inverter.

Single-stage PCSs have been proposed to reduce cost, increase efficiency, and prevent using complex hardware and control strategies [

16,

17]. A single-stage buck-boost inverter called impedance (Z-) source inverter (ZSI) has been proposed as a good candidate for PV applications. ZSI benefits from the high voltage gains, short-circuit protection, high power quality due to no deadtime, and less sensitivity to electromagnetic interference (EMI) [

17,

18]. The basic hardware design of PV system based on ZSI was explained by Hani in [

19], and various control methods such as multi-loop control scheme have been presented based on proportional–integral (PI) and proportional–resonant (PR) controllers [

13,

20,

21], sliding-mode control [

22], model predictive control [

23], and the adaptive backstepping approach [

24] have been applied to ZSI to improve the MPPT performance and enhance the transient response of the exchanged power with the grid and the quality of the grid current. The PI controller is used for controlling variables in DC side because of its capability to track the DC signals. The PR controller is able to track variables in AC side of PCS with zero steady-state errors, but it could not follow the DC reference, and it is sensitive to DC noise in the feedback loop [

24]. Sliding-mode and model predictive controllers provide high performance in MPP tracking and injecting standard current to the grid; however, their accuracy depends on the ZSI and PV modelling and parameters [

25].

Considering the advantages of ZSI, this paper presents a dual-input parallel PV system based on two ZSIs. Parallel ZSIs were already used for microgrid and uninterruptible power supply applications in [

26,

27,

28,

29] but have not been utilized for grid-connected PV applications yet. Previous structures of the parallel Z-source inverters either are independently working and only a slow outer control is used to coordinate them in [

29] or only have input in the DC side in [

27,

28,

30]. In this paper, however, parallel ZSIs are considered as a unified system with two DC inputs and one AC output. Additionally, only one control system, like a typical industrial multi-string PV system with DC/DC converters and inverters, is responsible of controlling both ZSIs. To realize this idea, the principle operation of parallel ZSI is explored in this paper, and a multi-loop control scheme consisting of DC side and AC side controllers is developed to control ZSIs. At the AC side, PI controllers compute the amplitude of grid current to regulate the voltages of the capacitors in ZSI networks. This approach indirectly controls the peak value voltage in the DC link. Besides, a proportional, multi resonant (PmR) controller is developed to control the grid current with a fast-transient response and zero steady-state error under normal and distorted grid voltages. At the DC side, an enhanced dual string MPPT (eDS-MPPT) is proposed to compute the shoot-through duty ratio to regulate the output voltage of the PV arrays and harvest the maximum available power. The eDS-MPPT is derived from the MPPT method, which was proposed in [

31,

32] for buck converters. This method, unlike conventional methods such as perturb and observe (P&O) [

33,

34], incremental conductance [

35,

36], neural network, and fuzzy logic [

37,

38], does not require measurement of PV modules voltages, power calculation, and memory for information storage; only the currents of the PV strings are used to determine MPPs through cross-referencing. In summary, the paper’s novelties are as follows:

- -
Using parallel ZSIs as single-stage power conversion system for multi-string PV systems.

- -
Proposing an effective control to perform MPPT and to inject high-quality current to the grid.

- -
Suggesting enhanced dual-string maximum power point tracking (eDS-MPPT) to reduce computational burden and to remove the need for using PV strings voltage sensors.

The remainder of the paper is organized as follows. In

Section 2, the configuration of the proposed system is introduced. The proposed control scheme and eDS-MPPT are presented in

Section 3. The simulation results are shown in

Section 4. Finally,

Section 5 concludes the paper.

## 2. Proposed Topology

The proposed configuration is shown in

Figure 3. This structure includes two AC modules; each of them has a PV string and a ZSI connected to the grid through an inductor. A typical microcontroller can be used to control both ZSIs simultaneously where the control scheme uses grid voltage, ZSI outputs currents, capacitor voltages of the ZSI network, and PV string currents for MPPT and exchanging with the grid.

Each ZSI includes the Z-source X shape and symmetrical network (C, L) and full-bridge inverter (S

_{1}–S

_{4}) [

11]. The conventional voltage source inverter (VSI) has two zero vectors and two active vectors. In the ZSI, a shoot-through vector is added to these vectors. A DC terminal of the inverter bridge,

u_{in}, is short-circuited through upper and lower switches of one or two legs in shoot-through mode. The shoot-through vector creates voltage boost capability for the ZSI, and this inverter would be able to produce the desired AC voltage despite variations of the DC voltage source [

39].

If the equations governing the Z-source network are written in shoot-through and non-shoot-through modes, then

u_{in} can be described as follows [

40]:

in which

V_{pv} is the PV string output voltage,

B is the boost coefficient, and

i indicates the ZSI’s number. The

B value is determined as follows:

If

T_{0} is the shoot-through vector interval in each switching period

T, then the shoot-through duty cycle,

D_{0}, will be calculated as:

In theory, the steady-state shoot-through duty ratio

D_{0} in Equation (3) can be between 0 and 0.5; however, it should be limited in practice by the zero-vector interval to avoid output voltage distortion. The peak value of output AC voltage

u_{i} and capacitor voltages can be expressed related as follows [

41]:

where

M is the modulation index.

The ZSI gain (G) is drawn based on the shoot-through duty cycle and the modulation index in

Figure 4, wherein ZSI with having two control inputs,

M and

D_{0}, can produce any voltage in the AC side. On the other hand, VSI with only one control variable

M, as a buck converter, can only generate AC voltage less than DC link voltage, and using a DC/DC converter is mandatory between PV array and VSI [

29,

42].

Figure 5 and

Figure 6 show the principle and implementation of the simple boost PWM method (SB-PWM) for switching of ZSI. The AC output voltage of ZSI is produced based on

V_{ref}, and the boost coefficient (B) is controlled by

U_{sc}.

U_{sc} and

-U_{sc} are two straight lines, which are used as shoot-through signals in this method. When a carrier wave (CW) is larger than

U_{sc} or smaller than

-U_{sc}, a shoot-through vector is created for ZSI. The

U_{sc} value is equal to:

## 4. Simulation Results

For verifying the performance of the proposed system, the system of

Figure 3 is simulated in MATLAB/SIMULINK. In the simulations, two photovoltaic strings are connected to a 110 V, 50 Hz grid through the ZSIs. The ZSIs parameters are given in

Table 1, and each ZSI is interfaced to the grid through a 1 mH inductor. The parameters of PV strings are listed in

Table 2. A 110 uF capacitor is installed in parallel to each PV string to reduce the level of PV current ripple and low-frequency voltage ripples. The controllers are tuned to ensure the best performance in the steady-state and transient situations, and their parameters are listed in

Table 3. The sampling period of the simulation is set 2 µs and switching frequencies of both ZSIs are 20 kHz. Since the DC link voltage of ZSI,

V_{in}, must be enough higher than the peak value of grid voltage (156 V), the reference of capacitor voltage is selected 170V. Therefore,

V_{in} and modulation index of ZSI will be regulated around 240 V and 0.65, respectively.

As shown in

Figure 10, the solar irradiance is changed from 1000 W/m

^{2} to 300 W/m

^{2} and vice versa for investigating the MPPT method performance. For evaluating the control scheme, both the ideal grid with sinusoidal voltage and distorted grid with high values of harmonics are considered. The grid voltage is considered sinusoidal until t = 1.2 s and then 10% of fifth and seventh harmonics, equal to total harmonic distortion (THD) of 14%, is added to the grid voltage. It is evident in

Figure 10 that both ZSIs inject active power (P) under solar irradiance changes, and the exchanged reactive powers (Q) with the grid are regulated around zero, i.e., unity power factor operation.

The instantaneous and filtered (average) values of voltage, current, and power of PV strings are presented in

Figure 11. Since ZSIs are connected to a single-phase grid, all variables have typical 100 Hz ripples [

47].

Figure 11 shows that ZSIs with the eDS-MPPT method accurately harvest the maximum powers of PV strings where the peak values of powers are close to MPP values (

P_{MPP} = 1600 W) and static MPPT efficiency is around 93.4%. The PV strings’ voltages do not change dramatically in

Figure 11a,d, but the strings’ currents have changed in proportion to the solar irradiance in

Figure 11b,e. Therefore, the presented results in

Figure 11 proved the performance of the proposed PCS with eDS-MPPT in absorbing maximum power from PV strings.

Figure 12 is presented to evaluate the adequacy of the proposed PCS in injecting high-quality currents to the grid. The injected currents are kept sinusoidal and in phase with the grid voltage for both sinusoidal and distorted grid voltages. As an example, the harmonic spectrum of the ZSI1 current is displayed in

Figure 13. It is observed that THD of current is around 3.2%, and all current harmonic components are less than 0.6%. Therefore, the tuned PmR controller has a highly desirable performance, and the ZSI currents comply with the power quality requirements of IEEE 1547 [

48].

The capacitors voltages,

V_{c}_{11} and

V_{c}_{21}, and DC link voltages of the Z-source networks,

u_{in}_{1} and

u_{in}_{2}, are shown in

Figure 14. It can be observed that the voltages of the capacitors are accurately controlled around their voltage references at 170 V. In this system, the DC link voltages jump to zero during shoot-through time intervals to track MPPs, as mentioned in

Section 3.2.

Figure 15 demonstrates the effectiveness of eDS-MPPT for unequal solar irradiances. Until t = 0.5 s, the solar irradiances of both strings are the same, 1000 W/m

^{2}, and then, the solar irradiance for string 2 steps down to 800 W/m

^{2}, while that of string 1 is still 1000 W/m

^{2} (see

Figure 15a). It can be seen from

Figure 15b,c that the maximum value of string 1 power is around 1600 W in the whole simulation, while the respective value of power string 2 reduces from 1600 to 1260 W (the expected value is 1300 W) at t = 0.5 s in response to the solar irradiance change. These results show that eDS-MPPT can track MPP in case of unequal solar irradiances with static MPPT efficiency around 91.1%.

In summary, the proposed parallel ZSIs as a single-stage PCS has fewer numbers of semiconductors compared to conventional PCSs. The proposed control scheme injects a low THD current with unity power factor to the grid with both sinusoidal and distorted grid voltages. On the other hand, the static MPPT efficiency of the proposed PCS with eDS-MPPT for equal and unequal solar irradiances is around 93.4% and 91.1%, respectively. Last but not least, this method reduces two voltage sensors compared to other PCSs. Therefore, it is a suitable candidate for multi-string PV systems.