**1. Introduction**

Solar energy is free and abundant [1]. Environmental concerns are widely reduced by using solar energy for power generation. Therefore, the photovoltaic (PV) energy is becoming the most emerging and promising solution to address environmental problems. Generally, the e fficiency of solar PV energy conversion using PV panels is low [2], and therefore, many researchers are working on improving the e fficiency and output energy yield [3]. Factors that may a ffect the conversion e fficiency generally include the e ffect of soiling, dirt and dust, elevated temperature, and sudden irradiance changes [4]. Similarly, the output power produced by PV arrays is remarkably reduced due to partial shading conditions [5,6]. Partial shading is generally induced over a PV module, string, or on a whole small PV system. It is due to cloud shadows, dust, permanent cracks on shields or surfaces; as well as shade due to various structures including trees, leaves, and buildings or towers [7]. Partial shading causes a reduction in the irradiance, and also distributes irradiance in a non-uniform pattern over the surface of various PV modules in an array [8,9]. Hence, the current from the PV array is constrained by the shaded PV modules, which in turn is detrimental for the other healthy PV modules connected in the series [10]. Consequently, in practice, a parallel-connected diode termed as a bypass diode (*D*1 and *D*2) is installed across it to minimize the e ffects of mismatching, as shown in Figure 1a. During mismatching, this bypass diode will be ON and the current starts flowing through it (as shown in Figure 1b). In this case, various maximas appear on the power–voltage (P–V) characteristics. These

multiple peaks are known as local maxima's, as examplified in Figue 1c. When multiple peaks are present, the conventional maximum power point techniques (MPPTs) may not work accurately. Therefore, a global maximum power point technique (GMPPT), capable to distinguish between local and global maxima is generally needed to maximize the overall output power from the array. In the literature, many conventional MPPT techniques have been presented and their behavior on partial shading conditions is analyzed [11–13]. Various artificial intelligence techniques including fuzzy logic [14,15], neural networks [16], and genetic algorithms [17] are generally employed to track the global maximum power point (GMPP). However, these techniques have limitations and exhibit false tracking over varying conditions of irradiance and temprature. Furthermore, the convential MPPT methods should be retrofitted with more sensoring and control requirements [18,19].

**Figure 1.** A PV module (M1 and M2) with parallel-connected bypass diodes *D*1 and *D*2: (**a**) schematic diagram, (**b**) schematic showing the current flow direction while shaded and bypassed [19], (**c**) P–V characteristic of series-connected two PV modules while one is shaded (mismatching occurs). Here, *Ib* is a bypass current through *D*1.

In addition to developing advanced MPPT algorithms, an alternative is to directly mitigate the local peaks under partial shading. Differential power processing (DPP) converters [20–25] are typical representatives, that enable each PV module to produce maximum output power. DPP converters eliminate the problem of multiple maximas in the PV string, as highlighted in Figure 2. In addition, Figure 3a further exemplifies one DPP configuration known as the PV–PV voltage balance converter [20]. This PV–PV converter only processes the mismatched power and thus, it is used in this paper. The working principle of the PV–PV DPP is shown in Figure 3b,c, where the PV module M1 is shaded and the PV module M2 in the non-shaded mode. *IL* is a mismatch current, which passes through the inductor *L*. The transistors *Q*1 and *Q*2 operate complementarily to each other. Nevertheless, the switching will induce power losses that can be found as [20]

$$P\_{SWLOSS} = 2k\_0 \left[ V\_G \sqrt{\frac{V\_G}{2V\_B}} + 4V\_D I\_L \sqrt{\frac{V\_D}{V\_B}} \right] f\_{SW} \tag{1}$$

in which *k*0 is a material property dependant device constant, *VB* is the breakdown voltage of the device, *VD* is the voltage at the device terminal, *VG* is the voltage at the gate terminal, *IL* is the current passing through the inductor, and *fsw* is the switching frequency of the power device. The PV–PV DPP topology is based on the switched-inductor between two PV modules. Therefore, it is named as switched-inductor (SL)-based topology. The SL-based topology can be represented by a simplified model as illustrated in Figure 4. To have the same voltage (i.e., *V*1 and *V*2) across both PV modules, the value of effective impedance *Z*EFF should be minimum. However, practically it is unavoidable to have zero value of *Z*EFF but since the value of *Z*EFF is frequency dependent. Therefore, it is possible to achieve the minimum value by operating the converter at frequencies near to the resonant frequency.

**Figure 2.** PV modules (M1 and M2) with parallel-connected DPP topologies: (**a**) schematic diagram when M1 is shaded and (**b**) P–V characteristic of series-connected two PV modules during mismatching and no mismatching.

**Figure 3.** Switched-inductor (SL)-based PV–PV voltage balance converter [20]: (**a**) schematic diagram containing two series-connected PV modules M1 and M2 without shading; (**b**) M1 is shaded, where *Q*1 is ON and *Q*2 is OFF; and (**c**) M1 is shaded and *Q*1 is OFF and *Q*2 is ON. Here, *IL* is a current passing through an inductor *L*.

**Figure 4.** Equivalent circuit for the SL-based DPP technique. Here, *Z*EFF is the effective impedance, *V*1, and *V*2 are the voltages across the PV module M1 and M2, respectively.

Moreover, another important factor to consider in the design of the SL-based topology is the quality factor *Q*, which is given by expression (2)

$$Q = \left(1/R\_{ESR}\right)\sqrt{L/C} \tag{2}$$

where *L* is the inductance shown in Figure 3 and *C* is the stray capacitance, which can be neglected as its value is very small. For practical reasons and to have adequate voltage stress across inductor *L*, the value of *Q* is selected in the range of 1–10 and the switching frequency is selected as 50 kHz.

The value of switching frequency is selected closer to the resonant frequency in order to have a minimum value of *Z*EFF. For better understanding, *Z*EFF can be considered as a series LC network whose impedance versus frequency curve is shown in Figure 5, which can be calculated by using (3). At lower frequencies (below resonant frequency), the topology behaves as overall capacitive. However, as the frequency increases, the value of *Z*EFF decreases to its minimum value at the resonant frequency where the impedances of *L* and *C* cancels each other. Similarly, beyond the resonant frequency and at higher frequencies, the nature of *Z*EFF is overall inductive. Therefore, the value of switching frequency is selected in the vicinity of resonant frequency to achieve a minimum value of *Z*EFF, which will, in turn, equalizes the voltages of PV modules in a system. Moreover, the value of switching frequency is selected to be higher than the resonant frequency to achieve soft-switching operation for all the switches, which can minimize the switching power loss.

**Figure 5.** A curve showing the variation of impedance with frequency for a series resonant circuit.

$$|X| = |X\_L| - |X\_C|\tag{3}$$

where *X*L is the inductive impedance and *X*C is the capacitive impedance.

The power losses during partial shading are dependent upon the patterns of shading. Various schemes have been presented in the literature to minimize the detrimental effects caused by non-uniform shading [26]. One possibility is to reconfigure the interconnection PV modules in case if there is partial shading. The most commonly used interconnection scheme for PV arrays is series-parallel (SP). Configurations like the bridge-linked (BL), central-cross-tied (CCT), and total-cross-tied (TCT) (see Figure 6) can also be adopted to minimize the mismatching effect due to partial shading [27]. Although, it has been reveailed that the TCT configuration yields maximum power for conventional bypass technique [28], more attempts have been made to mitigate the effects of partial shading using SP configurations due to its simplicity [29]. Using TCT enhances the longevity of the PV module with an estimated increase in a lifetime by 30% [30]. Alternately an electronic array reconfiguration scheme abbreviated as EAR has been proposed, which may modify the interconnection pattern of modules using electronic switches. In EAR, during operation and the decision of reconfiguration is based upon the pattern of shading, while control is achieved using a switch matrix [31]. The electrical reconfiguration using switches and relays, which can be effectively realized for small systems. However, for large PV arrays in solar parks, etc., the electronic switches, their interaction, and controllability becomes complex and difficult to handle due to the constraints of switching [32]. Similarly, another technique termed as disperse interconnection scheme (SDS) for multiple PV modules in an array has been presented in [33]. This technique is also based on changing the electrical configuration of the modules in the PV array. This technique has superior output yield in comparison to other interconnection schemes as discussed in [29]. However, cost and complexity associated with the changing connections in large PV arrays can be cumbersome, and the overall system yield may become infeasible [29]. Therefore, various aspects by including efficiency and cost must be carefully considered for the optimal system design. A static reconfiguration is considered effective over other dynamic interconnection techniques [23]. The static reconfiguration technique does not involve the dynamic change of interconnection. It is based upon the one-time constant arrangemen<sup>t</sup> of PV modules with predefined interconnection settings in an array under different partial shading conditions [34,35]. Different interconnection topologies, which are discussed above—namely, SP, BL, and TCT for PV arrays—have been proposed. These interconnection schemes are tested by using intelligent power electronics to minimize power losses due to mismatch. The power electronic-based technique replaces the shunting bypass diodes, which are generally connected in parallel to PV modules in the array.

**Figure 6.** PV array topologies: (**a**) series-parallel (SP), (**b**) total-cross-tied (TCT), (**c**) central-cross-tied (CCT), and (**d**) bridge-linked (BL).

The performance analysis of above-mentioned interconnection schemes has been widely discussed with traditional bypass diodes in the literature so far. However, when DPP converters have adopted the performance of those configurations has not ye<sup>t</sup> been explored. Therefore, in this paper, the four array interconnection schemes—i.e., the SP, TCT, CCT, and BL configurations with SL-DPP—are tested under different patterns of shading and irradiance. The performance of proposed schemes (SL-based interconnection schemes) is evaluated by introducing different shading patterns and its comparison with state of the art topology, i.e., bypass diode (for comparative analysis). This study uses a 4 × 4 PV array of system, which has a size of 968 W. The output power and mismatch losses under various shading patterns with SL-DPP and bypass diodes are presented. The organization of the rest of the paper is given below. Section 2 introduces the different interconnection configurations and shading pattern designs. Section 3 outlines various important results and based upon the highlighted results conclusions are outlined in Section 4.

#### **2. Configurations and Shading Pattern Designs**

The four interconnection schemes—i.e., the SP, TCT, CCT, and BL configurations—are compared at di fferent shading patterns for the 4 × 4 PV array. The PV array with these configurations using DPP converters and bypass diodes are evaluated. The rating of PV modules is given in Table 1. The rated maximum output power from the 4 × 4 PV system is 968 Watt at 1000 <sup>W</sup>/m<sup>2</sup> and STP. Di fferent types of shading patterns including, one module shading, short wide, long narrow shading, central shading, and diagonal shading are applied at all above discussed interconnection schemes on 4 × 4 PV array at di fferent irradiances, as shown in Figure 7. The variations in irradiance from 200 <sup>W</sup>/m<sup>2</sup> to 800 <sup>W</sup>/m<sup>2</sup> with a di fference of 100 <sup>W</sup>/m<sup>2</sup> is considered to compare the performance of SL-based DPPs with conventional parallel-connected bypass diodes. Various shading pattern designs for PV array configuration schemes are as follows.


**Table 1.** Specification of the PV module at STC (1000 <sup>W</sup>/m<sup>2</sup> and 25 ◦C).
