A Simple Mismatch Mitigating Partial Power Processing Converter for Solar PV Modules

: Partial shading affects the energy harvested from photovoltaic ( PV ) modules, leading to a mismatch in PV systems and causing energy losses. For this purpose, differential power processing ( DPP ) converters are the emerging power electronic-based topologies used to address the mismatch issues. Normally, PV modules are connected in series and DPP converters are used to extract the power from these PV modules by only processing the fraction of power called mismatched power. In this work, a switched-capacitor-inductor ( SCL )-based DPP converter is presented, which mitigates the non-ideal conditions in solar PV systems. A proposed SCL -based DPP technique utilizes a simple control strategy to extract the maximum power from the partially shaded PV modules by only processing a fraction of the power. Furthermore, an operational principle and loss analysis for the proposed converter is presented. The proposed topology is examined and compared with the traditional bypass diode technique through simulations and experimental tests. The efﬁciency of the proposed DPP is validated by the experiment and simulation. The results demonstrate the performance in terms of higher energy yield without bypassing the low-producing PV module by using a simple control. The results indicate that achieved efﬁciency is higher than 98% under severe mismatch (higher than 50%). comparison


Introduction
Energy production from coal and other fossil fuels leads to environmental hazards. Therefore, it is important to develop other various kinds of environmentally-friendly energy technologies. In recent years, energy production from renewable sources like solar energy has shown significant progress [1]. Compared to other energy resources, solar photovoltaic (PV) energy has grown at the highest rate. By 2023, the total installed PV capacity is expected to reach around 600 GWp [2,3].
Normally, PV systems compromise series-connected PV modules, and these systems are connected to converters, which are responsible for the extraction of maximum power out of the incident light energy, and transfer the energy from the PV modules to the load. The output power from PV modules is sensitive to non-ideal conditions such as dirt, manufacturing irregularities, thermal variations, aging, shadows, along with module placement orientations and angle of incidence. All these factors may induce a power mismatch in a PV system, which impacts the overall output and life of the PV system [4][5][6][7].
Normally, a PV module consists of 3-4 submodules, which are connected in series. Each of these submodules further consists of 20-24 series-connected PV cells [8]. In series, the power generated by these cells should be the same, otherwise it causes a mismatch. This mismatch is due to different amounts of currents produced by the series-connected PV cells. However, the current must be the same in series. Therefore, the extra-power generated by non-shaded panels starts to dissipate across the shaded cell, which is acting as a load to non-shaded cells. Hence, the dissipation of power due to the shaded cells also increases the temperature of these cells known as hotspots [9], which affects the long-term reliability of such cells [10][11][12][13][14].
In the commercial PV modules, a parallel-connected bypass diode is installed with each submodule, as shown in Figure 1a. This bypass diode reduces the mismatch effect under partial shading or other non-idealities, which are discussed above. When there is no mismatch, bypass diodes remain OFF and the same current I mod conducts through all submodules, as depicted in Figure 1b. If a mismatch occurs, the parallel-connected bypass diode turns ON due to the appearance of a negative voltage across the shaded PV submodule, and this shaded PV submodule is bypassed by that ON-state diode, as exemplified in Figure 1c. A current I by starts to flow through this bypass diode. However, the bypassed submodule causes a voltage mismatch, which results in several power peaks. Hence, the conventional maximum power point tracking (MPPT) algorithms are generally unable to distinguish between local and global maxima in the power-voltage (P-V) curve of PV systems, which also impacts the performance of the whole PV system. Therefore, global maximum power point tracking (GMPPT) algorithms are required to identify the global peak [15][16][17][18][19].
Energies 2021, 14, 2308 2 of 18 PV cells. However, the current must be the same in series. Therefore, the extra-power generated by non-shaded panels starts to dissipate across the shaded cell, which is acting as a load to non-shaded cells. Hence, the dissipation of power due to the shaded cells also increases the temperature of these cells known as hotspots [9], which affects the long-term reliability of such cells [10][11][12][13][14].
In the commercial PV modules, a parallel-connected bypass diode is installed with each submodule, as shown in Figure 1a. This bypass diode reduces the mismatch effect under partial shading or other non-idealities, which are discussed above. When there is no mismatch, bypass diodes remain OFF and the same current Imod conducts through all submodules, as depicted in Figure 1b. If a mismatch occurs, the parallel-connected bypass diode turns ON due to the appearance of a negative voltage across the shaded PV submodule, and this shaded PV submodule is bypassed by that ON-state diode, as exemplified in Figure 1c. A current Iby starts to flow through this bypass diode. However, the bypassed submodule causes a voltage mismatch, which results in several power peaks. Hence, the conventional maximum power point tracking (MPPT) algorithms are generally unable to distinguish between local and global maxima in the power-voltage (P-V) curve of PV systems, which also impacts the performance of the whole PV system. Therefore, global maximum power point tracking (GMPPT) algorithms are required to identify the global peak [15][16][17][18][19]. Recently, active mismatch mitigation techniques based on power electronics have been developed for PV systems, as categorized in Figure 2 [20][21][22][23][24][25][26]. In Figure 2, the distributed maximum power point tracking (DMPPT) systems, which consist of microconverters, have been developed to resolve the mismatch problems [27][28][29]. In the  In the search for a more effective solution, the differential power processing (DPP) converters are found to be a more viable solution. DPP converters usually use a ladder-based architecture, which has been previously explored in the battery voltage equalization [31][32][33], multicore CPU power delivery [34], and other PV applications [35][36][37][38]. In solar PV installations, DPP topologies have been found to be effective for the mitigation of the mismatch effects. When DPP converters are compared to the other power electronic-based solutions, these converters process only a fraction of power known as mismatched power. There exist a few DPP-based architectures in the literature [39][40][41] and these architectures are commonly divided into three categories, i.e., (a) PV to the non-isolated bus [37,42], (b) PV to the isolated bus [37,43], and (c) PV-PV DPP converters [37,42], as presented in Figure 2.
(a) In the first category [37,42], the secondary sides of the central inverter and the DC bus are connected in parallel and they share the same voltage. Furthermore, the switching devices on the secondary side of the module-level DC-DC converter experience high voltage stress, as the DC-bus voltage is the summation of all the PV module output voltages [44]. (b) The second category [37,43], which is known as an isolated bus, is formed by connecting the secondary ports of DC-DC converters in parallel. The selection of DCbus voltage in PV to an isolated bus DPP converter topology enhances the complexity of the design, as it can be selected independently from the PV module voltage. Also, in (a) and (b), the size and power loss increase due to the presence of more components along with the cost. (c) Lastly, the third DPP, which is known as the PV-PV DPP converter [42,45] are nonisolated DPP architectures, which can be built cost-effectively through modular combinations. These PV-PV DPP converters draw power from adjacent PV modules. The general structure of PV-PV DPP is shown in Figure 3. Moreover, this topology has one less power converter than the number of PV modules, i.e., one less PV-PV DPP converters is required than the total number of PV modules. The main benefit of this architecture is that its converters are designed according to the voltage characteristics of the PV module rather than that of the main bus voltage. Therefore, the PV-PV DPP converter is independent of bus voltage and need not withstand the high voltage stresses. PV-PV DPP converters are emerging DPP topologies, which are improving continuously in terms of performance, cost, and reliability [42,46].
In continuation, many attractive PV-PV DPP topologies are presented in the literature, i.e., energy recovery [47], buck-boost [35,48]  In the search for a more effective solution, the differential power processing (DPP) converters are found to be a more viable solution. DPP converters usually use a ladder-based architecture, which has been previously explored in the battery voltage equalization [31][32][33], multicore CPU power delivery [34], and other PV applications [35][36][37][38]. In solar PV installations, DPP topologies have been found to be effective for the mitigation of the mismatch effects. When DPP converters are compared to the other power electronic-based solutions, these converters process only a fraction of power known as mismatched power. There exist a few DPP-based architectures in the literature [39][40][41] and these architectures are commonly divided into three categories, i.e., (a) PV to the non-isolated bus [37,42], (b) PV to the isolated bus [37,43], and (c) PV-PV DPP converters [37,42], as presented in Figure 2.
(a) In the first category [37,42], the secondary sides of the central inverter and the DC bus are connected in parallel and they share the same voltage. Furthermore, the switching devices on the secondary side of the module-level DC-DC converter experience high voltage stress, as the DC-bus voltage is the summation of all the PV module output voltages [44]. (b) The second category [37,43], which is known as an isolated bus, is formed by connecting the secondary ports of DC-DC converters in parallel. The selection of DC-bus voltage in PV to an isolated bus DPP converter topology enhances the complexity of the design, as it can be selected independently from the PV module voltage. Also, in (a) and (b), the size and power loss increase due to the presence of more components along with the cost. (c) Lastly, the third DPP, which is known as the PV-PV DPP converter [42,45] are nonisolated DPP architectures, which can be built cost-effectively through modular combinations. These PV-PV DPP converters draw power from adjacent PV modules. The general structure of PV-PV DPP is shown in Figure 3. Moreover, this topology has one less power converter than the number of PV modules, i.e., one less PV-PV DPP converters is required than the total number of PV modules. The main benefit of this architecture is that its converters are designed according to the voltage characteristics of the PV module rather than that of the main bus voltage. Therefore, the PV-PV DPP converter is independent of bus voltage and need not withstand the high voltage stresses. PV-PV DPP converters are emerging DPP topologies, which are improving continuously in terms of performance, cost, and reliability [42,46]. contains an explicit analysis along with the experimental testing to describe the operation of the SCL DPP topology. The organization of the rest of this paper is given below. A conventional and state-of-the-art mismatch mitigation method, i.e., bypass diode topology is discussed in Section 2. The major features, working principle, and the power loss analysis of the proposed SCL topology are also detailed in Section 2. Section 3 presents the simulation results, which are compared with the bypass diode. In Section 4, experimental results are provided. Finally, Section 5 presents the conclusion of the work.

Conventional Mismatch Mitigation Method
Before introducing a proposed methodology, a traditional bypass diode solution is discussed. Their pros and cons are also presented during the discussion from the perspective of the mismatch effect. For this purpose, the experimental setup and the implementation findings are shown in Figure 4. During experiments, shading over a PV module is induced to create a mismatch by covering one of the cells from the 36 cells PV module shown in Figure 4a. Under one cell-shaded condition, the irradiance levels over the PV module are varied as 900 W/m 2 , 750 W/m 2 , and 500 W/m 2 . The P-V characteristics are obtained under these conditions, which is shown in Figure 4b. As observed in Figure  4b, the output power is reduced due to the bypassing of a submodule, which shows that the shading over a single PV cell can cause a bypassing of the whole PV sub-module, which consists of 12 series-connected PV cells. Additionally, the bypassed submodule has no contribution to the output power and the overall 150 W PV module has lost around 33% of its power due to shading over one PV cell when irradiance over the module is 900 W/m 2 . Therefore, it is highly desirable to extract the lost energy. Furthermore, the bypassed submodule becomes a cause of multiple power peaks due to the partial shading. Therefore, the proposed DPP technique is employed to extract the lost power due to the bypass diode method that is highlighted in the subsequent sections. In continuation, many attractive PV-PV DPP topologies are presented in the literature, i.e., energy recovery [47], buck-boost [35,48], and switched-capacitor (SC) topologies [45,[49][50][51]. For PV module-level applications, these DPP converters encounter several challenges such as high power conversion loss, voltage equalization, scalability, control structures, performance under severe mismatch (cell(s) or sub-module(s) that are completely blocked or there is irradiance difference between the shaded and non-shaded PV cells or sub-modules are around 70-80%) [7], and increased circuit component voltage stresses [46].
To overcome mismatch issues in the PV system, a simple concept based on a switchedcapacitor-inductor (SCL) is presented in this paper. The initial work containing the proposed concept was published in [52]. However, the presented circuit details and the analysis are not sufficient along with limited simulated results. Therefore, this work contains an explicit analysis along with the experimental testing to describe the operation of the SCL DPP topology. The organization of the rest of this paper is given below. A conventional and state-of-the-art mismatch mitigation method, i.e., bypass diode topology is discussed in Section 2. The major features, working principle, and the power loss analysis of the proposed SCL topology are also detailed in Section 2. Section 3 presents the simulation results, which are compared with the bypass diode. In Section 4, experimental results are provided. Finally, Section 5 presents the conclusion of the work.

Conventional Mismatch Mitigation Method
Before introducing a proposed methodology, a traditional bypass diode solution is discussed. Their pros and cons are also presented during the discussion from the perspective of the mismatch effect. For this purpose, the experimental setup and the implementation findings are shown in Figure 4. During experiments, shading over a PV module is induced to create a mismatch by covering one of the cells from the 36 cells PV module shown in Figure 4a. Under one cell-shaded condition, the irradiance levels over the PV module are varied as 900 W/m 2 , 750 W/m 2 , and 500 W/m 2 . The P-V characteristics are obtained under these conditions, which is shown in Figure 4b. As observed in Figure 4b, the output power is reduced due to the bypassing of a submodule, which shows that the shading over a single PV cell can cause a bypassing of the whole PV sub-module, which consists of 12 series-connected PV cells. Additionally, the bypassed submodule has no contribution to the output power and the overall 150 W PV module has lost around 33% of its power due to shading over one PV cell when irradiance over the module is 900 W/m 2 . Therefore, it is highly desirable to extract the lost energy. Furthermore, the bypassed submodule becomes a cause of multiple power peaks due to the partial shading. Therefore, the proposed DPP technique is employed to extract the lost power due to the bypass diode method that is highlighted in the subsequent sections.

Main Features and Qualitative Comparison with Other DPP Converter Topologies
There are many attractive PV-PV DPP topologies mentioned in Section 1 from the literature, i.e., energy recovery [47], buck-boost [35,48], and SC [45,[49][50][51]. For PV modulelevel applications, these DPP converters encounter several challenges such as high power conversion loss, voltage-equalization, scalability, control structures, performance under severe mismatch, and increased circuit component voltage stresses. For example, the energy recovery DPP topology [47] is suitable only for simple shading scenarios. Moreover, this topology has high power electronic conversion losses along with a large number of power electronic components. Besides, the complex control circuitry is also required to drive the active components in the energy recovery DPP topology. Another DPP topology, which is known as buck-boost topology, is presented in [35], which shows a significant performance degradation in the circumstances of higher levels of mismatch. Also, the switches have to stand with large voltage stresses (twice the proposed converter) in buck-boost DPP topology, which affects the long-term reliability of the active components. Therefore, switches with a high voltage rating are required for buck-boost DPP topology, which increases the size and price of the topology.
In continuation, the ladder-based SC DPP topologies are one of the most famous members of the adjacent PV-PV DPP class. In SC, the number of PV modules can be extended easily through modularly inter-connecting switches and capacitors. Many SCbased DPP topologies are presented in the literature [53][54][55]. Usually, the existed SC-based DPP topologies use additional active devices to process the mismatched power, especially during severe mismatch by introducing more switching states. These switching states make the control circuitry more complex. The most common SC topologies are resonant SC (RSC) [49], RSC gyrator [54,56], and simple SC [45]. In the RSC-based DPP topology [49], there are three modes of operation. Firstly, the resonant tank is charged while it discharges in the second mode of operation to release the energy that comes from a mismatch between series-connected PVs. Finally, in the last mode of operation, a short circuit is applied within the resonant tank to induce the requisite charge balance by discharging the residual energy. Notably, the operating switching sequences are important to obtain the desired output, which makes the circuit complex to control. Another SC-based DPP topology is presented in [22], which uses one inductor for four modules. Even when using one inductor, the circuit needs a high count of switching

Main Features and Qualitative Comparison with Other DPP Converter Topologies
There are many attractive PV-PV DPP topologies mentioned in Section 1 from the literature, i.e., energy recovery [47], buck-boost [35,48], and SC [45,[49][50][51]. For PV modulelevel applications, these DPP converters encounter several challenges such as high power conversion loss, voltage-equalization, scalability, control structures, performance under severe mismatch, and increased circuit component voltage stresses. For example, the energy recovery DPP topology [47] is suitable only for simple shading scenarios. Moreover, this topology has high power electronic conversion losses along with a large number of power electronic components. Besides, the complex control circuitry is also required to drive the active components in the energy recovery DPP topology. Another DPP topology, which is known as buck-boost topology, is presented in [35], which shows a significant performance degradation in the circumstances of higher levels of mismatch. Also, the switches have to stand with large voltage stresses (twice the proposed converter) in buck-boost DPP topology, which affects the long-term reliability of the active components. Therefore, switches with a high voltage rating are required for buck-boost DPP topology, which increases the size and price of the topology.
In continuation, the ladder-based SC DPP topologies are one of the most famous members of the adjacent PV-PV DPP class. In SC, the number of PV modules can be extended easily through modularly inter-connecting switches and capacitors. Many SCbased DPP topologies are presented in the literature [53][54][55]. Usually, the existed SC-based DPP topologies use additional active devices to process the mismatched power, especially during severe mismatch by introducing more switching states. These switching states make the control circuitry more complex. The most common SC topologies are resonant SC (RSC) [49], RSC gyrator [54,56], and simple SC [45]. In the RSC-based DPP topology [49], there are three modes of operation. Firstly, the resonant tank is charged while it discharges in the second mode of operation to release the energy that comes from a mismatch between series-connected PVs. Finally, in the last mode of operation, a short circuit is applied within the resonant tank to induce the requisite charge balance by discharging the residual energy. Notably, the operating switching sequences are important to obtain the desired output, Energies 2021, 14, 2308 6 of 18 which makes the circuit complex to control. Another SC-based DPP topology is presented in [22], which uses one inductor for four modules. Even when using one inductor, the circuit needs a high count of switching devices and diodes, i.e., for a system consisting of four series-connected PV modules, 8 switches and 10 diodes are required. Furthermore, during the charging and discharging phase of an inductor, only one combination of switches and diodes can work. Therefore, the optimal switching sequence has to be sought to extract MPP for non-ideal conditions (partial shading). During this process, the search for the most favorable switching state becomes difficult in several cases, which increases the computational time and control complexity. Therefore, effective tracking could not be guaranteed in rapidly changing environmental conditions. In order to overcome some of the challenges faced by existing DPP converters, the SCL-based DPP topology was proposed. This topology was derived from buck-boost and SC-based DPP topologies. Compared to buck-boost and SC-based DPP topologies, the proposed SCL topology has the following features: • a better performance under severe mismatching, • less inductor current ripple, • simple control circuitry, and • equalization of the series-connected PV submodule voltages.

Operational Analysis
The proposed topology has a ladder-based PV-PV architecture (see Figure 5). In this topology, a mismatched power is processed by the switched-capacitor C and inductor L. The SCL DPP topology has two operational modes and their equivalent circuits are depicted in Figure 5b,c. Four MOSFET devices (Q 1~4 ) are used during the operation, which is operating at a high frequency to distribute the mismatch charges equally between the submodules. These MOSFET devices are switched at a duty cycle of 50%. During the first cycle, Q 1 and Q 3 are switched OFF by keeping Q 2 and Q 4 in an ON-state, as demonstrated in Figure 5b. In the next cycle, the transistors Q 1 and Q 3 are switched ON while Q 2 and Q 4 are switched OFF, as shown in Figure 5c. The difference of the currents named as the mismatched current I L flows across the inductor L. The value of the current I L is maintained by the inductor L, which is represented in Figure 6a. Furthermore, the mismatch charges between SM1 and SM2 are distributed by the capacitor C in a way that the equalization of voltages is achieved at a submodule level with the proposed topology. Moreover, switching at a higher frequency allows maintaining the constant voltage on capacitor C. Additionally, the capacitor current is also shown in Figure 6b.
where IL is the mismatch current flowing across the inductor L, V2 is the voltage across the SM2, L is the value of the inductance, VC is the voltage across the switched-capacitor, and I1 is the current flowing across SM1.
In the next cycle, which is shown in Figure 5c, Q1 and Q3 are turned ON while keeping Q2 and Q4 in an OFF-state. In this scenario, the capacitor voltage VC and the current passing through SM2 can be represented by (3) and (4) where V1 is the voltage across the SM1.
Since the duty cycle for the proposed SCL-based DPP topology is fixed at 50%, the average mismatch inductor current IL is distributed equally into IS1 and IS2 (currents flowing through Q1, Q2, Q3, and Q4). The current following through the output and switches can be found by using (5) and (6). To further explain the operational principle of the proposed topology, a shade is applied on the submodule to induce the mismatch, as shown in Figure 5. Firstly, PV submodules are producing the same amount of energy. Hence, no mismatch power is processed by the converter. Now, if there is a power mismatch between SM1 and SM2, as shown in Figure 5, the proposed DPP converter starts to process and distributes the mismatched power between adjacent series-connected PV submodules through constant charging and discharging of the capacitor C. The schematic diagram of the equivalent SCL topology during mismatch is shown in Figure 5b,c, where voltages across SM1 and SM2 are represented as V 1 and V 2 , respectively. Considering the scenario of partial shading at SM1, the switching sequence and the associated equivalent circuit of the DPP converter are presented in Figure 5b,c. In the case when Q 2 and Q 4 are switched ON (Q 1 and Q 3 OFF), corresponding to Figure 5b, the differential current I L passes and charges the inductor L and a capacitor C. The voltage across the capacitor V C and the current I 2 flowing across SM2 can be mathematically represented by Equations (1) and (2) as below: where I L is the mismatch current flowing across the inductor L, V 2 is the voltage across the SM2, L is the value of the inductance, V C is the voltage across the switched-capacitor, and I 1 is the current flowing across SM1.
In the next cycle, which is shown in Figure 5c, Q 1 and Q 3 are turned ON while keeping Q 2 and Q 4 in an OFF-state. In this scenario, the capacitor voltage V C and the current passing through SM2 can be represented by (3) and (4) where V 1 is the voltage across the SM1.
Since the duty cycle for the proposed SCL-based DPP topology is fixed at 50%, the average mismatch inductor current I L is distributed equally into I S1 and I S2 (currents flowing through Q 1 , Q 2 , Q 3 , and Q 4 ). The current following through the output and switches can be found by using (5) and (6). I S1 = I S2 = I L 2 (5) where I out is the current flowing towards the output load.

Component Design
In general, there is a direct relationship between the inductor losses and the rootmean-square (RMS) inductor current ripple ∆I L . A high RMS current ripple results in a high-frequency RMS flux density and hence substantial core losses [57,58]. Furthermore, a high RMS current ripple (should be less than 5%) causes a high-frequency copper loss due to proximity and the skin effect. Therefore, the inductor current ripple ∆I L is a reasonable performance indicator for the design of the inductor, which should be as small as possible. On the other hand, the capacitance value should be large enough to limit the DC voltage ripple ∆V C to less than 5%. The inductance and capacitance can be calculated as where f sw is the switching frequency.

Power Loss Analysis
The loss of the DPP converter is briefly evaluated. The major power loss encountered in the proposed topology includes: (a) switching losses, (b) conduction losses, (c) losses in energy storage devices, and (d) leakage losses. Leakage losses are very small and therefore have been ignored in the analysis. Alternatively, remaining losses have been used to evaluate the performance of the proposed DPP. Firstly, the ON-state power loss (P on ) for the switches in the proposed topology can be calculated by where R on is the ON-state resistance of the MOSFETs and I Si(RMS) (i = 1 or 2) is the RMS value of mismatch current flowing across the switches while the switch is in an ON-state.
In each cycle, two MOSFETs are ON. Therefore, the ON-state losses are multiplied by a factor of 2.
A higher switching frequency f sw reduces the capacitor and inductor sizes. However, it enhances the switching losses [40]. At any switching instance, since two switches are involved, switching power losses (P swloss ) can be estimated as (10) (10) where i Si(tsw_on) is the instantaneous MOSFET current during the turn-ON, i Si(tsw_off) is the current during the turn-OFF, and t on and t off are the rise and fall time of the switch, which are mentioned in the datasheet. It can be seen from Figure 5 that I L always flows through L and C. Firstly, power losses of the inductor can be determined with the inductor's current (I L(RMS) ) and the inductor copper resistance R L at f sw . For the inductor L, the copper losses (P L_loss ) can be computed as P L_loss = I 2 L(RMS) R L ( f sw ). (11) Energies 2021, 14, 2308

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Once L is designed, the capacitor C is designed to be large enough for better charge distribution during mismatch. Similarly, for a capacitor C, the power losses (P C_loss ) can be calculated by P C_loss = I 2 L(RMS) R C ( f sw ) (12) where RC(f sw ) is the effective series resistance of C at f sw . Consequently, the overall power losses can be found by summing up all the losses in (9)- (12), which are given as P t = 2P on + 2P swloss + P L_loss + P C_loss (13) where P t is the total power loss. The overall loss evaluation for the proposed SCL-based DPP topology has been performed using (9)- (13), and the findings have been discussed in the subsequent sections.

Simulation Results
For the performance evaluation of the proposed SCL-based DPP topology, simulations are performed under various mismatch scenarios shown in Figure 7a. These mismatch cases are developed by varying the irradiance over the PV modules, i.e., E 1 for SM1 and E 2 for SM2. The rating of the used PV module is shown in Table 1. The converter is operating at a 50% duty cycle and the operating frequency is 100 kHz. The value of inductor L and a capacitor C are 100 µH and 50 µF, respectively by taking a consideration of the inductor current ripple ∆I L and capacitor voltage ripple ∆V C to be less than 5% according to (7) and (8).

• Scenario 1-No shading
During this scenario, there is no shading, SM1 and SM2 are producing the same amount of power. Therefore, the mismatch current I L between SM1 and SM2 is negligible, which can be seen from Figure 7b.

• Scenario 2-SM1 is shaded
The irradiance over SM1 is reduced to 500 W/m 2 , while it remains constant over SM2 to 1000 W/m 2 during this scenario. The simulation results are given in Figure 7b. In Figure 7b, the mismatch current I L is passing through the inductor. An average mismatch current is around 1.4 A.

• Scenario 3-SM2 is shaded
In this scenario, the irradiance over SM2 is reduced to 500 W/m 2 while it remains constant over SM1 to 1000 W/m 2 . The simulation results are shown in Figure 7b.
To further explain the operation of the proposed SCL-based topology, simulated results under scenario 2 are presented in Figure 8. In Figure 8, the current is flowing towards the output load (I out ) and PV modules (I 1 and I 2 ) in Figure 8a, inductor L (I L ) in Figure 8b, and MOSFET switches (I S1 and I S2 ) in Figure 8c,d during both operational states. For further assessment and evaluation, the performance of the SCL methodology in Figure 5 is compared with the conventional bypass diode method in Figure 1. For this purpose, several cases are developed and performed in PSIM, which are given in Table 2.
The simulation results are presented in Figures 9 and 10 for the traditional bypass diode and SCL-based DPP topology. In Figure 9, the P-V characteristics are shown under different mismatch cases. These mismatch cases are given in Table 2 by varying the irradiance (E 1 ) over SM1 (1000 W/m 2 , 750 W/m 2 , 500 W/m 2 , and 250 W/m 2 ) while keeping the irradiance (E 2 ) over SM2 constant (i.e., 1000 W/m 2 ) in Figure 5. In Figure 9, under these mismatch conditions, the proposed SCL-based DPP topology has achieved only one power peak while there are multiple peaks by using the conventional bypass diode method, as shown in Figure 9b-d. Therefore, the power is not fully extracted by the bypass diode methodology, but it is effectively extracted by the proposed SCL DPP topology. Overall, the results in Figures 9  and 10 have confirmed the effectiveness of the proposed DPP topology under non-ideal situations. Moreover, PV submodule voltages are also given in Table 3 under the similar mismatch conditions mentioned in Table 2. It may be observed that the proposed topology has equalized the voltages during all the mismatch cases. Therefore, the proposed topology requires a simple MPPT tracking algorithm.   In Figure 10, the maximum output power achieved from the proposed DPP topology and conventional bypass diode is shown. It is shown that the power achieved by using the proposed DPP is greater than using the traditional bypassing diode methodology during various mismatch cases mentioned in Table 2. Moreover, energy yield by the conventional bypass diode method during the mismatch cases 3 and 4 is similar (~45 W) and is significantly lower than the proposed DPP topology. During these cases, the conventional bypass diode method bypasses the low power-producing PV submodule. Therefore, the power is not fully extracted by the bypass diode methodology, but it is effectively extracted by the proposed SCL DPP topology. Overall, the results in Figures 9  and 10 have confirmed the effectiveness of the proposed DPP topology under non-ideal situations. Moreover, PV submodule voltages are also given in Table 3 under the similar mismatch conditions mentioned in Table 2. It may be observed that the proposed topology has equalized the voltages during all the mismatch cases. Therefore, the proposed topology requires a simple MPPT tracking algorithm.   (c) (d) Figure 9. P-V characteristics for the proposed topology under mismatch cases given in Table 2 Table 2.   Table 2  (c) (d) Figure 9. P-V characteristics for the proposed topology under mismatch cases given in Table 2 Table 2.   Table 2.
In Figure 10, the maximum output power achieved from the proposed DPP topology and conventional bypass diode is shown. It is shown that the power achieved by using the proposed DPP is greater than using the traditional bypassing diode methodology during various mismatch cases mentioned in Table 2. Moreover, energy yield by the conventional bypass diode method during the mismatch cases 3 and 4 is similar (~45 W) and is significantly lower than the proposed DPP topology. During these cases, the conventional bypass diode method bypasses the low power-producing PV submodule. Therefore, the power is not fully extracted by the bypass diode methodology, but it is effectively extracted by the proposed SCL DPP topology. Overall, the results in Figures 9 and 10 have confirmed the effectiveness of the proposed DPP topology under non-ideal situations. Moreover, PV submodule voltages are also given in Table 3 under the similar mismatch conditions mentioned in Table 2. It may be observed that the proposed topology has equalized the voltages during all the mismatch cases. Therefore, the proposed topology requires a simple MPPT tracking algorithm. Table 3. Voltages across PV submodules for proposed SCL-based DPP topology for the mismatch cases in Table 2.

Prototype and Experimental Setup
The prototype along with the experimental setup is presented in this section. For experimental validations, two solar PV modules (PV1 and PV2) are used. The prototype of 100 W is designed by considering the 45 W PV module to test it within a laboratory environment. The rating of PV modules used for hardware implementation is shown in Table 1. The parameters and components used for the experimental setup are listed in Table 4. In Table 4, the values of inductor L and a capacitor C are shown to be 100 µH and 50 µF, respectively by taking a consideration of the inductor current ripple ∆I L and capacitor voltage ripple ∆V C of less than 5% according to (7) and (8). Moreover, the proposed DPP converter only has to process the mismatched power. Therefore, the power rating requirement for the proposed DPP converter is lower. Hence, the low power components allow the use of small and fast-switching MOSFET transistors, which can operate at high switching frequencies. The inductance, capacitance, and switching frequency values were determined earlier. More importantly, this prototype is designed to prove the concept, and is not for practical use. Therefore, the components used during the testing should be replaced by the more efficient and small-size components for practical implementation. For the experimental setup, each PV module is connected in parallel with a DC power supply, as depicted in Figure 11a. The DC supply is operating in the constant-current (CC) mode to emulate the light-induced current, depicting the output current-voltage (I-V) curve. Details about this method to conduct repeatable indoor PV experiments can be found in [59]. Through the control of constant current mode, different conditions of mismatch can be emulated. The designed prototype is shown in Figure 11b.

Results
This section compromises experimental results along with the theoretical analysis of power loss distribution among different circuit components to verify the proposed work. For this purpose, three mismatch conditions are developed, which are shown in Table 5, i.e., Test 1, Test 2, and Test 3. The experimental results under these conditions are presented in Figure 12 for SCL-based DPP converters. Figure 12 shows the mismatch current process by the SCL-based DPP converters. In the first condition (Test 1), when there is no mismatch between the series-connected PV modules, the mismatch current IL is shown in Figure 12a. It can be seen from Figure 12a that the mismatch current during this test condition is zero. During Test 2, PV1 is producing more power than PV2. The mismatch current during this case is shown in Figure 12b. Lastly, in Test 3, PV2 is producing more power than PV1, while the difference of mismatch current IL between the two series-connected PV modules is shown in Figure 12c.

Results
This section compromises experimental results along with the theoretical analysis of power loss distribution among different circuit components to verify the proposed work. For this purpose, three mismatch conditions are developed, which are shown in Table 5, i.e., Test 1, Test 2, and Test 3. The experimental results under these conditions are presented in Figure 12 for SCL-based DPP converters. Figure 12 shows the mismatch current process by the SCL-based DPP converters. In the first condition (Test 1), when there is no mismatch between the series-connected PV modules, the mismatch current I L is shown in Figure 12a. It can be seen from Figure 12a that the mismatch current during this test condition is zero. During Test 2, PV1 is producing more power than PV2. The mismatch current during this case is shown in Figure 12b. Lastly, in Test 3, PV2 is producing more power than PV1, while the difference of mismatch current I L between the two series-connected PV modules is shown in Figure 12c. Table 5. Mismatch condition for the experiment. P-V characteristics for the proposed SCL topology are shown in Figure 13, which are measured by sweeping the variable load shown in Figure 11a. To measure the P-V characteristics, PV1 (30 W) is used as a reference PV module while PV2 is working at 90%, 50%, and 25% of PV1 to create a mismatch effect. It can be seen from Figure 13 that the P-V characteristics of the proposed SCL-based DPP methodology have no local maxima, as it has only one peak under all tested mismatch conditions. Hence, it becomes easy to track MPP by using simple MPPT control algorithms under partial shading or other non-ideal conditions, which causes a mismatch. Figure 13. Experimentally achieved P-V characteristics for the proposed technique when SM2 in Figure 5 is producing 90%, 50%, and 25% of SM1 (30 W).

Mismatch Conditions
The power loss breakdown across each component for the proposed topology is presented in Table 6. The ratings of each PV submodule along with other parameters,  Table 5 for SCL-based DPP topology. (a) Test 1 (b) Test 2 and (c) Test 3. P-V characteristics for the proposed SCL topology are shown in Figure 13, which are measured by sweeping the variable load shown in Figure 11a. To measure the P-V characteristics, PV1 (30 W) is used as a reference PV module while PV2 is working at 90%, 50%, and 25% of PV1 to create a mismatch effect. It can be seen from Figure 13 that the P-V characteristics of the proposed SCL-based DPP methodology have no local maxima, as it has only one peak under all tested mismatch conditions. Hence, it becomes easy to track MPP by using simple MPPT control algorithms under partial shading or other non-ideal conditions, which causes a mismatch.  Table 5 for SCL-based DPP topology. (a) Test 1 (b) Test 2 and (c) Test 3.
P-V characteristics for the proposed SCL topology are shown in Figure 13, which are measured by sweeping the variable load shown in Figure 11a. To measure the P-V characteristics, PV1 (30 W) is used as a reference PV module while PV2 is working at 90%, 50%, and 25% of PV1 to create a mismatch effect. It can be seen from Figure 13 that the P-V characteristics of the proposed SCL-based DPP methodology have no local maxima, as it has only one peak under all tested mismatch conditions. Hence, it becomes easy to track MPP by using simple MPPT control algorithms under partial shading or other non-ideal conditions, which causes a mismatch. Figure 13. Experimentally achieved P-V characteristics for the proposed technique when SM2 in Figure 5 is producing 90%, 50%, and 25% of SM1 (30 W).
The power loss breakdown across each component for the proposed topology is presented in Table 6. The ratings of each PV submodule along with other parameters, 25% irradiance on SM2 50% irradiance on SM2 90% irradiance on SM2 Figure 13. Experimentally achieved P-V characteristics for the proposed technique when SM2 in Figure 5 is producing 90%, 50%, and 25% of SM1 (30 W). The power loss breakdown across each component for the proposed topology is presented in Table 6. The ratings of each PV submodule along with other parameters, which are used for the loss calculation are mentioned in Tables 4 and 5, respectively. For the loss calculation, one submodule is producing half power, while the other is producing at its maximum capacity. The theoretically calculated on-state MOSFET power losses (P on ) and switching power losses (P swloss ) are 109.83 mW and 71.69 mW, respectively. Moreover, the calculated losses across the capacitor (P C_loss ) and inductor (P L_loss ) are 8.3 mW and 300 mW, correspondingly. The overall calculated efficiency (η c ) is 99.28% and the measured efficiency from the simulated results under similar conditions is 98.66%. Additionally, the calculated and simulated efficiencies are only considered because this prototype is designed only to prove the concept, not for practical use. Therefore, the components used during the testing should be replaced by the more efficient and small-size components for practical implementation for better performance and efficiency. As a continuation, it can be seen from Figure 14 that the losses associated with the inductor are the highest up to 61% because the copper loss is the most dominant material showing major losses at higher frequencies. Also, the ON-state switch losses are lower due to the low R on of the selected MOSFET. which are used for the loss calculation are mentioned in Tables 4 and 5, respectively. For the loss calculation, one submodule is producing half power, while the other is producing at its maximum capacity. The theoretically calculated on-state MOSFET power losses (Pon) and switching power losses (Pswloss) are 109.83 mW and 71.69 mW, respectively. Moreover, the calculated losses across the capacitor (PC_loss) and inductor (PL_loss) are 8.3 mW and 300 mW, correspondingly. The overall calculated efficiency (ƞc) is 99.28% and the measured efficiency from the simulated results under similar conditions is 98.66%. Additionally, the calculated and simulated efficiencies are only considered because this prototype is designed only to prove the concept, not for practical use. Therefore, the components used during the testing should be replaced by the more efficient and small-size components for practical implementation for better performance and efficiency. As a continuation, it can be seen from Figure 14 that the losses associated with the inductor are the highest up to 61% because the copper loss is the most dominant material showing major losses at higher frequencies. Also, the ON-state switch losses are lower due to the low Ron of the selected MOSFET. Figure 14. Theoretical analysis of power loss distribution among various components present in the proposed SCL-based DPP topology while one of the PV modules is half-shaded in Figure 5.
Overall, the proposed topology is simple and has the potential to withstand nonideal conditions by yielding the maximum power from a PV system. Moreover, the control circuitry is simple and easy to implement with only two modes of operations as compared to other complex SC topologies. Furthermore, the size of the proposed topology is compact, and thus, it is easily integrable into a PV module junction box. In a word, the proposed work has reduced the complexity and increased the output power yield with high efficiency.  Figure 14. Theoretical analysis of power loss distribution among various components present in the proposed SCL-based DPP topology while one of the PV modules is half-shaded in Figure 5.
Overall, the proposed topology is simple and has the potential to withstand non-ideal conditions by yielding the maximum power from a PV system. Moreover, the control circuitry is simple and easy to implement with only two modes of operations as compared to other complex SC topologies. Furthermore, the size of the proposed topology is compact, and thus, it is easily integrable into a PV module junction box. In a word, the proposed work has reduced the complexity and increased the output power yield with high efficiency.

Conclusions
A power electronic-based differential power processing (DPP) converter to mitigate the mismatch effects in solar PV modules is proposed in this paper. The proposed switched- For verification of the proposed topology, a simulation model was built in PSIM. Additionally, a hardware prototype was also built for the verification of the concept through experimental tests. The simulation and experimental results show that the SCLbased DPP converter overcomes the problem of multiple peaks in the output power of PV modules under various mismatch conditions by using simple control circuitry. The converter has achieved an efficiency above 98%. Moreover, the proposed DPP topology has been evaluated against the conventional traditional bypass diode. The comparison has shown that the proposed topology is simple, easy to integrate due to its small size, highly granular, reliable, and efficient even under a severe mismatch.