Dynamic Boost Based DMPPT Emulator

: The Distributed Maximum Power Point Tracking (DMPPT) approach is a promising solution to improve the energetic performance of mismatched PhotoVoltaic (PV) systems. However, there are still several factors that can reduce DMPPT energy e ﬃ ciency, including atmospheric conditions, the e ﬃ ciency of the power stage, constraints imposed by the topology, the ﬁnite rating of silicon devices, and the nonoptimal value of string voltage. In order to fully explore the advantages o ﬀ ered by the above solution, the implementation of a Boost based DMPPT emulator is of primary concern, especially if it behaves as a controlled voltage or current source. The repeatability of experimental tests, the tighter control of climatic conditions, the closing of the gap between the physical dimensions of a PV array and the space available in a university lab, the simplicity with which new algorithms can be tested, and the low maintenance costs are just some of the beneﬁts o ﬀ ered by an emulator. This paper describes the realization and use of a Boost based Distributed Maximum Power Point Tracking (DMPPT) emulator and shows its high ﬂexibility and potential. The device is able to emulate the output current vs. voltage ( I-V ) characteristics of many commercial PhotoVoltaic (PV) modules with a dedicated Boost DC / DC converter. The ﬂexibility is guaranteed by the ability to reproduce both I = f ( V ) and V = g ( I ) characteristics at di ﬀ erent values of not only the irradiance levels but also the maximum allowed voltage across the switching devices. The system design is based on a commercial power supply controlled by a low-cost Arduino board by Arduino (Strambino, Torino, Italy). Data acquisition is performed through a low-cost current and voltage sensor by using a multichannel board by National Instruments. Experimental results conﬁrm the capability of the proposed device to accurately emulate the output I-V characteristic of Boost based DMPPT systems obtained by varying the atmospheric conditions, the rating of silicon devices, and the electrical topology.


Introduction
Climate change and environmental degradation are issues of concern in the present world and represent the main challenges that we will face in the near future in order to prevent adverse socioeconomic consequences. A crucial aspect of Green New Deal action will be to decarbonize the production of electricity using renewable energy sources. To reinforce the distributed green energy generation, which represents another important challenge, photovoltaic (PV) systems are among the most promising renewable sources. In the last 20 years, the main objective of the scientific community has been to fully understand the factors that limit the energetic performance of PV systems [1][2][3][4][5][6][7] and propose possible solutions . What emerges is that commonly used grid-connected PV installations, made of strings of PV modules connected in parallel and feeding a central inverter, are ineffective when mismatching conditions occur (due to clouds, shadows, dirt, etc.). the finite rating of the silicon devices [32][33][34][35][36][37][38]. The above factors together with the nonoptimal value of the string voltage ( ) make the efficiency 1.
In order to clarify the above assumptions, it can be useful to compare two systems with the same topology, formed by series connection of two PV panels: in the first system (Figure 2a), DMPPT architecture is implemented; in the second system, the Central Maximum Power Point Tracking (CMPPT) function is adopted (Figure 2b). The electrical characteristics of commercial PV modules (Sunmodule SW225 by SolarWorld industries (Bonn, Germany) [43]) in standard test conditions (STC; = 25 °C, = 1000 W/m ) are reported in Table 1.  In order to clarify the above assumptions, it can be useful to compare two systems with the same topology, formed by series connection of two PV panels: in the first system (Figure 2a), DMPPT architecture is implemented; in the second system, the Central Maximum Power Point Tracking (CMPPT) function is adopted (Figure 2b). The electrical characteristics of commercial PV modules (Sunmodule SW225 by SolarWorld industries (Bonn, Germany) [43]) in standard test conditions (STC; T STC = 25 • C, S STC = 1000 W/m 2 ) are reported in Table 1.
In order to clarify the above assumptions, it can be useful to compare two systems with the same topology, formed by series connection of two PV panels: in the first system (Figure 2a), DMPPT architecture is implemented; in the second system, the Central Maximum Power Point Tracking (CMPPT) function is adopted (Figure 2b). The electrical characteristics of commercial PV modules (Sunmodule SW225 by SolarWorld industries (Bonn, Germany) [43]) in standard test conditions (STC; = 25 °C, = 1000 W/m ) are reported in Table 1.   In order to show and compare the energy performance of both systems, we can calculate their performance ratio (PR): in which P MAX represents the maximum power that can be extracted from the PV system in the considered atmospheric conditions, and P AV is the available maximum power obtained by the sum of maximum power (P MPP 1 , P MPP 2 ) that each shaded PV module is able to provide. The performance ratio is a function of the mismatching degree (MD) and the maximum allowed voltage V dsmax provided by silicon devices, where MD is defined as: where S 1 , S 1 are the irradiance values of modules 1 and 2.
In Figure 3, the PRs are plotted as a function of MD and voltage V dsmax .
Energies 2020, 13, x FOR PEER REVIEW 4 of 17 Different from DMPPT, the central approach performs its MPPT function on the entire PV plant rather than on each PV module. In order to show and compare the energy performance of both systems, we can calculate their performance ratio (PR): in which represents the maximum power that can be extracted from the PV system in the considered atmospheric conditions, and is the available maximum power obtained by the sum of maximum power ( , ) that each shaded PV module is able to provide. The performance ratio is a function of the mismatching degree ( ) and the maximum allowed voltage provided by silicon devices, where is defined as: where , are the irradiance values of modules 1 and 2. In Figure 3, the PRs are plotted as a function of and voltage . Figure 3. Performance ratio as a function of mismatching degree of the value assumed by Vdsmax. Figure 3 shows that for low values of MD, the energetic performance of the DMPPT approach is far superior than that obtained by CMPPT ( ). The same consideration cannot be extended for high values of MD, in that the difference between the two approaches does not promote employing one DC/DC converter for each PV module. Moreover, by looking at Figure 3, it  Figure 3 shows that for low values of MD, the energetic performance of the DMPPT approach is far superior than that obtained by CMPPT (PR DMPPT > PR CMPPT ). The same consideration cannot be extended for high values of MD, in that the difference between the two approaches does not promote Energies 2020, 13, 2921 5 of 16 employing one DC/DC converter for each PV module. Moreover, by looking at Figure 3, it is clear that the value of MD where PR DMPPT > PR CMPPT strongly depends on the maximum allowed voltage V dsmax provided by the silicon devices.
Moreover, it should also be considered that the value assumed by the string voltage seriously undermines the power extracted from the entire DMPPT PV system, if it does not belong to the best operating voltage (BOV) interval, as shown in Figure 4, which, as an example, shows the Performance ratio vs. Voltage characteristics obtained when MD = 0.4 and V dsmax = 60 V. closely related to the extracted power, by taking into account not only the efficiency but also the reliability of the entire PV system [38]. In order to fully explore the advantages offered by the above solution, the implementation of a Boost based DMPPT emulator is of primary concern, especially if it behaves as a controlled voltage or current source.
The repeatability of experimental tests, the tighter control of climatic conditions, the closing of the gap between the physical dimensions of a PV array and the space available in a university lab, the simplicity with which new algorithms can be tested, and the low maintenance costs are just some of the benefits offered by an emulator. Moreover, it is also evident that, in order to deeply understand the real potential of the DMPPT approach, a huge number of Boost converters, characterized by different values, are necessary. In fact, as shown before, silicon devices have a great influence on the achievement of high energy efficiency due to their finite voltage ratings. The enormous effort required in terms of both time and cost could be partly lessened by adopting a Boost based DMPPT emulator that foresees the possibility to swap the value of .

Mathematical Model of Boost Based PVU
A Boost based photovoltaic unit is shown in Figure 5. In the above figure, is the photoinduced current; diode D1 takes into account the effects at the silicon p-n junction of a PV cell; losses are considered by inserting series resistance and shunt resistance ; ( ) and ( ) are currents (voltages) at the input and output ports of the converter, respectively. The typical output static Current vs. Voltage (I-V) characteristics of a PV module (dashed line) and a controlled PV module (bold line) are represented, at constant irradiance ( ) and temperature ( ) values, in Figure  6. Losses occurring in the power stage of the Boost converter (switching, conduction, and iron losses) and the settling time of the step response of a closed or open loop PVU are neglected. In the following, in order to take the dynamic behavior of the considered system into account, a time delay will be Recent studies have shown the positive impact of the combined action of the distributed approach and dynamic reconfiguration from a broader perspective compared with approaches closely related to the extracted power, by taking into account not only the efficiency but also the reliability of the entire PV system [38]. In order to fully explore the advantages offered by the above solution, the implementation of a Boost based DMPPT emulator is of primary concern, especially if it behaves as a controlled voltage or current source.
The repeatability of experimental tests, the tighter control of climatic conditions, the closing of the gap between the physical dimensions of a PV array and the space available in a university lab, the simplicity with which new algorithms can be tested, and the low maintenance costs are just some of the benefits offered by an emulator. Moreover, it is also evident that, in order to deeply understand the real potential of the DMPPT approach, a huge number of Boost converters, characterized by different V dsmax values, are necessary. In fact, as shown before, silicon devices have a great influence on the achievement of high energy efficiency due to their finite voltage ratings. The enormous effort required in terms of both time and cost could be partly lessened by adopting a Boost based DMPPT emulator that foresees the possibility to swap the value of V dsmax .

Mathematical Model of Boost Based PVU
A Boost based photovoltaic unit is shown in Figure 5. In the above figure, I ph is the photo-induced current; diode D 1 takes into account the effects at the silicon p-n junction of a PV cell; losses are considered by inserting series resistance R S and shunt resistance R sh ; I PV (V PV ) and I PVU (V PVU ) are currents (voltages) at the input and output ports of the converter, respectively. The typical output static Current vs. Voltage (I-V) characteristics of a PV module (dashed line) and a controlled PV module (bold line) are represented, at constant irradiance (S) and temperature (T) values, in Figure 6. Losses occurring in the power stage of the Boost converter (switching, conduction, and iron losses) and the Energies 2020, 13, 2921 6 of 16 settling time of the step response of a closed or open loop PVU are neglected. In the following, in order to take the dynamic behavior of the considered system into account, a time delay will be introduced. The I-V curve is composed of three operating regions, OR1, OR2, and OR3, described in the following.
Energies 2020, 13, x FOR PEER REVIEW 6 of 17 introduced. The I-V curve is composed of three operating regions, OR1, OR2, and OR3, described in the following. Operating region 1: OR1 is defined for 0 , where is the MPP voltage that can be provided by the adopted PV module in the considered atmospheric conditions: where is the temperature coefficient of the voltage [44]. In such a region, the two characteristics of the PV module and the controlled PV module are coincidental. In fact, for 0 , the MPPT controller forces the Boost DC/DC converter to work with a duty cycle equal to one. In this condition it gives: where is the photo-induced current, which, in accordance with Equation (5), is linearly dependent on the irradiance level (S) and the PV module temperature ( ), is the current in diode D1 (Equation (6)), and is the shunt-resistor current (Equation (7)): where is the thermal voltage and is the diode reverse bias saturation current (Equation (8)): where = 1.38 J/K is the Boltzmann constant, is the band gap of the semiconductor material (in the following it is assumed E = 1.124 eV), and is the temperature coefficient [44]. Operating region 2: OR2, defined for , is described by a hyperbole of Equation (9), where is the maximum allowed voltage provided by the mosfet M1 ( Figure 5).
As shown in Figure 6, the current range ( ) associated with OR2 is as follows: where is the MPP current, the value of which is obtained by using Equation (4), setting in Equations (6) and (7) the value of is equal to , is the value of when = (Equation (11)).
Operating region 3: OR3 is defined by a vertical drop occurring at = , due to the action of the output overvoltage protection circuitry. The current range ( ) referring to OR3 is: Operating region 1: OR1 is defined for 0 ≤ V PVU ≤ V MPP , where V MPP is the MPP voltage that can be provided by the adopted PV module in the considered atmospheric conditions: where α V is the temperature coefficient of the voltage [44].
In such a region, the two characteristics of the PV module and the controlled PV module are coincidental. In fact, for 0 ≤ V PVU < V MPP , the MPPT controller forces the Boost DC/DC converter to work with a duty cycle equal to one. In this condition it gives: where I ph is the photo-induced current, which, in accordance with Equation (5), is linearly dependent on the irradiance level (S) and the PV module temperature (T), I d is the current in diode D 1 (Equation (6)), and I Rsh is the shunt-resistor current (Equation (7)): where V T is the thermal voltage and I sat is the diode reverse bias saturation current (Equation (8)): where k = 1.38 J/K is the Boltzmann constant, E gap is the band gap of the semiconductor material (in the following it is assumed E gap = 1.124 eV), and C is the temperature coefficient [44]. Operating region 2: OR2, defined for V MPP < V PVU ≤ V dsmax , is described by a hyperbole of Equation (9), where V dsmax is the maximum allowed voltage provided by the mosfet M 1 ( Figure 5).
As shown in Figure 6, the current range (R C OR2 ) associated with OR2 is as follows: where I MPP is the MPP current, the value of which is obtained by using Equation (4), setting in Equations (6) and (7) the value of V PV is equal to V MPP , I 0 is the value of I PVU when V PVU = V dsmax (Equation (11)).
Operating region 3: OR3 is defined by a vertical drop occurring at V PVU = V dsmax , due to the action of the output overvoltage protection circuitry. The current range (R C OR3 ) referring to OR3 is: The I-V output characteristics of a single PVU are strictly dependent on the irradiance and temperature levels (Equation (13)). As shown in Table 1, the acronym NOCT means Nominal Operating Cell Temperature. Typical curves are shown in Figure 7.
It is worth noting that in real environmental conditions, the temperature usually changes quite slowly with respect to variation of the irradiance level occurring during the day. Based on this, all subsequent results were obtained by considering a constant value of the PV module temperature of T = 57.5 • C (T ambient = 25 • C).

Design and Implementation of Boost Based PVU Emulator
A block diagram of the proposed Boost based PVU emulator is shown in Figure 8. The emulator is characterized by its simplicity of implementation and high flexibility. In order to be easily reconfigured, it consists of a current (voltage) controlled power supply, in which the output current ( ) (voltage ( )) is regulated by means of a proper controller. In other words, the system acts either as a controlled voltage source, if there is the need for a series connection, or as a controlled current source, if there is the need for a parallel connection. The input signals to the controlling unit are: ( ) (PVU output voltage), ( ) (PVU output current), (voltage signal, which is proportional to the maximum allowed voltage supported by the converter's mosfet M1), ( ) (time-varying voltage signal, which is proportional to desired irradiance level ; Equation (14)), and ( ) (voltage signal, which is proportional to the PV system settling time ; Equation (15)):

Design and Implementation of Boost Based PVU Emulator
A block diagram of the proposed Boost based PVU emulator is shown in Figure 8. The emulator is characterized by its simplicity of implementation and high flexibility. In order to be easily reconfigured, it consists of a current (voltage) controlled power supply, in which the output current I PVU (t) (voltage V PVU (t)) is regulated by means of a proper controller. In other words, the system acts either as a controlled voltage source, if there is the need for a series connection, or as a controlled current source, if there is the need for a parallel connection.  As highlighted in Figure 8, the core of the proposed PVU emulator is represented by an Arduino Mega 2560 microcontroller. Such a device can be programmed by means of Arduino IDE software by Arduino (Strambino, Torino, Italy), which is freely available online [45]. As one might expect, the analog input signals of the microcontroller, which are marked with an asterisk (Figure 8  The input signals to the controlling unit are: V PVU (t) (PVU output voltage), I PVU (t) (PVU output current), V dsmax (voltage signal, which is proportional to the maximum allowed voltage supported by the converter's mosfet M 1 ), V S (t) (time-varying voltage signal, which is proportional to desired Energies 2020, 13, 2921 9 of 16 irradiance level S; Equation (14)), and V td (t) (voltage signal, which is proportional to the PV system settling time t d ; Equation (15)): V td (t) = α td t d (15) with α S = 1 V m 2 /W and α td = 1 [V/s]. Corresponding with standard irradiance S STC , V S (t) assumes the value V SSTC ; corresponding with the maximum settling time t dMAX , V td (t) assumes the value V tdMAX . The calculation of t dMAX is reported in Appendix A. The output signal S re f (t) attained by the conditioning process is calculated according to the diagram shown in Figure 9. It depends on the operating region of the PV unit and is a proper function of the input signals (V PVU (t), I PVU (t), V S (t), V td (t) and V dsmax ). It includes a digital signal (CTR), which is settled in a high (low) state if a voltage (current) controlled source is needed. A proper digital analog converter (DAC) is used to obtain CTR.

Experimental Results
As a first step, preliminary test activity was carried out on the sole system composed of a microcontroller board "Arduino Mega 2560" and a 12-bit, fast response Digital to Analog Converter (DAC) Adafruit (New York, USA) MCP4725, in order to check the main features of the proposed emulator. In particular, the idea was to check the capability of the emulator to reproduce the I-V characteristics of a Boost based photovoltaic unit for different values of irradiance ( ) and maximum allowed voltage supported by the converter's mosfet. The preliminary results are shown on the display of a MDO 3034 oscilloscope by Tektronix (Beaverton, Oregon, USA), as illustrated in Figures 10 and 11. In both figures, a periodic (frequency 1 Hz) ramp signal has been applied at the microcontroller input * ( ) to scan the I-V characteristic of the proposed Boost based PVU. The amplitude of the adopted ramp signal varies from 0 to 5 V, which corresponds to PVU ramp voltage ( ) from 0 to ( = 100 V). The different time domain behavior of ( ) (corresponding to the output signal of the DAC) reported in Figures 11 and 12 is linked to the adoption of two different values of * ( ). In particular, in Figures 11 and 12, the value of * ( ) is equal to 2 and 1 V, corresponding to ( ) equal to 400 and 200 W/m 2 , respectively. By repeating the same tests with different values of = 50 V, the characteristics shown in Figure 12 were obtained. In this test case, the reference ramp signal rose linearly from 0 to 2.5 V.
In the next phase, the whole system was assembled and a set of representative experiments was carried out. The experimental setup was realized in the Circuit Laboratory of the University of Naples Federico II and is shown in Figure 13. It is composed of three fundamental blocks: power, control, As highlighted in Figure 8, the core of the proposed PVU emulator is represented by an Arduino Mega 2560 microcontroller. Such a device can be programmed by means of Arduino IDE software by Arduino (Strambino, Torino, Italy), which is freely available online [45]. As one might expect, the analog input signals of the microcontroller, which are marked with an asterisk (Figure 8), represent a scaled version of the corresponding signals V PVU (t), I PVU (t), V S (t), V dsmax , and V td . Such scaling is necessary to adapt the electrical characteristics of the above signals to the limited range [0, 5] V of the microcontroller. The scaled input signals, obtained as a result of the conditioning process, are defined as follows: where V MAX = 100 V and I MAX = 10 A are the maximum allowed values of the output voltage and current from the power unit, respectively. A flowchart of the routine written in Arduino code is shown in Figure 9.
In order to reduce the computation time of the code, two lookup tables (LUTs) for voltage and current controlled sources were implemented. Each LUT contains 256 samples of the scaled output variables (I * PVU and V * PVU ), representing the output values I * PVU V * PVU calculated corresponding with the 256 value of the input signal V * PVU I * PVU in the range [0, 5] V.

Experimental Results
As a first step, preliminary test activity was carried out on the sole system composed of a microcontroller board "Arduino Mega 2560" and a 12-bit, fast response Digital to Analog Converter (DAC) Adafruit (New York, USA) MCP4725, in order to check the main features of the proposed emulator. In particular, the idea was to check the capability of the emulator to reproduce the I-V characteristics of a Boost based photovoltaic unit for different values of irradiance S(t) and maximum allowed voltage V dsmax supported by the converter's mosfet. The preliminary results are shown on the display of a MDO 3034 oscilloscope by Tektronix (Beaverton, Oregon, USA), as illustrated in Figures 10  and 11. In both figures, a periodic (frequency 1 Hz) ramp signal has been applied at the microcontroller input V * PVU (t) to scan the I-V characteristic of the proposed Boost based PVU. The amplitude of the adopted ramp signal varies from 0 to 5 V, which corresponds to PVU ramp voltage V PVU (t) from 0 to V dsmax (V dsmax = 100 V). The different time domain behavior of S re f (t) (corresponding to the output signal of the DAC) reported in Figures 11 and 12 is linked to the adoption of two different values of V * S (t). In particular, in Figures 11 and 12, the value of V * S (t) is equal to 2 and 1 V, corresponding to S(t) equal to 400 and 200 W/m 2 , respectively. By repeating the same tests with different values of V dsmax = 50 V, the characteristics shown in Figure 12 were obtained. In this test case, the reference ramp signal rose linearly from 0 to 2.5 V.       Power block: The power block consists of two commercial power supplies BOP 100-4 [46], provided by Kepco (Flushing, New York, USA). One represents the power stage of the Boost based PV emulator and is used as a current-or voltage-controlled source. The other one is used as a controlled load in order to scan the I-V characteristics of the emulator. The two power supplies can work in all four quadrants of the current-voltage plane. They are linear power supplies with two bipolar control channels (voltage or current mode), selectable and individually controllable by either front panel controls or remote signals. In Table 2, the electrical characteristics of the proposed Boost based PVU emulator are reported.  In the next phase, the whole system was assembled and a set of representative experiments was carried out. The experimental setup was realized in the Circuit Laboratory of the University of Naples Federico II and is shown in Figure 13. It is composed of three fundamental blocks: power, control, and acquisition blocks. Control block: The core of the control block is composed of the embedded board "Arduino Mega 2560" in which the ATMega2560 microcontroller is integrated. The "Arduino Mega 2560" is powered via a USB connection and provides 54 digital input/output pins (15 of which can be used as PWM outputs) and 16 analog inputs, and it can be programmed through Arduino IDE software. Apart from the controller, the control block is composed of three units: (a) the input conditioning unit, which consists of two sensors: one current and one voltage sensor. The above sensors are used for sensing and adapting the PVU output current and voltage to the Arduino maximum allowed input voltage; (b) the output conditioning unit, which consists of the DAC MCP 4725 by Adafruit, and (c) the generation unit, which consists of the National Instruments (Austin, Texas, USA) generation board (BNC-2100 Series Connector Blocks), used to reproduce the input signals * ( ), * and * . In order to configure the data generation hardware (BNC-2100 Series Connector Blocks) Mathworks MATLAB Data Acquisition Toolbox is used. The adopted current sensor is an INA169 module, by Texas Instruments (Dallas, Texas, USA), which allows measurement of continuous current up to 5 A. The INA169 is a "high-side, unipolar, current shunt monitor," meaning that it measures the voltage drop across a shunt resistor, which is placed on the positive power side [47]. In order to reduce the PVU output voltage up to 20 times compared to the original, a voltage divider using a resistance of 220 and 11.5 kΩ was adopted as a voltage sensor. In other words, the adopted voltage sensor is based on the series connection of two resistors. Acquisition block: During the acquisition process, the experimental data were stored and plotted in MATLAB through a commercial multichannel USB data acquisition system NI CompactDAQ, provided by National Instruments, with NI9215 modules characterized by 16-bit resolution and maximum sampling frequency of 100 kS/s).  Power block: The power block consists of two commercial power supplies BOP 100-4 [46], provided by Kepco (Flushing, New York, USA). One represents the power stage of the Boost based PV emulator and is used as a current-or voltage-controlled source. The other one is used as a controlled load in order to scan the I-V characteristics of the emulator. The two power supplies can work in all four quadrants of the current-voltage plane. They are linear power supplies with two bipolar control channels (voltage or current mode), selectable and individually controllable by either front panel controls or remote signals. In Table 2, the electrical characteristics of the proposed Boost based PVU emulator are reported. Control block: The core of the control block is composed of the embedded board "Arduino Mega 2560" in which the ATMega2560 microcontroller is integrated. The "Arduino Mega 2560" is powered via a USB connection and provides 54 digital input/output pins (15 of which can be used as PWM outputs) and 16 analog inputs, and it can be programmed through Arduino IDE software. Apart from the controller, the control block is composed of three units: (a) the input conditioning unit, Energies 2020, 13, 2921 12 of 16 which consists of two sensors: one current and one voltage sensor. The above sensors are used for sensing and adapting the PVU output current and voltage to the Arduino maximum allowed input voltage; (b) the output conditioning unit, which consists of the DAC MCP 4725 by Adafruit, and (c) the generation unit, which consists of the National Instruments (Austin, Texas, USA) generation board (BNC-2100 Series Connector Blocks), used to reproduce the input signals V * S (t), V * dsmax and V * td . In order to configure the data generation hardware (BNC-2100 Series Connector Blocks) Mathworks MATLAB Data Acquisition Toolbox is used. The adopted current sensor is an INA169 module, by Texas Instruments (Dallas, Texas, USA), which allows measurement of continuous current up to 5 A. The INA169 is a "high-side, unipolar, current shunt monitor," meaning that it measures the voltage drop across a shunt resistor, which is placed on the positive power side [47]. In order to reduce the PVU output voltage up to 20 times compared to the original, a voltage divider using a resistance of 220 and 11.5 kΩ was adopted as a voltage sensor. In other words, the adopted voltage sensor is based on the series connection of two resistors. Acquisition block: During the acquisition process, the experimental data were stored and plotted in MATLAB through a commercial multichannel USB data acquisition system NI CompactDAQ, provided by National Instruments, with NI9215 modules characterized by 16-bit resolution and maximum sampling frequency of 100 kS/s). Figure 14a,b show a comparison between emulated I-V curves (shown in white) and theoretical curves (shown in black) in two cases. The two cases differ in the values assumed by S(t) and V dsmax . From these figures, it can be observed that the emulated and theoretical curves are nearly superimposed, thus confirming the excellent capability of the proposed solution of emulating PVU behavior. In order to fully exploit the potential of the proposed architecture, two Boost based PVU emulators were connected in parallel (series). The performance of this system is shown in Figures 15  and 16, in which the emulated I-V characteristics are shown together with the corresponding theoretical ones. The effectiveness of the obtained results highlights that the proposed emulator represents a useful tool to test the performance of shaded DMPPT PV systems.  In order to fully exploit the potential of the proposed architecture, two Boost based PVU emulators were connected in parallel (series). The performance of this system is shown in Figures 15 and 16, in which the emulated I-V characteristics are shown together with the corresponding theoretical ones. The effectiveness of the obtained results highlights that the proposed emulator represents a useful tool to test the performance of shaded DMPPT PV systems. In order to fully exploit the potential of the proposed architecture, two Boost based PVU emulators were connected in parallel (series). The performance of this system is shown in Figures 15  and 16, in which the emulated I-V characteristics are shown together with the corresponding theoretical ones. The effectiveness of the obtained results highlights that the proposed emulator represents a useful tool to test the performance of shaded DMPPT PV systems.

Conclusions
In this paper, a Boost based PVU emulator was presented and discussed. A detailed study was carried out in order to clearly understand the mathematical model of the Boost based PVU.
The proposed emulator was designed to reproduce both = ( ) and = ( ) characteristics at different values not only of the irradiance levels but also of the value of . The above properties make the proposed solution suitable for fully exploring the performance of the DMPPT approach, especially when the reconfiguration technique is also applied. Moreover, the possibility to swap the value of allows emulation of a large number of Boost converters, which results in a consistent reduction in time and cost. In particular, the proposed device represents a suitable compromise between time and cost insofar as the inexpensive choice to adopt a commercial power supply is compensated by the possibility to emulate the behavior of many commercial devices. In conclusion, the main advantages of the proposed solution are the following ones; it is possible to emulate: -both static and dynamic irradiance conditions; -not only uniform but also mismatching operating conditions; -both static and dynamic DMPPT configuration architectures; -Boost based DMPPT converters with different values of .
The proposed experimental tests fully confirm the validity of the proposed emulator. Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In this paper, a Boost based PVU emulator was presented and discussed. A detailed study was carried out in order to clearly understand the mathematical model of the Boost based PVU.
The proposed emulator was designed to reproduce both I PVU = f (V PVU ) and V PVU = g(I PVU ) characteristics at different values not only of the irradiance levels but also of the value of V dsmax . The above properties make the proposed solution suitable for fully exploring the performance of the DMPPT approach, especially when the reconfiguration technique is also applied. Moreover, the possibility to swap the value of V dsmax allows emulation of a large number of Boost converters, which results in a consistent reduction in time and cost. In particular, the proposed device represents a suitable compromise between time and cost insofar as the inexpensive choice to adopt a commercial power supply is compensated by the possibility to emulate the behavior of many commercial devices. In conclusion, the main advantages of the proposed solution are the following ones; it is possible to emulate: Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.

Calculation of t dMAX
In order to determine the maximum settling time t dMAX , we can consider an open-loop Boost based PVU (worst case) characterized by the electrical parameters reported in Table A1 [44]. In these conditions, t dMAX is defined as the settling time of the step response of a well-defined transfer function (G vd ) of the PVU under consideration. G vd is the small signal transfer function between the duty cycle and PV voltage. The expression of such a transfer function can be easily found by analyzing the small signal low-frequency equivalent circuit of a Boost based PVU and the load ( Figure A1).  In these conditions, tdMAX is defined as the settling time of the step response of a well-defined transfer function ( ) of the PVU under consideration. is the small signal transfer function between the duty cycle and PV voltage. The expression of such a transfer function can be easily found by analyzing the small signal low-frequency equivalent circuit of a Boost based PVU and the load ( Figure A1). Hat symbols indicate small signal low-frequency variations [44] of the corresponding variables. The resistance in Figure A1 is the differential resistance of the considered PV module [44]: The expression of is: The settling time ( ) of the step response of the above transfer function is equal to about 10 ms, if: Hat symbols indicate small signal low-frequency variations [44] of the corresponding variables. The resistance R MPP in Figure A1 is the differential resistance of the considered PV module [44]: The expression of G vd is: The settling time (t dMAX ) of the step response of the above transfer function is equal to about 10 ms, if: