A High Gain DC-DC Converter with Grey Wolf Optimizer Based MPPT Algorithm for PV Fed BLDC Motor Drive

: Photovoltaic (PV) water pumping systems are becoming popular these days. In PV water pumping, the role of the converter is most important, especially in the renewable energy-based PV systems case. This study focuses on one such application. In this proposed work, direct current (DC) based intermediate DC-DC power converter, i.e., a modiﬁed LUO (M-LUO) converter is used to extricate the availability of power in the high range from the PV array. The M-LUO converter is controlled e ﬃ ciently by utilizing the Grey Wolf Optimizer (GWO)-based maximum power point tracking algorithm, which aids the smooth starting of a brushless DC (BLDC) motor. The voltage source inverter’s (VSI) fundamental switching frequency is achieved in the BLDC motor by electronic commutation. Hence, the occurrence of VSI losses due to a high switching frequency is eliminated. The GWO optimized algorithm is compared with the perturb and observe (P&O) and fuzzy logic based maximum power point tracking (MPPT) algorithms. However, by sensing the position of the rotor and comparing the reference speed with the actual speed, the speed of the BLDC motor is controlled by the proportional-integral (PI) controller. The recent advancement in motor drives based on distributed sources generates more demand for highly e ﬃ cient permanent magnet (PM) motor drives, and this was the beginning of interest in BLDC motors. Thus, in this paper, the design of a high-gain boost converter optimized by a GWO algorithm is proposed to drive the BLDC-based pumping motor. The proposed work is simulated in MATLAB-SIMULINK, and the experimental results are veriﬁed using the dsPIC30F2010 controller.


Introduction
The brushless DC (BLDC) motor is commonly used for low and medium power applications because of its high torque/inertia ratio, high efficiency, low electromagnetic interference and lower maintenance. The BLDC motor is also widely used in aerospace, medical, servo appliances, electric vehicles and robotic applications [1,2]. These motors need electronic commutators, which require information about the rotor position to achieve commutation using a voltage source inverter. The speed-torque characteristics of BLDC motors are very significant, and there is no need for affected due to the environmental conditions [22]. The closed-loop speed control of the BLDC motor is implemented with the dSPACEDS1103 controller for controlling the speed at a reference value for low to high speeds [22]. Additionally, by self-tuning the fuzzy proportional-integral-derivative (PID) controller, the rotor speed is forced to track the reference speed at all times [23]. The closed-loop speed control of the BLDC motor is obtained from the optimized fuzzy algorithm [24]. A DC-DC boost converter is utilized between the solar PV array and permanent magnet motors, by which the friction between the brushes increases and the torque is lowered [25].
A simple and efficient solar water pumping system using a modified LUO converter has been proposed in this paper. A BLDC motor is attracting much interest, because of its higher efficiency, better performance and simple control when applied in many applications. The induction motors have a nearly 10% lower efficiency than PM motor drives for energy saving applications. The increase in energy demand spurs higher demands for variable speed PM motor drives. A modified LUO converter with an efficient grey wolf optimizer (GWO) MPPT algorithm extracts the maximum power from the PV panel. This converter also provides a low starting current for the BLDC motor, which overcomes the torque ripple problems in the BLDC motor.
The manuscript is structured as follows, in six different sections: in Section 2, the systematic working of the proposed system is presented. In Section 3, the design of the proposed system considering each electrical component is discussed, and detailed mathematical modelling is given. Section 4 presents a brief theory on the perturb and observe (P&O), fuzzy and GWO MPPT algorithms, as well as a detailed flow chart of the GWO algorithm. The simulation and experimental results of the proposed system are presented and discussed in Section 5. Finally, the main conclusions are drawn from the study and views on future works are given in Section 6.

Systematic Working of the Proposed System
The configuration of the developed solar-fed BLDC motor using a modified LUO converter is shown in Figure 1. The proposed modified LUO converter operates with a single switch in a continuous conduction mode. This increases the efficiency and suppresses the ripple in the output voltage. The single switch operation reduces the switching stress of the converter. The continuous conduction mode reduces the heat produced in the power semiconductor devices.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 19 with a zeta converter was designed, where the sensors and PI controllers in the system often got affected due to the environmental conditions [22]. The closed-loop speed control of the BLDC motor is implemented with the dSPACEDS1103 controller for controlling the speed at a reference value for low to high speeds [22]. Additionally, by self-tuning the fuzzy proportional-integral-derivative (PID) controller, the rotor speed is forced to track the reference speed at all times [23]. The closed-loop speed control of the BLDC motor is obtained from the optimized fuzzy algorithm [24]. A DC-DC boost converter is utilized between the solar PV array and permanent magnet motors, by which the friction between the brushes increases and the torque is lowered [25]. A simple and efficient solar water pumping system using a modified LUO converter has been proposed in this paper. A BLDC motor is attracting much interest, because of its higher efficiency, better performance and simple control when applied in many applications. The induction motors have a nearly 10% lower efficiency than PM motor drives for energy saving applications. The increase in energy demand spurs higher demands for variable speed PM motor drives. A modified LUO converter with an efficient grey wolf optimizer (GWO) MPPT algorithm extracts the maximum power from the PV panel. This converter also provides a low starting current for the BLDC motor, which overcomes the torque ripple problems in the BLDC motor.
The manuscript is structured as follows, in six different sections: in Section 2, the systematic working of the proposed system is presented. In Section 3, the design of the proposed system considering each electrical component is discussed, and detailed mathematical modelling is given. Section 4 presents a brief theory on the perturb and observe (P&O), fuzzy and GWO MPPT algorithms, as well as a detailed flow chart of the GWO algorithm. The simulation and experimental results of the proposed system are presented and discussed in Section 5. Finally, the main conclusions are drawn from the study and views on future works are given in Section 6.

Systematic Working of the Proposed System
The configuration of the developed solar-fed BLDC motor using a modified LUO converter is shown in Figure 1. The proposed modified LUO converter operates with a single switch in a continuous conduction mode. This increases the efficiency and suppresses the ripple in the output voltage. The single switch operation reduces the switching stress of the converter. The continuous conduction mode reduces the heat produced in the power semiconductor devices.   The proposed GWO-optimized algorithm reduces the maximum power tracking time and makes the output voltage nearly constant. This constant voltage is fed to the three-phase electronic commutator, which converts the DC into three-phase AC voltage. For find the rotor position, three hall sensors are set up in the rotor displaced by 60 • mechanicals. The input current is continuous because of the modified LUO converter, and this makes the BLDC motor make a soft starting. The proportional-integral (PI)-based motor speed control achieves a constant speed of operation [26]. This makes the proposed work highly efficient in a way that could easily be carried out in a low-cost budget. The proposed system is developed using the dsPIC30F2010 microcontroller by Microchip Technology Inc., USA, and the experimental results are verified using the MATLAB Simulink tool by MathWorks, USA.
This system consists of a 1000 W solar panel, insulated-gate bipolar transistor (IGBT)-based modified LUO (M-LUO) converter with an active snubber circuit and IGBT-based VSI with a 3 phase, 1 horsepower (HP) BLDC motor employed with a Hall Effect sensor. Additionally, a dsPIC30F2010 controller is used as a pulse generator, which is controlled by the GWO algorithm. The driver circuit drives the IGBT switch. The system functions when the input from the solar array voltage is given to the modified, LUO converter for maintaining constant voltage, with less ripple content delivered to the inverter system.
The output of the LUO converter is used as an input for the GWO algorithm. For tracking the maximum power, the proposed GWO algorithm is advantageous. This algorithm produces PWM pulses based on the variation of the PV panel voltage, thereby adjusting the duty cycle of the M-LUO converter. In the M-LUO converter, the elementary LUO converter is added with one extra inductor. This converter acts as a second-order low pass filter, and therefore it does not require another filter circuit. This converter with the GWO algorithm provides a constant voltage to all the three phases of the electronic commutator. Switching is done with the help of Hall Effect voltage sensors. The three-phase voltage source inverter converts the DC voltage into AC voltage to provide power to the BLDC motor. The inverter system works at a fundamental frequency to eliminate the high-frequency noise in the inverter output, and high efficiency is thus attained.

Proposed System Design
The modelling steps are explained appropriately to make a compelling design of the proposed system, capable of operating in certain determined conditions. A BLDC motor with 1 HP power and a solar panel of the maximum power capacity of 800 W under standard test conditions (STC) are deliberated. Figure 2 shows a schematic representation of the solar cell. In Figure 2a,b, the simplified diagram and the equivalent diagram of the solar cell are represented, respectively. The current I ph represents the current generated due to photons. I ph mainly depends on the incident radiant energy emitted by the sun and its temperature. One single solar cell is designed by using one photon source current, one diode and one set of series and shunt resistors grouped in a series and parallel fashion, forming a photovoltaic cell. The proposed GWO-optimized algorithm reduces the maximum power tracking time and makes the output voltage nearly constant. This constant voltage is fed to the three-phase electronic commutator, which converts the DC into three-phase AC voltage. For find the rotor position, three hall sensors are set up in the rotor displaced by 60° mechanicals. The input current is continuous because of the modified LUO converter, and this makes the BLDC motor make a soft starting. The proportional-integral (PI)-based motor speed control achieves a constant speed of operation [26]. This makes the proposed work highly efficient in a way that could easily be carried out in a low-cost budget. The proposed system is developed using the dsPIC30F2010 microcontroller by Microchip Technology Inc., USA, and the experimental results are verified using the MATLAB Simulink tool by MathWorks, USA.
This system consists of a 1000 W solar panel, insulated-gate bipolar transistor (IGBT)-based modified LUO (M-LUO) converter with an active snubber circuit and IGBT-based VSI with a 3 phase, 1 horsepower (HP) BLDC motor employed with a Hall Effect sensor. Additionally, a dsPIC30F2010 controller is used as a pulse generator, which is controlled by the GWO algorithm. The driver circuit drives the IGBT switch. The system functions when the input from the solar array voltage is given to the modified, LUO converter for maintaining constant voltage, with less ripple content delivered to the inverter system.
The output of the LUO converter is used as an input for the GWO algorithm. For tracking the maximum power, the proposed GWO algorithm is advantageous. This algorithm produces PWM pulses based on the variation of the PV panel voltage, thereby adjusting the duty cycle of the M-LUO converter. In the M-LUO converter, the elementary LUO converter is added with one extra inductor. This converter acts as a second-order low pass filter, and therefore it does not require another filter circuit. This converter with the GWO algorithm provides a constant voltage to all the three phases of the electronic commutator. Switching is done with the help of Hall Effect voltage sensors. The threephase voltage source inverter converts the DC voltage into AC voltage to provide power to the BLDC motor. The inverter system works at a fundamental frequency to eliminate the high-frequency noise in the inverter output, and high efficiency is thus attained.

Proposed System Design
The modelling steps are explained appropriately to make a compelling design of the proposed system, capable of operating in certain determined conditions. A BLDC motor with 1 HP power and a solar panel of the maximum power capacity of 800 W under standard test conditions (STC) are deliberated. Figure 2 shows a schematic representation of the solar cell. In Figure 2a,b, the simplified diagram and the equivalent diagram of the solar cell are represented, respectively. The current ℎ represents the current generated due to photons. ℎ mainly depends on the incident radiant energy emitted by the sun and its temperature. One single solar cell is designed by using one photon source current, one diode and one set of series and shunt resistors grouped in a series and parallel fashion, forming a photovoltaic cell.

Modelling of the Solar Cell
The output current from the solar cell is: The diode thermal voltage is given as: The shunt current is given as: where N P is the number of modules connected in parallel; R s is the series resistance; R sh is the shunt resistance; and the diode thermal voltage is V t . With the available physical and mathematical model, various parameters of the solar cell can be estimated. These include the estimated power, output voltage and maximum short circuit current. In the proposed study, a solar panel with the specifications shown in Table 1 is used.

Design of the Proposed System
The design of the M-LUO converter-fed BLDC for the water pumping application is discussed in this section. The components, such as the input inductor, capacitors L 1 and C 1 respectively, output inductors L 2 , L 3 and output dc-link capacitor C 2 work in a continuous conduction mode with low stress on the devices and its elements. Depending on the duty cycle, the mode of operation can be changed.
where V out is the average value of the output voltage of the LUO converter, which is equal to the BLDC motor's input voltage. The estimated output current can be written as: The BLDC motor rating is taken as P out = 746 W: Appl. Sci. 2020, 10, 2797 6 of 20 Then, the estimated maximum permitted ripple values of L 1 and C 1 are: The inductor L 1 in the modified LUO converter is calculated by the following equation: The inductances L 2 & L 3 in the modified LUO converter are calculated by the following equation: The change in the capacitor voltage across C 1 is given by: The following equation calculates the capacitor C 1 in the modified LUO converter:

Modelling of DC-Link Capacitor
For the estimate, the VSI DC-link capacitor, the harmonic content present in the AC supply is reflected on the DC side as a prior harmonic in the three-phase supply system. The minimum and the maximum speeds for the BLDC motor can be calculated through the fundamental frequencies of the VSI. These two frequencies ω max and ω min are further used to calculate the dc link capacitance value which would satisfy the operation of the solar panel when working below the reduced level of irradiance. The highest capacitor value is chosen for designing a DC-link capacitor.
The fundamental output frequency of VSI corresponding to the maximum and minimum pumping speed requirement is: ω min = 2π f min = 2πN min P 120 = 2π × 1000 × 6 120 = 314.15 rad/s (13) where f max is the maximum fundamental frequency in Hz, f min is the minimum fundamental frequency in Hz, and P is the number of poles of the BLDC motor. The corresponding capacitor can be calculated as: where ∆V out is the amount of the maximum permissible ripple voltage. Finally, C 0 min is chosen to construct the DC link capacitor.

Water Pump Design
The water pump design relating to the power and speed for the proportionality constant has to be calculated: where P is the BLDC motor's rated power, and ω max is the motor's rated speed in rad/s.

BLDC Motor Controlled by Electronic Commutation
The BLDC motor is an electronically commutated device and requires data regarding the rotor position for the proper commutation of the stator current. The BLDC motor needs a quasi-rectangular shaped input current drawn into the machine. The back emf of each phase is trapezoidal and 120 electrical degrees-displaced. The BLDC motor is rotated in a sequence to energize the stator winding. Hall sensors sense the rotor position, and it is embedded into the stator. Whenever the magnetic poles of the rotor are nearer to the hall sensors, the sensors feed a low or high signal. The complete commutation sequence can be found by integrating the three-hall sensor output. Another important key factor of electronic commutation is high-frequency switching loss, which can be eliminated by providing the fundamental switching frequency of VSI. The switching sequences for the electronic commutation of the BLDC motor are the same as those employed in [18].

Maximum Power Point Tracking (MPPT) Algorithm
An MPPT algorithm is implemented to keep track of the changes caused by the environment and to extricate high power from the solar array. In a system with MPPT, voltage collapse is shunned when Maximum Power Point (MPP) is near to the operating point. The benefits of using the MPPT algorithm lie in its robustness and simplicity in implementation. In this paper, P&O, fuzzy logic and GWO algorithms are compared to extricate high power from the PV system. There are different control algorithms available to monitor the maximum power point. Among these, P&O and Fuzzy logic are better choices of control algorithms. The main aim of this control algorithm is to adjust the variation of the voltage, current and power at the maximum power point obtained under the specific values of irradiance and temperature.

P&O Algorithm
In this algorithm based on the previous value of the power, the value of the reference voltage and current keeps on changing (i.e., increasing or decreasing) until it attains the maximum power point [27,28]. This perturbation causes changes in the power of the solar module. If the power increases due to the perturbation, it moves the operating point of the PV array to MPP and continues to disturb the PV voltage in the same direction. After reaching the maximum power, the next instant power reduces and consequently reverses the perturbation. The size of the perturbation kept is minimal in order to maintain the power variation. For set the reference perturbation voltage, the additional Proportional Integral controller was utilized to calibrate the duty cycle ratio of the MPPT-based converter. It was observed that there was some power loss due to this perturbation and that it sometimes also failed to track the power under rapidly varying atmospheric conditions. However, this algorithm is well known for its simplicity, showing better stability in the response under slow transient conditions and at a very high voltage oscillation.

FUZZY Algorithm
The Fuzzy algorithm overcomes the disadvantages of the P&O algorithm. Fuzzy is one of the most optimal and attractive technical tools in all control fields as it deals with indefinite and uncertain information and makes decisions like humans. Thus, fuzzy control is applied to non-linear systems. The solar panel is a powerful, non-linear system. Various control algorithms have been worked out under the maximum power point tracking algorithm [29,30]. The fuzzy-based control algorithm is efficient because it can automatically adjust the output deviation to a constant value based on specific fuzzy rules. The control rules are framed, and the elements are determined based on the theory that in the transient state significant errors need coarse control which requires coarse input/output, while small errors need fine control which requires excellent input/output variables. Based on this, the elements of the rule table are obtained.

GWO Algorithm
The grey wolf optimization algorithm is being employed to achieve a better MPPT [9]. Mirjalili first proposed the Grey wolf algorithm in 2014. It is a mathematical model which follows the social behaviour of the grey wolf pack when hunting prey. The wolves in the pack are divided into different categories based on their fitness and strength. The different categories are alpha (α), beta (β), delta (δ) and omega (ω). The fittest wolf in the pack is alpha (α), while the wolves with a fitness close to alpha are beta (β) and delta (δ), and the rest of the wolves constitute omega (ω). The same structure is then used by the pack to hunt the prey by tracking, encircling and attacking. Here, the alpha (α), beta (β) and delta (δ) wolves play the primary role.
The same phenomenon is considered in the GWO optimization model. The model divides the available solutions for a given problem into different categories as per their closeness to the desired output and also moves the solutions towards the desired values, just like the wolf pack tracking the prey, encircling the solution and finally achieving the desired solution. The solution which falls into alpha (α) is used by the mathematical model to reach the optimal solution. The equation used by the GWO to achieve this is given below: Here, it indicates the current iteration. D represent the vector coefficients, and these vectors are calculated using the below formula: where the values of the vector a are linearly decreased from 2 to 0 as the iterations proceed, and r 1 , r 2 are randomly chosen vectors in [0, 1]. In this paper, the GWO math model is used to achieve the maximum power point tracking with the help of a modified LUO converter whose switching pulse's duty cycle can be varied in an optimal way to achieve the maximum power from the PV array. The GWO performs the desired calculations to achieve MPP. The flow chart for the GWO-based MPPT is shown in Figure 3. The duty cycle (D) of the switching pulse of the modified Luo converter represents the Grey wolf. Therefore, we can rewrite Equation (17) as: The duty cycle (D) of the switching pulse of the modified Luo converter represents the Grey wolf. Therefore, we can rewrite Equation (17) as: The objective function of the proposed GWO algorithm is given by: where V indicates the output voltage, d is the duty cycle, 'i' is the number of current Grey wolves and k is the number of iterations. For the MPPT tracking presented in this paper, the duty cycle of the DC-DC converter is referred to like the positions of the wolves in each state, and during iteration, the best value is considered as the K P , K i values of the PI controller.

Simulation and Experimental Results of the Proposed System
The proposed method is simulated using MATLAB. Here, in the DC-DC converters, IGBTs are utilized to reduce the switching power losses. The MPPT algorithm regulates the control signal produced by the PI controller, PWM pulses for the LUO converter and the input to the three-phase inverter. The proposed method is developed, modeled and simulated under starting and steady-state conditions.

Performance of the Converter
The solar panel is consistently operated at the minimum and maximum power level utilizing the proposed GWO optimized algorithm. The tracking of the maximum power is purposely increased at the start in order to achieve the smooth start of the BLDC drive. The perturbation size is appropriately selected in order to avoid oscillation during the peak powerpoint. The DC link voltage across the capacitor is supplied to the VSI for the smooth start of the BLDC drive. The solar panel is operated under the conditions of dynamic variation due to changes in the irradiation level. Using the GWO algorithm, the proportional and integral gain is varied as it is mainly designed to obtain an excellent dynamic response under conditions of uncertainty and external disturbances. The GWO-based closed-loop control algorithm tracks the maximum power from the system. The output voltage (see in Figure 4a) and current (see in Figure 4b inverter. The proposed method is developed, modeled and simulated under starting and steady-state conditions.

Performance of the Converter
The solar panel is consistently operated at the minimum and maximum power level utilizing the proposed GWO optimized algorithm. The tracking of the maximum power is purposely increased at the start in order to achieve the smooth start of the BLDC drive. The perturbation size is appropriately selected in order to avoid oscillation during the peak powerpoint. The DC link voltage across the capacitor is supplied to the VSI for the smooth start of the BLDC drive. The solar panel is operated under the conditions of dynamic variation due to changes in the irradiation level. Using the GWO algorithm, the proportional and integral gain are varied as it is mainly designed to obtain an excellent dynamic response under conditions of uncertainty and external disturbances. The GWO-based closed-loop control algorithm tracks the maximum power from the system. The output voltage (see in Figure 4a) and current (see in Figure 4b) waveforms of the solar PV panel are shown in Figure 4. From Figure 4, it is observed that the output voltage from the PV panel is approximately 55 Volts, and the output current generated by the PV panel is 17 Amps. Here, the PV panel is integrated with the MPPT technique. For prove the effectiveness of the proposed controller in MPPT tracking, a comparative study was done using various MPPT algorithms.
In Figure 5, the output waveform of the modified LUO converter using the GWO algorithm is shown. Initially, a peak is observed, and later at the time > 0 s the voltage value settles to a value of approximately 300 Volts. The output voltage produced by the proposed modified LUO converter is compared with the P&O and Fuzzy logic algorithms. From Figure 4, it is observed that the output voltage from the PV panel is approximately 55 Volts, and the output current generated by the PV panel is 17 Amps. Here, the PV panel is integrated with the MPPT technique. For prove the effectiveness of the proposed controller in MPPT tracking, a comparative study was done using various MPPT algorithms.
In Figure 5, the output waveform of the modified LUO converter using the GWO algorithm is shown. Initially, a peak is observed, and later at the time > 0 s the voltage value settles to a value of approximately 300 Volts. The output voltage produced by the proposed modified LUO converter is compared with the P&O and Fuzzy logic algorithms.
with the MPPT technique. For prove the effectiveness of the proposed controller in MPPT tracking, a comparative study was done using various MPPT algorithms.
In Figure 5, the output waveform of the modified LUO converter using the GWO algorithm is shown. Initially, a peak is observed, and later at the time > 0 s the voltage value settles to a value of approximately 300 Volts. The output voltage produced by the proposed modified LUO converter is compared with the P&O and Fuzzy logic algorithms.  The input and output currents drawn by the proposed system are shown in Figure 6a,b, respectively. Here, the current ripples are maintained within the permissible limit. The three-phase output voltage waveform of the voltage source inverter is shown in Figure 7. The input and output currents drawn by the proposed system are shown in Figure 6a,b, respectively. Here, the current ripples are maintained within the permissible limit. The three-phase output voltage waveform of the voltage source inverter is shown in Figure 7.

BLDC Motor Pump Performance
Here, the starting and steady-state performances of the BLDC motor pump are exhibited. If there is any change in the level of irradiance, all the parameters in the BLDC motor pump vary according to the irradiance level. Usually, the BLDC runs above 1100 rpm. However, the required speed to pump water is below this speed at a low irradiance level of a minimum of 200 W/m 2 . The proposed work is not intended to find the one among the best optimization algorithms, rather than to prove that the optimization technique can outperform the competitive fuzzy and elementary P&O algorithms. The Luo converter and its modified versions are considered to measure the comparative performance of the BLDC motor. Figure 8 shows the output current waveforms of the BLDC motor The input and output currents drawn by the proposed system are shown in Figure 6a,b, respectively. Here, the current ripples are maintained within the permissible limit. The three-phase output voltage waveform of the voltage source inverter is shown in Figure 7.

BLDC Motor Pump Performance
Here, the starting and steady-state performances of the BLDC motor pump are exhibited. If there is any change in the level of irradiance, all the parameters in the BLDC motor pump vary according to the irradiance level. Usually, the BLDC runs above 1100 rpm. However, the required speed to pump water is below this speed at a low irradiance level of a minimum of 200 W/m 2 . The proposed work is not intended to find the one among the best optimization algorithms, rather than to prove that the optimization technique can outperform the competitive fuzzy and elementary P&O

BLDC Motor Pump Performance
Here, the starting and steady-state performances of the BLDC motor pump are exhibited. If there is any change in the level of irradiance, all the parameters in the BLDC motor pump vary according to the irradiance level. Usually, the BLDC runs above 1100 rpm. However, the required speed to pump water is below this speed at a low irradiance level of a minimum of 200 W/m 2 . The proposed work is not intended to find the one among the best optimization algorithms, rather than to prove that the optimization technique can outperform the competitive fuzzy and elementary P&O algorithms. The Luo converter and its modified versions are considered to measure the comparative performance of the BLDC motor. Figure 8 shows the output current waveforms of the BLDC motor for phases A, B and C, respectively. In Figure 9, the back emf of the BLDC motor is shown. The back emf cuts the magnetic flux and opposes the current flowing through the conductor. The starting value of the back emf is zero, and the values depend on the speed of rotation of the armature conductor.        Figure 10 shows the starting and steady-state behaviour of the BLDC motor. The speed and electromagnetic torque reach their steady-state value when the maximum power is tracked by the GWO algorithm. Figure 9. The back emf of the BLDC motor. Figure 10 shows the starting and steady-state behaviour of the BLDC motor. The speed and electromagnetic torque reach their steady-state value when the maximum power is tracked by the GWO algorithm. Figure 10. Steady-state response of the BLDC motor speed. Figure 10. Steady-state response of the BLDC motor speed. Figure 11 shows the torque waveform of the BLDC motor before using the LUO converter. Here, the starting torque is high and is equal to 6 Nm, and the steady-state torque occurs at 0.12 s with a ripple of 5.5 Nm. Figure 12 shows the torque characteristics of the BLDC motor after using the LUO converter, as a result of which the ripples are reduced.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 19 Figure 11 shows the torque waveform of the BLDC motor before using the LUO converter. Here, the starting torque is high and is equal to 6 Nm, and the steady-state torque occurs at 0.12 s with a ripple of 5.5 Nm. Figure 12 shows the torque characteristics of the BLDC motor after using the LUO converter, as a result of which the ripples are reduced.  The comparative results are given in Table 2, where it is seen that the proposed system is more efficient when compared to other MPPT algorithms and converter topologies, with an efficiency of 97.8%. The settling time and the output voltage gain are also better when compared to other methods. Usually, the optimization technique consumes significantly more time, which is, however, less than the manual tuning of the PI controller. Table 2 mentions the time taken by the system to settle after Figure 11. Output load torque characteristics of the BLDC motor before using the LUO converter.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 19 Figure 11 shows the torque waveform of the BLDC motor before using the LUO converter. Here, the starting torque is high and is equal to 6 Nm, and the steady-state torque occurs at 0.12 s with a ripple of 5.5 Nm. Figure 12 shows the torque characteristics of the BLDC motor after using the LUO converter, as a result of which the ripples are reduced.  The comparative results are given in Table 2, where it is seen that the proposed system is more efficient when compared to other MPPT algorithms and converter topologies, with an efficiency of 97.8%. The settling time and the output voltage gain are also better when compared to other methods. Usually, the optimization technique consumes significantly more time, which is, however, less than the manual tuning of the PI controller. Table 2 mentions the time taken by the system to settle after The comparative results are given in Table 2, where it is seen that the proposed system is more efficient when compared to other MPPT algorithms and converter topologies, with an efficiency of 97.8%. The settling time and the output voltage gain are also better when compared to other methods. Usually, the optimization technique consumes significantly more time, which is, however, less than the manual tuning of the PI controller. Table 2 mentions the time taken by the system to settle after the tuning process is completed. The literature also shows that for a particular PI controller, it takes 10 s, whereas it is reduced to 4 s when using an optimization technique.  Figure 13 shows the output voltage comparison of different MPPT methods. As the progression reaches the proposed method, the performance (higher output voltage) of the developed method (modified LUO converter with GWO) shows more improvement than the existing approaches. Figure 14 shows the efficiency comparison of the different MPPT methods. As the progression reaches the proposed method, the performance (higher efficiency) of the developed method (modified LUO converter with GWO) shows more improvement than the existing approaches.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 19 Figure 13 shows the output voltage comparison of different MPPT methods. As the progression reaches the proposed method, the performance (higher output voltage) of the developed method (modified LUO converter with GWO) shows more improvement than the existing approaches. Figure  14 shows the efficiency comparison of the different MPPT methods. As the progression reaches the proposed method, the performance (higher efficiency) of the developed method (modified LUO converter with GWO) shows more improvement than the existing approaches.

Experimental Results
The proposed method was verified experimentally by conducting a real-time test study. A practical setup was developed: first, the LUO converter and controller circuit designs were developed as demanded by the simulation requirements. The experimental setup shown in Figure 15 includes this designed controller and converter, along with the few additional components like the voltage source inverter, autotransformer, rheostat and BLDC motor. In Figure 16a, the output voltage of the PV panel is shown. This voltage consists of higher-order ripple contents which are oscillatory. To reduce this problem, the voltage is fed to the modified LUO converter. Figure 16b shows the modified LUO converter output voltage. This constant and ripple-free voltage is achieved using the LUO converter and its optimized MPPT algorithm. This constant voltage is fed to the three-phase inverter which converts the DC voltage into AC voltage.

Experimental Results
The proposed method was verified experimentally by conducting a real-time test study. A practical setup was developed: first, the LUO converter and controller circuit designs were developed as demanded by the simulation requirements. The experimental setup shown in Figure 15 includes this designed controller and converter, along with the few additional components like the voltage source inverter, autotransformer, rheostat and BLDC motor. In Figure 16a, the output voltage of the PV panel is shown. This voltage consists of higher-order ripple contents which are oscillatory. For reduce this problem, the voltage is fed to the modified LUO converter. Figure 16b shows the modified LUO converter output voltage. This constant and ripple-free voltage is achieved using the LUO converter and its optimized MPPT algorithm. This constant voltage is fed to the three-phase inverter which converts the DC voltage into AC voltage.     Figure 17 shows the PWM pulses fed to the switching devices of the voltage source inverter. The PI controller manages the pulse width for speed compensation. The dsPIC produces PWM pulses with a switching frequency of 10 kHz.         Figure 18 shows the position of the rotor signal from the three hall effect sensors which are mounted on the stator. Based on the rotor position signals, the electronic commutator switches are energised. Figure 19 shows the output voltage from the three-phase voltage source inverter, which also includes back emf. Due to the presence of this back emf, the supply voltage is trapezoidal. Figure 20 shows the BLDC motor output current waveform. The modified LUO converter maintains the current within a specific limit. Figure 21 illustrates the speed waveform of the BLDC motor using the closed-loop PI control technique. Here, the reference speed and actual speed are compared and shown in the graph. The PI controller makes the speed constant in terms of the load.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 19 Figure 18 shows the position of the rotor signal from the three hall effect sensors which are mounted on the stator. Based on the rotor position signals, the electronic commutator switches are energised. Figure 19 shows the output voltage from the three-phase voltage source inverter, which also includes back emf. Due to the presence of this back emf, the supply voltage is trapezoidal.   Figure 20 shows the BLDC motor output current waveform. The modified LUO converter maintains the current within a specific limit. Figure 21 illustrates the speed waveform of the BLDC motor using the closed-loop PI control technique. Here, the reference speed and actual speed are compared and shown in the graph. The PI controller makes the speed constant in terms of the load.   Figure 18 shows the position of the rotor signal from the three hall effect sensors which are mounted on the stator. Based on the rotor position signals, the electronic commutator switches are energised. Figure 19 shows the output voltage from the three-phase voltage source inverter, which also includes back emf. Due to the presence of this back emf, the supply voltage is trapezoidal.   Figure 20 shows the BLDC motor output current waveform. The modified LUO converter maintains the current within a specific limit. Figure 21 illustrates the speed waveform of the BLDC motor using the closed-loop PI control technique. Here, the reference speed and actual speed are compared and shown in the graph. The PI controller makes the speed constant in terms of the load.

Conclusions
The modified LUO converter-fed VSI-BLDC motor with a solar PV array for a water pumping application was developed using MATLAB/Simulink and the Simpower system toolbox, whose suitability was exhibited by simulated results. Initially, to meet the various desired objectives, the developed system was logically designed.
The proposed method was simulated and modelled to evaluate the performance under initial and steady-state conditions. The integration of the modified LUO converter was justified by evaluating its performance with the SPV array-based water pumping BLDC motor drive. The developed method availed many desired operations such as the absorption of MPP from the SPV array, BLDC motor soft starting, the fundamental switching frequency of the VSI (resulting in low switching losses), a reduction in the switch stress and the continuous conduction mode of the modified LUO converter for stable operation. Even at a very low solar irradiance, the developed method was operated successfully.
The GWO-optimized algorithm optimally extracted maximum power from the PV system when compared to the P&O and Fuzzy logic MPPT algorithms. The scaling-up of the power rating of the

Conclusions
The modified LUO converter-fed VSI-BLDC motor with a solar PV array for a water pumping application was developed using MATLAB/Simulink and the Sim-power system toolbox, whose suitability was exhibited by simulated results. Initially, to meet the various desired objectives, the developed system was logically designed.
The proposed method was simulated and modelled to evaluate the performance under initial and steady-state conditions. The integration of the modified LUO converter was justified by evaluating its performance with the SPV array-based water pumping BLDC motor drive. The developed method availed many desired operations such as the absorption of MPP from the SPV array, BLDC motor soft starting, the fundamental switching frequency of the VSI (resulting in low switching losses), a reduction in the switch stress and the continuous conduction mode of the modified LUO converter for stable operation. Even at a very low solar irradiance, the developed method was operated successfully.
The GWO-optimized algorithm optimally extracted maximum power from the PV system when compared to the P&O and Fuzzy logic MPPT algorithms. The scaling-up of the power rating of the motor and converter did not affect the performance of the pumping system unless the incoming torque of the motor was not affected by the converter. Hence, the proper design of the converter ensured the overall performance of the system. The system may be economical if it is operating with better performance; as stated earlier, the incoming torque has a direct effect on the performance, which affects the overall economic value. While scaling up the system, considering the performance based on the systems' service life is essential, and this will allow us to make decisions on when to change the converter if any operating issues occur. The regular maintenance of the converters may ensure economic gains from the system. Furthermore, from the results, it was seen that the proposed system was more efficient when compared to other MPPT algorithms and converter topologies, with a maximum efficiency of 97.8%. In comparison, the average performance shown by the Fuzzy optimized modified Luo converter was 94%, and the lowest performance, about 86%, as shown by the conventional P&O algorithm. The settling time was also better when compared to other methods, with a minimum settling time of 0.009 s for GWO and of 0.02 s for the P&O algorithm. Similarly, the voltage gain of the proposed method was higher, with a voltage of 298 V, while for Fuzzy and P&O it was 289 V and 280 V. The experimental outcomes were validated with the simulated results.
Furthermore, this work plans to extend the performance analysis of the BLDC pumping motor for a higher-rated three-phase power system with the proposed converter.