*2.2. Luo Converter Mathematical Modeling*

Renewable technology comprises DC-DC topologies for yield of energy harvest with admissible proficiency. With respect to other DC-DC converters, modern Luo topology depicted in Figure 3 delivers reasonable cost, better power/density ratio and enhanced transformation efficiency. It comprises the least ripple content with geometric output voltage and surpasses the parasitic element action. The auxiliary benefit of this topology is switched components, which take ground as a reference. In addition to that, the input inductor smoothes the ripple present to input source. Employed capacitors get charged to stated value to accomplish high voltage leveled. Table 1 presents the designed parameters of Luo Converter used during practical implementation.

**Figure 3.** Power Circuit Luo converter.

**Table 1.** Luo converter parameter.


Transfer gain voltage is evaluated as [24,25]:

$$\frac{V\_0}{V\_S} = \frac{2 - d\_{duty}}{1 - d\_{duty}}\tag{3}$$

Relation between inductor ripple current and duty cycle is expressed as:

$$
\Delta I\_{L\_{Ripple}} = \frac{V\_S \times d\_{duty}}{f\_{Pulsc} \times L} \tag{4}
$$

Capacitors (*C*=*C*1) values are determined mathematically as:

$$\mathcal{C} = \mathcal{C}\_1 = \frac{\left(1 - d\_{duty}\right) \times V\_0}{f\_{Pulse} \times R\_{Load} \times \Delta V\_0} \tag{5}$$

where,

*dduty* = Duty ratio *fPulse* = Frequency of Switched pulse *V*<sup>0</sup> = Output Voltage of Luo Converter

#### *2.3. A Hybrid Proposed FLC-ANN Tuned FPA MPPT*

In this proposed scheme, the hybrid ANFIS-FPA MPPT algorithm is realized for maximizing PV outturn and accurate motion control with PV-pump interface. The FLC data is trained by ANN which is finally optimized by FPA method, leading to minimum RMSE of FLC and ANN. It comprises the dominance of both FLC and ANN. The threshold and weight of NN models are optimized by FPA algorithm to produce minimum RMSE. Figure 4 depicts the complete structure of hybrid learning in which learning data has been achieved from FLC architecture. The FLC architecture comprises fuzzification, Inference Rule base and defuzzification as elemental constituents. Real variables are converted to linguistic parameters using fuzzification. The requisite output is introduced by the Mamdani fuzzy inference rule deployed by max-min composition. With the help of centroid method, the defuzzification process converts the linguistic parameters to real values. Parameters used in FLC and ANN are presented using Table 2. Employed membership values are illustrated in Figure 5. The FPA method of MPPT is predicted by reproduction of flower of transferring pollen. This convection is possible through biotic/cross and abiotic/self-pollination. In cross-pollination the pollens are translated between two unlike flowers. On the other hand, abiotic pollination takes place between distant species. It is noted that in flower pollination 90% possibility of cross-pollination and only 10% possibility of self-pollination happen, which is limited in the probability range R*ε*[1,0]. Table 3 describes ANFIS-FPA parameters used for practical validation of BLDC-driven PV pumping. The complete process is based on the following 4 rules [22]. The min-max composition (Mamdani's rule) is employed to calculate the fuzzy error (*E*) and change in error (*dE*/*CE*) input as [23]:

$$E(r) = \frac{dP\_{PV}(r)}{dV\_{PV}(r)}\tag{6}$$

$$dE = E(r) - E(r-1) \tag{7}$$

$$
\mu\_{P \to Q}(\mathbf{x}y) = \min \left[ \mu\_P(\mathbf{x}), \mu\_Q(y) \right], \qquad \forall P \in X, \forall Q \in Y \tag{8}
$$

where,

*μP*(*x*) = Membership function of *P* fuzzy set in *X* Universe of discourse

*μQ*(*y*) = Membership function of *Q* fuzzy set in *Y* Universe of discourse

*X*,*Y* = *x*, *y* variables defined in Universe *X* and *Y*, respectively

**Figure 4.** Complete structure of hybrid ANFIS-FPA.

**Table 2.** Parameters used in FLC and ANN.


**Figure 5.** Employed membership values.

**Table 3.** ABC-FPA Parameters.


Output *D* is calculated as:

$$\mathcal{D} = \frac{D \in \mathcal{S}^{\int \mu\_D(D) dD}}{D \in \mathcal{S}^{\int \mu\_D(D)}} \tag{9}$$

where,

*D*ˆ = Crisp output *μD*(*D*) = Membership function (Aggregated) *D* = Fuzzy output *S* = Subarea/Universe of discourse

Also, neural-fuzzy network output (*D*) expressed mathematically as:

$$
\overrightarrow{D} = \mu\_A(E) \times \mu\_B(dE) \times \mathcal{W}\_{Li} \tag{10}
$$

where,

*μA*(*E*) = Membership function of fuzzy set *A* in *E* universe of discourse *μB*(*dE*) = Membership function of fuzzy set *B* in *dE* universe of discourse *WLi* = Weight of consequent *i*th layer

The ANFIS objective function is expressed mathematically as:

$$RMSE = \left[ \frac{1}{P} \sum\_{i=1}^{P} (D - \overline{D})^2 \right]^{1/2} \tag{11}$$

where,

*P* = Total sample

*D* = Fuzzy output

*D* = Neural network output

Rule I: Biotic pollination uses levy flight for transferring pollens and is called global pollination in which the *i*th pollen solution vector is expressed mathematically using Equation (12). The Levy flight factor is accountable for pollens transport which improves the methodology of pollination where scaling factor is responsible to limit step size.

$$\mathbf{X}\_{i}^{T+1} = \mathbf{X}\_{i}^{T} + \mathbf{L}\_{f} \times \gamma\_{\text{scaling}} \times \left(\mathbf{X}\_{i}^{T} - \mathbf{G}\_{\text{best}}\right) \tag{12}$$

where,

*X<sup>T</sup> <sup>i</sup>* = Vector representing solution *T* = No. of iteration *Lf* = Levy flight factor *γscaling* = Scaling factor *Gbest* = Global best solution

Rule II: Self-pollination is termed as local pollination and characterized mathematically as:

$$X\_i^{T+1} = X\_i^T + P\_f \times \left(X\_m^T - X\_n^T\right) \tag{13}$$

*X<sup>T</sup> <sup>m</sup>* and *X<sup>T</sup> <sup>n</sup>* = two unlike pollen in the species

*Pf* = Switched probability

Rule III: The performance of the flower is assumed to be identical to the probability of reproduction which is equivalent to resemblance of two concerned flowers.

Rule IV: Pollination is interchanged between global and local, which depends on switching probability which lies between 0 and 1.

The proposed nature-inspired FPA algorithms are responsible for providing proper learning of the neural network to reduce root mean square error between outcomes of *D*(Fuzzy output) and *D* (Neural network output). Pollen position (duty ratio) is updated using biotic/abiotic pollination for the next iteration. Under step variation in solar insolation, the corresponding variance in voltage/current threshold is expressed mathematically as [22]:

$$\frac{dP\_{PV}(n)}{dV\_{PV}(n)} \ge 0.2\tag{14}$$

$$\frac{dI\_{PV}(n)}{I\_{PV}(n)} \ge 0.1\tag{15}$$

where,

*VPV*(*n*) =*n*th iteration PV voltage *IPV*(*n*) =*n*th iteration PV current *dVPV*(*n*) = change in PV voltage (*n*th and (*n* − 1)th iteration)

#### *2.4. Electronic BLDC Commutator and VSI Switching*

Commutation in Permanent Magnet DC Motor (PMDC) is obtained by a commutator and brushes. Nevertheless, hall sensors are important components employed in BLDC motors which sense the position of a rotor as the commutation wave. Coils and permanent magnets are employed as stator and rotor respectively, in which stator's magnetic field rotates the rotor. Armature of a BLDC motor consists of a permanent magnet as a substitute of the coil which does not require brushes. Figure 6 demonstrates BLDC-driven structure with induced EMF and reference current. The electronic commutation process is used to control the VSI-employed BLDC motor in which winding current is adjusted with the help of decoder in proper sequence. In this method, symmetrical DC currents are situated in the phase voltage at 120◦. Based on the motor alignment, the hall sensors produce signals of 60◦ phase difference. The gating signal for 3-phase VSI generated by transforming hall signals using the decoder is illustrated in Figure 7. The pulse width modulated pulses are generated by comparing triangular signal with duty cycle produced through MPPT. Table 4 portrays Hall signals and Switching states of BLDC used with electronic commutation. The high-frequency PWM pulses and six fundamental signals are operated with an AND gate, which produces 6 gating pulses for VSI inverter. As the atmospheric conditions change, the duty cycle is also regulated using MPPT methods which control the VSI and finally the BLDC motor is adjusted accordingly.

The BLDC motor is analyses mathematically as [27]:

$$
\begin{bmatrix} V\_{ap} \\ V\_{bp} \\ V\_{cp} \end{bmatrix} = \begin{bmatrix} R\_T & 0 & 0 \\ 0 & R\_T & 0 \\ 0 & 0 & R\_T \end{bmatrix} \begin{bmatrix} I\_{dp} \\ I\_{bp} \\ I\_{cp} \end{bmatrix} + \begin{bmatrix} L\_1 - M\_1 & 0 & 0 \\ 0 & L\_1 - M\_1 & 0 \\ 0 & 0 & L\_1 - M\_1 \end{bmatrix} \frac{d}{dx} \begin{bmatrix} I\_{dp} \\ I\_{bp} \\ I\_{cp} \end{bmatrix} + \begin{bmatrix} E\_{bd} \\ E\_{bb} \\ E\_{bc} \end{bmatrix} \tag{16}
$$

Developed electromagnetic torque (*TEM*) by BLDC motor can be expressed mathematically as:

$$T\_{EM} = \frac{E\_{ba} \times I\_{ap} + E\_{bb} \times I\_{bp} + E\_{bc} \times I\_{cp}}{\omega\_{rotor}} \tag{17}$$

where,

*Vap*, *Vbp*, *Vcp* = Phase voltage of a 3-Phase BLDC motor *Iap*, *Ibp*, *Icp* = Phase Currents *Eba*, *Ebb*, *Ebc* = Phase Back EMF of BLDC motor *L*<sup>1</sup> = Each Phase self-inductance *M*<sup>1</sup> = Two phase's mutual inductance

*TEM* = Developed Electromagnetic torque of BLDC motor *ωRotor* = Rotor Speed

**Figure 6.** (**a**) BLDC driven structure (**b**) induced EMF and reference current.

**Figure 7.** Gating signal for 3-phase VSI.


**Table 4.** Hall signals and Switching states.

#### **3. Experimental Results**

Performance justification of the BLDC-driven PV pumping-employed Luo converter has been done through the dSPACE controller. For the purposes of MPPT operation, LA-55/LV-25 as current/voltage sensors are employed during practical implementation. Figure 8 portrays the BLDC-driven Luo converter-employed PV-pumping hardware developed in the laboratory. With the help of an A/D converter, analog pulses are transformed to digital and fed to the dSPACE interface. Electronic commutation/controlling BLDC has been executed by obtaining hall pulses from the input/output terminal and then generated pulses are outturned to the inverter.

**Figure 8.** BLDC-driven Luo converter-employed PV-pumping hardware.

#### *3.1. Steady-State Performance*

The experimental behaviors of the PV module and motor pumping system have been tested under steady-state condition of irradiance level 1000 W/m2. The proposed MPPT design technique is working effectively and tracks optimal power from PV module with unity duty cycle at 1000 W/m2 solar insolation level depicted in Figure 9. Practical results obtained for the BLDC-driven Luo converter-employed PV pumping are described in Figure 9a PVG at 1000 W/m2. (Figure 9b) BLDC performance at 1000 W/m2. (Figure 9c) generated hall sensor pulses at 1000 W/m2 (Figure 9d) switched and hall pulses at 1000 W/m2 (Figure 9e) BLDC performance at 300 W/m<sup>2</sup> (Figure 9f) switched and hall pulses at 300 W/m2.The corresponding BLDC motor and torque (1500 rpm) has been demonstrated in Figure 9d presents the obtained hall sensor pulses with motor torque. The performance of the BLDC motor-pumping system has been evaluated with 300 W/m2 solar irradiance. The motor torque is experimentally obtained, which is sufficient to operate PV water pumping. Based on duty cycle generation using the MPPT algorithm, the corresponding hall signals have been generated to trigger six switches of the inverter.

**Figure 9.** BLDC-driven Luo converter-employed PV pumping (**a**) PVG at 1000 W/m2;(**b**) BLDC performance at 1000 W/m2; (**c**) generated hall sensor pulses at 1000 W/m2; (**d**) switched and hall pulses at 1000 W/m2; (**e**) BLDC performance at 300 W/m2; (**f**) switched and hall pulses at 300 W/m2.
