*3.6. Modeling and Motor Choice*

In recent years, many electric motors have been used in electric vehicles. In the erickshaw, the DC motor's dynamic properties are better; the main disadvantage of the DC motor is that it needs more maintenance due to the brush and commutator. Induction motors are therefore a better option, because they are often suitable for such circumstances, but the induction motor needs huge control. Thus, in automotive applications, the induction motor is not usually employed. After that, the researchers take an alternative and find a trustworthy and effective motor. The BLDC motors are easy to regulate, require less maintenance, and have a high roughness. It has high torque, fast dynamic responses, a low operating voltage range, and a good performance ratio.

The BLDC motor consists of a permanent magnet stator and three-phase windings in the rotor. The currents generated in the rotor can be neglected, and there is no need to model damper windings if the stainless-steel retaining sleeves and magnet have high resistance. The analogous circuit of a BLDC motor is depicted in Figure 8, where R is a stator resistance, L is self-inductance and mutual inductance, and e is phase back-EMF voltage of A, B, and C, respectively. The 3 φ winding governing equation for the phase variables is

$$
\begin{bmatrix} V\_a^\* \\ V\_b^\* \\ V\_c^\* \end{bmatrix} = \mathbb{R}^\* \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} i\_a^\* \\ i\_b^\* \\ i\_c^\* \end{bmatrix} + \begin{bmatrix} l-m & 0 & 0 \\ 0 & l-m & 0 \\ 0 & 0 & l-m \end{bmatrix} \frac{d}{dt} \begin{bmatrix} i\_a^\* \\ i\_b^\* \\ i\_c^\* \end{bmatrix} + \begin{bmatrix} E\_a^\* \\ E\_b^\* \\ E\_c^\* \end{bmatrix} \tag{9}
$$

**Figure 8.** BLDC motor equivalent circuit.

*R\** = phase resistance, *m* = mutual inductance, *l* = phase inductance. The mechanical equation is shown below:

$$J^\* \cdot \frac{d\omega\_r^\*}{dt} = T\_\varepsilon^\* - T\_l^\* - f\_r^\* \omega\_r^\* \tag{10}$$

Finite element analysis is used to calculate the three back-EMFs, and Fourier series equations are used to display the results. It is a ratio of speeds.

#### **4. Control Method Using MPA Technique**

As shown in Figure 1, to carry out the required operation and to get the output from PV, MPPT with a DC-DC converter is needed. In the implementation of MPPT, a control variable (duty cycle) is controlled by the MPPT controller. This generates a control signal in the range [0, 1] which is given in Equations (11) and (12):

$$\mathbf{V}\_{\text{out}} = \frac{\mathbf{V}\_{\text{in}}}{1 - \mathbf{d}} \tag{11}$$

$$\mathbf{d} = \frac{\mathbf{T}\_{\text{on}}}{\mathbf{T}\_{\text{Switching}}} \tag{12}$$

where, Vout and Vin are boost converter output and input voltages, and d denotes the duty cycle. This article gives a new bioinspired algorithm based on marine predators' social behavior pattern.
