## 2 Materials and Methods  
This section summarizes the various aspects associated with research on induction machines. The phasor diagram of indirect vector control is shown in Figure 1, while the synchronous reference frame mode of the induction machine can be expressed as in Equation (1):  
\[ \begin{bmatrix}\text{V}_{\text{qs}}^{\text{e}}\\ \text{V}_{\text{qs}}^{\text{e}}\\ \text{V}_{\text{qr}}^{\text{e}}\\ \text{V}\end{bmatrix} = \begin{bmatrix}\text{R}_{\text{s}}+\text{L}_{\text{s}} \text{P}\;\omega_{\text{s}}\text{L}_{\text{s}}\;\text{L}_{\text{m}}\text{P}\; \omega_{\text{s}}\text{L}_{\text{m}}\\ -\omega_{\text{s}}\text{L}_{\text{s}}\;\text{R}_{\text{s}}+\text{L}_{\text{s}} \text{P}-\omega_{\text{s}}\text{L}_{\text{m}}\text{P}\\ \text{L}_{\text{m}}\text{P}\;(\omega_{\text{s}}-\omega_{\text{r}})\text{L}_{ \text{m}}\;\text{R}_{\text{r}}+\text{L}_{\text{r}}\;(\omega_{\text{s}}-\omega _{\text{r}})\text{L}_{\text{r}}\\ -(\omega_{\text{s}}-\omega_{\text{r}})\text{L}_{\text{m}}\;\text{L}_{\text{m}} \text{P}\;-(\omega_{\text{s}}-\omega_{\text{r}})\text{L}_{\text{r}}\;\text{R} _{\text{r}}+\text{L}_{\text{r}}\text{P}\end{bmatrix} . \begin{bmatrix}\text{i} _{\text{qs}}^{\text{e}}\\ \text{i}_{\text{qs}}^{\text{e}}\\ \text{i}_{\text{qr}}^{\text{e}}\\ \text{i}_{\text{dr}}^{\text{e}}\end{bmatrix} . \tag{1}\]  
Electromagnetic torque can be expressed as in Equation (2):  
\[\text{T}_{\text{e}}=\frac{3}{2}\frac{\text{P}}{2}\text{L}_{\text{m}}\left( \text{i}_{\text{qs}}^{\text{e}}\text{i}_{\text{dr}}^{\text{e}}-\text{i}_{ \text{ds}}^{\text{e}}\text{i}_{\text{qr}}^{\text{e}}\right) \tag{2}\]  
where:  
\(\omega_{\text{s}}\): Synchronous speed  
\(\omega_{\text{r}}\): Electrical speed (rotor speed)  
P: Number poles of IM  
T\({}_{\text{e}}\): Electromagnetic torque
Making the appropriate choice of DC battery with effective performance is of considerable importance in many real-life applications. The Li-ion battery type is emerging as a source of enhanced energy, a better rating of power, and an improved charging/discharging cycle, with proficiency in the pulsated types of energy conversion systems. A preselected value for the charge/discharge cycle is essential to increase the lifetime of the Li-ion battery. Battery life-restrictive issues are defined as a drop in battery ability and are caused by a rise in the internal source resistance of DC batteries [3]. Generally, EVs are powered by a commercial battery management system (CBMS). The CBMS provides an alternative to traditional battery packs, which can cause thermal runaway loss. For this reason, individual batteries are often replaced by a commercial battery management system [4]. An inverter-fed mechanism is used to deliver a 3-phase supply to the IM. An IGBT inverter, operating at a higher switching frequency, performs better than the older models. A hysteresis-band PWM (pulse-width modulation) provides optimum performance over the inverter losses. The terminal voltages and respective currents or flux sense windings are included when determining the field angle for a direct vector control strategy [5]. PI-based  
Figure 1: Phasor diagram of indirect vector control. controllers are more applicable as a way to regulate the torque and flux feedback toward reference values. The proportional controller decreases the rise time, whereas an integral controller eliminates steady-state error in order to attain the set parameters efficiently [6]. In a speed-sensorless vector-controlled induction drive, both torque and flux are controlled independently. Previous studies suggest that peak power is achieved by using incremental and conductance-based MPPT (maximum power point tracking) algorithms. [7]. The MRAS (model reference adaptive system) is another technique that can be used to provide a robust defense and effectively ensures good performance against variations in the parameters, noise removal, and error measurements The space vector modulation (SVM) technique imposes a tension vector through the vector modulation of space for a predictive selection of torque and flux [8].