**1. Introduction**

The most popular motors utilized in economic mobility automation applications and primary-supply residential electrical consumables are AC induction machines. The key benefits of AC induction machines are their simplicity and robust construction, competitive prices, minimal servicing, and straightforward integration into an AC power supply. There are many different kinds of AC induction machines accessible in the industry. Several machines are appropriate for various functions [1]. However, AC induction machines are convenient to construct compared to DC machines. Controlling the rpm and torque in different varieties of AC induction machines requires a deeper grasp of the configuration and features of such motors. However, DC motors are efficient at commencing and moderating speed. Such machines have a great torque concentration [2]. A DC machine works quietly and has a hugely variable speed. The electromagnetic disturbance is minimal, and the overcurrent or inrush tolerance is substantial. The construction or assembly of a

**Citation:** Le Roux, P.F.; Ngwenyama, M.K. Static and Dynamic Simulation of an Induction Motor Using Matlab/Simulink. *Energies* **2022**, *15*, 3564. https:// doi.org/10.3390/en15103564

Academic Editor: Ryszard Palka

Received: 6 March 2022 Accepted: 18 April 2022 Published: 12 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

DC machine is one of its limitations. The commutator and the brush [3] have a rubbing connection, resulting in sparks and mechanical degradation. As a result, DC machines possess a comparatively limited operating lifespan, requiring a high service expense. This also casts uncertainties about the system's durability and safety. As a result, the usage of DC machines in some industrial applications is restricted nowadays [4].

Over the years, motors have revolutionised the mining and automation industry. Processes such as hoisting conveyor belt systems for moving minerals, e.g., gold, coal, diamonds, etc., from underground and opencast mines, depend largely on the utilisation of induction motors [5]. Thus, for the reliable operation of these machines, proper protection needs to be implemented for safe operation under load conditions. Any malfunction of an induction motor can be described as an electrical fault, environmental factor, or mechanical breakdown. Rotor bearings could result in overheating, wear, and tear due to mechanical stresses [6]. Drawing enormous magnitudes of currents ensure high temperatures. Modelling an induction motor is somewhat complex, stemming from its non-linear behaviour triggered by electromagnetic exhaustion and the significant temperature influence from the synchronous motor settings [7].

Furthermore, the shaft time constant of an induction motor can change due to rotor heat. Such characteristics render the mathematical modelling of induction motors somewhat insurmountable. Most researchers use simplified models that do not consider the factors mentioned above. Production of these machines is imperative and requires urgency in reproduction during their idle state [8].

Chitra and Prabhakar [9] presented a simulation of an induction machine by utilising the fuzzy logic approach. The authors applied the approach in their study in order to regulate the velocity of an induction machine to obtain the optimum torque with the least amount of loss. They used the field-oriented control approach to create a fuzzy logic controller that enables improved control of motor torque with greatly variable performance. Their simulated design was evaluated by utilising multiple Matlab toolboxes. They observed that the induction motor's efficiency increased in stable conditions. The results show that the suggested speed regulator was efficient and reliable.

Elnaghi et al. [10] proposed using a genetic algorithm (GA) to process experimental loads on an inductive machine. The principle of predicting motor parameters from testing data was demonstrated using a genetic algorithm-based technique. The specifications were determined using typical no-load and blocked rotor experiments. The cost equation—the graded sum of the stator currents and rotor velocity—was studied and improved for various motor parameter values. The impact of differential equations on the estimates was also shown. The estimated speed and torque parameters from the mathematical equation were compared to the experimental findings, and both exhibited a strong connection, proving the validity of the mathematical equation and the genetic algorithm method for improvement.

Sadasivan and Mammen [11] applied the same algorithm to obtain parameters that linked the proposed technique and the loading of the electric motor using the evaluation function. They used the genetic algorithm on three separate situations of simulated loading and found that the outcomes were superior in terms of the overall losses induced by the motor. The authors' technique proved to be effective in terms of parameter estimation.

Jirdehi and Rezaei [12] presented a simulation of an induction motor by utilising an artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS) to investigate variables that are often difficult to obtain. They used both methods to test 20 induction motors of varying power outputs. The experimental results consisted of the starting torque, current, maximum torque, full-load slip, efficiency, rated active power, and reactive power. The authors compared the findings produced by the proposed ANN and ANFIS models and the practical results. They discovered a good relationship between the projected values and the practical data. However, the proposed ANFIS model was more precise than the proposed ANN model.

Keerthipala et al. [13] explained the ANN algorithm and how it may be used to monitor an induction motor's torque and speed regulation using linear and non-linear models. The authors reported that the linear observer approach is simple to apply in real-time; however, it does not accurately estimate the rotor and vector angle since the induction machine generally works in the saturated region. The non-linear observer approach considers the impact of the magnetic saturation of the induction machine; however, it cannot be practically applied using conventional techniques because estimating the angle requires too much time. Their suggested technique compensates for the effect of saturation and estimates the angle in a few milliseconds, which is well within the real-time limit.

This study presents an adaptable simulation of an induction motor with a downstream protective scheme [9]. In this work, a direct dq0-direct axis algorithm is presented to implement both static and dynamic modelling of a three-phase induction machine due to possible faults and high-performance requirements in induction machines. The proposed algorithm was tested against several conventional methods, and it was observed that under a stable condition of the machinery, the proposed algorithm could remove any developing faults. This conserves time and minimises the labour required of the operator, which makes the proposed algorithm more efficient. Furthermore, the machine is demonstrated in a steady-state performance with respect to current, active power, efficiency, reactive power, power factor, and speed when the torque loads range from 0 to 125% of its nominal torque. The transient behaviour of the machine was shown through the current, electromagnetic torque, electromagnetic torque versus speed, and speed under no-load, half-load (50%), and full-load (100%) conditions. Finally, the proposed technique was compared to the results of the measured parameters. It was observed that when the load changed from half load (50%) to full load (100%), the supply voltage was suddenly halved with the load at full load (100%). It was observed that the proposed algorithm provides accurate estimates with a deviation of not more than +/−2% from the measured parameters.
