# The Principle Of Operation Engineering Essay

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The use of AC Induction motors (Figure 1) in the industry dates back to almost 20 years. It's because of its cost effectiveness, simplicity and ease of use that it is being used for a wide range of applications. The machine can be highly customized, parameters like speed, torque, etc can be altered to suit various needs and for varieties of applications. With advances in technology, manufacturers have been able to control the speed of the AC induction motor with great versatility. From simple use like phase control to highly complex applications involving closed loop system that uses vector orientations in its field control, the AC Motor has progressed with time.

The principle behind the operation of induction motors was first demonstrated by the British scientist Michael Faraday when he showed in one of his experiments that when a current is passed through a wire, the wire rotates around a magnet proving that current gave rise to rotating magnetic fields.

It was Tesla, a Serbian inventor who found the concept of AC induction motors in the year 1888. He also stated that motors don't need brushes for the rotor to commutate and can be done by an induced rotating magnetic field.

Contributions from Italian physicist, Galileo Ferraris have also been synonymous with the development of AC induction motors.

And finally, Mikhail Dolivo-Dobrovolsky has been credited for the development of the induction motor with a cage.

## 1.3 PRINCIPLE OF OPERATION

The basic principle on which the motor works is the electromagnetic induction. The motor consists of two parts: a stator which is the stationary part and a rotor which is the rotating part.

The stator consists of three pairs of copper wires threaded across its cylindrical surface, a poly-phase current is then fed to these wires in turns so that they get energized and start acting like electromagnets. These electromagnets then interact with the rotor and induce current in the rotor; the electromagnets force this current to move in a direction which is perpendicular to the direction of the magnetic field and thus causes the rotor to rotate.

However, for these currents to be induced the speed of the rotating magnetic field in the stator must be greater than the speed of the material rotor or else the magnetic field will not be moving comparative to the conductors of the rotor and hence current would not be induced. If in any case this happens, the rotor would typically slow down slightly until the current is re-induced and then again the rotor continues as before. This difference between speed of the rotating magnetic field in the stator and the speed of the rotor is known as slip. It is a unit less quantity and is the ratio between the relative speeds of the magnetic field as seen by the rotor (the slip speed) to the speed of the rotating stator field. Due to this phenomenon, an induction motor is also referred to as an asynchronous machine.

## 1.4 AN OVERVIEW OF THE PROJECT

The project report is based on the behavioural study of a three phase induction motor when it is subjected to non-sinusoidal excitation by modelling and simulation of its equivalent circuit.

It highlights the background of the induction motor and its invention; it details its construction and then explains the harmonic effects and torque-slip characteristics of the induction motor. Then it goes on to explain the various losses under non-sinusoidal excitation and proposes various mathematical models and formulae to calculate these losses, it also gives suggestions on reducing the harmonics and thereby curbing these losses. A simple modelling and simulation of the induction motor based on its equivalent circuit illustrates the various efficiency drops in the torque output of the motor.

## 1.4.1 OBJECTIVE

The objective of the project is to give an introduction about the working principle of an induction motor and highlighting its construction. It further details the harmonic characteristics of the motor and its torque-slip characteristics. It provides a detailed discussion about the various losses suffered by an induction motor under non-linear loads having non-sinusoidal excitation, the harmonics that come into picture and the various methods that can be implied to reduce this hampering. It also discusses the modelling and simulation of the motor under such excitation and highlights the losses that are incurred by the motor.

## 1.5 REPORT PREVIEW

This report is presented in 6 chapters.

Chapter 1: Gives an overview of the project, describing the historical background and principle of operation of the three phase induction motor.

Chapter 2: Details about the construction of the three phase induction motor and its constructional features with suitable illustrations.

Chapter 3: Discusses the various equivalent circuit models of the induction motor and its torque-slip characteristics.

Chapter 4: Explains about the various deterrent effects of non-sinusoidal voltage in an induction motor, it also gives various mathematical models to predict the losses and other harmonic effects.

Chapter 5: Illustrates the modelling technique applied to generate the results of an induction motor and explains the various simulations that were applied.

Chapter 6: Gives a conclusion to the report.

## CHAPTER 2

## CONSTRUCTION OF INDUCTION MOTORS

The following chapter explains in details about the constructional features of the three phase induction motors. It highlights the various components and materials used for the construction of the motor with various illustrations.

The two basic components of the motor are- the stationary part called the Stator and the rotational part called the rotor (Figure 2).

## 2.1 GENERAL ARRANGEMENT

The three phase induction motor varies constructionally from the d.c. machine in various fundamentals: it is shorter, has a uniform air-gap, there is absence of a commutator, speed limitation, it contains simple windings and has a laminated stator. In a.c. induction machines it is not possible to use the frame as a part of the magnetic circuit as compared to the d.c. machines where this can be done. The stator core is carried in a shell (frame) or housing which provides a means for protecting the stator and insulating it. The shell is also responsible for carrying the end covers, bearings and the terminal box, it also supports all the other various peripheries in the motor.

The housing carries the stator core and the windings. The rotor is made out of cast copper or aluminium.

Figure 2: Stator & Rotor

## 2.2 FRAMES

The frame of a motor carries the general assembly; there are two methods to produce the frame. The conventional method is to cast the frame in one piece using a single mould or the other method is to fabricate the individual pieces separately and then welding all the pieces together to form the frame. The former method is still common for small and miniature rotors, but medium-sized and large machines are almost entirely fabricated. The main advantage of fabricated construction is in its application to new designs and modifications, which can be made without reference to existing patterns. The principal constructional difficulty that fabricated motors face is the avoidance of distortion when the parts are welded together.

Essentially the frame is a short cylinder with end plates and axial ribs on the inner surface (Figure 3). In larger sizes housing is made in a box form. When the ribs have been machined and ends turned where necessary for the end covers the frame is ready to receive the stator core.

Figure 3: Frame Showing Slots For Windings

## 2.3 CORES

Thin sheets of special core steel are used to build the cores of the stator and the rotor. They are insulated from one another by means of varnish or sprayed china clay. The gap surfaces of the plates have suitable slots punched out which are either open, semi-closed or completely closed.

For small machines, both rotor and stator punching are complete rings; also the rotor core is mounted directly on the shaft to which it is keyed.

## 2.4 WINDINGS

For large motors or those for high voltage the stator phases may be fashioned by single layer concentric coils. But even here, as for most medium-sized machines, the double layer winding is common.

For large sized slip ring rotors, bar windings can be used because the choice of voltage is usually free. For smaller machines wire wound rotors (Figure 4) can be used with coil arrangements analogous to those of the stator. Cage rotors in small and miniature motors can be cast in one piece in copper or aluminium with the end rings moulded to form simple fan blades.

Large rotors have copper or brass bars (Figure 5) driven through slots, the endings being electrically welded or silver soldered to the end rings and the fans are separately moulded.

Figure 4: Wire Wound Rotor Figure 5: Cage Rotor With Brass Bars

And End Rings

## 2.5 SHAFTS AND BEARINGS

The induction motor shaft which is responsible for delivering the mechanical output is kept short and stiff in order to have as small an air-gap as mechanically possible. The type of bearing used to make accurate centering of the rotor is known as a ball and roller type bearing. These bearings are packed with grease and sealed after manufacturing and can generally be relied upon to work for long periods without any maintenance.

Alternatively for small machines a roller bearing may be used at the pulley end and a ball bearing at the other.

The material used for slip-rings in many cases is of brass or phosphor-bronze which is shrunk onto a cast-iron sleeve with molded mica insulation. The entire assembly is pressed onto the rotor shaft and located either between the rotor core and the bearing or on the shaft extension. In the latter case a slip-ring cover is provided and the shaft has to be bored to take the slip-ring leads through the bearing.

## CHAPTER 3

## EQUIVALENT CIRCUIT MODELS AND TORQUE-SLIP CHARACTERISTICS

The following chapter discusses the equivalent circuit model of an induction motor and gives a detailed elaboration on the torque-slip characteristics of the induction motor with suitable plots.

## 3.1 EQUIVALENT CIRCUITS

The induction motor can be studied under three types of equivalent circuit models.

## 3.1.1 TRANSFORMER CIRCUIT MODEL

Circuit elements:

Stator resistance and leakage reactance: R1 and X1

Core Loss resistance RC and Magnetizing reactance Xm

E1 = Primary internal stator voltage coupled to secondary rotor voltage ER via effective turns ratio aeff.

Primary difference with respect to transformer lies in effects of varying rotor frequency on the rotor voltage ER and the rotor impedances RR and XR.

Figure 6: Transformer Model Equivalent Circuit

## 3.1.2 ROTOR CIRCUIT MODEL

Stator voltage induces voltage on rotor windings

The greater the relative motion between the rotor and stator magnetic fields, the greater the induced rotor voltage and frequency: eind=vBl

Maximum induced voltage at locked rotor condition: ER0

Voltage and frequency directly proportional to slip of the rotor: ER = sERO , fr = sfe

Rotor contains both reactance and resistance

RR is independent of slip

XR depends on rotor inductance LR and frequency of induced voltage and current:

XR = wrLR = 2 Ï€frLR = 2Ï€sfeLR = s(2Ï€feLR) = sXR0 with XR0 the locked rotor reactance.

Resulting equivalent circuit:

Figure 7: Rotor Circuit Equivalent Model

All rotor affects due to varying rotor speed accounted forby varying impedance, or rather varying resistance.

At low slip RR/S >> XR0, IR varies linearly with slip

At high slip XR0>> RR/s, IR approaches steady state value.

## 3.1.3 PER PHASE EQUIVALENT CIRCUIT

Need to refer rotor part of model to the stator side.

Figure 8: Per-Phase Equivalent Circuit

E1=E'R=aeffER0

Problem for cage motors: Almost impossible to determine RR, XR0 and aeff.

Possible to directly determine the referred values.

## 3.2 TORQUE-SLIP CHARACTERISTICS

Depending on the value of the slip, the induction machine can be operated under three modes: Motoring, generating and Plugging (Figure 8).

## 3.2.1 MOTORING

Here the slip value lies between 0 and 1, as the slip value decreases the torque developed in the machine increases and reaches a maximum value (Tmax) and with further decrease in the slip value the torque also starts to drop and reaches the breakdown value and then comes down to zero. The steady-state speed is less than the synchronous speed (ns>n) and the direction of the torque produced and the mechanical power output is in the same direction as the rotation of the rotor.

## 3.2.2 GENERATING

For this mode of operation the value of the slip is negative, i.e. the rotor speed is greater than the synchronous speed (n>ns) and the motor is ruuning at super synchronous speed. The system rotates in the same direction as the stator rotating field. The induction machine will produce a generating torque, that is, a torque acting opposite to the rotation of the rotor (or acting opposite to the stator rotating magnetic field). The generating mode of operation is utilized in some drive applications to provide regenerative braking.

For example, suppose an induction machine is fed from a variable-frequency supply to control the speed of a drive system. To stop the drive system, the frequency of the supply is gradually reduced. In the process, the instantaneous speed of the drive system is higher than the instantaneous synchronous speed because of the inertia of the drive system. As a result, the generating action of the induction machine will cause the power to flow to reverse and the kinetic energy of the drive system will be fed back to the supply. The process is known as regenerative braking.

Figure 9: Torque-Slip Curve

## 3.2.3 PLUGGING / BRAKING

If the motor is adjusted so that the system rotates in a direction opposite to the stator rotating magnetic field, the torque will be in the direction of the rotating field but will oppose the motion of the rotor. This torque is a braking torque. The slip value is greater than 1for this mode of operation.

Plugging is sometimes utilized in drive applications where the drive system is required to stop very quickly. Suppose an induction motor is running at a steady-state speed. If its terminal phase sequence is changed suddenly, the stator rotating field will rotate opposite to the rotation of the rotor, producing the plugging operation. The motor will come to zero speed rapidly and will accelerate in the opposite direction, unless the supply is disconnected at zero speed.

## CHAPTER 4

## NON-SINUSOIDAL EXCITATION

Until the recent past electrical systems were mainly constituting of loads which were linear in nature. Recent developments in technology have led to an increased use of electronic devices which have loads pertaining to non-linear nature and they require non-sinusoidal excitation for their operation.

As a result the waveforms of the supply voltage are being distorted, they have asymmetry and are unbalanced and introduce inequalities in the supply network.

## 4.1 GENERAL EFFECTS

Different loads react differently to the effects of non-sinusoidal excitation in the supply network. Not all the loads are affected by inequalities in the supply voltage but some of the loads are very sensitive to such changes; they may not function properly and may even be damaged.

A phenomenon called electromagnetic capability is used to measure the disruption which various types of loads can accept without incongruous behaviour.

Non-sinusoidal voltages when applied to the electrical machines may also cause various other problems like overheating, torque which is pulsating in nature and noise in the electrical system.

## 4.2 GENERATION OF NON-SINUSOIDAL VOLTAGE

Non-sinusoidal voltage can be generated using many techniques.

The most common method is by using inverters to convert direct current to alternating current and then using a pulse width modulator or a voltage source inverter to get the required non-sinusoidal waveform.

The non-sinusoidal supply (Figure 10) voltage output from a PWM inverter can be expressed in a general form as:

Where:

V1 is the fundamental supply voltage.

Vn represents harmonic voltages of order n.

Î˜n is the harmonic phase angle.

The fundamental and the [3n+1] for n=1, 2... order voltage harmonics contribute to a rotating magneto-motive force (MMF) in the direction of motion and hence constitutes a positive torque.

The [3n+2] for n=0,1,2,.... order voltage harmonics result in a rotating magneto-motive force in a direction opposite to that of the motion and hence it contributes to negative torque.

Whereas the [3n+3] for n=0, 1, 2.... order voltage harmonics produces no rotating magneto-motive force and therefore no torque. If there are a certain number of pulses per quarter cycle and it is an odd number the harmonic order will be even number only.

Figure 10: Non-Sinusoidal PWM Signals

## 4.3 INDUCTION MOTOR UNDER NON-SINUSOIDAL EXCITATION

An induction motor operating under non-sinusoidal excitation suffers from various types of losses due to the asymmetry and the unbalance in the supply voltage.

Induction motors are generally designed to operate under normal sinusoidal supply voltage coming from the mains. When instead of that a non-sinusoidal voltage generated using a voltage source inverter or a PWM is supplied to it, it suffers from the following losses:

Copper loss; also know as joules effect loss is significant in the stator and the rotor conductors.

Harmonic dispersion flows lead to losses in the terminal section.

Figure 11: Voltage Harmonics-Non Linear Loads

The harmonic limit is set by an IEEE standard-519 called the "Distortion factor" which is used to establish the amount of voltage distortion. 5% is the average acceptable value of harmonic content present in the supply voltage (Figure 12) of industrial power systems, wherein no derating of the motor would be necessary.

Various losses are incurred in the iron core due to the harmonics involved (Figure 11). Hysterics and eddy current effects also come into picture and they increase with the order of the harmonics and reach significant values.

Voltage flickering is also one of the major causes of harmonics in electrical systems.

All these losses contribute to the deterioration of the motors life, the copper loss which intensifies with increased harmonics helps augmenting the skin effect that reduces the conductor's effective section and increases its physical resistance.

The output of any induction motor depends on heating and it also reduces the overall life of the motor if it is overheated. A major factor in determining the performance of a motor is the temperature rise resulting from losses. The harmonics generated from the applied non-sinusoidal voltages may cause excessive heating.

Figure 12: Harmonic Distortion

Many of the automated industrial processes require fast and efficient control of ac motors, this is achievable only through input power fed from a pulse width modulated inverter. These inverters make use of semiconductor switches to transfer the electrical energy from the source to the various controlled industrial processes. These switches are turned on and off are very fast and rapid rates, hence selection of the PWM generating technique is also very important in reducing the harmonics in the system.

## 4.4 MATHEMATICAL MODELLING

All the major calculations done regarding the induction motor are based on its equivalent circuit.

The various harmonics have a deterring effect on the motor and changes are observed in the source current. To determine the source current due to 'n' harmonics the following fourier series has been established:

'n' represents the harmonic order

Where:

Is is the source current of the equivalent circuit.

The RMS value of nth harmonic in the source current is:

Where 'a' and 'b' can be found using the equations mentioned above.

The phase displacement of the nth harmonic is given by:

Because of the half-wave symmetry only the odd harmonics will be present like the positive 5th or the negative 7th, etc and the zero sequence harmonics.

They only contribute to the losses of the motor and do not contribute to the output power of the motor. Such harmonics decrease the efficiency of the motor and increase its thermal loading.

They also produce pulsating torques, which result in a stepped or jerked motion of the motor. For example the positive 7th harmonic produces a forward moving mmf at a speed seven times the fundamental synchronous speed, the relative speed between the 7th harmonic and the fundamental harmonic being six times the fundamental synchronous speed and thus their interaction produces a pulsating torque at six times the fundamental frequency. Similarly the negative 5th harmonic produces a negative mmf moving backwards at a relative speed of 5 times the fundamental synchronous speed and the difference in that speed compared to that of the fundamental synchronous speed is six times. Thus their interaction also produces a pulsating torque moving at a speed six times the fundamental frequency and so on. These torque pulsations cause fluctuations in the motor speed.

Larger harmonics result in a greater decrease in the efficiency and a major increase in the thermal loading.

The fundamental component of the slip does not coincide with the slip in the harmonic current and thus and effect will appear simultaneously on the equivalent resistance of the rotor as seen from stator and also on the loads equivalent resistance.

The single phase value of the equivalent resistance for any given harmonic frequency is given by:

; h-harmonic order

Where:

r1h-physical resistance of the stator winding

r2h-physical resistance of the rotor winding

sh-harmonic split

Authors like Murphy and Egan have simplified this occurrence by introducing a factor for copper loss in their studies which is defined as follows:

Where, 'Vh' and 'fh' are values of voltage and frequency for h order harmonic in the voltage waveform.

Various other formulae have been developed to calculate the losses, one of the empirical relations is:

Where 'A' is the function parameter, 'Peh' are the losses, 'Ih' and 'fh' are the current and frequency of the harmonic involved and 'a' and 'b' are coefficients which are determined experimentally.

The combined effect of harmonic duality is zero, though each of them have an effect separately which can be calculated by taking the fundamental as a reference and applying the following formula:

Where:

Th-harmonic torque of order h.

X1-Stator impedance

The Williamsons formula can be used to calculate the pair pulsations when both positive and negative sequence harmonics are present.

Order of harmonics present: h+ = 3k+1 and h- = 3k-1

Where:

Ih+ - Harmonic current for the order 3k+1

Ih- - Harmonic current for the harmonic order 3k-1

The copper loss generated by the harmonics can be calculated using the following formula and applying the various parameters from the equivalent circuit.

Where I can be given by:

Here 'k' is the harmonic order

## 4.5 METHODS TO REDUCE THE LOSSES

Linear loads which have very low power factor can be easily corrected by using passive inductive or capacitive networks.

For non-linear loads filters (active and passive) containing capacitors and inductors can be designed to reduce the distortions and harmonic effects in the network. Also capacitive banks can be implied for corrections of non linearity in the waveforms.

The passive filter requirement is that it needs large valued high current conductors which are not economical and their bulky size is also a major problem.

The active filters on the other hand are more effective than passive filters but they are more costly.

An active filter continuously monitors the power drawn by the load and regulates it such that the power factor is maintained as close as possible to unity.

One more device which can be employed to correct the non sinusoidal voltage is the Matrix Converter. It is a direct AC/AC converter which is capable of transfiguring input voltage to inconsistent voltage with unobstructed frequency. It consists of 9 bi-directional switches and hence it can assume 29=512 forms and states of switching

It also offers sinusoidal output and input waveforms (Figure 13), hence can be clubbed with a PWM inverter to get the output wave in a sinusoidal form. It is also capable of reducing the higher order harmonics.

Figure 13: Output Of A Matrix Converter Compared To An Inverter

## CHAPTER 5

## MODELLING AND SIMULATION

The following chapter describes the modelling techniques that were implemented to simulate the working of an induction motor under non-sinusoidal excitation.

Using PSPICE - release 9 the design of the equivalent circuit was redrawn and the various input parameters were fed to the design.

## 5.1 MODELLING

For modelling and simulating the working of any induction machine , its equivalent circuit is required.

By giving variable inputs to the equivalent circuit model different simulations can be achieved to obtain the various outputs.

Given below is the screenshot of the design of the equivalent circuit with the input parameters defined for the various factors present on the model:

Figure 14: Equivalent Circuit Modelling Using Pspice

## 5.2 SIMULATIONS

The equivalent circuit was simulated for the odd harmonics by varying the frequency in odd multiples and accordingly changing the constraints on the circuit to obtain the value of the secondary current.

Using this current the value of the torque and the mechanical power output has been calculated.

Fundamental Frequency 50Hz:

Figure 15: Circuit Model For 50Hz

Using the voltage and current markers the respective current and voltage have been plotted and their values are noted down.

The value of the voltage in the fundamental frequency is in a perfect sinusoid form.

V = 230 Volts

I'2 = 140 Amperes

The following plot shows these values

Figure 16: Voltage And Current Plot at 50Hz

Hence,

Torque:

Substituting the corresponding values-

I'2 = 140 Amperes s = 0.00279

R'2 = 0.4ohm ws = 314 rad/sec

We get Torque=26.8X103 Nm

And mechanical power output:

Substituting the corresponding values we get

Pm = 8.4X106 kW

Similarly calculations are done when harmonics are introduced into the system.

Following are the plots and circuits for the various odd harmonics.

3rd Harmonic, when frequency = 150 Hz:

When the frequency is increased, the voltage experiences asymmetry and changes into a non-sinusoidal form

Figure 17: Circuit Model For 150Hz

The voltage source parameter for the frequency is now changed to a value of 150hz.

Since the frequency has been changed (made thrice) the values of the inductors will also change correspondingly.

Figure 18: Current Plot For 150Hz

Figure 19: Voltage Plot For 150Hz

Using the above plots the value of secondary current is:

I'2=22.2 Amperes

Therefore,

Torque, T = 225.02 Nm

And mechanical power output, Pm = 211.3 kW

5th Harmonic, when frequency = 250 Hz:

Figure 20: Circuit Model For 250Hz

Figure 21: Current Plot For 250Hz

I'2=2.5 Amperes

Therefore,

Torque, T = 1.71 Nm and

Mechanical power output, Pm = 2.6 kW

7th harmonic, when frequency is 350 Hz:

Figure 22: Circuit Model For 350Hz

Following is the current plot for the 7th harmonic

Figure 23: Current Plot For 350Hz

Therefore,

I'2=1.7 Amperes

Hence,

Torque, T = 0.56 Nm

And Mechanical power output, Pm = 1.23 kW

## 5.3 INFERENCE

By using the following simulations and observing their outputs, we can easily infer that with each increasing harmonic the value of the secondary current decreases rapidly.

The secondary current is directly proportional to the torque developed by the motor and its mechanical power output; hence when the current reduces these values also diminish rapidly.

Thus we can conclude that the introduction of harmonics due to non-sinusoidal signals hampers the working of the three phase induction motor.

## CHAPTER 6

## CONCLUSIONS

The use of AC induction motor for industrial purposes dates back to almost 20 years. Because of its high customization, ease of use and various advantages it has gained tremendous popularity for many industrial and domestic purposes.

It was Michael Faraday who gave the concept of rotating magnetic fields, Tesla in the year 1888 came up with the design for the motor and finally it was Mikhail Dolivo-Dobrovolsky who has been credited with the design for the cage motors.

The working principle of the induction motor is based on electromagnetic induction and Lorentz force. The two main parts involved in its working are the stator and the rotor. The current in the stator wires produce a magnetic field which interact with the rotor and causes it to move thus giving the mechanical output.

The construction of the motor is done in several parts, the stator consist of laminations of silicon steel whereas the rotor is of cast copper or aluminium. The frame of the motor may either be cast or fabricated and then welded together. The cores are made of thin sheets of steel and contain slots. The windings are present on stator as well as rotor, for large motor the rotor windings are replaced with thick bars of copper or aluminium. The shafts of the rotor are made of rigid steel which deliver the mechanical output.

The equivalent circuit of an induction motor is like a model that represents the motor in the form of a circuit. Using this model the values of the various constraints are fed and the different results can be obtained. The motor can be operated under 3 modes depending on its slip viz. motoring, generating and braking.

The induction motor when fed with non sinusoidal voltage suffers from a variety of losses. The non-linear loads present in the electrical system draw non linear currents which give rise to harmonics. These harmonics bring into being an assortment of losses which include copper loss, hysteresis and eddy current losses. These losses affect the efficiency of the motor and increase thermal loading which in turn hampers the life of the motor. Various mathematical models can be proposed to calculate these harmonic losses and factors that affect the mechanical power output.

Based on the equivalent circuit a model was developed on psipce and different odd harmonics were applied to it to get the results. These harmonics reduce the current value in the circuit which is directly related to the mechanical power output and the torque produced.

Thus the results that have been presented with this project are that three phase induction motors operating under non-sinusoidal excitation suffer from various losses, these losses hamper the currents which have direct relation with the mechanical power output.

From the simulations it is clear that non-sinusoidal voltage produces harmonics in the electrical system which leads to torque pulsations and other losses, thus devices like filters and matrix converters can be used to decrease these asymmetries and restore the efficiency.

It is also clear from the simulations that the torque and the mechanical power output of the motor reduces significantly with the harmonics.

## REFRENCES

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