ENCHANCING THE PERFORMANCE OF SPEED CONTROL OF THREE PHASE INDUCTION MOTOR USING VOLTAGE/FREQUENCY SPEED CONTROL TECHNIQUE
USER'S INSTRUCTIONS: The project work you are about to view is on "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique". Please, sit back and study the below research material carefully. This project topic "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" have complete 5(five) Chapters. The complete Project Material/writeup include: Abstract + Introduction + etc + Literature Review + methodology + etc + Conclusion + Recommendation + References/Bibliography.Our aim of providing this "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" project research material is to reduce the stress of moving from one school library to another all in the name of searching for "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" research materials. We are not encouraging any form of plagiarism. This service is legal because, all institutions permit their students to read previous projects, books, articles or papers while developing their own works.
TITLE PAGE
BY
---
--/H2013/01430
DEPARTMENT OF ----
SCHOOL OF ---
INSTITUTE OF ---
APPROVAL PAGE
This is to certify that the research work, "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" by ---, Reg. No. --/H2007/01430 submitted in partial fulfillment of the requirement award of a Higher National Diploma on --- has been approved.
By
--- . ---
Supervisor Head of Department.
Signature………………. Signature……………….
……………………………….
---
External Invigilator
DEDICATION
This project is dedicated to Almighty God for his protection, kindness, strength over my life throughout the period and also to my --- for his financial support and moral care towards me.Also to my mentor --- for her academic advice she often gives to me. May Almighty God shield them from the peril of this world and bless their entire endeavour Amen.
ACKNOWLEDGEMENT
The successful completion of this project work could not have been a reality without the encouragement of my --- and other people. My immensely appreciation goes to my humble and able supervisor mr. --- for his kindness in supervising this project.
My warmest gratitude goes to my parents for their moral, spiritual and financial support throughout my study in this institution.
My appreciation goes to some of my lecturers among whom are Mr. ---, and Dr. ---. I also recognize the support of some of the staff of --- among whom are: The General Manager, Deputy General manager, the internal Auditor Mr. --- and the ---. Finally, my appreciation goes to my elder sister ---, my lovely friends mercy ---, ---, --- and many others who were quite helpful.
PROJECT DESCRIPTION: This work "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" research material is a complete and well researched project material strictly for academic purposes, which has been approved by different Lecturers from different higher institutions. We made Preliminary pages, Abstract and Chapter one of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" visible for everyone, then the complete material on "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" is to be ordered for. Happy viewing!!!
- INTRODUCTION
Three-phase induction motor drives are employed in several industrial areas with a good power, ranging from few 100W to many MW. In industrial-oriented countries, more than half the total electrical energy used is converted to mechanical energy through AC induction motors. Induction motors have industrial and household applications and expend over 50% of the total generated electrical energy. Single phase induction motors are widely utilized in home appliances and industrial control. During the last few years, speed and torque control principle are asynchronous with motor drives which gained significant popularity. It is possible to combine the induction-motor structural robustness with the control simplicity and efficiency of a direct current motor. This evolution resulted to the replacement of the dc machines by induction motors in many applications in the last few years. Earlier only dc motors were employed for drives requiring variable speeds due to facilities of their speed control methods ( Zubek, 2010). The conventional methods of speed control in an induction motor are very expensive or too inefficient thus restricting their level of application to only constant speed drives. Examples include to drive pumps, fans, compressors, mixers, agitators, mills, conveyors, crushers, machine tools and cranes. They are very simple, reliable, low maintenance and low cost. Today, with advancements in power electronics, microcontrollers, and digital signal processors (DSPs), electric drive systems have improved drastically. Initially the principle of speed control was based on steady state consideration of the induction motor. Voltage/frequency control was suitable for the open-loop speed control of drives with low dynamic requirements.
There are different methods of controlling induction motor for industrial application. Voltage/frequency ratio method offers an easy way to regulate both the frequency and magnitude of the voltage applied to a motor. However, better efficiency can be obtained by these motor drives with less noise. The most rampant technique is the constant Voltage/frequency principle which requires that frequency and the magnitude of the voltage applied to the stator of a motor maintain a constant ratio. So, by this, the
magnetic field in the stator is kept almost constant for all operating points. Thus, constant torque is maintained.
Figure.1.1: Block diagram of closed loop Voltage/frequency control of induction motor
2.0 AIM AND OBJECTIVES
AIM
The main aim of this study is to enhance the performance of speed control using voltage/frequency ratio method of speed control for three phase induction motor.
OBJECTIVE
The objectives are:
- To develop a model for implementation of Voltage/Frequency control scheme in a three-phase induction motor.
- To enhance the efficiency of motor speed control techniques, using Voltage/Frequency speed control technique for a three phase induction motor.
3.0 INDUCTION MOTOR CONTROL APPROACHES
Recently, revolutionary advances in technology, power electronics, modern control and artificial intelligence have led to a replacement generation of induction control which will provide significant economic benefits. The voltage or current supplied to an induction motor are often expressed as a sinusoidal function of magnitude and frequency or magnitude and phase. Accordingly, induction motor control methods are classified into two categories: scalar control in which the voltage magnitude and frequency are adjusted, and vector control in which the voltage magnitude and phase are adjusted. Various control approaches of induction motor are as follows:
Scalar Control: - Scalar control is predicated on steady state relationships; usually only magnitude and frequency are controlled, not space vector orientation. Making terminal voltage magnitude proportional to frequency leads to an approximately constant stator flux, which is desirable to maximise capability of the motor? The classical variable frequency V/f scheme may be a scalar control supported this principle, with voltage boost at low frequency usually introduced to counteract the larger effect of stator resistance at low speeds. Scalar control, often open-loop aside from stator current monitoring for fault detection, gives a cheap drive with good behavior, but transients might not be controlled. More sophisticated variants can improve behavior, perhaps with better handling of parameter variations, particularly of stator resistance. Buja and Kazmierkowski describe the evolution of the still widely used scalar control methods and their progression to vector control.
- Vector Control (VC): -In Vector Control, the instantaneous position of voltage, current, and flux space vectors are controlled, ideally giving correct orientation both in steady state and during transients. Coordinate transformations (three phases to two or d − q axes) to new field coordinates are a key component of standard VC, giving a linear relationship between control variables and torque. It is ideally suited to current control via PWM voltage switching. VC are often introduced by considering a DC machine. In a DC drive the rotating commutator acts as both current switch and rotor position sensor. A DC drive is shown during a schematic diagram in Figure. 2.1, where ia is often chopper controlled. The commutator maintains the most flux and therefore the armature MMF directions to be approximately perpendicular under all operational conditions, illustrated by the vector diagram in Figure.2.1 This basic arrangement defines the aim of a VC for a high-performance ac drive, as given in equψiation 2.1 where electrical torque (
is shown as the product of magnetic flux linkage(ψ) and current(i) .
Te∝ψi (2.1)
Figure. 2.1 Flux and MMF in a DC drive.
The VC usually separates current into field and torque producing components. The perpendicular field system makes the relationships between the machine variables simple, in theory. The flux is a function of the field (producing component) or d-axis current, the torque is proportional to the product of this flux and the torque (producing component) or q-axis current. If the flux is established and may be held constant, the torque response is governed by the present and may be fast and well-controlled. Full advantages of VC are given as long as the instantaneous position of the rotor flux vector are often established. The usual Induction Motor (IM) cast cage rotor aids in robustness and economy, but rotor quantities aren't accessible. Two variants of VC are used, direct and indirect. In the direct method, the instantaneous rotor position for this flux is found either by sensors, or more usually by estimators, or a combination; Blaschke was a pioneer of the approach. Indirect VC for an Induction Motor combines an error calculation with use of rotor position or speed. Slip calculation involves the rotor time constant which can vary considerably mainly due to changes in rotor resistance with temperature. This need for rotor position or velocity is most obviously required in an Synchronous Machine such as a brushless Permanent Magnet machine since stator excitation must be synchronous to the rotor. It also applies to an Induction Motor drive, although the essential symmetry of the rotor implies only relative velocity is originally needed. A straightforward method is to connect a rotor sensor, e.g., an encoder to live rotor position or speed, and this is often still preferred in many cases, but sensorless schemes are gaining ground. The vector controllers are expensive and high-performance drives, which aim to regulate the magnitude and phase of voltage or current vectors. Vector control methods include Field Oriented Control (FOC) and Direct Self-Control (DSC). Both methods plan to reduce the complex nonlinear control structure into a linear one, a process that involves the evaluation of definite integrals. FOC uses the integral to get the rotor flux angle, whereas DSC uses the integral to get the stator flux space vector. Although the implementation of both methods has largely been successful, they suffer from the following drawbacks:
- Sensitivity to parameter variations;
- Error accumulation when evaluating the definite integrals; if the control time is long, degradation in the steady-state and transient responses will result due to drift in parameter values and excessive error accumulation;
- In both the methods, the control must be continuous and the calculation must begin from an initial state.
(b) Direct Torque Control (DTC): - DTC also exploits vector relationships, but replaces the coordinate transformation concept of standard VC with a form of bang- bang action, dispensing with PWM current control in standard VC the q-axis current component is employed because the torque control quantity. With constant rotor flux it directly controls the torque. In a standard three-phase converter, simple action of the six switches can produce a voltage vector with eight states, six active and two zero. The voltage vector and stator flux then move around a hexagonal trajectory; with sinusoidal PWM this becomes a circle. With either, the motor acts as a filter, so rotor flux rotates continuously at synchronous speed along a near-circular track. In Direct Torque Control the bang-bang or hysteresis controllers impose the time duration of the active voltage vectors, moving stator flux along the reference trajectory, and determining duration of the zero voltage vectors to control motor torque. At every sampling time the voltage vector selection block chooses the inverter switching state to reduce the flux and torque error. Depending on the Direct Torque Control switching sectors, circular or hexagonal stator flux vector path schemes are possible. Types of Direct Torque Control include: switching table based, direct self-control, space vector modulation and constant switching frequency. Direct Torque Control has these features compared to standard Vector Control.
- No current control loops, so current not directly regulated. Coordinate transformation not required.
- No separate voltage PWM is required.
- Stator flux vector and torque estimation is required.
Figure.2.2. Basic direct VC scheme with an observer used for rotor flux estimation.
(c) Sensorless Control Method: - There is intensive research worldwide devoted to sensorless methods. Motor drives without a speed or position sensor have received much research attention in recent years, both for IMs and PM brushless types . Such techniques typically measure stator quantities, usually current, directly via existing transducers normally present within the inverter and voltage, although rarely with an immediate measurement. SI methods are also used. Figure 2.3 shows a typical schematic of a sensorless scheme. Advantages of such “sensorless” schemes include.
More compact drive with less maintenance;
- No cable to machine transducers, easier application particularly to existing machines, reduced electrical noise;
- Transducer cost is avoided.
- Suitable for hostile environments, including temperature. Despite much effort and progress, operation at very low speed remains problematic particularly for an IM sensorless drive. Proper comparative analysis of the many variants in the extensive literature on this topic is difficult. This is mainly because a typical set of tests or benchmarks has not been agreed. Even quite simple schemes can give results which are adequate for undemanding applications. Such simple schemes can usually demonstrate operation through zero speed provided the transition is fairly rapid. Hence, a reversal over say 1000 r/min during a short time could also be useful to offer an summary, but it's not an appropriate test unless it's all the application requires. This benchmark issue has been commendably addressed by Ohyama. In a most valuable contribution to standardizing tests. Benchmark tests are proposed in four categories, including a staircase speed transient over 150 r/min in ten steps, i.e., of 30 r/min, with drive data to be fully specified, including moment of inertia since large values can make results look impressive. Sensitivity to parameter change is also critically important.
Figure.2.3: Schematic of a speed sensorless scheme = demand, est = estimated.
SPEED CONTROL BY FREQUENCY VARIATION
Variable Frequency Control a method which is employed to regulate the speed of an induction motor. The synchronous speed and therefore, the speed of the motor can be controlled by varying the supply frequency.
By varying supply frequency (on small amount), we will vary the speed. But a decrease in supply frequency decreases the speed and increases the flux, core losses which leads heating and low efficiency. Increase in frequency increases the speed and reduces the torque. A separate costlier auxiliary equipment is required to provide a variable frequency. So this method is not used in practical.
The synchronous speed of an induction motor is given by the relation shown below:
2.7
The EMF induced in the stator of the induction motor is given by the equation shown below.
2.8
Therefore, if the availability frequency is modified induced EMF also will change to take care of an equivalent air gap flux. The terminal voltage V1 is equal to the induced EMF E1 if the stator voltage drop is neglected.
In order to minimize the losses and to avoid the saturation, the motor is operated at rated air gap flux. This condition is obtained by varying the terminal voltage with frequency so on maintain (V/f) ratio constant at the speed value. This type of control is understood as Constant Volts Per Hertz.
Thus, the speed control of an induction motor using variable frequency supply requires a variable voltage power source. The variable frequency supply is obtained by the subsequent converters.
• Voltage source inverter
• Current source inverter
• Cyclo converter
An inverter converts a hard and fast voltage DC to a hard and fast or variable voltage AC with variable frequency. Cyclo converter converts a hard and fast voltage and glued frequency AC to a variable voltage and variable AC frequency.
The variable frequency control allows good running and transient performance to be obtained from a cage induction motor. Cyclo converter-controlled induction motor drive is suitable just for large power drives and to urge lower speeds.
f. SPEED CONTROL BY POLE CHANGING
Pole Changing Method is one among the most methods of the speed control of an induction motor. This method of controlling the speed by pole changing is employed mainly for cage motor only because the cage rotor automatically develops variety of poles, which is equal to the poles of the stator winding. The change of number of poles is completed by having two or more entirely independent stator windings within the same slots. Each winding gives a special number of poles, so we'll get different speeds. Due to cost and sophisticated switching arrangements, it's not practical to supply quite two arrangements of poles (ie, two normal speeds).
The number of stator poles are often changed by the subsequent three methods. They are referred to as multiple stator windings, method of consequent poles and pole AM (PAM). The detail explanation of every pole changing method is given below.
Multiple Stator Winding
In the multiple stator winding method, two windings are provided on the stator which are wound on the 2 different numbers of pole. One winding is energized one at a time. Let us consider that the motor has two windings for six and 4 poles. For the frequency of fifty hertz, the synchronous speeds are going to be 1000 and 1500 revolutions per minute respectively. This method of speed control is less efficient and more costly.
Pole Amplitude Modulation (PAM) Technique
Pole AM may be a flexible method of pole changing which may be utilized in applications where speed ratios aside from 2:1 are required. The motors designed for speed changing supported the poled AM scheme are referred to as PAM motors.
g. SPEED CONTROL BY VARYING SUPPLY VOLTAGE
The speed of induction motor can be varied by changing supply voltage. The torque developed during this method is proportional to the square of the availability voltage.
T ∝ V2. 2.9
This is the most cost effective and simplest way, but it's rarely used due to the below reasons. A small change in speed requires an outsized change in voltage. This large change in voltage will end in an outsized change within the flux.
2.10
The torque produced by running three phase induction motor is given by
2.12
2.11
Since rotor resistance, R2 is constant so the equation of torque further reduces to
We know that rotor induced emf E2∝ V. So, T ∝ sV2.
The equation above clears that if we decrease supply voltage torque also will decrease. But for supplying an equivalent load, the torque must remain an equivalent, and it's only possible if we increase the slip and if the slip increases the motor will run at a reduced speed. This method of speed control is never used because a little change in speed requires an outsized reduction in voltage, and hence the present drawn by motor increases, which cause overheating of the induction motor.
4.0 THREE PHASE INDUCTION MOTOR CONSTRUCTION
These three phase motors contain a stator and a rotor and between which no electrical connection exists. These stator and rotors are constructed with the utilization of high-magnetic core materials so as to scale back hysteresis and eddy current losses.
Figure 2.7: Induction motor composition
Stator frame can be constructed using cast iron, aluminum or rolled steel.
Stator frame provides necessary mechanical protection and support for stator laminated core, windings and other arrangements for ventilation. Stator is wounded with three-phase windings which are overlapped with each other at 120 degree phase shift fitted into slotted laminations. The six ends of the three windings are brought out and connected to the terminal box in order that these windings are excited by three-phase main supply.
These windings are of copper wire insulated with varnish fitted into insulated slotted laminations. At all working temperatures, this impregnated varnish remains rigid. These windings have high-insulation resistance and high resistance to saline atmosphere, moisture, alkaline fumes, oil and grease, etc. Whichever suits the voltage level, these windings are connected in either star or delta connections.
The rotor of three phase AC induction motor is different for the slip-ring and squirrel-cage induction motors. Rotor in slip-ring type consists of heavy aluminum or copper bars shorted on both ends of the cylindrical rotor. The shaft of the induction motor is supported on two bearings at each ends to ensure free rotating within the stator and to reduce the friction. It consists of stack of steel laminations evenly spaced slots that are punched around of its circumference into which un-insulated heavy aluminum or copper bars are placed.
A slip-ring-type rotor consists of three-phase windings are internally starred at one end, and the other ends are brought outside and connected to the slip rings mounted on the rotor shaft. And for developing a high-starting torque these windings are connected to rheostat with the assistance of carbon brushes. This external resistors or rheostat is employed at the starting period only. Once the motor attains the normal speed, the brushes are short circuited, and the wound rotor works as squirrel cage rotor.
5.0 PRINCIPLE OF OPERATION OF 3-PHASE INDUCTION MOTOR
Figure 2.8: Principle of Operation of Three Phase Induction Motor
• When the motor is excited with three-phase supply, three-phase stator winding produce a rotating magnetic field with 120 displacements at constant magnitude which rotates at synchronous speed. This changing magnetic flux cuts the rotor conductors and induces a current in them consistent with the principle of Faraday’s laws of electromagnetic induction. As these rotor conductors are shorted, the present starts to flow through these conductors.
• In the presence of magnetic field of stator, rotor conductors are placed, and therefore, according to the Lorenz force principle, a mechanical force acts on the rotor conductor. Thus, all the rotor conductors force, i.e., the sum of the mechanical forces produces torque within the rotor which tends to maneuver it within the same direction of rotating magnetic field.
• This rotor conductor’s rotation can also be explained by Lenz’s law which tells that the induced currents in the rotor oppose the cause for its production, here this opposition is rotating magnetic field. This result the rotor starts rotating within the same direction of the stator rotating magnetic flux . If the rotor speed quite stator speed, then no current will induce within the rotor because the rationale for rotor rotation is that the relative speed of the rotor and stator magnetic fields. This stator and therefore the rotor fields difference is named as slip. This how 3-phase motor is called as asynchronous machine due to this relative speed difference between the stator and the rotors.
• As we discussed above, the relative speed between the stator field and the rotor conductors causes to rotate the rotor in a particular direction. Hence, for producing the rotation, the rotor speed Nr should be but the stator field speed Ns, and therefore the difference between these two parameters depends on the load on the motor.
The difference of speed or the slip of the AC induction motor is given as
2.12
2.13
• When the stator is stationary, Nr=0; so, the slip becomes 1 or 100%.
• When Nr is at synchronous speed, the slip becomes zero; so, the motor never runs at synchronous speed.
• The slip in the 3-phase induction motor from no load to full load is about 0.1% to 3%; that’s why the induction motors are called as constant-speed motors.
6.0 STATIC KRAMER DRIVE
A static ramer drive is a method to obtain an injected voltage that is in phase with the rotor current. The schematic circuit for a static ramer drive is shown below
Figure 2.9:Static Kramer Drive
The voltage at the slip rings is forced to be in phase with the rotor currents by the diode rectifier. The magnitude of the connection voltage is about by the DC link voltage, which is successively set by the inverter connected back to the AC supply. In the diagram above and the analysis presented, the inverter used is a thyristor converter. However, a PWM inverter can also be used.
Simple Analysis of staticramer drive
This simple analysis of the static ramer drive illustrates the operation of the drive. It neglects the voltage drops within the drive and any possible commutation overlap within the diode rectifier.
The voltage at the input to the diode rectifier is given by
=
2.142.15
Considering the thyristor converter, this circuit are often thought of as a thyristor rectifier connected in reverse, and therefore the DC link voltage is said to the line-line inverter voltage as
2.16
Substituting the above expressions, the voltage injected into the rotor are often calculated as
2.17
In the case that the inverter line-line voltage is connected to the availability through a transformer, as shown within the diagram above, the injected voltage are often associated with the supply voltage as
2.18
Torque-Speed curve of a motor
Because the slip ring voltage is derived using a diode bridge, the torque speed curve for a motor operated using a static ramer drive does not produce a negative torque as soon because the speed exceeds the no-load speed. If the slip is just too low for a given injected voltage, the voltage induced within the rotor circuit by the stator will have a lower magnitude than the DC link voltage. As a result, no rotor current will flow and therefore the torque are going to be zero. Torque speed curves for various injected voltages are animated below
7.0 STATIC SCHERBIUS DRIVES
Static scherbius drives are capable of bi-directional power flow, with both positive and negative injected voltages possible, in phase with or opposing the rotor current. As a result, a wider set of operating conditions is possible. Considering the torque equation for slip energy recovery:
2.19
When motoring, torque is positive, when generating torque is negative.
Operating Modes
Sub-synchronous motoring
In this mode, operation is similar to that obtained with a static kramer drive. Slip and torque are both positive, therefore injected voltage must be in phase with rotor current. Power flows into the stator and back out of the rotor circuit.
Super-synchronous motoring
Above synchronous speed, the slip is negative. In order for the torque to be positive, must be negative. Therefore, voltage and current must be out of phase with each other. Power is being injected into the rotor from the drive circuit connected to the slip rings, additionally to input power flowing into the stator
Sub-synchronous generating
If generation below synchronous speed is required, torque must be negative whilst slip is positive. Again,
Must be negative. Power is being injected into the rotor from the slip rings.
Super-synchronous generating
If generating above synchronous speed, slip and torque are both negative, therefore is positive and injected voltage is in phase with rotor current. In this case, mechanical input power is being supplied from the shaft and both the stator and rotor circuits are providing output power.
Digital Signal Processor
Adigitalsignalprocessorisatechnicalmicroprocessorschip,withitsarmatureoptimizedforthefunctionalrequirementsofdigitalsignalprocessing.DigitalsignalprocessorsarefabricatedonMetalOxideSemiconductorintegratedcircuitchips.They areextensivelyusedinaudiosignalprocessing,telecommunications,digitalimageprocessing, radar, sonar andspeechrecognitionsystems, and incommonconsumerelectronicbiassimilarasmobilephones,fragmentdrivesandhigh-descriptionTVproducts.
ThethingofaDigitalSignalProcessorisgenerallytomeasure,sludgeorcompressnonstopreal-worldanalogsignals.Utmostgeneral-purposemicroprocessorscanalsoexecutedigitalsignalprocessingalgorithmssuccessfully,butmaynotbesuitabletokeepupwithsimilarprocessingcontinuouslyinreal-time.Also,devotedDigitalSignalProcessorsgenerallyhavebetterpowereffectiveness,thereforethey aremoresuitableinmovablebiassimilarasmobilephonesbecauseofpowerconsumptionconstraints.DigitalSignalProcessorsfrequentlyusespecialmemoryinfrastructuresthataresuitabletocostmultipledataorinstructionsat the same time.DigitalSignalProcessorsfrequentlyalsoapplydatacontractiontechnology,withtheseparatecosinetransfigureinparticularbeingaextensivelyusedcontractiontechnologyinDigitalSignalProcessors.
Microcontroller unit
Microcontrollerisasmallcomputerona single essence-oxide-semiconductorintertwinedcircuitchip.Amicrocontrollercontainsoneorurthercentralprocessingunitprocessorcoresalongwithmemoryandprogrammableinput/affairperipherals.ProgrammemoryintheformofferroelectricRAM,NORflashorOTPROMisalsofrequentlyincludedonchip,aswellasasmallquantumofRAM.Microcontrollersaredesignedforbeddedoperations,indiscrepancytothemicroprocessorsusedinparticularcomputersorothergeneralpurposeoperationsconformingofcolorfulseparatechips.
Inultramodernlanguage,amicrocontrollerisanalogousto,butlesssophisticatedthan,asystemonachipwhichmayincludeamicrocontrollerasoneofitsfactors,butgenerallyintegratesitwithadvancedperipheralslikeaplatesprocessingunit,aWi-Fimodule,oroneorfurthercoprocessors.
Microcontrollersareusedinautomaticallycontrolledproductsandbias, similar asmachinecontrolsystems,implantablemedicalbias,remotecontrols,officemachines,appliances,powertools,toysandotherbeddedsystems.Byreducingthesizeandcostcomparedtoadesignthatusesaseparatemicroprocessor,memory,andinput/affairbias,microcontrollersmakeitprovidenttodigitallycontrolindeedmorebiasandprocesses.
8.0 INDUCTION MOTOR DESIGNS
An electric motor consists of an iron rotor wheel mounted on a shaft, supported by bearings at each end, spinning within a multi-coil cage of wire called a stator. Copper or aluminum bars are imbedded in the outside surface of the rotor and connected together to form a circuit. The wire windings within the stator are arranged to make an electromagnet. Figure 1 shows a simplified motor design. The electric currents flowing through the surface stator coils create a magnetic flux through the rotor while inducing an electrical current within the rotor bars.
Figure 2.5.A simple cage induction electric motor design.
When alternating current (AC) flows through the stator coil, reciprocating north and south magnetic poles are created at the ends of each coil. At an equivalent time, sort of a transformer, the electrical fields within the stator coils also create an electrical current within the rotor. When an electrical current is cut by a moving magnetic flux a reaction force occurs within the current carrying conductor. The bars within the rotor, now induced with current, react in response to the magnetic flux and force the rotor to show. The alternating magnetic flux is then created within the neighboring coil and therefore the rotor continues to show.
For motion to be induced on the rotor the electric carrying conductor must cut the magnetic field. This means the rotor must move slower than the cycling magnetic flux . It is only by cutting through the lines of magnetism that torque is generated on the rotor. An electric motor will always run at a rather slower speed than the cycling magnetic flux .
The motor speed depends on the number of separate magnetic fields created by the coils in the stator. A two-pole motor has one coil and one magnetic flux arranged round the stator, a four-pole motor has two coils arranged round the stator with each winding placed between the other in sequence. A six-pole motor has three coils with the windings spaced in sequence round the stator, and so on.
9.0 The Squirrel cage Induction Motor
The Induction motor (IM) is composed of a group of thin laminated steel sheets arranged into a cylinder with slots. Coils are inserted into the slots. Each coil group constitutes an electromagnet. The number of poles depends on the internal connection of the stator coils. The squirrel cage rotor is a cylinder made of aluminum bars. The bars are connected mechanically and electrically by ending rings. Considering the stator connected to the source, the generated magnetic field of the stator rotates at synchronous speed
; therefore, the rotor is inside of an electromagnetic field. An electromotive force is produced in the rotor. The rotor current, produced by the rotor induced EMF, generates an electromagnetic field that has opposed polarity with respect to the stator electromagnetic field. Consequently, the interaction between both fields produces an electromagnetic torque in the rotor which makes it rotate in the direction of the stator electromagnetic field.
There is a difference between synchronous speed (
and the rotor speed (
). The speed difference is named slip speed and the slip, is expressed, according to equation (3.1).
rev/ min (3.2)
Where f is the stator voltage frequency and p (equation (3.2), is the number of stator poles expressed by the number of slots in a pole per phase (n) , as:
= 2n. (3.3)
From equation (3.1), we can derivate equation (3.4) in order to express the rotor speed as:
(3.4)
This equation indicates that rotor speed can be adjusted with the frequency of the Induction Motor source. If the rotor is blocked (s =1) and the stator connected to the power source, the frequency of the sinusoidal voltages and currents induced in the rotor (
), is equal to f. In theory, if 
, there would have not been induced any EMF in the rotor and the rotor would not rotate. The frequency of the induced EMF in the rotor changes in inverse proportion to 
. The frequency variation starts in a maximum point (power source frequency) and is decreasing as 
increases (with s » 0).
The frequency of the rotor induced EMF is expressed by equation (3.5):
f= 
(3.5)
The rotor bars have low electrical resistance as well as inductance (
and inductive reactance (
properties. The inductive reactance of the rotor (
) is computed with the rotor blocked [3.18]. Considering that 
increases proportionally to the value of S, the rotor inductive reactance can be expressed by equation (3.6):
The EMF induced in the rotor when it is blocked, is defined by equation (3.7):
Where k is a constant that represents rotor bars features and j is the stator magnetic field. The induced EMF in the rotor ( 
), expressed by equation (3.8), for any value of 
can be expressed as a function of r 
and S:
The frequency of the induced EMF in the rotor (
starts at the value of the stator voltage frequency ( f ) with the rotor is blocked (s = 1) , and decreases down to zero when the shaft attains the synchronous speed (s » 0) .
The torque with the rotor blocked can be determined by the current in the rotor according to equation (3.9):
where
is a constant that depends on the stator coil characteristics, and 
*cosq is the current component of the rotor in phase with j .
The equivalent circuit of the single cage IM is shown in Figure 3.1. The circuit is a model in steady state and allows obtaining the equations that define the IM behavior [3.19-3.20]. The mutual reactance m j
represents the difference between stator and rotor inductances. The impedance of the stator is represented by 
and
. The effective rotor resistance is represented by 
. The effective rotor resistance is represented by
. The s term takes into account the apparent increment of 
when the rotor is moving. 
represents the reactance when s =1.
Figure 3.1: (a) Induction Motor equivalent circuit (b) Reduction of the equivalent circuit
From figure 3.1(a), it can be seen that the rotor current magnitude Ir, with the rotor blocked, is expressed according to equation (3.10):
(3.10)
By substituting equation (3.10) into equation (3.9) and considering that 
equation (3.11) expresses the initial value of the rotor torque [3.21]:
For any value of s, considering equations (3.6) and (3.8), equation (3.12) indicates that rotor current is:
The term, at any value of s , is 2 
Hence, equation (3.13) expresses that, for a given sliding the torque of the IM is:
The equation (3.14) can be derived considering equations (3.7) and (3.8):
Therefore, the stator magnetic field, expressed by equation (3.15),
By substituting equation (3.15) into equation (3.13), the torque magnitude is expressed by equation (3.16) as:
As stated before, a region of constant torque is demanded for speeds below the nominal. Commonly, the voltage magnitude of the motor power source is modified in direct proportion to the frequency. When the frequency is larger than the nominal, the voltage magnitude becomes the nominal value. In order to determine the values of 
the losses of the stator are neglected, then 
To determine the real value of 
, and the real value of the torque, 
and Xsshould be considered. The equivalent circuit of the IM can be reduced to the circuit shown in figure 3.1(b). The magnitude of the equivalent impedance is expressed by equation (3.17):
When the rotor is blocked, equation (3.17) reduces to equation (3.18):
According to the circuit of Figure 3.1(b), the magnitude of V can be expressed by equation (3.19):
and the stator current, s I , is expressed according to equation (3.20):
(3.20)
Hence, by substituting equation (3.20) into equation (3.19),r E1 is given by equation (3.21) shown in (3.22):
The equation (3.22) expresses r E1 when the rotor is blocked:
The proposed V - f relationship
The method of computing the proposed V - f relationship allows the Induction motor to approach the torque-speed to improve the speed response. Taking into account equation (3.16), the torque at nominal frequency (fn) can be expressed by equation (3.23):
The torque for a given frequency, lower than the nominal frequency and that we call operation frequency (fm) , is expressed by equation (3.24) as:
Considering the torque invariant for any power source frequency, that is, Tn= Tm, if the relation between nominal frequency and the given frequency is expressed, by equation (3.25) through an unknown variable X= 
, called frequency factor [24]:
Then
The frequency factor must be calculated for each operation speed of the induction motor (IM); in order to include the frequency influence in the elements of the equivalent circuit shown in Figure 3.1. Hence, this factor appears in the calculation of the magnitude of V .
Replacing equation (3.25) inTn= Tm, the equation (3.26) is obtained:
Then, the induced EMF in the rotor (
) for a given frequency is expressed by equation (3.27):
From equation (3.22), the power source voltage magnitude required to produce 
at the nominal frequency is obtained with equation (3.28):
Hence, the power source voltage magnitude required for any given frequency is expressed by equation (3.29) as:
Where equation (3.30) must be considered:
Equations (3.27) and (3.30) are defined by the IM parameters. There exist several methods to determine the induction motor (IM) parameters.
Equation development
Three-phase induction motors are represented by set of equations.
The slip
The slip is given by the equation below
(3.31)
Where
The rotor speed can otherwise be written as
(3.32)
The Synchronous speed is given as
(3.33)
or
(3.34)
Where
f = the frequency
P = the number or poles
If the unit of the synchronous speed is to be determined in radians, then the speed has to be multiplied by the factor (2
(3.35)
Similarly, the angular value of the rotor speed is give as
(3.36)
The rotor current is given as
(3.37)
The electromagnetic torque is given as
(3.38)
Where
T is the electromagnetic torque, [Nm]
if the synchronous speed is in revolutions per minute then the torque is given by
(3.39)
The power analyses of the circuit is given as follows
The power transferred across the air gap to the rotor is given as
(3.40)
The rotor copper loss is given as
(3.41)
(3.42)
(3.43)
Thus, torque is given as
(3.44)
The torque developed is proportional to the air gap power 𝑃𝑔. The air gap power 𝑃𝑔 is usually known as torque measured in synchronous watts
Figure 3.2: Equivalent circuit of three phase induction motor
This dissertation contributes in developing models for the implementation of V/f control scheme and integrating a PID and vector controllers to control the speed of a three-phase induction motor.
10. CONCLUSION
The torque-speed characteristics for different methods of speed control of an induction motor were obtained and analsyzed. These achievement were made possible by developing MATLAB programming codes. Real motor parameters were used for the creation of the program. The graph results of the various methods were analyses.
In rotor resistance control method the starting torque can be varied with the variation of rotor resistance. The maximum torque however, remains unaffected. Thus for operations requiring high starting torque, the rotor resistance can be varied to even obtain the maximum torque during starting. But simultaneously the copper losses will increase due to increase of resistance. So this method is highly inefficient and cannot be used throughout the operation. In variable supply voltage control method of speed control, the maximum torque decreases with the decrease of supply voltage and thus the motor remains underutilized. So then the variable stator voltage control method cannot be used for good performance due to the weakness.
In constant employing the techniques of constant v/f ratio control, the supply voltage as well as the supply frequency can varied such that the flux remain constant. So we can get different operating zone for various speeds and torques can be achieved at constant flux. Achieving different synchronous speed with almost same maximum torque makes the motor completely utilized and also we have a good range of speed control.
Maintain the V/F ratio helps us to maintain a constant maximum torque while controlling the speed.
11.0 RECOMMENDATION
The advantages of V/F control on induction motor is that it provides good range of speed and it has low starting current requirement. Operators can choose the reference speed to maintain based on the loads. Even if the load is changing with time, the speed can be maintained. To ensure the motor is fully utilized the following suggestions are imperative and therefore recommended.
- The ratio of the change in voltage and frequency must be constant in order to keep the flux content. Thus by maintaining a constant V/f ratio maximum torque of the motor becomes constant for changing speed.
- The initial starting load torque should be zero. This will make the motor speed to move from the incremented of zero to the synchronous speed
- From this work, of the above mentioned methods, V/f control is the most popular and has found widespread use in industrial and domestic applications because of the ease-of-implementation. However, it has inferior dynamic performance compared to vector control. Thus in areas where precision is required, V/f control are not used. Further work can be done on vector method for continual monitoring and control over the operating state of a system without operator intervention: and for more precision or faster response, automatic control systems are needed.
- From this work, of the above mentioned methods, V/f control is the most popular and has found widespread use in industrial and domestic applications because of its ease-of-implementation.
- Implementation of this scalar method (close loop control) on hardware can also be done.
REFERENCE
Agrebi-Zorgani, Y., Koubaa, Y. and Boussak, M. (2010).Simultaneous Estimation of Speed and Rotor Resistance in Sensorless ISFOC Induction Motor Drive Based on MRAS Scheme. IEEE International Conference on Electrical Machines ICEM, Rome,6-8 September, IEEE, pp. 1–6.
AlirezaDavari, D. A. Khaburi, F. Wang, and R. M. Kennel, (2012) "Using full order and reduced order observers for robust sensorless predictive torque control of induction motors," IEEE Trans. Power Electron., vol. 27, pp.3424-3433.
Anwin John and Jayanand B (2014) “Speed and Current Observer for Induction Motor using Extended Kalman Filter” International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181Vol. 3 Issue 7,pp.218-436.
B. Prathap Reddy, MadhukarRao, AManoranjanSahooandSivakumarKeerthipati, (2003) “A Fault Tolerant Multi level Inverter for Improving the Performance of Pole-Phase Modulated Nine-Phase Induction Motor Drive, ”IEEE Transactions On Industrial Electronics, vol. 14, pp.54-112.
Benchaib, A., A. Rachid, E. Audrezet, and M. Tadjine,(1999) “Real time sliding mode observer and control of an induction motor, "IEEE Trans. on Ind. Electronics,vol.46, no.1,Febuary,pp.128-138.
BidyutMahato, Ravi Raushan, Kartick Chandra Jana, (2005)“Modulation and Control of Multilevel Inverter for an Open-end Winding Induction Motor with Constant Voltage Levels and Harmonics, ”IET PowerElectronics.vol.9,pp.47-83.
Bilal A., Umit O., Aydin E., Mehrded E., (2004) “A Comparative Study on Non- Linear State Estimators Applied to Sensorless AC Drives: MRAS and Kalman Filter,” 30 Annual Conf. of the IEEE Ind. Electron. Society .Busan , Korea.vol.11.pp74-135.
Blaschke, (1972)"The principle of field-orientation as applied to the Trans vector closed-loop control system for rotating-field machines", in Siemens, vol.34,pp.217-222.
Cheng Z. C., Hai P. L., (2002) “An Application of Fuzzy-Inference-Based Neural Network in DTC System of Induction Motor,” In Proc. First Int. Conf. on Machine Learning and Cybernetics, Beijing, pp.354-359.
Chul-Woo Park and Woo-Hyen Kwon, (2004)"Simple and robust speed sensorless vector control of induction motor using stator current based MRAC," Electric Power Systems Research, Elsevier, Vol. 71, pp.257–266.
Cirrincione M., Pucci M., (2005)“Sensorless direct torque control of an induction motor by a TLS-based MRAS observer with adaptive integration,” Automatica, vol. 41, pp. 1843-1854.
EKF-algorithm,” Int. J. Power and Energy Sys, p. 1-20.
F. Blaschke,(2010)“The principle of field orientation as applied to the new transvector closed- loop control system for rotating-field machines, ”Siemens Rev., vol. 34,pp.217– 220.
F.A.Toliyat, E. Levi and M. Raina (2003) “A Review of RFO Induction Motor Parameter Estimation Techniques”, IEEE Trans. on Energy Conversion, Vol. 18, No.2, June pp.18-11.
- Harnefors, M. Hinkkanen, (2008) “Complete stability of reduced-order and full-order observers for sensorless IM drives”, IEEE Transactions on Industrial Electronics, Vol. 55, No. 3, pp. 1319–1329.
K. Hinkkanen, (2004) “Stabilization of regenerating-mode operation in sensorless induction motor drives by full- order flux observer design”, IEEE Transactions on Industrial Electronics, Vol. 51, No. 6, pp. 1318–1328.
I.Gonzalez-Prieto, M.J.Duran ,J.J.Aciego, C. Martin, and F.Barrero,(2005)“Model Predictive Control of Six-phase Induction Motor Drives Using Virtual Voltage Vectors ”,IEEE Transactions On Industrial Electronics, pp.10-24.
Ignacio González-Prieto1, Mario. J. Duran1 and Federico J. Barrero,(2014)“Fault-tolerant Control of Six-phase Induction Motor Drives with Variable Current Injection ”, IEEE Transactions On Power Electronics. Edition one ,pp.123-126.
J. Zubek, A. Abbondanti, and C. J. Norby,(2010) “Pulse width modulate diverter motor drives with improved modulation,” IEEE Trans. Ind. Applicat., vol. 11,Nov./Dec ,pp.695–703.
J.H. Song I. Choy K.B. Kim J. Song, K.B. Lee, (2000) “Sensorless vector control of induction motor using a novel reduced-order extended luenberger observer” Conference Record of the IEEE Industry Applications Conference ,vol. 3,pp.1828-1834.
Joachim Holtz, (2002) "Sensorless Control of Induction Machines—With or Without Signal Injection, "IEEE Trans. on Ind. Electrical., Vol. 53, No. 1,February, pp.7-30.
Joachim Holtz, (2002) "Sensorless Control of Induction Motor Drives," IEEE Proc., Vol. 90, No. 8, August, pp.1359-1394.
Kim Y. R., S. K. Sul and M.H. Park, (1994) “Speed sensorless vector control of induction motor using extended Kalman filter,” IEEE Transaction on Ind. Appl., Vol. 30, no. 5, pp. 1225-1233.
KyoB.L., FredeB.,(2006)“Reduced-Order Extended Luenberger Observer Based Sensorless Vector Control Driven by Matrix Converter With Non linearity Compensation ,”IEEE Trans. Ind .Electron., vol.53,no.1,p.66-75.
- L. Shi, T. F. Chan, Y. K. Wong, S.L. HO; (2002) “Speed Estimation of an Induction Motor Drive Using an Optimized Extended Kalman Filter” IEEE transactions on industrial electronics, vol. 49, no.1.pp.382-420.
Lipo , T. & Novotny, D. (1985). Introduction to field orientation and high performance drives. Tutorial course, IEEE LAS, pp.21-264.
LongyaXu, Ernesto Inoa, Yu Liu, and Bo Guan; (2012) “A New High-Frequency Injection Method for Sensorless Control of Doubly Fed Induction Machines” IEEE transactions on industry applications, vol. 48, no.5, September/October ,pp.315-424.
- Asher, A. Ferrah, K. J. Bradley; (1992) “Sensorless speed detection of inverter fedinduction motors using rotor slot harmonics and fast Fourier transforms” IEEE PES meeting, pp.279-286.
M. N. Marwali and A. Keyhani, (1997) "A comparative study of rotor flux based MRAS and back EMF based MRAS speed estimators for speed sensorless vector control of induction machines, "Proc. of the IEEE-IAS Annual Meeting ,pp. 160–166.
Negm , (2000)” Torque optimized speed control of a three phase induction motor”, in Proc .Int. Conf. power system technology pp. 67-72.
Mario Bermudez, Ignacio Gonzalez-Prieto, Federico Barrero, Hugo Guzman , Xavier Kestelynland Mario J. Duran, (2006)“An Experimental Assessment of Open-Phase Fault-Tolerant Virtual Vector Based Direct Torque Controlin Five-Phase Induction Motor Drives”, IEEE Transactions On Power Electronics.pp.48-57.
- Yoo G. Park S. Kim, T. Park, (2001) “Speed-sensorless vector control of an induction motor using neural network speed estimation. IEEE Trans. Ind. Electronics,vol.48,no.3, June, pp.609-614.
MortezaMajdi and FarzanRashidi, (2005) “Sensorless Speed and Position Control of Induction Motor Servo Drives Using MLP Neural Network and Sliding Mode Controller” 4th WSEAS int. conf. on non-linear analysis, non-linear systems and chaos, sofia, bulgaria, October , pp.94-102.
MugdhaBhandari, ShivajiGavade, Shwetha S H, (2015) “Model Reference Adaptive Technique for Sensorless Speed Control of Induction Motor Using MATLAB\SIMULINK” International Journal of Emerging Technology in Computer Science & Electronics (IJETCSE) ISSN: 0976-1353 Volume 14 Issue 2.pp.488-493.
Ouhrouche M. A., (2002)“Estimation of speed, rotor flux and rotor resistance in cage induction motor using the EKF-algorithm," Int. J. Power and Energy system,pp.1-20.
Park, R.H. (1929). "Two-Reaction Theory of Synchronous Machines Generalized Method of Analysis - Part I", AIEE Transactions, Vol. 48, pp. 716-727
Pavel, Brandstetter, MarekDobrovsky, (2013) “Speed Estimation Of Induction Motor Using Model Reference adaptive system with kalman filter” theoretical and applied electrical engineering, vol. 12, no.1.pp.72-98.
Peng and T. Fukao, (1994) "Robust speed identification for speed-sensorless vector control of induction motors," IEEE Transactions on Industry Applications, vol. 30, no. 5, pp. 1234- 1240.
Prasad, B .Suresh ,K. Raghuveer (2012). “Field Oriented Control of PMSM Using SVPWM Technique ”Global Journal of Advanced Engineering Technologies, Vol1, Issue2- ISSN: 2277-6370.
Pratibha Naganathan1,SriramaSrinivasandHridyaIttamveettil,(2017)“Five-level torque controller-based DTC method for a cascaded three level inverter fed induction motor drive”, IET Power Electron.,© The Institution of Engineering and Technology , Vol. 10,pp. 1223-1230.
Rashidi, F., Rashidi, M. (2012) “Design of robust sliding mode speed control with fuzzy approach for induction motor”, IEEE international conference on industrial technology (ICIT03),pp. 27-30.
S. Ambrosii C. Ilas R. Magureanu M. Cuibus, V. Bostan, (2000) “Luenberger ,kalman and neural network observers for sensorless induction motor control” Power Electronics and Motion Control Conference, vol.3,pp.1256-1261.
S.Rahman ,B.E. ,M.Sc ,Ph.D. ,and W .Shepherd ,D.Sc.(Eng.),(1977)“Thyristor and diode controlled variable voltage drives for 3-phaseinductionmotors”,IEE, Vol124,No.9,pp.221-243.
Said A. Deraz and Haitham Z. Azazi1,“Current limiting soft starter for three phase induction motor drive system using PWM AC chopper ”,IET Power Electronics.2004, P.34-44.
Schauder, C. (1992)"Adaptive speed identification for vector control of induction motors without rotational transducers," IEEE Transactions on Industry Applications, vol. 28, no. 5, September ,pp.1054-1061.
Seyed Mohammad Jalal Rastegar Fatemi1,Navid Reza Abjadi, JafarSoltani, and SaeedAbazari,(2014)” Speed sensor less control of a six-phase induction motor drive using back stepping control”, IET PowerElectron.pp.418-720.
W. Novotny and T. A. Lipo, (1996) “Vector Control and Dynamics of AC Drives” Oxford University Press Inc., New York,pp.41-154.
YifanTang , Member , IEEE, and Long yaXu, Senior Member, IEEE, (1995) “Aflexible Active and Reactive Power Control Strategy for a Variable Speed Constant Frequency Generating System ”IEEE Transactions On Power Electronics,Vol.10,No.4,July.pp.110-214.
Zwicky ,B .Haemmerli ,R .Tanner;(1987)“A rotor speed detector for induction machines utilizing rotors lot harmonics and active three-phase injection” EPE, Grenoble, pp. 599-603.
CHAPTER TWO: The chapter one of this work has been displayed above. The complete chapter two of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" is also available. Order full work to download. Chapter two of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" consists of the literature review. In this chapter all the related work on "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" was reviewed.
CHAPTER THREE: The complete chapter three of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" is available. Order full work to download. Chapter three of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" consists of the methodology. In this chapter all the method used in carrying out this work was discussed.
CHAPTER FOUR: The complete chapter four of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" is available. Order full work to download. Chapter four of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" consists of all the test conducted during the work and the result gotten after the whole work
CHAPTER FIVE: The complete chapter five of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" is available. Order full work to download. Chapter five of "enchancing the performance of speed control of three phase induction motor using voltage/frequency speed control technique" consist of conclusion, recommendation and references.
To "DOWNLOAD" the complete material on this particular topic above click "HERE"
Do you want our Bank Accounts? please click HERE
To view other related topics click HERE
To "SUMMIT" new topic(s), develop a new topic OR you did not see your topic on our site but want to confirm the availiability of your topic click HERE
Do you want us to research your new topic? if yes, click "HERE"
Do you have any question concerning our post/services? click HERE for answers to your questions
For more information contact us through any of the following means:
Mobile No 
:+2348146561114 or +2347015391124 [Mr. Innocent]
Email address 
:engr4project@gmail.com
Watsapp No 
:+2348146561114
COUNTRIES THAT FOUND OUR SERVICES USEFUL
Australia, Botswana, Canada, Europe, Ghana, Ireland, India, Kenya, Liberia, Malaysia, Namibia, New Zealand, Nigeria, Pakistan, Philippines, Singapore, Sierra Leone, South Africa, Uganda, United States, United Kindom, Zambia, Zimbabwe, etc
Support: +234 8146561114 or +2347015391124
Watsapp No :+2348146561114
Email Address :engr4project@gmail.com
FOLLOW / VISIT US VIA:
