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EE6352 -ELECTRICAL ENGINEERING AND INSTRUMENTATION UNIT I DC MACHINE 9 Three phase circuits, a review. Construction of DC machines – Theory of operation of DC generators – Characteristics of DC generators- Operating principle of DC motors – Types of DC motors and their characteristics – Speed control of DC motors- Applications. UNIT II TRANSFORMER 9 Introduction – Single phase transformer construction and principle of operation – EMF equation of transformer-Transformer no–load phasor diagram - Transformer on–load phasor diagram Equivalent circuit of transformer – Regulation of transformer –Transformer losses and efficiencyAll day efficiency –auto transformers. UNIT III INDUCTION MACHINES AND SYNCHRONOUS MACHINES 9 Principle of operation of three-phase induction motors – Construction –Types – Equivalent circuit –Construction of single-phase induction motors – Types of single phase induction motors – Double revolving field theory – starting methods - Principles of alternator – Construction details – Types –Equation of induced EMF – Voltage regulation. Methods of starting of synchronous motors – Torque equation – V curves – Synchronous motors. UNIT IV BASICS OF MEASUREMENT AND INSTRUMENTATION 9 Static and Dynamic Characteristics of Measurement – Errors in Measurement - Classification of Transducers – Variable resistive – Strainguage, thermistor RTD – transducer - Variable Capacitive Transducer – Capacitor Microphone - Piezo Electric Transducer – Variable Inductive transducer – LVDT, RVDT UNIT V ANALOG AND DIGITAL INSTRUMENTS 9 DVM, DMM – Storage Oscilloscope. Comparison of Analog and Digital Modes of operation, Application of measurement system, Errors. Measurement of R, L and C, Wheatstone, Kelvin, Maxwell, Anderson, Schering and Wien bridges Measurement of Inductance, Capacitance, Effective resistance at high frequency, Q-Meter. TOTAL (L:45+T:15): 60PERIODS TEXT BOOKS: 1. I.J Nagarath and Kothari DP, “Electrical Machines”, McGraw-Hill Education (India) Pvt Ltd 4 th Edition ,2010 2. A.K.Sawhney, “A Course in Electrical & Electronic Measurements and Instrumentation”, Dhanpat Rai and Co, 2004. REFERENCES: 1. Del Toro, “Electrical Engineering Fundamentals” Pearson Education, New Delhi, 2007. 2. W.D.Cooper& A.D.Helfrick, “Modern Electronic Instrumentation and Measurement Techniques”, 5 th Edition, PHI, 2002. 3. John Bird, “Electrical Circuit Theory and Technology”, Elsevier, First Indian Edition, 2006. 4. Thereja .B.L, “Fundamentals of Electrical Engineering and Electronics”, S Chand & Co Ltd, 2008. 5. H.S.Kalsi, “Electronic Instrumentation”, Tata Mc Graw-Hill Education, 2004. 6. J.B.Gupta, “Measurements and Instrumentation”, S K Kataria & Sons, Delhi, 2003.
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EE6352
ELECTRICAL ENGINEERING AND INSTRUMENTATION
UNIT I DC MACHINES
Construction of DC Machines DC Machines are D.C. Generator and D.C Motor. The construction of both the types of d.c. machines remains same. D.C. Generator : These machines converter mechanical energy into electrical energy. D.C .motor: The machines convert electrical energy into mechanical energy.
It consists of 1. 2. 3. 4. 5. 6. 7. 3
Constructional View of DC Machine
Yoke Field system Armature core Armature winding Commutator Brushes Bearings Visit : www.EasyEngineeering.net
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1.Yoke: It act as the protecting cover for the whole machine and provides mechanical support. It also supports the field system by housing the magnetic poles and field winding of the dc motor.It carries magnetic flux produced by the poles.Yoke is usually made of magnetic material. For small machines: cast iron For large machines: cast steel,silicon steel, rolled steel(for high permeability i.e low reluctance).
2.Field system: (i)poles: Each pole is divided into two parts(1) pole core(2) pole shoe Pole core: The pole core is of small cross-sectional area and its function0 is to just hold the pole shoe over the yoke.It basically carries a field winding , which produce the flux. It directs the flux produced through air gap to armature core, to the next pole. 4
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Pole shoe: pole shoe having a relatively larger cross-sectional area spreads the flux produced over the air gap between the stator(field) and rotor(armature) to reduce the loss due to reluctance. The pole shoe also carries slots for the field windings that produce the field flux. The end of the pole core towards armature is expanded to reduce reluctance of the air gap.It is made up of a magnetic material like cast iron or Cast steel. (ii)Field Winding: The field winding of DC motor are made with field coils (copper wire can bend easily) wound over the slots of the pole shoes in such a manner that when field current flows through it, then adjacent poles have opposite polarity are produced. The field winding basically form an electromagnet, that produces field flux within which the rotor armature of the DC motor rotates, and results in the effective flux cutting. As it helps in producing magnetic field it is called as field winding or exciting winding. Armature Divided into two parts (1)Armature core (2) Armature winding 3.Armature core: It is cylindrical in shape mounted on the shaft.It consists of slots on its periphery and air ducts to permit the air flow through armature which serves cooling purpose.It provides house for armature winding and to provide a path of low reluctance to the magnetic flux produced by the field winding.It is made with several low-hysteresis silicon steel lamination, to reduce the magnetic losses like hysteresis and eddy current loss respectively. 4.Armature winding: It is nothing but the interconnection of armature conductors placed in the slots provided on the armature core. The armature winding of DC motor is attached to the rotor, or the rotating part of the machine, and as a result is subjected to altering magnetic field in the path of its rotation which directly results in magnetic losses. For this reason the rotor is made of armature core. Lap Winding
In this case the number of parallel paths between conductors A is equal to the number of poles P. 5
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i.e A = P ***An easy way of remembering it is by remembering the word LAP----→ L A=P Wave Winding
Here in this case, the number of parallel paths between conductors A is always equal to 2 irrespective of the number of poles. Hence the machine designs are made accordingly.
5.Commutator: It collects current from the armature conductors it is made up of copper segments stacked together, but insulated from each other by mica.It is used to convert alternating emf into unidirectional emf in the case of d.c generators.It provides unidirectional torque in the case of d.c motor.
6.Brushes: The purpose of brushes is to provide electrical connection between rotating commutator and stationary external load circuit. made up of carbon or graphite. They are rectangular in shape. Brushes are housed in brush holder. 7.Bearings: A bearing is a device that is used to enable rotational or linear movement, while reducing friction and handling stress. Resembling wheels, bearings literally 6
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enable devices to roll, which reduces the friction between the surface of the bearing and the surface it’s rolling over. It’s significantly easier to move, both in a rotary or linear fashion, when friction is reduced—this also enhances speed and efficiency. Ball bearing for more reliable. Roller bearing for heavy duty machine(heavy equipment like lift, truck etc).
Operation Of DC Generators A DC generator produces direct power. A generator works on the principles of Faraday’s law of electromagnetic induction.It states that “Whenever a conductor is moved in the magnetic field, an emf is induced andthe magnitude of the induced emf is directly proportional to the rate of change of flux linkage”. This emf causes a current flow if the conductor circuit is closed. The most basic two essential parts of a generator are 1. A magnetic field 2. Conductors which move inside that magnetic field.
The pole pieces (marked N and S) provide the magnetic field. The loop of wire that rotates through the field is called the ARMATURE. The ends of the armature loop are connected to rings called commutator they rotate with the armature. The brushes, usually made of carbon, with wires attached to them, ride against the rings. The generated voltage appears across these brushes
1.Initial position
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The elementary generator produces a voltage in the following manner. Let's us consider, the rectangular loop of conductor is ABCD which rotates inside the magnetic field about its own axis ab. The armature conductors are moving parallel to the magnetic field and not cutting any magnetic lines of flux. No voltage is induced. 2.Zero to 90 degrees When the loop rotates from its vertical position to its horizontal position, it cuts the flux lines of the field. As during this movement two sides, i.e. AB and CD of the loop cut the flux lines there will be an emf induced in these both of the sides (AB & BC) of the loop in the positive direction.
As the loop is closed there will be a current circulating through the loop. The direction of the current can be determined by Flemming's right hand Rule. This rule says that if you stretch thumb, index finger and middle finger of your right hand perpendicular to each other, then thumbs indicates the direction of motion of the conductor, index finger indicates the direction of magnetic field i.e. N - pole to S pole, and middle finger indicates the direction of flow of current through the conductor. Now if we apply this right hand rule, we will see at this horizontal position of the loop, current will flow from point A to B and on the other side of the loop current will flow from point C to D. 8
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3.90 to 180 degrees
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Now if we allow the loop to move further, it will come again to its vertical position, but now upper side of the loop will be CD and lower side will be AB (just opposite of the previous vertical position). At this position the tangential motion of the sides of the loop is parallel to the flux lines of the field. Hence there will be no question of flux cutting and consequently there will be no current in the loop.Cutting less lines of flux. The induced voltage decreases from a maximum positive value to zero.
4.180 to 270 degrees If the loop rotates further, it comes to again in horizontal position. But now, said AB side of the loop comes in front of N pole and CD comes in front of S pole, i.e. just opposite to the previous horizontal position as shown in the figure beside. The conductor cuts more and more lines of flux but in the opposite direction voltage induced in the negative direction building upto a max at 270 degrees.
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Here the tangential motion of the side of the loop is perpendicular to the flux lines, hence rate of flux cutting is maximum here and according to Flemming's right hand rule, at this position current flows from B to A and on other side from D to C. Now if the loop is continued to rotate about its axis, every time the side AB comes in front of S pole, the current flows from A to B and when it comes in front of N pole, the current flows from B to A. Similarly, every time the side CD comes in front of S pole the current flows from C to D and when it comes in front of N pole the current flows from D to C. 5.270 to 360 degrees
Induced voltage decreases from a maximum negative value to zero .This completes one cycle.
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It is seen that in the first half of the revolution current flows always along ABLMCD i.e. brush no 1 in contact with segment a. In the next half revolution, in the figure the direction of the induced current in the coil is reversed. But at the same time the position of the segments a and b are also reversed which results that brush no 1 comes in touch with the segment b. Hence, the current in the load resistance again flows from L to M. The wave from of the current through the load circuit is as shown in the figure. This current is unidirectional.
waveform
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output
voltage
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EE6352
ELECTRICAL ENGINEERING AND INSTRUMENTATION
EMF Equation of Generator(Electromagnetic Force Equation) Let Φ = flux/pole in webers Z = total number of armature conductors = No. of slots x No. of conductors/slot P = No. of poles A = No. of parallel paths in armature N = Armature rotation in revolutions per minute (r.p.m) E = e.m.f induced in any parallel path in armature Average e.m.f generated /conductor = dΦ/dt volt (n=1) Now, flux cut/conductor in one revolution dΦ = ΦP Wb No. of revolutions/second = N/60 Time for one revolution, dt = 60/N second According to Faraday's Laws of Electromagnetic Induction E.M.F generated/conductor is
=
For a simplex wave-wound generator No. of parallel paths A = 2 No. of conductors (in series) in one path = Z/2 E.M.F. generated/path is
60
∗
2
=
120
For a simplex lap-wound generator No. of parallel paths A= P No. of conductors (in series) in one path = Z/P E.M.F.generated/path
60
In general , generated e.m.f
∗
= =
60
ZPN
Note: electromagnetic force, a type of physical interaction that occurs between electrically charged particles. Characteristics of DC Generators The magnetic field in a d.c. generator is normally produced by electromagnets rather thanpermanent magnets. Generators are generally classified according to their methods of fieldexcitation. On this basis, d.c. generators are divided into the following two classes: (i) Separately excited d.c. generators : Field winding is supplied from external or separate d.c.supply 12
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(ii) Self-excited d.c. generators : Generated voltage itself is used to excite the field winding The behaviour of a d.c. generator on load depends upon the method of field excitation adopted. Separately Excited D.C. Generators characteristics A d.c. generator whose field magnet winding is supplied from an independent external d.c.source (e.g., a battery etc.) is called a separately excited generator. The connections of aseparately excited generator are shown below. The voltage output depends upon the speed ofrotation of armature and the field current. The greater the speed and field current, greater is thegenerated e.m.f. It may be noted that separately excited d.c. generators are rarely used inpractice. The d.c. generators are normally of self-excited type.
1. Magnetic (no load or open circuit) characteristics This curve shows the relation between the generated e.m.f. at no-load (E 0) and the field current(If) at constant speed. It is also known as magnetic characteristic or no-load saturation curve. Its shape is practically the same for all generators whether separately or self-excited. The data for O.C.C. curve are obtained experimentally by operating the generator at no load and constant speed and recording the change in terminal voltage as the field current is varied. ∝
The induced emf increases directly as If increases. But after certain If core gets saturated and flux also remains constant through If increases. Hence after saturation voltage also remains constant. For various speed magnetization characteristics are plotted we will get family of parallel characteristics. 13
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2.Load Saturation curve This is the graph of terminal voltage Vt against field current If. When generator is loaded, armature current Ia flows and armature reaction exists. Due to this, terminal voltage Vt is less than the no load rated voltage. On no load, current Ia is zero and armature reaction is absent. Hence less number of ampere turns are required to produce rated voltage Eo .
These ampere-turns are equal to OB as shown in the Fig. On load, to produce same voltage more field ampere-turns are required due to demagnetization effect of armature reaction. These are equal to BC as shown in the Fig. Similarly there is drop Ia Ra across armature resistance. Hence terminal voltage Vt = E - Ia Ra . This graph OR is also shown in the Fig. The triangle PQR is called drop reaction triangle. 14
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ThusOP is no load saturation curve, OQ is the graph of generated voltage on load and OR is the graph of terminal voltage on load. Note: Armature reaction : The effect of flux produced by armature on the main flux produced by the field winding. Armature reaction reduces the generated emf. Demagnetizationeffect :A suitably intense magnetic field applied in a direction opposite to that of the existing magnetization will serve to reduce or destroy that magnetization. 3. Internal and External characteristics Internal characteristics This curve shows the relation between the generated e.m.f. on load (E or Eg) and the armaturecurrent (Ia). The e.m.f. E is less than E0 due to the demagnetizing effect of armature reaction. Therefore, this curve will lie below the open circuit characteristic (O.C.C.). The internalcharacteristic is of interest chiefly to the designer. It cannot be obtained directly by experiment.It is because a voltmeter cannot read the e.m.f. generated on load due to the voltage drop inarmature resistance. The internal characteristic can be obtained from external characteristic ifwinding resistances are known because armature reaction effect is included in bothcharacteristics. External characteristics This curve shows the relation between the terminal voltage (Vt) and load current (IL). The terminal voltage Vt will be less than E due to voltage drop in the armature circuit. Therefore, this curve will lie below the internal characteristic. This characteristic is very important indetermining the suitability of a generator for a given purpose. Armature current, Ia = IL Terminal voltage, Vt = Eg – IaRa-Vbrush Electric power developed = EgIa Power delivered to load = VtIL
Note : E=Eg for all the case 15
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D.C. Shunt Generator In these type of DC generators the field windings are connected in parallel with armature conductors as shown in figure below. In shunt wound generators the voltage in the field winding is same as the voltage across the terminal. So, Ia=Ish + IL The effective power across the load will be maximum when IL will be maximum. So, it is required to keep shunt field current as small as possible. For this purpose the resistance of the shunt field winding generally kept high (100 Ω) and large no of turns are used for the desired emf. Let, Rsh = Shunt winding resistance Ish = Current flowing through the shunt field Ra = Armature resistance Ia = Armature current IL = Load current Vt = Terminal voltage Eg = Generated emf
Shunt field current, Ish = Vt/Rsh Armature current, Ia = IL + Ish Terminal voltage, Vt = Eg - IaRa -Vbrush Power developed(generated) in armature = EgIa Power delivered to load = Vt IL Internal characteristics: The induced e.m.f is not depend on the load current or armature current Ia. But as load current increases the armature current Ia increases to supply load demand. As Ia increases, armature flux increases. Due to armature reaction main flux gets distorted. Hence lesser flux gets linked with the armature conductors.This reduces the induced emf. Note: Armature reaction: The effect of flux produced by armature on the main flux produced by the field winding. 16
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External characteristics: When load current increases,armature current also increases. The drop IaRa increases and terminal voltage decreases. But the value of armature resistance is very small,the drop in terminal voltage as IL changes from no load to full load is very small.Hence d.c shunt generator is called constant voltage generator.
D.C. Series Generator In these type of generators, the field windings are connected in series with armature conductors as shown in figure below. So, whole current flows through the field coils as well as the load. As series field winding carries full load current it is designed with relatively few turns of thick wire. The electrical resistance of series field winding is therefore very low (nearly 0.5Ω ). Let, Rse = Series winding resistance Ise = Current flowing through the series field Ra = Armature resistanceIa = Armature current IL = Load current Vt = Terminal voltage Eg = Generated emf
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Armature current, Ia = Ise = IL Terminal voltage, Vt = Eg - Ia(Ra + Rse)-Vbrush Power developed in armature = EgIa Power delivered to load = VtIa or VtIL No load and Load Characteristics In series generatorIa = Ise = IL,As load current increases,Ise increases.The flux is directly proportional to Ise.So flux also increases.The induced emf E is proportional to flux hence induced emf also increases.Thus the characteristics of E (Or) Eg increasing nature.As Ia increases,armature reaction increases but its effect is negligible compared to increases in E.But for high load current,saturation occurs and flux remains constant. In such case E starts decreasing as shown in figure by dotted line. Thus the external characteristics also of rising as E increases but it will be below internal characteristics due to Ia(Ra+Rse) drop. When there is no load IL=0 then there exists certain induced emf due to residual flux retained by the field winding. Hence characteristics do not pass through origin.
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Note: Residual Magnetism In ferromagnetic materials, the magnetic power and the generated voltage increase with the increase of the current flow through the coils. When current is reduced to zero, there is still magnetic power left in those coils core. This phenomenon is called residual magnetism. The core of a DC machine is made of ferromagnetic material. D.C. Compound Generator: In series wound generators, the output voltage is directly proportional with load current. In shunt wound generators, output voltage is inversely proportional with load current. A combination of these two types of generators can overcome the disadvantages of both. This combination of windings is called compound wound DC generator. Compound wound generators have both series field winding and shunt field winding. One winding is placed in series with the armature and the other is placed in parallel with the armature. This type of DC generators may be of two typesshort shunt compound wound generator and long shunt compound wound generator. In a compound wound generator, the shunt field is stronger than the series field. When the series field assists the shunt field, generator is said to be commutatively compound wound. On the other hand if series field opposes the shunt field, the generator is said to be differentially compound wound. Short Shunt Compound Wound DC Generator
The generators in which only shunt field winding is in parallel with the armature winding as shown in figure. Series field current, Ise = IL Shunt field current, Ish = (V+IseRse) / Rsh 19
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Terminal voltage, Vt = Eg–IaRa -IseRse – Vbrush Power developed in armature = EgIa Power delivered to load = VtIL
Long Shunt Compound Wound DC Generator The generators in which shunt field winding is in parallel with both series field and armature windingas shown in figure.
Armature current, Ia = series field current,Ia= Ise Ia=Ish+IL 20
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Shunt field currentIsh=Vt/Rsh
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Terminal voltage=Eg – IaRa-IseRse-V brush Load Characteristics of compound Generator: The characteristics depends on whether generator is cumulatively compound or differentially compound.
External characteristic of DC compound wound generator is drawn between the terminal voltage and the load current.By adjusting the no. of amp-turns in the series field winding we can get following external characteristics:
1. If the series turns are so adjusted that with the increase in load current the terminal voltage also increases, then the generator is called over compounded. The curve AB in the figure showing this characteristic. When the load current increases then the flux provides by the series field also increases. It gives the additional generated voltage. If the increase in generated voltage is greater than the voltage drops due to armature reaction and ohmic drop then, terminal voltage of the generator is increased.
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2. If the series turns are so adjusted that with the increase in load current the terminal voltage remains constant, then the generator is called flat compounded. The curve AC in the figure showing this characteristic. When the load current increases then the flux provides by the series field also increases and gives the additional generated voltage. If the increase in generated voltage is equal to the voltage drops due to armature reaction and ohmic drop then, rated terminal voltage of the generator remains same as no load voltage.
3. If the series field winding has lesser no. of turns then the rated terminal voltage becomes less than the no load voltage, then the generator is called under compounded. Because, the increase in generated voltage is lesser than the voltage drops due to armature reaction and ohmic drop. Curve AD in the figure is showing this characteristic. In differentially compound the net flux is difference between the shunt field flux and series field flux.As IL increases ϕsh is almost constant but ϕse increases rapidly.Hence net flux reduces.Hence E and Vt decreases drastically.
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D.C.MOTOR Operating Principle of DC Motors
It is based on the principle that when a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force whose direction is given by Fleming's Left-hand rule and whose magnitude is given by Force, F = B I l Newton Where, B is the magnetic field in weber/m2. I is the current in amperes and l is the length of the coil in meter.
In dc motor field winding produces a required magnetic field while armature conductors play a role of a current carrying conductors and hence experience a force. The torque is the product of force and the radius at which this force acts due to this torque armature starts rotating. Position1 Single conductor placed in magnetic field produced by permanent magnet or field winding supplied by current.
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Position1
Position2
Position2 Conductor is excited by a separate supply so it carries a current in a particular direction and produces its own magnetic field around it. Direction of this flux is in clockwise. Position3 Now there are two fluxes 1.Flux produced by permanent magnet called main flux. 2.Flux produced by the current carrying conductor. From the figure we can see that on one side of the conductor both the fluxes are in the same direction(left) there is a gathering of flux lines as two fluxes help each other. On the right side of conductor the two fluxes are in opposite direction and cancel each other. So density of the flux in this area gets weakened. Hence on the left there exists high flux density area while on the right of the conductor low flux density area.
Position 3 24
Position 4
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Position4 This flux distribution around the conductor acts like a stretched rubber band under tension. This exerts a mechanical force on the conductor which acts from high flux density area towards low flux density area. Left to right armature starts move. So motor rotates.
Torque Equation
Turning or twisting force about an axis is called torque.
Consider a wheel of radius R meters acted upon by a circumferential force F Newton’s as shown in above figure. The wheel is rotating at a speed of N rpm. The angular speed of the wheel ω = 2πN/60 rad/sec
Work done in one revolution W= Force x distanced travelled in one revolution W = FX2πR joules Power developed, P = Work done/time = W/Time for 1 rev. P = FX2πR/(60/N) = (FXR)(2πN/60) P = T x ω watts
Power in armature = armature torque x ω EbIa = Ta x (2ΠN/60)
Where, Ta = Armature torque. Eb = (PΦZN)/60A Substituting Eb values, we get,
Ta = 0.159ΦIaPZ N-m A
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Types of DC Motors
1. D.C Shunt Motor In shunt wound motor the field winding is connected in parallel with armature. The current through the shunt field winding is not the same as the armature current. Shunt field windings are designed to produce the necessary m.m.f. by means of a relatively large number of turns of wire having high resistance. Therefore, shunt field current is relatively small compared with the armature current
= = 26
+
DC Shunt Motor
+
=
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Now flux produced by the field winding is proportional to the current passing through it.∅ ∝ Note: Supply voltage is constant the flux produced is constant,so d.c shunt motor is called constant flux motor 2. D.C Series Motor
In series wound motor the field winding is connected in series with the armature. Therefore, series field winding carries the armature current. Since the current passing through a series field winding is the same as the armature current, series field windings must be designed with much fewer turns than shunt field windings for the same mmf. Therefore, a series field winding has a relatively small number of turns of thick wire and, therefore, will possess a low resistance.
DC Series Motor
=
+
+
= +
=
=
+
+
+
Supply voltage has to overcome the drop across series field winding in addition to Eb and drop across armature winding. Note:In series motor entire armature current is passing through the series field winding. So flux produced is proportional to the armature current. 3. D.C Compound Motor
Compound wound motor has two field windings; one connected in parallel with the armature and the other in series with it. There are two types of compound motor connections 1) Short-shunt connection 2) Long shunt connection
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1) Short-shunt connection
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When the shunt field winding is directly connected across the armature terminals it is called short-shunt connection. = = + = + + + But = = + + + Drop across shunt field winding is = − = =
=
+
+
DC Compound Motor (Short shunt) 2) Long shunt connection When the shunt winding is so connected that it shunts the series combination of armature and series field it is called long-shunt connection.
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DC Compound Motor (Long shunt) But
=
=
+
=
+
= = But =
+
= + (
+ +
+ )+
Note: Cumulatively compound motor: If the two windings are wound in such a manner that the fluxes produced the two always help each other. Differential compound motor: If the fluxes produced by the two field windings are trying to cancel each other Note:Back EMF in motor: In a DC Motor, the induced EMF of rotation of the armature is known as Back EMF or Counter EMF. When the current is supplied to the armature conductors placed in the main magnetic field, the torque develops, and the armature of the motor rotates. The armature conductors cut the magnetic flux of the main magnetic field. It can be seen in the figure above that the direction of this induced EMF is opposite to the applied voltage. This is the reason that this induced EMF in the armature, when the machine works as a motor, is called Back EMF (Eb).
Since the back Emf is induced due to the generator action, its magnitude is given by the same expression as that for the generated EMF in a DC generator. It is expressed by the relation shown below. supply voltage is always greater than the induced or back emf i.e. (V > Eb). Therefore, the current is always supplied to the motor from the mains and the relation among the various quantities will be given as Eb = V – IaRa. 29
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EE6352
D.C Motor Characteristics
ELECTRICAL ENGINEERING AND INSTRUMENTATION
1. D.C Shunt Motor a. Torque versus Armature current
Ta is proportional toϕIa .For a constant values of Rsh and supply voltage
V,Ish is also constant and hence flux is also constant.TaαIa.This equation represents a straight line passing through the orgin that indicate torque increases linearly with armature current. Shunt motor requires a large value of armature current at start and hence starting torque high. This may damage the motor hence d.c shunt motors can develop moderate starting torque and suitable for applications where moderate starting torque is required. Shaft torque Tsh is less than armature torque so lies below Ta.
Torque Vs Armature Current
b. Speed versus Armature current As flux ɸ is assumed to be constant, we can say N ∝ Eb. But, as back emf is also almost constant, the speed should remain constant. But practically, ɸ as well as Eb decreases with increase in load. Back emf Eb decreases slightly more than ɸ, therefore, the speed decreases slightly. Generally, the speed decreases only by 5 to 15% of full load speed. Therefore, a shunt motor can be assumed as a constant speed motor. In speed vs. armature current characteristic in the following figure, the straight horizontal line represents the ideal characteristic and the actual characteristic is shown by the dotted line.
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Speed Vs Armature Current
c. Speed versus Torque This characteristic is also called as mechanical characteristic.These characteristics can be derived from the above two characteristics.This curve is similar to N VsIa ,this shows that the speed almost remains constant though torque changes from no load to full load conditions
Speed Vs Torque
2.D.C Series Motor
a. Torque versus Armature current
This characteristic is also known as electrical characteristic. We know that torque is directly proportional to the product of armature current and field flux, T a∝ ɸ.Ia. In DC series motors, field winding is connected in series with the armature, i.e. Ia = If. Therefore, before magnetic saturation of the field, flux ɸ is directly proportional to Ia. Hence, before magnetic saturation Ta α Ia2. Therefore, the Ta-Ia curve is parabola for smaller values of Ia. After magnetic saturation of the field poles, flux ɸ is independent of armature current Ia. Therefore, the torque varies proportionally to Ia only, T ∝Ia.Therefore, after magnetic saturation, Ta-Ia curve becomes a straight line. The shaft torque (Tsh) is less than armature torque (Ta) due to stray losses. Hence, the curve Tsh vs Ia lies slightly lower. In DC series motors, (prior to magnetic saturation) torque increases as the square of armature current, these motors are used where high starting torque is required.
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Torque Vs Armature Current
b. Speed versus Armature current We know the relation, N ∝ Eb/ɸ For small load current (and hence for small armature current) change in back emf Eb is small and it may be neglected. Hence, for small currents speed is inversely proportional to ɸ. As we know, flux is directly proportional to Ia, speed is inversely proportional to Ia. Therefore, when armature current is very small the speed becomes dangerously high. That is why a series motor should never be started without some mechanical load. But, at heavy loads, armature current Ia is large. And hence, speed is low which results in decreased back emf Eb. Due to decreased Eb, more armature current is allowed.
Speed Vs Armature Current
c. Speed versus Torque This characteristic is also called as mechanical characteristic. In case of series motors T α Ia 2 and N α 1/Ia Hence we can write N α 1/√ From the above two characteristics of DC series motor, it can be found that when speed is high, torque is low and vice versa.
Speed Vs Torque
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EE6352
ELECTRICAL ENGINEERING AND INSTRUMENTATION
3.D.C Compound Motor
DC compound motors have both series as well as shunt winding. In a compound motor, if series and shunt windings are connected such that series flux is in direction as that of the shunt flux then the motor is said to be cumulatively compounded. And if the series flux is opposite to the direction of the shunt flux, then the motor is said to be differentially compounded. Characteristics of both these compound motors are explained below. (a) Cumulative compoundmotor Cumulative compound motors are used where series characteristics are required but the load is likely to be removed completely. Series winding takes care of the heavy load, whereas the shunt winding prevents the motor from running at dangerously high speed when the load is suddenly removed. These motors have generally employed a flywheel, where sudden and temporary loads are applied like in rolling mills. (b) Differential compound motor Since in differential field motors, series flux opposes shunt flux, the total flux decreases with increase in load. Due to this, the speed remains almost constant or even it may increase slightly with increase in load (N ∝ Eb/ɸ). Differential compound motors are not commonly used, but they find limited applications in experimental and research work.
DC Compound Motor Characteristics 33
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SpeedControl of DCMotors
DC shunt motor i. Flux control
Flux Control
Speed equation is
∝
∅
∝
∅
Speed Vs Shunt Field Current
As speed is inversely proportional to the flux. The flux is dependent on the current through the shunt field winding. Thus flux can be controlled by adding a rheostat (variable resistance in series with the shunt field winding as shown in above figure. At the beginning the rheostat is kept at minimum. The supply voltage is at rated value. So current through the shunt field winding is also its rated value. Hence the speed is also the rated value. 34
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Resistance is increased, shunt field current is reduced (flux is reduced) and speed is increased beyond its rated value. Advantage: 1.Provide smooth and easy control 2.Speed control above rated speed is possible 3.Power loss is less so more economical and efficient
Disadvantage: 1.Speed below rated speed is not possible. 2.As flux reduces, speed increases. Affects commutation.
ii. Armature voltage control or rheostatic control
Rheostatic Control
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Speed Vs Voltage across Armature Visit : www.EasyEngineeering.net
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The speed is directly proportional to the voltage applied across the armature. As the supply voltage is normally constant, the voltage across the armature can be controlled by adding a variable resistance in series with the armature as shown in figure above. Initially the rheostat position is minimum and rated voltage gets applied across the armature.So speed is also rated. For a given load armature current is fixed. When extra resistance is added in the armature circuit Ia remains same and there is voltage drop across the resistance added.Hence voltage across the armature decreases speed also decreases. iii. Applied voltage control
Multiple Voltage Control Shunt field of the motor is permanently connected to the fixed voltage supply. Armature is supplied with various voltages by means of suitable switchgear arrangements. iv. Potential divider control
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Speed Vs Voltage
When the variable rheostat position is at start point shown, voltage across the armature is zero. As rheostat is moved towards minimum point shown, the voltage across the armature increases, increasing the speed. At maximum point the voltage is maximum and speed is rated value. SPEED CONTROL OF D.C SERIES MOTOR The flux produced by the winding depends on the magnetomotive force which is the product of current and the number of turns of the winding through which current is passing. So flux can be changed either by changing the current by adding a resistance or by changing the number of turns of the winding. Flux control method: 1.Field diverter method: This method uses a diverter. Here the field flux can be reduced by shunting a portion of motor current around the series field. Lesser the diverter resistance(Rx) less is the field current, less flux therefore more speed. This 37
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method gives speed above normal and the method is used in electric drives in which speed should rise sharply as soon as load is decreased.
2.Armature diverter method: This method is used for the motor which require constant load torque. An armature is shunted with an external variable resistor(Rx).Due to this armature current decreases. But asTαΦIa and load torque is constant the flux is to be increased. So motor draws more current. So current through field winding increases so flux increases and speed of motor reduces.
3.Tapped field method This is another method of increasing the speed by reducing the flux and it is done by lowering number of turns of field winding through which current flows. In this method a number of tapping from field winding are brought outside. This method is employed in electric traction.
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4.Series -Parallel connection of field Field coil is divided into various parts. For the same torque if the field coil is arranged in series or parallel mmf produced by the coils changes ,hence the flux produced also changes. Some fixed speed only can be obtained by this method. In parallel grouping the mmf produced decreases hence higher speed can be obtained this method is used in fan motors.
Rheostatic control method In this method Rx is connected in series with the motor .There is a voltage drop across inserted resistor. This drop reduces armature voltage. So speed also reduces.AS entire current passes through Rx there is large power loss.
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Applied voltage control In this method a series motor is excited by the voltage by a series generator.The generator is driven by prime mover.The voltage obtained from the generator is controlled by a field diverter resistance connected across series field winding of the generator.
Ward Leonard control system is introduced by Henry Ward Leonard in 1891. Ward Leonard method of speed control is used for controlling the speed of a DC motor. It is a basic armature control method. This control system is consisting of a DC motor M1 and powered by a DC generator G. In this method the speed of the DC motor (M1) is controlled by applying variable voltage across its armature. This variable voltage is obtained using a motor-generator set which consists of a motor M2 (either AC or DC motor) directly coupled with the generator G. It is a very widely used method of speed control of DC motor.
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The speed of motor M1 is to be controlled which is powered by the generator G. The shunt field of the motor M1 is connected across the DC supply lines. Now, generator G is driven by the motor M2. The speed of the motor M2 is constant. When the output voltage of the generator is fed to the motor M1 then the motor starts to rotate. When the output voltage of the generator varies then the speed of the motor also varies. Now controlling the output voltage of the generator the speed of motor can also be controlled. For this purpose of controlling the output voltage, a field regulator is connected across the generator with the dc supply lines to control the field excitation. The direction of rotation of the motor M1 can be reversed by excitation current of the generator and it can be done with the help of the reversing switch R.S. But the motor-generator set must run in the same direction. Advantages of Ward Leonard System
1. It is a very smooth speed control system over a very wide range (from zero to normal speed of the motor). 2. The speed can be controlled in both the direction of rotation of the motor easily. 3. The motor can run with a uniform acceleration. 4. Speed regulation of DC motor in this Ward Leonard system is very good. 5. It has inherent regenerative braking property. Disadvantages of Ward Leonard System
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1. The system is very costly because two extra machines (motor-generator set) are required. 2. Overall efficiency of the system is not sufficient especially if it is lightly loaded. 3. Larger size and weight. Requires more floor area. 4. Frequent maintenance. 5. The drive produces more noise. Application of Ward Leonard System
This Ward Leonard method of speed control system is used where a very wide and very sensitive speed control is of a DC motor in both the direction of rotation is required. This speed control system is mainly used in colliery winders, cranes, electric excavators, mine hoists, elevators, steel rolling mills, paper machines,diesel-locomotives, etc.
APPLICATIONS Type of Motor Shunt
Series
Cumulative
Characteristics Speed is fairly constant and medium starting torque.
High starting torque. No load condition is dangerous. Variable speed.
compound
High starting torque. No load condition is allowed.
Differential compound
Speed increases as load increases.
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Applications
1. Blowers and fans 2. Centrifugal and reciprocating pumps 3. Lathe machines 4. Machine tools 5. Milling machines 6. Drilling machines 1. Cranes 2. Hoists, Elevators 3. Trolleys 4. Conveyors 5. Electric locomotives 1. Rolling mills 2. Punches 3. Shears 4. Heavy planers 5. Elevators Not suitable for any practical applications
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43
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UNIT-II-TRANSFORMERS
Introduction – Single phase transformer construction and principle of operation – EMF equation of transformer-Transformer no–load phasor diagram - Transformer on–load phasor diagram -Equivalent circuit of transformer – Regulation of transformer –Transformer losses and efficiency-All day efficiency –auto transformers. TRANSFORMERS
It is a static device ( doesn’t contains rotating parts, hence no friction losses) which transform ac electrical energy from one circuit to another circuit without change in frequency. • There are two or more stationary electric circuits that are coupled magnetically. • It involves interchange of electric energy between two or more electric systems. • Transformers provide much needed capability of changing the voltage and current levels easily. • They are used to step-up generator voltage to an appropriate voltage level for power transfer. • Stepping down the transmission voltage at various levels for distribution and power Utilization. Types: In terms of number of windings Conventional transformer: two windings Autotransformer: one winding Others: more than two windings In terms of number of phases Single-phase transformer Three-phase transformer Depending on the voltage level at which the winding is operated Step-up transformer: primary winding is a low voltage (LV) winding 1 Visit : www.EasyEngineeering.net
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Step-down transformer : primary winding is a high voltage (HV) winding
Single Phase Transformer Construction and Principle of Operation Construction It consists of two electric circuits linked by a common magnetic circuit helped the voltage and current levels to be changed keeping the power invariant. The various parts are 1. Windings
2. Magnetic core 3.Insulation
4.Conservator 5.Breather
6.Buchholz relay
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1.Windings:
Primary Winding - which produces magnetic flux when it is connected to electrical source. Secondary winding – winding to which an electrical load is connected and from which output energy is drawn. Windings are made of copper. 2.Magnetic core:
It is made-up of silicon steel sheets. The sheets are laminated and insulated from each other by thin layer of varnish. The magnetic flux produced by the primary winding, that will pass through this low reluctance path linked with secondary winding and create a closed magnetic circuits. The vertical portion on which coils are wound s called limb while horizontal portions is called yoke. Types of Transformers w.r.t Cores • Core Type Transformer • Shell Type Transformer • Berry Type Transformer Core Type Transformer: In core type transformer, windings are cylindrical former wound, mounted on the core limbs as shown in the figure above. The cylindrical coils have different layers and each layer is insulated from each other. Materials like paper, cloth or mica can be used for insulation. Low voltage windings are placed nearer to the core, as they are easier to insulate.
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Shell Type Transformer: Here the core surrounds the windings. It has two magnetic path and three limbs. Laminated sheets are cut in E and I shape. The coils are of sand width type.
Berry type Transformer:
This has distributed magnetic circuit.The number of independent magnetic circuits are more than 2.Its core construction is like spokes of a wheel.
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Conservator:
The conservator conserves the transformer oil. It is an airtight, metallic, cylindrical drum that is fitted above the transformer. The conservator tank is vented to the atmosphere at the top, and the normal oil level is approximately in the middle of the conservator to allow the oil to expand and contract as the temperature varies. The conservator is connected to the main tank inside the transformer, which is completely filled with transformer oil through a pipeline. Breather:
• The breather controls the moisture level in the transformer. Moisture can arise when temperature variations cause expansion and contraction of the insulating oil, which then causes the pressure to change inside the conservator. Pressure changes are balanced by a flow of atmospheric air in and out of the conservator, which is how moisture can enter the system. • If the insulating oil encounters moisture, it can affect the paper insulation or may even lead to internal faults. Therefore, it is necessary that the air entering the tank is moisture-free. • The transformer's breather is a cylindrical container that is filled with silica gel. When the atmospheric air passes through the silica gel of the breather, the air's moisture is absorbed by the silica 5 Visit : www.EasyEngineeering.net
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crystals. The breather acts like an air filter for the transformer and controls the moisture level inside a transformer. It is connected to the end of breather pipe. Buchholz Relay :
The Bochholz Relay is a protective device container housed over the connecting pipe from the main tank to the conservator tank. It is used to sense the faults occurring inside the transformer. It is a simple relay that operates by the gases emitted due to the decomposition of transformer oil during internal faults. It helps in sensing and protecting the transformer from internal faults. Explosion Vent:
The explosion vent is used to expel boiling oil in the transformer during heavy internal faults in order to avoid the explosion of the transformer. During heavy faults, the oil rushes out of the vent. The level of the explosion vent is normally maintained above the level of the conservatory tank.
Insulation:
• Insulating paper and cardboard are used in transformers to isolate primary and secondary windings from each other and from the transformer core.
• Transformer oil is another insulating material. Transformer oil can actually have two functions: in addition to insulating it can also work to cool the core and coil assembly. The transformer's core and windings must be completely immersed in the oil. Normally, hydrocarbon mineral oils are used as transformer oil. Oil contamination is a serious problem because contamination robs the 6 Visit : www.EasyEngineeering.net
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oil of its dielectric properties and renders it useless as an insulating medium.
Principle of operation: The working principle of transformer is very simple. It depends upon Faraday's law of electromagnetic induction. Actually, mutual induction between two or more winding is responsible fortransformation action in an electrical transformer. Note:
Faraday's Laws of Electromagnetic Induction According to these Faraday's laws, "Rate of change of flux linkage with respect to time is directly proportional to the induced EMF in a conductor or coil". It consists of two inductive coils which are electrically separated but magnetically coupled to a core. If the coil is connected to a source of alternating voltage an alternating flux is produced in the laminated core. Most of the flux islinked with the coil. Thus flux is called mutual flux. As per faraday s laws of electromagnetic induction, an emf is induced in the secondary coil. If the secondary coil circuit is closed, a current flow in it and thuselectrical energy is transferred from the first coil to the second coil.Then as per Faradays law of electromagnetic induction emf E1 and E2 are induced in primary and secondary winding.The emf E2 can be delivered to any load.The magnitude of the emf E2 induced in the secondary winding depends upon the number of turns of winding. STEP UP TRANSFORMER: If the number of turns in the secondary winding is greater than the number of turns in the primary winding,then it is called as step-up transformer.
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STEP-DOWN TRANSFORMER:
If the number of turns in the secondary winding isles than the number of turns in the primary winding,then it is called as step-down transformer.
EMF Equation of Transformer
Let, N1=Primary number of turns N2 =Secondary number of turns f = Frequency of supply in Hz The flux in the core will be sinusoidally as shown below
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The flux in the core increases from zero to Φm in one quarter cycle (1/4 second) Therefore, average rate of change of flux = Φm/(1/4f) = 4f Φm Average emf induced per turn = Average rate change of flux x 1 =4f Φm Volts Since the flux is varying sinusoidaly,r.m.s value is obtained by multiplying average value with the form factor. Form factor of sine wave = RMS value of induced emf per turn = 1.11 x 4f Φm = 4.44f Φm Volts RMS value of induced emf in primary, E1 = 4.44f ΦmN1 Volts RMS value of induced emf in secondary, E2 = 4.44f ΦmN2 Volts In an ideal transformer on no load, V1 = E1, V2 = E2 Transformation Ratios Ideal Transformer
An ideal transformer is a transformer which has no loses, i.e. it’s winding has no ohmic resistance, no magnetic leakage, and therefore no I2 R and core loses. However, it is impossible to realize such a transformer in practice. Voltage ratio: =
=K
Current ratio: =
=
Where K is called as transformation ratio
If N2 > N1 , K1 then transformer is a step up transformer
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If N2=N1 ,K=1 ,1:1 Transformer or isolation transformer. Theory of Transformer on No-Load
Theory of Transformer On No-load, and Having No Winding Resistance and No Leakage Reactance of Transformer If the primary winding is connected to a a.c supply and the secondary winding is left open, then it is called as transformer on No-load.
When an alternating source is applied in the primary, the source will supply the current for magnetizing the core of transformer.
But this current is not the actual magnetizing current, it is little bit greater than actual magnetizing current. Actually, total current supplied from the source has two components, one is magnetizing current which is merely utilized for magnetizing the core and other component of the source current is consumed for compensating the core losses in transformer. Because of this core loss component, the source current in transformer on no-load condition supplied from the source as source current is not exactly at 90° lags of supply voltage, but it lags behind an angle θ is less than 90°. If total current supplied from source is Io, it will have one component in phase with supply voltage V1 and this component of the current Iw is core loss component. This component is taken in phase with source voltage, because it is associated with active or working losses in transformer. Other component of the source current is denoted as I μ. This component produces the alternating magnetic flux in the core, so it is watt10 Visit : www.EasyEngineeering.net
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less; means it is reactive part of the transformer source current. Hence I μ will be in quadrature with V1 and in phase with alternating flux Φ.
No load input power, W0 = V1 I0 cos Φ0
In primary side for I0 we get two components Iw and Im.
The component Im is known as magnetizing component. This component produces mutual flux Φ in the core. Im lagging behind V1 by 90˚. Im = I0 sin Φ0
The component Iw is known as iron loss or active or working component. It is in phase with the applied voltage V1. It supplies a very small primary copper loss and iron loss. Iw = I0 cos Φ0
It is clear that I0 is the phasor sum of Im and Iw. I0 = √(Im2 + Iw2)
No load power factor, cos Φ0 = Iw / I0
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At no load practical transformer primary copper loss I02R is very small and this loss may be neglected. Hence, primary no load input power of practical transformer is equal to the iron loss. No load input power, W0 = Iron loss
As primary loss in practical transformer is quite small so it can be written at no load, V1 = E1. There is no load in secondary so E2 = V2. Transformer On-load When the secondary winding is connected to a load, then it is called as transformer on load. Due to load, current I2 flow through the load.
The phase angle between V2 and I2 depends on load. Resistive load- V2 and I2 are in phase Inductive load – I2 lags V2
Capacitive load – I2 leads V2
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IO flows through primary winding and produces flux.Then emf E1 and E2 are induced in primary and secondary wingding. Due to E2 current I2 flows and produces flux2. Flux 2 opposes the flux as shown in fig. Due to this E1 is reduced.
This causes an additional current I2’ to flow through primary winding. I2’ is known as load component of primary current. I2’ produces flux 2’shown in fig.
Flux 2’ opposes the flux 2 and cancel each other as shown in fig. Flux is constant at no load as well as at loaded condition. The total current I1 will be vector sum of IO and I2’.
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Primary Leakage flux:
The flux that links only the primary winding is called as primary leakage fluxand it induces emf E1. Secondary leakage flux:
The flux that links only the secondary winding is called as secondary leakage flux and it induces emf E2. VECTOR DIAGRAM OF TRANSFORMER ON LOAD CASE1:No winding resistance and leakage reactance
Assume V1=E1 and V2=E2
Let us consider a inductive load.Here I2 lags V2 by a angle 2. 14 Visit : www.EasyEngineeering.net
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The primary current I1 has to supply IO and I2’ ′
∗
′
=
′
=
=
′
+
=
=
I1 is the vector sum of I2’ and IO ,
I2’ is 180 out of phase with I2
PROCEDURE TO DRAW VECTOR DIAGRAM: 1.Draw the flux line .It is the reference vector
2.Draw the V1 vector. The angle between V1 and is 90.
3.Draw the induced emfs E1 and E2 vector. They opposes V1 180 out of phase. 4.Draw the no load current IO.The current IO is lagging V1 by an angle o. 5.Draw the secondary current I2. UPF: V2 and I2 are in phase
Lagging p.f: I2 lags V2 by an angle 2
Leading p.f: I2 leads v2 by an angle 2
6.Draw the load component of primary current I2’.It is opposite and equal in magnitude toI2.
7.Draw the current I1.I1 lags V1 by an angle 1.I1 is a vector sum of IO and i2’. = ′ + Case(ii)Transformer with resistance and leakage reactance 15 Visit : www.EasyEngineeering.net
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Consider a transformer supplying the load as shown in the Fig
The various transformer parameters are, R1 = Primary winding resistance X1 = Primary leakage reactance R2 = Secondary winding resistance X2 = Secondary leakage reactance ZL = Load impedance I1= Primary current I2 = Secondary current = IL = Load current now Ī1 = Īo + Ī2' where Io = No load current I2'= Load component of current decided by the load = K I2 where K is transformer component There is a voltage drop in R1 and X1 .So E1 is less than V1.
There is also voltage drop in R2 and X2.So V2 is less than E2. =
+j
+
=
=
=
+
=
=
=
′
+
+
+
+
+
+
−
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PROCEDURE TO DRAW VECTOR DIAGRAM 1.Draw the vector flux .It acts as reference line.
2.Draw the induced emfE1.The angle between E1 and is 90 lag. 3.Draw the line –E1 It is opposite to E1. 4.Draw the no load primary current IO.
5.Draw the secondary terminal voltage V2 in a particular direction. 6.Draw the I2 vector.
For UPF: I2 &V2 are inphase
For Lag p.f:I2 lags V2 by 2
For Lead p.f: I2 leads V2 by 2
7.Draw I2R2 drop line, parallel to vector I2
8.Draw I2X2 drop line, perpendicular to vector I2.
9.I2X2 line is joined with E1 line .This point is E2. 10.Draw line I2’ at 180 to I2. 11.Draw I1 line .
=
′
+
12.Draw I1R1 drop line, parallel to vector I1.
13.Draw I2X1 drop line, perpendicular to vector I1.
14.Join I1X1 point and “o”.We get V1.The angle between V1 and I1 is 1. Load p.f=cos2 17 Visit : www.EasyEngineeering.net
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Primary p.f=cos1
Input power to transformer p=V1I1 COS Output power=V2I2COS.
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Note: leakage reactance
All the flux in transformer will not be able to link with both the primary and secondary windings. A small portion of flux will link either winding but not both. This portion of flux is called leakage flux. Due to this leakage flux in transformer, there will be a self-reactance in the concerned winding. This self-reactance of transformer is alternatively known as leakage reactance of transformer. This self-reactance associated with resistance of transformer is impedance. Due to this impedance of transformer, there will be voltage drops in both primary and secondary transformer winding. Equivalent circuit of Transformer
Representing transformer as electrical circuit is known as equivalent circuit. 19 Visit : www.EasyEngineeering.net
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With the help of equivalent circuit voltage drop, regulation, efficiency can be calculated.
(a) Some leakage flux is present at both primary and secondary sides. This leakage gives rise to leakage reactances at both sides, which are denoted as X1 and X2 respectively. (b) Both the primary and secondary winding possesses resistance, denoted as R1 and R2 respectively. These resistances causes voltage drop as, I1R1 and I2R2 and also copper loss I12R1 and I22R2. (c) Permeability of the core can not be infinite, hence some magnetizing current is needed. Mutual flux also causes core loss in iron parts of the transformer. I1=Full load primary current I2= secondary current IO=Noload primary current IW=Working component of current IM=Magnetizing component of current RO=No load resistance XO=No load reactance XL=Load reactance RL= load resistance K=transformation ratio ZL=Load impedance
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The no load current I0 is divided into, pure inductance X0 (taking magnetizing components Iμ) and non induction resistance R0 (taking working component Iw) which are connected into parallel across the primary. The value of E1 can be obtained by subtracting I1Z1 from V1. The value of R0 and X0 can be calculated as, R0 = E1 / Iw and X0 = E1 / Iμ. But, using this equivalent circuit does not simplifies the calculations. To make calculations simpler, it is preferable to transfer current, voltage and impedance either to primary side or to the secondary side. In that case, we would have to work with only one winding which is more convenient. EQUIVALENT CIRCUIT REFFERED TO PRIMARY SIDE R2,X2,ZL,V2 and I2 are shifted to primary side as R2’,X2’,ZL’,V2’ and I2’. ′
=
,
′
,
=
′
=
,
′
′
=
=
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=
,
=
,
=
+
′
,
R01=Total equivalent resistance referred to primary X01=Total equivalent reactance referred to secondary
=
+
′
+
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EQUIVALENT CIRCUIT REFFERED TO SECONDARY SIDE R1,X1,I1 and V1 are shifted to secondary side as R1’,X1’,I1’ and V1’ ′
=
,
′
=
,
′
=
,
′
=
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