Presentation on theme: "OUTPUT EQUATION OF SINGLE PHASE TRANSFORMER"— Presentation transcript:
1OUTPUT EQUATION OF SINGLE PHASE TRANSFORMER · The equation which relates the rated kVA output of a transformer to the areaof core and window is called output equation.· In transformers the output kVA depends on flux density and ampere-turns.· The flux density is related to core area and the ampere-turns is related towindow area.· The simplified cross-section of core type and shell type single phasetransformers are shown in figures (4-1) and (4-2).· The low voltage winding is placed nearer to the core in order to reduce theinsulation requirement.· The space inside the core is called window and it is the space available foraccommodating the primary and secondary winding.· The window area is shared between the winding and their insulations.
2· The induced emf in a transformer, · Emf per turn,· The window in single phase transformer contains one primary and onesecondary winding.
3· The window space factor Kw is the ratio of conductor area in window to total area of window.· Conductor area in window,· The current density is same in both the windings. Therefore Current density,· Area of cross - section of primary conductor,· Area of cross - section of secondary conductor,
4· If we neglect magnetizing mmf then primary ampere turns is equal to secondary ampere turns. Therefore ampere turns,· Total copper area in window,Ac = Copper area of primary winding + Copper area of secondary winding= (Number of primary turns x area of cross-section of primaryconductor) + (Number of secondary turns x area of cross - section ofsecondary conductor)
5· On equating the above equations, we get, · Therefore Ampere turns,· The kVA rating of single phase transformer is given by· On substituting for E and AT from equations we get,The above equation is the output equation of single phase transformer.
6OUTPUT EQUATION OF THREE PHASE TRANSFORMER · The simplified cross-section of core type three phase transformer is shown infigure.· The cross-section has three limbs and two windows.· Each limb carries the low voltage and high voltage winding of a phase.· The induced emf per phase,· Emf per turn,· In case of three phase transformer, each window has two primary and twosecondary windings.
7· The window space factor K is the ratio of conductor area in window to total area of window,· Therefore Conductor area in the window,· The current density is same in both the windings.where, I = Primary current per phase= Secondary current per phase· Area of cross - section of primary conductor,· Area of cross - section of secondary conductor,
8· If we neglect magnetizing mmf then primary ampere turns per phase is equal to secondary ampere turns per phase.· Total copper area in window, Ac = (2 x Number of primary turns x area ofcross-section of primary conductor) + ( 2 x Number of secondary turns x areaof cross - section of secondary conductor)· On equating we get,
9· The kVA rating of three phase transformer is given by, · On substituting for E and AT from equations we get,· The above equation is the output equation of three phase transformer.
10DESIGN OF CORES· For core type transformer the cross-section may be rectangular, square orstepped.· When circular coils are required for distribution and power transformers, thesquare and stepped cores are used.· For shell type transformer the cross-section may be rectangular.· When rectangular cores are used the coils are also rectangular in shape.· The rectangular core is suitable for small and low voltage transfor· In core type transformer with rectangular cores, the ratio of depth to width ofthe core is 1.4 to 2.· In shell type transformers with rectangular cores the width of the central limbis 2 to 3 times the depth of the core.· The figure shows the cross-section of transformer cores.
11· In square cores the diameter of the circumscribing circle is larger than the diameter of stepped cores of same area of cross-section.· Thus when stepped cores are used the length of mean turn of winding isreduced with consequent reduction in both cost of copper and copper loss.· However with larger number of steps a large number of different sizes oflaminations have to be used.· This results in higher labor charges for shearing and assembling differenttypes of laminations.· Let d = diameter of circumscribing circle· Also, d = diagonal of the square core and a = side of square· Diameter of circumscribing circle,
12· Therefore Side of square, · Gross core area, Agj = area of square = a2· Let stacking factor, Sf = 0.9· Net core area, Ai = Stacking factor x Gross core area= 0.9 x 0.5 d2 = 0.45 d2· Area of circumscribing circle,
13· Another useful ratio for the design of transformer core is core area factor. · It is the ratio of net core area and square of the circumscribing circleTWO STEPPED CORE FOR CRUCIFORM CORE· In stepped cores the dimensions of the steps should be chosen, such as tooccupy maximum area within a circle. The dimensions of the two step to givemaximum area for the core in the given area of circle are determined asfollows.· Let, a = Length of the rectangleb = Breadth of the rectangled = Diameter of the circumscribing circle
14Also, d= Diagonal of the rectangle ϴ = Angle between the diagonal and length of the rectangle.· The cross-section of two stepped core is shown in figure.
15MULTI-STEPPED CORES· We can prove that the area of circumscribing circle is more effectively utilizedby increasing the number of steps.· The most economical dimensions of various steps for a multi-stepped core canbe calculated as shown for cruciform (or two stepped) core. The results aretabulated in table.
16CHOICE OF FLUX DENSITY IN THE CORE · The flux density decides the area of cross-section of core and core loss.· Higher values of flux density results in smaller core area, lesser cost,reduction in length of mean turn of winding, higher iron loss and largemagnetizing current.· The choice of flux density depends on the service condition (i.e., distributionor transmission) and the material used for laminations of the core.· The laminations made with cold rolled silicon steel can work with higher fluxdensities than the laminations made with hot rolled silicon steel.· Usually the distribution transformers will have low flux density to achievelesser iron loss.· When hot routed silicon steel is used for laminations the following values canbe used for maximum flux density (Bm)Bm = 1.1 to, 1.4 Wb/m2 - For distribution transformersBm = 1.2 to 1.5 Wb/m2 - For power transformers· When cold rolled silicon steel is used for laminations, the following valuescan be used for maximum flux density (Bm)Bm = 1.55 Wb/m - For transformers with voltage rating upto 132 kVBm= 1.6 Wb/m - For transformers with voltage rating 132 kV to 275 kYBm = 1.7 Wb/m - For transformers with voltage rating 275 kV to 400 Kv
17OVERALL DIMENSIONS OF THE TRRNSFORMER · The main dimensions of the transformer are Height of window (Hw) andWidth of window (Ww).· The other important dimensions of the transformer are width of largeststamping (a), diameter of circumscribing circle (d), and distance between corecentres (D), height of yoke (Hy), depth of yoke (Dy), overall height oftransformer frame (H) and overall width of transformer frame (W).· These dimensions for various types of transformers are shown in figures.
18· The above figure shows a vertical and horizontal cross-section of the core and winding assembly of a core type single phase transformer.· The following figure shows a vertical and horizontal cross-section of the coreand winding assembly of a core type three phase transformer.· The next figure shows a vertical and horizontal cross-section of a shell typesingle phase
19· The figure shows a vertical and horizontal cross-section of a shell type single phase transformer.
20TRANSFORMER CONSTRUCTION · A transformer consists of two windings coupled through a magnetic medium.· The two windings work at different voltage level.· The two windings of the transformer are called High voltage winding andLow voltage winding.· Both the windings are wound on a common core.· One of the winding is connected to ac supply and it is called primary.· The other winding is connected to load and it is called secondary.· The transformer is used to transfer electrical energy from high voltagewinding to low voltage winding or vice-versa through magnetic field.· The construction of transformers varies greatly, depending on theirapplications, winding voltage and current ratings and operating frequencies.· The two major types of construction of transformers (used in transmission anddistribution of electrical energy) are core type and shell type.· Depending on the application, these transformers can be classified asdistribution transformers and power transformers.· The transformer is extremely important as a component in many differenttypes of electric circuits, from small-signal electronic circuits to high voltagepower transmission systems.· The most important function performed by transformers are,Changing voltage and current level in an electric system.Matching source and load impedances for maximum powertransfer in electronic and control circuitry.Electrical isolation.
21CORE TYPE TRANSFORMER· In core type transformer, the magnetic core is built of laminations to form arectangular frame and the windings are arranged concentrically with eachother around the legs or limbs.· The top and bottom horizontal portion of the core are called yoke.· The yokes connect the two limbs and have a cross sectional area equal to orgreater than that of limbs.· Each limb carries one half of primary and secondary.· The two windings are closely coupled together to reduce the leakagereactance.· The low voltage winding is wound near the core and high voltage winding iswound over low voltage winding away from core in order to reduce theamount of insulating materials required.
22SHELL TYPE TRANSFORMER · In shell type transformers the windings are put around the central limb and theflux path is completed through two side limbs.· The central limb carries total mutual flux while the side limbs forming a partof a parallel magnetic circuit carry half the total flux.· The cross sectional area of the central limb is twice that of each side limbs.CORE TYPESHELL TYPE1. Easy in design and construction.2. Has low mechanical strength due to nonbracingof windings.3. Reduction of leakage reactance is noteasily possible.4. The assembly can be easily dismantledfor repair work.5. Better heat dissipation from windings.6. Has longer mean length of core andshorter mean length of coil turn. Hence bestsuited for EHV (Extra High Voltage)requirements.1. Comparatively complex.2. High mechanical strength.3. Reduction of leakage reactance is highlypossible.4. It cannot be easily dismantled for repairwork.5. Heat is not easily dissipated fromwindings since it is surrounded by core.6. It is not suitable for EHV (Extra HighVoltage) requirements.
23Choice of core lengthThe factors to be considered for the choice of core length areCostVentilationVoltage between adjacent commutator segmentsSpecific magnetic loadingWhen the length of the core is large, the ratio of inactive copper to activecopper will be small. Hence the machine may cost less.When the core length is very large then ventilation of the core will bedifficult. The centre portion of the core tends to attain a high temperature rise andso the core must be ventilated (or cooled) by special methods.An expression for maximum value of core length can be derived as shownbelow.For better commutation the voltage between adjacent commutatorsegments at load is to be limited to 30V. To achieve this, the inducedemf in a conductor should not exceed 7.5/TcNcwhere, Tc = Turns per coilNc = Number coils between adjacent segmentsNc = 1, for simplex lap windingNc = p/2, for simplex wave windingp = Number of poles
24CHOICE OF SPECIFIC MAGNETIC LOADING The choice of average gap density or specific magnetic loading depends onthe followingFlux density in teethFrequency of flux reversalSize of machineLarge values of flux density in teeth results in increased field mmf.Higher values of field mmf increase the iron loss, copper loss and cost ofcopper.The Bav is chosen such that the flux density at the root of the teeth does notexceed 2.2 Wb/m2.If the frequency of flux reversals is high then iron losses in armature core andteeth would be high. Therefore we should not use a high value of flux density inthe air gap of machines which have a high frequency.It is possible to use increased values of flux density as the size of the machineincreases.As the diameter D of the machine increases, the width of the tooth alsoincreases, permitting an increased value of gap flux density without causingsaturation in the machine.The value of Bg varies between 0.55 to 1.15 Wb/m2 and the correspondingvalues Of Bav are 0.4 to 0.8 Wb/m2
25CHOICE OF SPECIFIC ELECTRIC LOADING The choice of specific electric loading depends on the followingTemperature rise Size of machine Speed of machineArmature reaction Voltage CommutationA higher value of ac results in a high temperature rise of windings.The temperature rise depends on the type of enclosure and cooling techniquesemployed in the machine.If the speed of machine is high, the ventilation of the machine is better andtherefore, greater losses can be dissipated. Thus a higher value of ac can be usedfor machine having high speed.In high voltage machines, large space is required for insulation and thereforethere is less space for conductors. This means that in high voltage machines, thespace left for conductors is less and therefore we should use a small value of ac.In large size machines it is easier to find space for accommodatingconductors. Hence specific electric loading can be increased with increase inlinear dimensions.With high values of ac, armature reaction will be severe. To counter this, thefield mmf is increased and so the cost of the machine goes high.High values of ac worsen the commutation condition in machines. From thepoint of view of commutation a small value of ac is desirable. The value of acusually lies between to amp.cond/m.
26TRANSFORMER CORE DESIGN The core of a transformer consists of core and winding.The armature core is cylindrical in shape with slots on the outer periphery ofthe armature.The core is formed with circular laminations of thickness 0.5 mm.The winding is placed on the slots in the armature core.The design of armature core involves the design of main dimensions D & L,number of slots, slot dimensions and depth of core.Number of transformer slotsThe factors to be considered for selection of number of transformers slots areSlot width (or pitch)Cooling of armature conductorsFlux pulsationsCommutationCost
27A large number of slots results in smaller slot pitch and so the width of tooth is also small. This may lead to difficulty in construction.But large number of slots will lead to less number of conductors per slot andso the cooling of armature conductors is better.If the air-gap reluctance per pair of pole is constant then the flux pulsationsand oscillations can be avoided.It can be proved that the air-gap reluctance is constant if the slots per pole isan integer plus 1/2.For sparkless commutation the flux pulsations and oscillations under theinterpole must be avoided. This can be achieved with large number of slots perpole.In fact, the number of slots in the region between the tips of two adjacentpoles should be at least 3.The slots per pole should be greater than or equal to 9, for better commutation.When large number of slots are used the cost of lamination and the cost ofinsulation will be high
28Depth of transformer core The depth of core cannot be independently designed, because it depends onthe diameter of armature (D), inner diameter of armature (Di) and the depth of slot(ds). The figure shows the cross-section of armature.From figure,D = Di + 2dc + 2ds
29Depth of core, d = 1/2(D-Di-2ds) After estimating D, Di and ds the available depth of core dc can be calculated.With this value of dc, the flux density in the core can be estimated and if itdoes not exceed 1.5 Wb/m2, then the available depth of core is sufficient.Otherwise we have to increase the diameter of the armature D to giveufficient depth for core. The usual value of flux density in the core is 1.0 to 1.5Wb/m2Finally, the depth of the core is given by,dc= ½( φ/iBLc)where, φ = Flux per poleLi = Net iron length of the armatureB = Flux density in the core
30Types of transformer winding DC machines employ two general types of double layer windings. They areSimplex lap windingSimplex wave windingThese two types of windings primarily differ from each other in the followingtwo factors.The number of circuits between the positive and negative brushes,i.e., number of parallel paths.The manner in which the coil ends are connected to the commutator segments.In simplex lap winding the number of parallel paths is equal to number ofpoles, whereas in simplex wave winding the number of parallel paths is two.In simplex lap winding the finish of a coil is connected to start of next coil. Insimplex wave winding the finish of a coil is connected to start of a coil which islying one pitch away from the finish.The simplex lap or wave windings are suitable for most of the dc machinesused for various applications. But occasionally the number of parallel paths has tobe increased to a value more than that provided by simplex windings. In suchcases the multiplex windings are employed..
32Definition of various terms used in transformer winding Conductor: The active length of copper or aluminium wire in the slot iscalled conductor.Turn: Two conductors connected for additive emf is called a turn. The twoconductors of a turn are placed approximately a pole pitch apart.Coil: A coil consists of a number of turns and it is the principal element ofarmature winding. The coil with single turn is called single turn coil and thecoil with several turns is called multi turn coil.Coil side: The active portions of the conductors in a coil are called coil sides.A coil will have two sides and they are upper coil side and lower coil side.Usually the top coil side is represented by solid line and bottom coil side bydotted line. The top coil side is placed in the upper portion of a slot and thebottom coil side is placed at the lower portion of another slot. The distancebetween the two coil sides is kept approximately as one pole pitch.Overhang: The end portion of the coil connecting the two coil sides is calledoverhang.
33the coils are called short pitched or short chorded coils. Coil span: The distance between the two coil sides of a coil is called coilspan. It is expressed in terms of number or slots or in electrical degrees.Full pitch coil: When the coil span is equal to pole pitch, the coils are calledfull pitched coils.Short pitched or chorded coil: When the coil span is less than the pole pitch,the coils are called short pitched or short chorded coils.Single layer winding: When the coil sides are arranged in a single layer in aslot, the winding is called single layer winding.Double layer winding : When the coil sides are arranged in two layers in aslot, the winding is called double layer winding.Back Pitch (Yb): The distance between top and bottom coil sides of a coilmeasured around the back of the armature (away from the commutator) iscalled the back pitch. The back pitch is measured in terms of coil sides. SinceYb is difference between odd and even number, it is always an odd number.The back pitch of a coil determines the size of the coil and is nearly equal tocoil sides per pole or pole pitch.
34Front Pitch (Yf): The distance between two coil sides connected to the same commutator segment is called the front pitch (Yf). The front pitch determinesthe type of the winding only and it does not affect the size of the coils.Winding Pitch (Y): The distance between the starts of two consecutive coilsmeasured in terms of coil sides is called winding pitch (Y). The winding pitchis always an even integer.Y = Yb - Yf for lap windingY = Yb + Yf for wave windingCommutator Pitch (Yc): The distance between the two commutator segmentsto which the two ends (start and finish) of a coil are connected is called thecommutator pitch (Yc) and it is measured in terms of commutator segment.Number of armature coils: The number of turns per coil and the number ofcoils are so chosen that the voltage between adjacent commutator segments islimited to a value where there is no possibility of a flashover. Normally, themaximum voltage between adjacent segments at load should not exceed 30V.
35SIMPLEX LAP WINDINGIn simplex lap winding the finish of a coil is connected to start of next coil.This winding scheme results in a number of parallel paths which is equal tonumber of poles.The simplex lap winding is a closed winding. In a closed winding if we tracethe winding starting from one point, we will reach the same point after travelingthrough all the turns.But the electrical circuit closes through external load in case of generator andthrough external supply in case of motor. The simplex winding has one closedelectrical circuit. (i.e., all the parallel paths electrically closes through externalload or supply).The two types of simplex lap winding used areprogressive lap winding andRetrogressive lap winding.In the progressive lap winding the joining to the commutator progress aroundthe commutator in the same direction as the coils progress around the armature, asshown in figure.
37In the retrogressive lap winding the joining to the commutator segment progresses around the commutator in the opposite direction to the progress ofcoils around the armature, as shown in figure.
38Steps for designing of lap winding for transformers Step 1: Find the range of slots from the range of slot pitch. Armature slotpitch, Ysa = 25 to 35 mm. Slots, itD/y where D is diameter of armatureStep 2: In the above range of slots, list the values of slots which are multiplesof pole pairs.Step 3: In order to reduce flux pulsations, the slots per pole should be aninteger ± 1/2. The integer should be in the range of 8 to 16. List all themultiples of integer ± 1/2 from the list obtained in step 2.Step 4: Choose the suitable slot from the list obtained in step 3.Step 5: Estimate the total number of armature conductors, Z using theequation of induced ernf. Find the conductors per slot and choose it to thenearest even number.Step 6: Find the minimum number of coils.Step 7: Assume, u = 2, 4, 6, 8 etc., where u = coil sides per slot.Step 8: For each value of u, calculate the number of coils. Choose the numberof coils such that, it is greater than minimum number of coils. Also the valueof u should be a divisor of conductors per slot.Step 9: Once the number of coils and slots are finalized, Estimate the newvalue of total number of conductors and number of turns per coil.Total armature conductors, Z = Slots x Conductor per slot.Number of turns per coil = Z/2C.If a suitable value of C is not obtained to satisfy the above condition, thenmake another choice of slots from the list obtained in step 3.
41COOLING OF TRANSFORMERS · The losses developed in the transformer cores and windings are converted intothermal energy and cause heating of corresponding transformer parts.· The heat dissipation in transformer occurs by Conduction, Convection andRadiation.· The paths of heat flow in transformer are the followingFrom internal most heated spots of a given part (of core orwinding) to their outer surface in contact with the oil.From the outer surface of a transformer part to the oil that cools it.From the oil to the walls of a cooler, eg. Wall of tank.From the walls o the cooler to the cooling medium air or wIn the path 1 mentioned above heat is transferred by conduction. In the path 2and 3 mentioned above heat is transferred by convection of the oil. In path 4the heat is dissipated by both convection and radiation.
42· The various methods of cooling transformers are Air naturalForced circulation of oilAir blastOil forced-air naturalOil naturalOil forced-air forcedOil natural-air forcedOil forced-water forcedOil natural-water forced· The choice of cooling method depends upon the size, type of application andtype of conditions obtaining at the site where the transformer in installed.· Air natural is used for transformers up to 1.5 MVA. Since cooling by air is notso effective and proves insufficient for transformers of medium sizes, oil isused as a coolant.· Oil is used for almost all transformers except for the transformers used forspecial applications.· Both plain walled and corrugated walled tanks are used in oil cooledtransformer.· In oil natural-air forced method the oil circulating under natural head transfersheat to tank walls. The air is blown through the hollow space to cool the
43· In oil natural-water forced method, copper cooling coils are mounted above the transformer core but below the surface of oil. Water is circulated throughthe cooling coils to cool the transformer.· In oil forced-air natural method of cooling, oil is circulated through thetransformer with the help of a pump and cooled in a heat exchanger by naturalcirculation of air.· In oil forced-air forced method, oil is cooled in external heat exchanger usingair blast produced by fans.· In oil forced-water forced method, heated oil is cooled in a water heatexchanger. In this method pressure of oil is kept higher than that of water toavoid leakage of oil.· Natural cooling is suitable up to 10 MVA. The forced oil and air circulationare employed for transformers of capacities 3Q MVA and upwards.