Transformer DesignA transformer transfers electric power from one circuit to another circuit without a change in frequency. It contains primary and secondary winding. The primary winding is connected to the main supply and secondary to the required circuit. In our project circuit, we have taken the design of low power (10 KVA) single phase 50 hertz power transformer as per our requirement in the project.The transformer is basically of three types: Core TypeShell TypeToroidalIn core, type windings surround a part of the core whereas in shell type core surrounds windings. In the Core type, there are two main types namely E-I type and U-T type. In this transformer design, we used E-I core type. We chose E-I core as the winding is much easier when compared to toroidal, but efficiency is very high (95%-96%). It is so because flux loss is very less in toroidal cores comparatively.The transformers employed in the project areSeries transformer: To provide the required boost or buck voltage andControl transformer: For sensing the output voltage and for power supply.Design Formulas:Here we take the reference of winding data on enameled copper wire table and dimensions of transformer stampings table to select input and output windings SWG and core of the transformer for given specifications.The design procedure is followed assuming that the following specification of a transformer are given:- Secondary voltage (Vs)Secondary current (Is) Turns ratio (n2/n1)From these given details we calculate Tongue width, stack height, core type, window area as follows:-Secondary Volt-Amps (SVA) = secondary voltage (Vs) * secondary current(Is)Primary Volt-Amps (PVA) = Secondary Volt-Amps (SVA) / 0.9 (assuming efficiency of the transformer as 90%)Primary voltage (Vp)= Secondary voltage(Vs)/ turns ratio(n2/n1)Primary current (Ip) = Primary Volt-Amps(PVA)/ Primary voltage(Vp)The require cross-sectional area of the core is given by:- Core area (CA) = 1.15 * sqrt (Primary Volt-amps(PVA)) Gross core area (GCA) = Core area(CA) * 1.1The number of turns on the winding is decided by the ratio given as:- Turns per volt (Tpv) = 1/(4.44 * 10-4 * core area* frequency * flux density)Winding data on Enameled copper wire(@ 200A/cm²)Max. Current Capacity (Amp.)Turns/Sq. cmSWGMax. Current Capacity (Amp.)Turns/Sq. cmSWG0.00181248500.1874711290.001562134490.2219609280.002639706480.2726504270.004127546470.3284415260.005920223460.4054341250.007914392450.4906286240.010411457440.5838242230.01319337430.7945176220.01627755421.0377137210.01976543411.313106200.02335595401.62287.4190.02744838392.33560.8180.03653507383.17845.4170.04692800374.15135.2160.05862286365.25426.8150.07151902356.48721.5140.08581608348.57916.1130.101313083310.96112.8120.118211373213.63810.4110.13649973116.68.7100.158888130Dimension of Transformer stampings (Core table):Type NumberTongue Width (cm)Window Area (Sq. cm)Type NumberTongue Width (cm)Window Area (Sq. cm)171.271.21392.2237.86512A1.5881.8979A2.2237.865741.7482.28411A1.9059.072231.9052.7234A3.33510.284302321.90510.891 1.5883.329163.8110.891312.2233.70333.8112.704101.5884.4394AX2.38313.039152.544.839133.17514.117332.85.88752.5415.32411.6676.55542.5415.865142.546.55575.0818.969111.9057.25963.8119.356341.5887.52935A3.8139.31633.1757.56285.0849.803For operation on mains supply, the frequency is 50HZ, while the flux density can be taken as 1Wb/sq cm. for ordinary Steel stampings and 1.3Wb/sq cm for CRGO stampings, depending on the type to be used.HencePrimary turns (n1) = Turns per volt(Tpv) * Primary voltage(V1)Secondary turns (n2) = Turns per volt(Tpv) * secondary voltage(V2) * 1.03 (Assume that there is 3% drop in transformer windings)The width of the tongue of laminations is approximately given by:-Tongue width (Tw) = Sqrt * (GCA) Current densityIt is the current carrying capacity of a wire per unit cross sectional area. It is expressed in units of Amp/ cm². The above mentioned wire table is for a continuous rating at current density of 200A/cm². For non-continuous or intermittent mode of operation of transformer one can choose a higher density up to 400A/cm² i.e., twice the normal density to economize the unit cost. It is opted as, the temperature rise for the intermittent operational cases are less for the continuous operational cases.So depending on the current densities choosen we now calculate the values of primary and secondary currents that are to searched in wire table for selecting SWG:-n1a = Primary current (Ip) calculated / (current density/200)n2a = Secondary current (Is) calculated / (current density/200)For these values of primary and secondary currents we choose the corresponding SWG and Turns per sqcm from the wire table. Then we proceed to calculate as follows:-Primary area(pa)= Primary turns(n1) / (Primary turns per sqcm)Secondary area(sa)= Secondary turns(n2) / (Secondary turns per sqcm)The total window area required for the core is given by:-Total area (TA) = Primary area (pa) + Secondary area (sa)Extra space required for the former and insulation may be taken as 30% extra space of what is required by the actual winding area. This value is approximate and may have to be modified, depending on the actual winding method.Window area (Wacal) = Total area (TA) * 1.3For the above calculated value of tongue width, we choose core number and window area from the core table ensuring that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain approximately constant gross core area.Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core tableStack Height = Gross core area / Tongue width ((available) (atw)).For commercially available former size purposes, we approximate stack height to tongue width ratio to the nearest following figures of 1.25, 1.5, 1.75. At the worst case we take the ratio equal to 2. However any ratio till 2 can be taken which would call for making ones own former.If the ratio is greater than 2 we select a higher tongue width (aTw) ensuring all the conditions as above.Stack height(ht) / tongue width(aTw) = (some ratio)Modified stack height = Tongue width(aTw) * Nearest value of standard ratioModified Gross core area = Tongue width (aTw) * Modified stack height.Same design procedure applies for control transformer, where in we need to ensure that stack height equals Tongue width.Thus we find core number and stack height for the given specifications.Designing a transformer using an example:The given details are as follows:-Sec. voltage(Vs) = 60VSec current(Is) = 4.44ATurns per ratio (n2/n1) = 0.5Now we have to calculations as follows:-Sec.Volt-Amps(SVA) = Vs * Is = 60 * 4.44 =266.4VA Prim.Volt-Amps(PVA) = SVA / 0.9 = 296.00VA Prim.Voltage (Vp) = V2 / (n2/n1) = 60/0.5= 120V Prim.current (Ip) = PVA/Vp = 296.0/ 120 = 2.467A Core Area(CA) = 1.15 * sqrt(PVA) = 1.15 * sqrt(296) = 19.785 cm² Gross core area(GCA) = CA * 1.1 = 19.785 * 1.1 = 21.76 cm² Turns per volt(Tpv) = 1 / (4.44 * 10-4 * CA *frequency * Flux density) = 1 / (4.44 * 10-4 * 19.785 * 50 *1) = 2.272 turns per volt Prim.Turns(N1) = Tpv * Vp = 2.276 * 120 = 272.73 turns Sec.Turns(N2) = Tpv * Vs * 1.03 = 2.276 * 60 * 1.03 = 140.46 turns Tongue width(TW) = Sqrt*(GCA) = 4.690 cm We are choosing the current density as 300A/cm², but the current density in the wire table is given for 200A/cm², then Primary current search value = Ip / (current density/200) = 2.467 / (300/200) = 1.644A Secondary current search value = Is / (current density/200) = 4.44 / (300/200) = 2.96AFor these values of primary and secondary currents we choose the corresponding SWG and Turns per sqcm from the wire table.SWG1=19 SWG2=18Turn per sqcm of primary = 87.4 cm² turns per sqcm of secondary =60.8 cm² Primary area(pa) = n1 / turns per sqcm(primary) = 272.73 / 87.4 = 3.120 cm² Secondary area(sa) = n2 / turns per sqcm(secondary) = 140.46 / 60.8 = 2.310 cm² Total area(at) = pa + sa = 3.120 + 2.310 = 5.430 cm² Window area (Wa) = total area * 1.3 = 5.430 * 1.3 = 7.059 cm²For the above calculated value of tongue width, we choose core number and window area from the core table ensuring that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain approximately constant gross core area.Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table: So tongue width available (atw) = 3.81cm Window area available (awa) = 10.891 cm² Core number = 16 Stack Height = gca / atw = 21.99 / 3.810 = 5.774cmFor performance reasons, we approximate stack height to tongue width (aTw) ratio to the nearest following figures of 1.25, 1.5, and 1.75. At the worst case we take the ratio equal to 2.If the ratio is greater than 2 we select a higher tongue width ensuring all the conditions as above.Stack height(ht) / tongue width(aTw) = 5.774 / 3.81 = 1.516 Modified stack height = Tongue width(aTw) * Nearest value of standard ratio = 3.810 * 1.516 = 5.715cm Modified Gross core area = Tongue width (aTw) * Modified stack height = 3.810 * 5.715 = 21.774 cm²Thus we find core number and stack height for the given specifications. Design of a small control transformer with example:The given details are as follows:-Sec. voltage(Vs) = 18V Sec current(Is) = 0.3A Turns per ratio (n2/n1) = 1Now we have to calculations as follows:-Sec.Volt-Amps(SVA) = Vs * Is = 18 * 0.3 = 5.4VAPrim.Volt-Amps(PVA) = SVA / 0.9 = 5.4 / 0.9 = 6VAPrim. Voltage (Vp) = V2 / (n2/n1) = 18/1 = 18VPrim. current (Ip) = PVA/Vp = 6 / 18 = 0.333ACore Area(CA) = 1.15 * sqrt(PVA) = 1.15 * sqrt(6) = 2.822 cm²Cross core area(GCA) = CA * 1.1 = 2.822 * 1.1 = 3.132 cm²Turns per volt(Tpv) = 1 / (4.44 * 10-4 * CA *frequency * Flux density) = 1 / (4.44 * 10-4 * 2.822 * 50 *1) = 15.963 turns per voltPrim. Turns(N1) = Tpv * Vp = 15.963 * 18 = 287.337 turnsSec.Turns(N2) = Tpv * Vs * 1.03 = 15.963 * 60 * 1.03 = 295.957 turnsTongue width(TW) = Sqrt*(GCA) = sqrt * (3.132) = 1.770 cmWe are choosing the current density as 200A/cm², but the current density in the wire table is given for 200A/cm², thenPrimary current search value = Ip / (current density/200) = 0.333 / (200/200) = 0.333ASecondary current search value = Is / (current density/200) = 0.3 / (200/200) = 0.3AFor these values of primary and secondary currents we choose the corresponding SWG and Turns per Sq. cm from the wire table.SWG1=26 SWG2=27Turn per Sq. cm of primary = 415 turns Turns per Sq. cm of secondary = 504 turnsPrimary area(pa) = n1 / turns per sqcm(primary) = 287.337 / 415 = 0.692 cm²Secondary area(sa) = n2 / turns per sqcm(secondary) = 295.957 / 504 = 0.587 cm²Total area(at) = pa + sa = 0.692 + 0.587 = 1.280 cm²Window area (Wa) = total area * 1.3 = 1.280 * 1.3 = 1.663 cm²For the above calculated value of tongue width, we choose core number and window area from the core table ensuring that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain approximately constant gross core area.Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core tableSo tongue width available (atw) = 1.905cm Window area available (awa) = 18.969 cm² Core number = 23 Stack Height = gca / atw = 3.132 / 1.905 = 1.905cmHence the control transformer is designed. Share This Post: Facebook Twitter Google+ LinkedIn Pinterest Post navigation ‹ Previous Servo Voltage StabilizerNext › 300+ Electronics Mini Projects Ideas for Engineering Students Related Content What is RL Circuit : Working & Its Uses What is a Current Mirror : Circuit & Its Working What is a Form Factor & Its Significance What is Peak Inverse Voltage & Its Working 13 CommentsDear sir. Thanks for ur valuable information ,please help us to find EI core selection calculation and to find the Stack calculation sir..,ReplyVery good post on transformer design. I also have an article regarding types of CTs on my page if anyone is interested in learning more about Current Transformer Theory. Cheers!ReplyDear sir. Thanks for ur valuable information ,please help us to find EI core selection calculation and to find the core area of a line and load inductorsReplyHello sir, This site is very informative and I learn a lot . thank you for sharing the design in detail. One doubt sir in example 1 and 2 how you select turn per ratio 0.5 Hope to listen from you soon regardsReplyreally very useful in our industryReplyhaving any calculation formula for designReplyHi Raakesh,Please visit our website once https://www.elprocus.com For any assistance or for customization of projects please email us on team@elprocus.comuse full information but i can’t understand what is 4.44*10 to the power minus 4 please reply its urgent.Replythis is very useful information.. Thnx A ton for sharing… Its very helpful…Replytnx & nice1!ReplyIts very useful to learn any transformer Design.ReplyUseful information. I bookmarked it…Replyrealy usefulReplyAdd Comment Cancel replyComment:Name * Email * Website
Dear sir. Thanks for ur valuable information ,please help us to find EI core selection calculation and to find the Stack calculation sir..,Reply
Very good post on transformer design. I also have an article regarding types of CTs on my page if anyone is interested in learning more about Current Transformer Theory. Cheers!Reply
Dear sir. Thanks for ur valuable information ,please help us to find EI core selection calculation and to find the core area of a line and load inductorsReply
Hello sir, This site is very informative and I learn a lot . thank you for sharing the design in detail. One doubt sir in example 1 and 2 how you select turn per ratio 0.5 Hope to listen from you soon regardsReply
Hi Raakesh,Please visit our website once https://www.elprocus.com For any assistance or for customization of projects please email us on team@elprocus.com
use full information but i can’t understand what is 4.44*10 to the power minus 4 please reply its urgent.Reply