CONTENTS + 0 ) 2 6 - 4 ! Learning Objectives ➣ Working Principle of TRANSFORMER Transformer ➣ Transformer Construction ➣ Core-type Transformers ➣ Shell-type Transformers ➣ E.M.F. Equation of Transformer ➣ Voltage Transformation Ratio ➣ Transformer with losses ➣ Equivalent Resistance ➣ Magnetic Leakage ➣ Transformer with Resistance and Leakage Reactance ➣ Total Approximate Voltage Drop in Transformer ➣ Exact Voltage Drop ➣ Separation of Core Losses ➣ Short-Circuit or Impedance Test ➣ Why Transformer Rating in KVA? ➣ Regulation of a Transformer ➣ Percentage Resistance, Reactance and Impedance ➣ Kapp Regulation Diagram ➣ Sumpner or Back-to-back- 6LAH?AIIAIJDAAA?JHE?EJOBH= Test CAAH=JHEI 1116 Electrical Technology 32.1. Working Principle of a Transformer A transformer is a static (or stationary) piece of apparatus by means of which electric power in one circuit is transformed into electric power of the same frequency in another circuit. It can raise or lower the voltage in a circuit but with a correspond- ing decrease or increase in current. The physical basis of a transformer is mutual induction between two circuits linked by a common magnetic flux. In its simplest form, it consists of two inductive coils which are electrically separated but magnetically linked through a path of low reluctance as shown in Fig. 32.1. The two coils possess high mutual inductance. If one coil is connected to a source of alternating voltage, an alternating flux is set up in the laminated core, most of which is linked with Fig. 32.1 the other coil in which it produces mutually-in- duced e.m.f. (according to Faraday’s Laws of Electromagnetic Induction e = MdI/dt). If the second coil circuit is closed, a current flows in it and so electric energy is transferred (entirely magnetically) from the first coil to the second coil. The first coil, in which electric energy is fed from the a.c. supply mains, is called primary winding and the other from which energy is drawn out, is called secondary winding. In brief, a transformer is a device that 1. transfers electric power from one circuit to another 2. it does so without a change of frequency 3. it accomplishes this by electromagnetic induction and 4. where the two electric circuits are in mutual inductive influence of each other. 32.2. Transformer Construction iron core The simple elements of a transformer consist of two coils having mutual inductance and a laminated steel core. The primary secondary two coils are insulated from each other and coil coil the steel core. Other necessary parts are : some suitable container for assembled core 110/120 220/240 and windings ; a suitable medium for volts volts insulating the core and its windings from its container ; suitable bushings (either of porcelain, oil-filled or capacitor-type) for secondary insulating and bringing out the terminals coil of windings from the 110/120 220/240 tank. volts volts In all types of Principle of transformer transformers, the core is constructed of transformer sheet steel laminations assembled to provide a continuous magnetic path with a minimum of air-gap included. The steel used is of high silicon content, sometimes heat treated to produce a high permeability and a low hysteresis loss at the Fig. 32.2 Laminated Core f Secondary Primary Transformer 1117 usual operating flux densities. The eddy current loss is minimised by Normal Operation laminating the core, the laminations being insulated from each other by a Low High voltage voltage light coat of core-plate varnish or by an oxide layer on the surface. The Oil thickness of laminations varies from 0.35 mm for a frequency of 50 Hz to Iron Core 0.5 mm for a frequency of 25 Hz. The core laminations (in the form of strips) are joined as shown in Fig. 32.2. It is seen that the joints in the alternate layers are staggered in order to avoid the presence of narrow gaps right through the cross-section of the core. Such staggered joints are said to be ‘imbricated’. Magnetic Flux Constructionally, the transformers are of two Paper Insulation Laminated general types, distinguished from each other Ground core merely by the manner in which the primary Leads Core-type transformer and secondary coils are placed around the laminated core. The two types are known as (i) core-type and (ii) shell- type. Another recent development is spiral-core or wound-core type, the trade name being spirakore transformer. Primary In the so-called core type transformers, the windings surround a Winding Secondary Winding considerable part of the core whereas in shell-type transformers, the core surrounds a considerable portion of the windings as shown schematically Shell-Type transformer in Fig. 32.3 (a) and (b) respectively. Fig. 32.3 Fig. 32.4 In the simplified diagram for the core type transformers [Fig. 32.3 (a)], the primary and secondary winding are shown located on the opposite legs (or limbs) of the core, but in actual construction, these are always interleaved to reduce leakage flux. As shown in Fig. 32.4, half the primary and half the secondary winding have been placed side by side or concentrically on each limb, not primary on one limb (or leg) and the secondary on the other. Fig. 32.5 Fig. 32.6 In both core and shell-type transformers, the individual laminations are cut in the form of long strips of L’s, E’s and I’s as shown in Fig. 32.5. The assembly of the complete core for the two types of transformers is shown in Fig. 32.6 and Fig. 32.7. Lamination Coils Butt Joint 1118 Electrical Technology As said above, in order to avoid high reluctance at the joints where the laminations are butted against each other, the alternate layers are stacked differently to eliminate these joints as shown in Fig. 32.6 and Fig. 32.7. Fig. 32.7 32.3. Core-type Transformers The coils used are form-wound and are of the cylindrical type. The general form of these coils may be circular or oval Coil Coil Coil Coil Coil or rectangular. In small size core-type transformers, a simple rectangular core is used with cylindrical coils which are either 2-leg core 3-leg core 4-leg core circular or rectangular in form. But for Single-Phase Transformer Cores large-size core-type transformers, round or circular cylindrical coils are used which are so wound as to fit over a cruciform core section as shown in Fig. 32.8(a). The circular cylindrical coils are used in most of the core-type transformers because of their mechanical strength. Such cylindrical coils are wound in helical layers with the different layers insulated from each other by paper, cloth, micarta board or cooling ducts. Fig. 32.8(c) shows the general arrangement of these coils with respect to the core. Insulating cylinders of fuller board are used to separate the cylindrical windings from the core and from each other. Since the low- voltage (LV) winding is easiest to insulate, it is placed nearest to the core (Fig. 32.8). Fig. 32.8 (a) Fig. 32.8 Butt Joint Core H.V. Winding Insulating L.V. Winding Cylinder L.V.H.V. H.V. L.V. L.V. H.V. (b) (c) Transformer 1119 Because of laminations and insulation, the net or effective core area is reduced, due allowance for which has to be made (Ex. 32.6). It is found that, in general, the reduction in core sectional area due to the presence of paper, surface oxide etc. is of the order of 10% approximately. As pointed out above, rectangular cores with rectangular cylindrical coils can be used for small-size core-type transformers as shown in Fig. 32.9 (a) but for large-sized transformers, it becomes wasteful to use rectangular cylindrical coils and so circular cylindrical coils are preferred. For such purposes, square cores may be used as shown in Fig. 32.9 (b) where circles represent the tubular former carrying the coils. Obviously, a considerable amount of useful space is still wasted. A common improvement on square core is to employ cruciform core as in Fig. 32.9 (c) which demands, at least, two sizes of core strips. For very large transformers, further core-stepping is done as in Fig. 32.9 (d) where at least three sizes of core plates are necessary. Core-stepping not only gives high space factor but also results in reduced length of the mean 2 turn and the consequent I R loss. Three stepped core is the one most commonly used although more steps may be used for very large transformers as in Fig. 32.9 (e). From the geometry of Fig. 32.9, it can be shown 2 2 that maximum gross core section for Fig. 32.9 (b) is 0.5 d and for Fig. 32.9 (c) it is 0.616 d where d is the diameter of the cylindrical coil. Fig. 32.9 32.4. Shell-type Transformers In these case also, the coils are form-would but are multi-layer disc type usually wound in the form of pancakes. The different layers of such multi-layer discs are insulated from each other by paper. The complete winding consists of stacked discs with insulation space between the coils–the spaces forming horizontal cooling and insulating ducts. A shell-type transformer may have a simple rectangular form as shown in Fig. 32.10 or it may have distributed form as shown in Fig. 32.11. Fig. 32.10 A very commonly-used shell-type transformer is the one known as Berry Transformer–so called after the name of its designer and is cylindrical in form. The transformer core consists of laminations arranged in groups which radiate out from the centre as shown in section in Fig. 32.12. 1120 Electrical Technology It may be pointed out that cores and coils of transformers must be provided with rigid mechanical bracing in order to prevent movement and possible insulation damage. Good bracing reduces vibration and the objectionable noise–a humming sound–during operation. The spiral-core transformer employs the newest development in core construction. The core is as- sembled of a continuous strip or ribbon of transformer steel wound in the form of a circular or elliptical cylinder. Such construction allows the core flux to follow the grain of the iron. Cold-rolled steel of high silicon content enables the designer to use considerably higher operating flux densities with lower loss per kg. The use of higher flux density reduces the weight per kVA. Hence, the advantages of such construction are (i) a relatively more rigid core (ii) lesser weight and size per kVA rating (iii) lower iron losses at higher operating flux densities and (iv) lower cost of manufacture. Fig. 32.11 Fig. 32.12 Transformers are generally housed in tightly-fitted sheet-metal ; tanks filled with special insulating oil*. This oil has been highly developed and its function is two-fold. By circulation, it not only keeps the coils reasonably cool, but also provides the transformer with additional insulation not obtainable when the transformer is left in the air. In cases where a smooth tank surface does not provide sufficient cooling area, the sides of the tank are corrugated or provided with radiators mounted on the sides. Good transformer oil should be absolutely free from alkalies, sulphur and particularly from moisture. The presence of even an extremely small percentage of moisture in the oil is highly detrimental from the insulation viewpoint because it lowers the dielectric strength of the oil considerably. The importance of avoiding moisture in the transformer oil is clear from the fact that even an addition of 8 parts of water in 1,000,000 reduces the insulating quality of the oil to a value generally recognized as below standard. Hence, the tanks are sealed air-tight in smaller units. In the case of large-sized transformers where complete air-tight construction is impossible, chambers known as breathers are provided to permit the oil inside the tank to expand and contract as its temperature increases or decreases. The atmospheric moisture is entrapped in these breathers and is not allowed to pass on to the oil. Another thing to avoid in the oil is sledging which is simply the decomposition of oil with long and continued use. Sledging is caused principally by exposure to oxygen during heating and results in the formation of large deposits of dark and heavy matter that eventually clogs the cooling ducts in the transformer. No other feature in the construction of a transformer is given more attention and care than the insulating materials, because the life on the unit almost solely depends on the quality, durability and handling of these materials. All the insulating materials are selected on the basis of their high quality and ability to preserve high quality even after many years of normal use. * Instead of natural mineral oil, now-a-days synthetic insulating fluids known as ASKARELS (trade name) are used. They are non-inflammable and, under the influence of an electric arc, do not decompose to produce inflammable gases. One such fluid commercially known as PYROCLOR is being extensively used because it possesses remarkable stability as a dielectric and even after long service shows no deterioration through sledging, oxidation, acid or moisture formation. Unlike mineral oil, it shows no rapid burning. Cylindrical Magnetic Winding Core (a) (b) Transformer 1121 All the transformer leads are brought out of their cases through suitable bushings. There are many designs of these, their size and construction depending on the voltage of the leads. For moderate voltages, porcelain bushings are used to insulate the leads as they come out through the tank. In general, they look almost like the insulators used on the transmission lines. In high voltage installations, oil-filled or capacitor- type bushings are employed. The choice of core or shell-type construction is usually determined by cost, because similar character- istics can be obtained with both types. For very high-voltage transformers or for multiwinding design, shell- type construction is preferred by many manufacturers. In this type, usually the mean length of coil turn is longer than in a comparable core-type design. Both core and shell forms are used and the selection is decided by many factors such as voltage rating, kVA rating, weight, insulation stress, heat distribution etc. Another means of classifying the transformers is according to the type of cooling employed. The following types are in common use : (a) oil-filled self-cooled (b) oil-filled water-cooled (c) air-blast type Small and medium size distribution transformers–so called because of their use on distribution systems as distinguished from line transmission–are of type (a). The assembled windings and cores of such transformers are mounted in a welded, oil-tight steel tank provided with steel cover. After putting the core at its proper place, the tank is filled with purified, high quality insulating oil. The oil serves to convey the heat from the core and the windings to the case from where it is radiated out to the surroundings. For small size, the tanks are usually smooth-surfaced, but for larger sizes, the cases are frequently corrugated or fluted to get greater heat radiation area without increasing the cubical capacity of the tank. Still larger sizes are provided with radiators or pipes. Construction of very large self-cooled transformers is expensive, a more economical form of construction for such large transformers is provided in the oil-immersed, water-cooled type. As before, the windings and the core are immersed in the oil, but there is mounted near the surface of oil, a cooling coil through which cold water is kept circulating. The heat is carried away by this water. The largest transformers such as those used with high-voltage transmission lines, are constructed in this manner. Oil-filled transformers are built for outdoor duty and as these require no housing other than their own, a great saving is thereby effected. These transformers require only periodic inspection. For voltages below 25,000 V, transformers can be built for cooling by means of an air-blast. The transformer is not immersed in oil, but is housed in a thin sheet-metal box open at both ends through which air is blown from the bottom to the top by means of a fan or blower. 32.5. Elementary Theory of an Ideal Transformer An ideal transformer is one which has no losses i.e. its windings have no ohmic resistance, there is no 2 magnetic leakage and hence which has no I R and core losses. In other words, an ideal transformer consists of two purely inductive coils wound on a loss-free core. It may, however, be noted that it is impossible to realize such a transformer in practice, yet for convenience, we will start with such a trans- former and step by step approach an actual transformer. Fig. 32.13 1 e2 V 1 F F e1 o V 90 2 E 1 E2 0 F V 1 i i o 90 E 1 Primary Secondary E 2 (b) (a) 1122 Electrical Technology Consider an ideal transformer [Fig. 32.13 (a)] whose secondary is open and whose primary is con- nected to sinusoidal alternating voltage V . This potential difference causes an alternating current to flow in 1 the primary. Since the primary coil is purely inductive and there is no output (secondary being open) the primary draws the magnetising current I only. The function of this current is µ merely to magnetise the core, it is small in magnitude and lags V by 90°. This alternating current I 1 µ produces an alternating flux φ which is, at all times, proportional to the current (assuming Step-up transformer permeability of the magnetic circuit to be Primary coil Secondary coil constant) and, hence, is in phase with it. This changing flux is linked both with the primary If the primary coil and the secondary windings. Therefore, it has 3 loops and the produces self-induced e.m.f. in the primary. secondary coil has This self-induced e.m.f. E is, at every in- 30, the voltage is 1 stepped up 10 stant, equal to and in opposition to V . It is 1 times. also known as counter e.m.f. or back e.m.f. of the primary. Step-down transformer Similarly, there is produced in the sec- ondary an induced e.m.f. E which is Primary coil Secondary coil 2 known as mutually induced e.m.f. This If the primary coil has 30 loops and e.m.f. is antiphase with V and its magni- 1 the secondary coil tude is proportional to the rate of change has 3, the voltage of flux and the number of secondary turns. is stepped down 10 The instantaneous values of applied times. voltage, induced e.m.fs, flux and magnetising current are shown by sinu- Step-up transformer soidal waves in Fig. 32.13 (b). Fig. 32.13 (c) shows the vectorial representation of the effective values of the above quantities. 32.6. E.M.F. Equation of a Transformer Let N = No. of turns in primary 1 N = No. of turns in secondary 2 Φ = Maximum flux in core in webers m = B × A m f = Frequency of a.c. input in Hz As shown in Fig. 32.14, flux increases from its zero value to maximum value Φ in one quarter of the cycle i.e. in 1/4 f second. m Φ m ∴ Average rate of change of flux = 1/ 4 f Fig. 32.14 = 4 f Φ Wb/s or volt m Now, rate of change of flux per turn means induced e.m.f. in volts. ∴ Average e.m.f./turn = 4 f Φ volt m If flux Φ varies sinusoidally, then r.m.s. value of induced e.m.f. is obtained by multiplying the average value with form factor. r.m.s. value Form factor = = 1.11 average value ∴ r.m.s. value of e.m.f./turn = 1.11 × 4 f Φ = 4.44 f Φ volt m m Now, r.m.s. value of the induced e.m.f. in the whole of primary winding = (induced e.m.f/turn) × No. of primary turns E = 4.44 f N Φ = 4.44 f N B A ...(i) 1 1 m 1 m Cycle F m T f 4 Time 1 T = / f Transformer 1123 Similarly, r.m.s. value of the e.m.f. induced in secondary is, E = 4.44 f N Φ = 4.44 f N B A ...(ii) 2 2 m 2 m It is seen from (i) and (ii) that E /N = E /N = 4.44 f Φ . It means that e.m.f./turn is the same in both 1 1 2 2 m the primary and secondary windings. In an ideal transformer on no-load, V = E and E = V where V is the terminal voltage 1 1 2 2 2 (Fig. 32.15). 32.7 Voltage Transformation Ratio (K) From equations (i) and (ii), we get E 2 N2 = = K E 1 N1 This constant K is known as voltage transformation ratio. (i) If N > N i.e. K > 1, then transformer is called step-up 2 1 transformer. (ii) If N < N i.e. K < 1, then transformer is known as 2 1 step-down transformer. Again, for an ideal transformer, input VA = output VA. I 2 V1 1 Fig. 32.15 V I = V I or = = 1 1 2 2 I V K 1 2 Hence, currents are in the inverse ratio of the (voltage) transformation ratio. Example 32.1. The maximum flux density in the core of a 250/3000-volts, 50-Hz single-phase 2 transformer is 1.2 Wb/m . If the e.m.f. per turn is 8 volt, determine (i) primary and secondary turns (ii) area of the core. (Electrical Engg.-I, Nagpur Univ. 1991) Solution. (i) E = N × e.m.f. induced/turn 1 1 N = 250/8 = 32; N = 3000/8 = 375 1 2 (ii) We may use E = − 4.44 f N B A 2 2 m 2 ∴ 3000 = 4.44 × 50 × 375 × 1.2 × A; A = 0.03m . Example 32.2. The core of a 100-kVA, 11000/550 V, 50-Hz, 1-ph, core type transformer has a cross-section of 20 cm × 20 cm. Find (i) the number of H.V. and L.V. turns per phase and (ii) the e.m.f. per turn if the maximum core density is not to exceed 1.3 Tesla. Assume a stacking factor of 0.9. What will happen if its primary voltage is increased by 10% on no-load ? (Elect. Machines, A.M.I.E. Sec. B, 1991) 2 Solution. (i) B = 1.3 T, A = (0.2 × 0.2) × 0.9 = 0.036 m m ∴ 11,000 = 4.44 × 50 × N × 1.3 × 0.036, N = 1060 1 1 550 = 4.44 × 50 × N × 1.3 × 0.036; N = 53 2 2 or, N = KN = (550/11,000) × 1060 = 53 2 1 (ii) e.m.f./turn = 11,000/1060 = 10.4 V or 550/53 = 10.4 V Keeping supply frequency constant, if primary voltage is increased by 10%, magnetising current will increase by much more than 10%. However, due to saturation, flux density will increase only marginally and so will the eddy current and hysteresis losses. Example 32.3. A single-phase transformer has 400 primary and 1000 secondary turns. The 2 net cross-sectional area of the core is 60 cm . If the primary winding be connected to a 50-Hz supply at 520 V, calculate (i) the peak value of flux density in the core (ii) the voltage induced in the secondary winding. (Elect. Engg-I, Pune Univ. 1989) F V1 E1 E2 V2 1124 Electrical Technology Solution. K = N /N = 1000/400 = 2.5 2 1 (i) E /E = K ∴ Ε = ΚΕ = 2.5 × 520 = 1300 V 2 1 2 1 (ii) E = 4.44 f N B A 1 1 m −4 2 or 520 = 4.44 × 50 × 400 × B × (60 × 10 ) ∴ B = 0.976 Wb/m m m Example 32.4. A 25-kVA transformer has 500 turns on the primary and 50 turns on the second- ary winding. The primary is connected to 3000-V, 50-Hz supply. Find the full-load primary and secondary currents, the secondary e.m.f. and the maximum flux in the core. Neglect leakage drops and no-load primary current. (Elect. & Electronic Engg., Madras Univ. 1985) Solution. K = N /N = 50/500 = 1/10 2 1 Now, full-load I = 25,000/3000 = 8.33 A. F.L. I = I /K = 10 × 8.33 = 83.3 A 1 2 1 e.m.f. per turn on primary side = 3000/500 = 6 V ∴ secondary e.m.f. = 6 × 50 = 300 V (or E = KE = 3000 × 1/10 =300 V) 2 1 Also, E = 4.44 f N Φ ; 3000 = 4.44 × 50 × 500 × Φ ∴ Φ = 27 mWb 1 1 m m m Example 32.5. The core of a three phase, 50 Hz, 11000/550 V delta/star, 300 kVA, core-type transformer operates with a flux of 0.05 Wb. Find (i) number of H.V. and L.V. turns per phase. (ii) e.m.f. per turn (iii) full load H.V. and L.V. phase-currents. (Bharathithasan Univ. April 1997) Solution. Maximum value of flux has been given as 0.05 Wb. (ii) e.m.f. per turn = 4.44 f φ m = 4.44 × 50 × 0.05 = 11.1 volts (i) Calculations for number of turns on two sides : Voltage per phase on delta-connected primary winding = 11000 volts Voltage per phase on star-connected secondary winding = 550/1.732 = 317.5 volts T = number of turns on primary, per phase 1 = voltage per phase/e.m.f. per turn = 11000/11.1 = 991 T = number of turns on secondary, per phase 2 = voltage per phase/e.m.f. per turn = 317.5/11.1 = 28.6 Note : (i) Generally, Low-voltage-turns are calculated first, the figure is rounded off to next higher even integer. In this case, it will be 30. Then, number of turns on primary side is calculated by turns-ratio. In this case, T = T (V /V ) = 30 × 11000/317.5 = 1040 1 2 1 2 This, however, reduces the flux and results into less saturation. This, in fact, is an elementary aspect in Design-calculations for transformers. (Explanation is added here only to overcome a doubt whether a fraction is acceptable as a number of L.V. turns). (ii) Full load H.V. and L.V. phase currents : Output per phase = (300/3) = 100 kVA 100 × 1000 H.V. phase-current = = 9.1 Amp 11, 000 L.V. phase-current = (100 × 1000/317.5) = 315 Amp Example 32.6. A single phase transformer has 500 turns in the primary and 1200 turns in the secondary. The cross-sectional area of the core is 80 sq. cm. If the primary winding is connected to a 50 Hz supply at 500 V, calculate (i) Peak flux-density, and (ii) Voltage induced in the secondary. (Bharathiar University November 1997)