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Transformers Fe O CO 1 Ota BR ÃçttoOoãà fm [e») Transformer Principles Vector Diagrams Transformer Classification Transformer Circuitry Transformer Cooling Tap Changers Transformer Connections Special Transformers Reactors Transformer Maintenance Appendix Glossary Index 103 117 155 169 237 247 261 287 305 313 TRANSFORMER PRINCIPLES Alternating current can be more economi- cally transmitted over long distances than direct current. AC voltages may be stepped up to a high voltage or stepped down to a low voltage through the use of transformers. High-voltage transmission makes it possible to generate electrical energy more cheaply in large, efficient central generating stations and transmit it considerable distances. POWER DISTRIBUTION The success of the transformer is due to George Westinghouse and Wil- liam Stanley. Westinghouse secured two English patents in 1885 and turned them over to Stanley to develop. In 1886, Stanley succeeded in lighting some stores in Great Barrington, MA. The transformer he de- signed was capable of stepping down 500 V on a line from a generator a half-mile away. Increase of Voltage Transformers are used in the transmission and distribution of electrical power to reduce the size of the conductors carrying the power. Electrical power is the product of voltage and current. To calculate power, apply the formula: P=ExI where P = power (in W) E = electrical pressure (in V) 1 = electric current (in A) 2 TRANSFORMERS Example: Calculating Power What is the power in a 120 V circuit carrying 1 A? P=ExT P=120x1 P=120W The electrical power remains the same if the circuit is carrying 1 A at 100 V or 10 A at 10 V. For example, 100 V x 1 A = 100 W and 10 V x 10 A = 100 W. The size of the conductor necessary for transmitting a given amount of power a given distance depends inversely on the square of the voltage. Tf the voltage between transmission lines is doubled, a conductor only Ya as large is necessary to transmit the same power over the same distance with the same line loss. If the voltage is increased three times, the size of the conductor is only 4 as large. In the transmission of electrical power, a transformer is used to raise (step up) the voltage at the generator to a high value, reducing the size of the transmission conductor. The installation and maintenance costs are less for a small conductor. AC generators (alternators) normally produce voltages of up to 22,000 V which are stepped up to a higher voltage for economical transmission to the load or to the place where the power is used. Transmission lines usually operate at voltages from 7200 V to 69,000 V for transmitting industrial power short distances or for low power demand areas, such as residential areas. Very high voltages such as 1,300,000 V are necessary to transmit large amounts of power over considerable distances. Reduction of Voltage High voltages are required for economical transmission. Such voltages are undesirable when electrical power is distributed among buildings or within densely populated areas. Transformers lower (step down) the volt- age at the load or building where the power is required to a value that is safe and economical to use inside residential, commercial, or industrial buildings. For residential wiring, the normal voltage is 115/230 V. The voltage in a commercial or industrial building is usually 120/208 V for appliances and incandescent lighting and 277/480 V for fluorescent light- ing and power. 4 TRANSFORMERS A conductor is connected in series with a battery. The battery sends a current through the conductor in a counterclockwise direction. The magnetic flux surround the conductor in the form of complete curves. This is also the case when a straight wire moves some distance from other current-carrying conductors. Right-Hand Screw Rule. A definite relationship exists between the di- rection of the current in a conductor and the direction of the magnetic flux surrounding the conductor. The right-hand screw rule states that the direction of advance of a right-hand screw corresponds with the direction of current flow through a conductor. The direction in which the screw is rotated corresponds with the direction of the magnetic flux surrounding the conductor. See Figure 1-2. In a conductor, when the right hand is used with the thumb pointing in the direction of the current flow, the fingers point in the direction of the magnetic flux surrounding the conductor. The magnetic flux produced by the current flow through a conductor consists of circular magnetic lines flowing in a clockwise direction. = RIGHT-HAND SCREW RULE — a DIRECTION OF DIRECTION OF SCREW ROTATION ] MAGNETIC FLUX SCREWDRIVER +, CONDUCTOR +, N | A A 4 Vo | Sa 1 | ES 7 / ZA, ) À NDA E pirecTION OF RIGHT-HAND SCREW + / CURRENT FLOW DIRECTION OF / ADVANCE OF SCREW “ Figure 1-2. The direction of advance of a right-hand screw corresponds with the direction of current flow through a conductor. The direction in which the screw is rotated corresponds with the direction of the magnetic flux surrounding the conductor. When two conductors are placed close to each other, the fluxes combine to increase the flux density between the two conductors. See Figure 1-3. The current is flowing in opposite directions in each conductor. reremeinrertretrem Transformer Principles 5 MAGNETIC FLUX FLOWS IN SAME DIRECTION BETWEEN CONDUCTORS CURRENT-CARRYING CONDUCTOR—, MAGNETIC FLUX LINES Louemenreanmena CONDUCTOR Figure 1-3. Two conductors placed close to each other increase the flux density between the conductors. When the right-hand screw rule is applied to each conductor, the magnetic flux from each conductor flows in the same direction between the two conductors. Current flowing around a coil in a counterclockwise direction produces a north magnetic pole at the top of the coil. Magnetic Flux A magnetomotive force must be applied to establish magnetic flux in a magnetic circuit. Magnetomotive force (MMF) is the magnetic pressure that determines the number of flux lines through a medium. This force may come from the magnetic field around a permanent magnet or from the flow of electric current through a conductor or coil of wire. The unit of measure of magnetomotive force is the gilbert. The flux lines always form closed loops and travel in a path known as the magnetic circuit. The magnetic field is represented by the flux lines. The total number of flux lines are the magnetic flux. Magnetic flux is measured in maxwells. One maxwell is equal to one magnetic flux line. The magnetomotive force produces the magnetic flux. The magnetizing force is the magnetomotive force that produces the magnetic flux per unit length of the magnetic circuit. An oersted is the magnetomotive force per unit length. The magnetizing force is found by dividing the Transformer Principles 7 Magnetic permeability is the measure of the case with which certain substances conduct magnetic flux lines. The Greek letter | is often used to denote permcability. While iron is the best conductor of magnetic flux lines, the various grades of iron differ greatly in magnetic conducting ability. The softer the iron, the greater its conductivity (permeability). Pure soft iron is used in the cores of most transformers. Retentivity The magnetic flux lines disappear when the current is removed from a circuit. If the circuit is looped around an iron core when the current is stopped, a considerable number of magnetic lines remain in the iron. Re- tentivity is the ability of a substance to retain magnetic flux lines after the magnetizing force has been removed. The harder the iron, the greater the number of the retained magnetic flux lines. Many lines are retained if hard steel is used as a core instead of soft iron. The hard steel becomes a per- manent magnet. Only soft iron should be used in transformer coils because high retentivity values are undesirable in transformers. Magnetic Induction Steel is composed of molecules. Each molecule is regarded as a tiny magnet in which its poles are distributed at random in a demagnetized steel bar. Demagnetized steel may be magnetized to a small degree if it is rubbed by a permanent magnet. The same pole of the permanent magnet must be used to rub the demagnetized steel in the same direction each time. When the demagnetized steel bar is rubbed with the pole of a permanent magnet, some of the molecular magnets respond by lining up end-to-end thus having a combined field that makes the stccl bar a weak permanent magnet. Magnetic induction is the setting up of flux lines in a material by an electric current. The magnetic lines may be in air, steel, or iron. For example, when the current in a circular loop is 1 A, a certain number of magnetic lines are produced in the air. Because the unit for electric current (amperes) is not the same as the unit for magnetic lines, the relationship between the number of amperes of current and the number of magnetic lines must be expressed symbolically. To produce a magnetic field of a given number of lines, a current of a certain number of amperes 8 TRANSFORMERS must exist in the circular loop. Am- pere-turns is a unit of magnetomo- tive force which is obtained by multiplying the current in amperes by the number of turns in a coil. Thus the magnetic flux lines are di- rectly proportional to the ampere- turns of the coil. The saturation point of a magnetic circuit is the point where an increase in magnet- izing force (ampere-turns) does not greatly increase the flux density. At the saturation point, it is no longer practical to increase the current or turns of a coil. See Figure 1-5. Electromotive Force of Induction 7 SATURATION POINT ANNEALED SHEET STEEL STEEL — cASL casUIReE FLUX DENSITY (GAUSS) MAGNETIZING FORCE (OERSTEDS) Figure 1-5. At the saturation point, an increase in current or turns of a coil does not significantly increase the magnetiz- ing force. Magnetic induction is the setting up of magnetic flux lines by an electric current. Given the proper conditions, a changing magnetic field can in- duce an electric current. See Figure 1-6. CURRENT FLOW CAUSED BY INDUCED VOLTAGE IN BAR +, RECTANGULAR CIRCUIT / POINTA— MAGNETIC FLUX LINES BAR , POINT B BAR DIRECTION À INDUCED VOLTAGE FROM MAGNETIC FLUX LINES Figure 1-6. Electric current can be induced by magnetic flux lines. E E E É E É Ê E E E E Ê E 10 TRANSFORMERS Relative Motion Between Circuit and Magnetic Field An electrical voltage can only be induced while there is a relative motion between a conductor or a circuit and a magnetic field. There can be no induced voltage if the magnetic field that flows through a circuit has a steady value and the circuit is stationary. A direct current that does not vary in its amount from one second to the next cannot be employed in transformers to effect changes in voltages. No current can flow in a circuit if the circuit, through which the number of magnetic flux lines is changing, is an open circuit. Induced voltage from the magnetic flux lines is present in the bar moving across the open circuit. See Figure 1-8. MAGNETIC FLUX LINES BAR a BAR DIRECTION NO CURRENT FLOW IN CIRCUIT » INDUCED VOLTAGE FROM MAGNETIC FLUX LINES Figure 1-8. No current can flow in a circuit if the circuit, through which the number of magnetic flux lines is changing, is an open circuit. The voltage exists in the portions of the circuit and according to the right-hand rule, T2 is positive with respect to TI. If, while the bar is moving and the voltage is being induced, TI and T2 are brought together, thus closing the circuit, the induced current can flow. Left-Hand Rule In the design of transformers the left-hand rule is as important as the right-hand rule. The left-hand rule is the relationship between the current in a conductor and the magnetic field existing around the conductor. With the left-hand rule, the left hand is held so that the thumb, index berro emerenteroteprremmren enero Transformer Principles H finger, and middle finger are perpendicular to one another. Placing the hand in a magnetic field so that the index finger points in the direction of the flux lines and the middle finger points in the direction of the current in a conductor placed in the field perpendicular to the lines of force, the thumb points in the direction in which the conductor tends to move. See Figure 1-9. LEFT-HAND RULE DIRECTION OF | CONDUCTOR POINTA BarteRv MOVEMENT =—s NORTH POLE -DIRECTION OF MAGNETIC LINES —— / OFFORCE — DIRECTION OF E + CURRENT IN O po CONDUCTOR — T=POINTB, me Figure 1-9. The left-hand rule is the relationship between the current in a conductor and the magnetic field existing around the conductor. This is shown when a bar is allowed to slide along two parallel conductors that have magnetic flux lines flowing in the downward direction. À battery sends current through the circuit in a counterclockwise direction. According to the left-hand rule, the sliding bar tends to move to the left. This motion removes flux lines from the circuit. See Figure 1-10. Counter Electromotive Force According to the right-hand rule, the induced voltage is clockwise around a conductor moving across a magnetic field whenever the number of flux lines flowing through a circuit is decreased. Tf the current in the movable conductor is in such a direction and of such an amount as to cause the conductor to actually move to the left (left-hand rule), thus reducing the number of flux lines, a voltage is simultaneously induced in the circuit in a clockwise direction or directly opposite to that of the applied voltage. Tm Transformer Principles 13 When the conductor is moving to the left, the current in the circuit is less than when the conductor is stationary due to the induced counter clectromotive force (counter EMF). To calculate current when the con- ductor is in motion, apply the formula: — E-e 2 R where r TF = current in circuit with counter EMF (in A) = applied voltage (in V) induced voltage (in V) E e R = total resistance (in Q) Example: Calculating Current-Induced Voltage Present What is the current in a 200 V circuit that has 1 92 of resistance and 100 V of counter EMF? » — E-e [="R 7 = 200100 1 + = 100 F= 1 Tr =100A The induced voltage (e) is directly opposite in direction to the applied battery voltage. This voltage is counter EMF because of its opposite direction. The counter EMF is produced by induction or relative motion between an inductor and a magnetic field and is referred to as the EMF of induction. If the direction of the current around the circuit is reversed, the movable portion of the conductor moves to the right, according to the left-hand rule. Tn this case, the number of flux lines flowing through the circuit is increased if the movable conductor moves. The resulting induced volt- age is counterclockwise, according to the right-hand rule, in a direction exactly opposite to that of the applied voltage from the power supply. Introducing flux lines into a circuit produces an induced voltage equal in value to, but in opposite direction to the voltage produced by removing the same number of flux lines in the same length of time. 14 TRANSFORMERS Rate of Change in Magnetic Flux 1 an inductor moves across a circuit at a certain rate, the number of flux lines flowing through the circuit is changed in exact proportion to that rate. If the distance moved by an inductor is 10 feet per second (ft/sec) or 120”, its velocity is expressed as feet or inches per second. 1 the length of the inductor is 10” and its velocity is 120 inches per second (in./sec), it sweeps over an area of 1200 sq in. (120 x 10 = 1200). JÉ the number of magnetic flux lines per square inch flowing downward through a circuit is 20,000, the number of lines traversed by the moving inductor during one second of its motion, is 24,000,000 (1200 x 20,000 = 24,000,000). The total area swept over by the moving portion of any circuit, mul- tiplied by the magnetic density (number of flux lines per unit area), gives the number of lines introduced to or removed from the circuit. The in- duced voltage in any circuit, due to the rate of change in the magnetic flux lines induced by the circuit is obtained by dividing the number of flux lines cut in one second by 100,000,000. According to Lenz's law, it is necessary for 100,000,000 (102) magnetic flux lines to be cut in one second to produce 1 V. If the number of magnetic flux lines per square inch, traversed by a moving induetor during one second of its motion is 24,000,000, the voltage produced by the conductor equals .24 V (24,000,000 + 100,000,000 = .24). Rate of Change in Current 1f an inductor remains stationary and if 24,000,000 flux lines are uniformly removed each second from flowing through the circuit, the voltage induced in the circuit is exactly the same as though the conductor were moved across the circuit at the rate of 120 in./sec, (if its length between the portions of the circuit upon which it slides is 107 and if the magnetic density is 20,000 flux lines per square inch). Induced voltage always depends on the relative motion of any circuit and a magnetic field flowing through the circuit. The number of lines flowing through the circuit may be removed by reducing the amount of current used to produce the field. 16 TRANSFORMERS MAGNETIC souTH our . peço FLUX LINES CIRCUIT ABCD NO CURRENT FLOW IN CIRCUIT SOFT IRON CONDUCTORS FORM CORE BATTERY —. —COIL aa DIRECTION OF CURRENT FLOW THROUGH COIL Figure 1-12. A simple transformer may be developed from a round bundle of soft iron conductors and a coil of wire. If the coil circuit is opened and the magnetizing current in the coil surrounding the iron core drops to zero, the number of flux lines flowing downward through circuit ABCD decreases rapidly and a current is in- duced in circuit ABCD in a clockwise direction. See Figure 1-13. The induced current in circuit ABCD is in the same direction as the current in the coil surrounding the core that produced the magnetic flux lines that flow through circuit ABCD. The coil surrounding the core may be designated as the primary, and circuit ABCD as the secondary of a trans- former. The two electrical circuits are connected (interlinked) by the mag- netic circuit consisting of the flux lines flowing through the iron core, the primary, and the secondary. If the battery circuit is closed by joining TI and T2, the current through the coil increases, increasing the number of flux lines flowing through the secondary (circuit ABCD), and a coun- terclockwise current is produced in the secondary. DTERROS ROLE RaTA LA LARA NASA Ra LADA AA DA ARA A A A A A AAA AA AAA A AAA AAA ARA AA A AAA Magnetic Leakage Not all the magnetic flux lines pro- duced by the magnetizing force of the ampere turns of the primary pass through the secondary. The shape of the magnetic field pro- duced by the magnetizing force of the primary coil tends to arc out- ward from the coil. See Figure 1-14. Leakage lines are the magnetic lines produced by the primary coil which do not pass through the sec- ondary. The greater the number of leakage lines, the less useful effect realized. The primary and secondary must be arranged so that as many of the magnetic flux lines as possible flow through both the primary and sec- ondary. This is accomplished by making the magnetic circuit (core) a complete, circular, closed circuit of iron, and winding the primary on this in close turns. See Figure 1-15. The secondary may be wound over the primary. This is the most magnetically efficient form of a transformer. There are no joints to interrupt the passage of the mag- netic flux lines, and the path of the Transformer Principles 17 CURRENT INDUCED IN CLOCKWISE DIRECTION SOUTH POLE o abra [e “orcur" JÁ! ABCD COIL CIRCUIT || OPEN mes Coll Ho enorme POLE Figure 1-13. Current is induced in circuit ABCD in a clockwise direction if the coil circuit is opened and the magnetizing current in the coil surrounding the iron core drops to zero. magnetic circuit is circular. The disadvantage of this form is the increased labor required in its construction. Each turn of the primary and secondary must be threaded through the center hole by hand. Labor is considerable if there are many turns to be wound on the core. 
