POWER TRANSFORMERS IN AND OUT MANSOOR Transformers in and out MANSOOR Page 1

CHAPTERS AND CONTENTS POWER TRANSFORMERS.............................................................. .............................................. 1 IN AND OUT .................... ................................................................................ ................................ 1 1 INTRODUCTION............................... ................................................................................ ..... 6 1.1 1.2 1.3 1.4 2 Brief Overview of Transformers ....................... ................................................................. 6 Flux couplin g laws.......................................................................... .................................. 8 Transformer ratings........................ ................................................................................ 10 Understand the terminology ................................................. ........................................... 13 MAGNETISM AND MAGNETIC FIELDS................................................... ....................... 17 2.1 2.2 2.3 2.4 Magnetism: quantities, units and rela tionships ................................................................ 17 Ma gnetic phenomena in ferromagnetic materials..................................... ........................ 31 Magnetics Properties of Transformers................ ............................................................ 32 Typical construc tion of a transformer core ..................................................... ................. 35 3 TRANSFORMERS EQUATIONS ......................................................... ............................... 40 3.1 3.2 3.3 3.4 Magnetic circuit excited by a lternating current.............................................................. .. 40 Single-phase transformer ................................................. ............................................... 46 Three-phase transformers .... ................................................................................ ........... 59 Auto-transformer ................................................ ............................................................ 64 4 INSTRUMENT TRANSFORMERS......................................................... ............................. 67 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 Introd uction.......................................................................... .......................................... 67 Current transformers ............. ................................................................................ ......... 67 Measuring and protective current transformers ..................... .......................................... 68 Selecting core material .......... ................................................................................ ......... 68 Connection of a CT ................................................ ......................................................... 71 Construction of a C urrent Transformer ............................................................. .............. 73 Standard Burdens for Current Transformers with ............... ............................................. 74 Voltage Transformers .......... ................................................................................ ........... 75 Standard Burdens for Voltage Transformers........................ ............................................ 78 Construction of a Voltage Transf ormer .......................................................................... . 79 5 TRANSFORMER BUSHINGS & SURGE ARRESTOR........................................... ........... 81 Transformers in and out MANSOOR Page 2

5.1 5.2 5.3 5.4 5.5 5.6 6 Bushing design theory........................................................... .......................................... 81 Construction of a Transformer bush ing ........................................................................... 82 Voltage and BIL.............................................................. ................................................ 84 Bushing Storage............. ................................................................................ ................. 84 Surge Arrestors............................................ ................................................................... 85 Transform er Neutral Grounding............................................................ .......................... 87 TRANSFORMER TANK AND COOLING SYSTEM ............................................ ............. 90 6.1 6.2 6.3 Transformer Tank Requirements ..................... ................................................................ 90 Tank Constru ction........................................................................... ................................ 91 Transformer Cooling......................... .............................................................................. 9 4 7 TRANSFORMER WINDINGS ........................................................... .................................. 97 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Winding Co nstruction ..................................................................... ................................ 97 Insulation and drying system................ ........................................................................... 99 T ransformer Impedance ........................................................... ..................................... 101 Insulation system .................... ................................................................................ ...... 102 Megger details and Usage............................................. ................................................ 103 Transformer Oil............ ................................................................................ ................ 105 Transformer Oil Quality Tests.............................. ......................................................... 106 Gas analysis of tr ansformer ...................................................................... .................... 109 8 TRANSFORMER CONSERVATOR TANK.................................................... .................. 111 8.1 8.2 8.3 Function of the Conservator Tank ............ ..................................................................... 111 Buchho lz Relay connection............................................................. ............................... 112 Transformer Breathers....................... ........................................................................... 113 9 THREE-PHASE TRANSFORMERS ....................................................... ........................... 115 9.1 9.2 9.3 9.4 Three Phase Connection.......... ................................................................................ ...... 115 Parallel operation of Power transformer.............................. ......................................... 119 Vector Groups and Diagrams........ ................................................................................ 121 Vector groups and parallel operation....................................... ..................................... 124 10

TRANSFORMER PROTECTION.......................................................... ............................ 125 10.1 10.2 Types of protection.................. ................................................................................ ...... 125 Thermal Overload protection ......................................... ............................................... 126 Page 3 Transformers in and out MANSOOR

10.3 10.4 10.5 10.6 11 Over-flux protection............................................................ .......................................... 129 Transformer differential protecti on ............................................................................. .. 130 Protection of parallel transformer....................................... .......................................... 139 Internal Fault Protection........ ................................................................................ ....... 141 TRANSFORMER TAP CHANGER ........................................................ ........................... 146 11.1 11.2 11.3 Selection of On Load Tap Changers ............................................................................. 1 47 Mechanical tap changers ..................................................... ......................................... 148 Tap changer troubleshooting....... ................................................................................ .. 151 12 TRANSFORMER TESTING ............................................................ .................................. 154 12.1 12.2 12.3 Types of Tests ........... ................................................................................ .................... 154 Type Tests............................................. ........................................................................ 157 Rou tine Tests ..................................................................... ........................................... 167 13 GENERAL AND PREVENTIVE MAINTENANCE ............................................. ............ 174 13.1 13.2 13.3 Importance of Maintenance....................... ................................................................... 175 Causes o f electrical failure............................................................ ................................ 175 Checks to be carried out................... ............................................................................. 17 7 1. Condition of paint work.................................................... ............................... 178 2. Operation of door handles................ ................................................................ 178 3. Operatio n of doors and hinges .......................................................... ............... 178 4. Condition of door seal .................................. ................................................... 178 5. Door switches working ................................................................................ .... 178 6. Lights working...................................................... .......................................... 178 7. Heater working................ ................................................................................ 178 8. Thermostats working..................................................... .................................. 178 9. Operation of heating and lighting swit ches....................................................... 178 10. Mounting of equipment secure ............................................................... ..... 178 11. Manual operation of switches satisfactory ........................ ........................... 178 12. Checking of tightness of cable terminations. ................................................ 178 13. Checking of operation o f contractors (isolating the trip signal, if any) .......... 178 14. HRC fuses a nd their rating................................................................. ......... 178 15. Operation of local alarm annunciator by pushing push buttons p rovided for lamp test, acknowledge, reset, system test, mute etc. to cover all s ystem function ...... 178 16. Source change over test check by putting off power sources alternatively .... 178 17. Check for plugs for dummy holes and replacem ent, if found missing. .......... 178 Maintenance and testing procedures .......

...................................................................... 182 Maint enance tests recommended ....................................................... ............................ 184 13.4 13.5 OIL SAMPLING PROCEDURES......................................................... ....................................... 192 Transformers in and out MANSOOR Page 4

TRANSFORMER DATA SHEET SMALL TRANSFORMERS....................................... .......... 195 TYPICAL TECHNICAL PARTICULARS FOR A 315 MVA, 400/220/33KV TRANSFO RMER ........................................................................... ............................................................................ 196 Transformers in and out MANSOOR Page 5

Chapter-1 1 1.1 INTRODUCTION Brief Overview of Transformers Power generation transmission and distribution throughout the world is through A .C system and the voltages are different at each level of the network. A transfo rmer is a device that transfers energy from one AC system to another. A transfor mer can accept energy at one voltage and deliver it at another voltage. This per mits electrical energy to be generated at relatively low voltages and transmitte d at high voltages and low currents, thus reducing line losses, and again it is stepped down from higher to lower levels to be used at safe voltages. Power tran sformers are necessary for increasing the voltage from generation to transmissio n system and then decreasing from transmission to sub-transmission and distribut ion system. The total transformer capacity is usually 8 to 10 times the total ge nerating capacity, therefore transformers are a very important apparatus in the electrical network, it is a capital equipment with a life expectancy of several decades and care should be taken about selection and ratings for which a good un derstanding of the basics and principles of operation is essential. The KVA (Pow er) rating of a power transformer covers a wide range between 5 KVA to 750 MVA. Very big transformers are installed in generating stations and HVDC converter st ations very small transformers are used in low voltage and electronic circuits. The KVA rating of the transformer depends on the load connected which is normall y on the secondary winding An analogy The transformer may be considered as a sim ple two-wheel 'gearbox' for electrical voltage and current. The primary winding is analogous to the input shaft and the secondary winding to the output shaft. I n this comparison, current is equivalent to shaft speed, voltage to shaft torque . In a gearbox, mechanical power (speed multiplied by torque) is constant (negle cting losses) and is equivalent to electrical power (voltage multiplied by curre nt) which is also constant. The gear ratio is equivalent to the transformer step -up or step-down ratio. A step-up transformer acts analogously to a reduction ge ar (in which mechanical power is transferred from a small, rapidly rotating gear to a large, slowly rotating gear): it trades current (speed) for voltage (torqu e), by transferring power from a primary coil to a secondary coil having more tu rns. A step-down transformer acts analogously to a multiplier gear (in which mec hanical power is transferred from a large gear to a small gear): it trades volta ge (torque) for current (speed), by transferring power from a primary coil to a secondary coil having fewer turns. Transformers in and out MANSOOR Page 6

Fig 1.1 Diagram showing the location of different power transformers from genera tion to the L.T (domestic) power network (circuit breakers and other equipment a re not shown) A transformer is an electrical device that transfers energy from o ne circuit to another purely by magnetic coupling. Relative motion of the parts of the transformer is not required. Transformers in and out MANSOOR Page 7

1.2 Flux coupling laws Fig 1.2 An idealized step-down transformer showing resultant flux in the core A simple transformer consists of two electrical conductors called the primary wind ing and the secondary winding. If a time-varying voltage (Sinusoidal) is applied to the primary winding of turns, a current will flow in it producing a magneto motive force (MMF). Just as an electromotive force (EMF) drives current around a n electric circuit, so MMF drives magnetic flux through a magnetic in the core ( shaded grey), and circuit. The primary MMF produces a varying magnetic flux indu ces a back electromotive force (EMF) in opposition to. In accordance with Farada y's Law, the voltage induced across the primary winding is proportional to the r ate of change of flux: Similarly, the voltage induced across the secondary winding is: With perfect flux coupling, the flux in the secondary winding will be equal to t hat in the primary winding, and so we can equate and . It thus follows that Hence in an ideal transformer, the ratio of the primary and secondary voltages i s equal to the ratio of the number of turns in their windings, or alternatively, the voltage per turn is the same for both windings. This leads to the most comm on use of the transformer: to convert electrical energy at one voltage to energy at a different voltage by means of windings with different numbers of turns. Th e EMF in the secondary winding, if connected to an electrical circuit, will caus e current to flow in the secondary circuit. The MMF produced by current in the s econdary opposes the MMF of the primary and so tends to cancel the flux in the c ore. Since the reduced flux reduces the EMF induced in the Transformers in and out MANSOOR Page 8

primary winding, increased current flows in the primary circuit. The resulting i ncrease in MMF due to the primary current offsets the effect of the opposing sec ondary MMF. In this way, the electrical energy fed into the primary winding is d elivered to the secondary winding. Neglecting losses, for a given level of power transferred through a transformer, current in the secondary circuit is inversel y proportional to the ratio of secondary voltage to primary voltage. For example , suppose a power of 50 watts is supplied to a resistive load from a transformer with a turns ratio of 25:2. P = EI (power = electromotive force current) 50 W = 2 V 25 A in the primary circuit Now with transformer change: 50 W = 2 A 25 V in t he secondary circuit. The high-current low-voltage windings have fewer turns of wire. The high-voltage, low-current windings have more turns of wire. Since a DC voltage source would not give a time-varying flux in the core, no back EMF woul d be generated and so current flow into the transformer would be unlimited. In p ractice, the series resistance of the winding limits the amount of current that can flow, until the transformer either reaches thermal equilibrium or is destroy ed. The Universal EMF equation If the flux in the core is sinusoidal, the relati onship for either winding between its number of turns, voltage, magnetic flux de nsity and core cross-sectional area is given by the universal emf equation: E=4. 44 n a b Where E is the sinusoidal root mean square (RMS) voltage of the winding , is the frequency in hertz, n is the number of turns of wire, a is the area of the core (square units) and b is magnetic flux density in webers per square unit . The value 4.44 collects a number of constants required by the system of units. Invention Those credited with the invention of the transformer include: Michael Faraday, who invented an 'induction ring' on August 29, 1831. This was the firs t transformer, although Faraday used it only to demonstrate the principle of ele ctromagnetic induction and did not foresee the use to which it would eventually be put. Lucien Gaulard and John Dixon Gibbs, who first exhibited a device called a 'secondary generator' in London in 1881 and then sold the idea to American co mpany Westinghouse. This may have been the first practical power transformer, bu t was not the first transformer of any kind. They also exhibited the invention i n Turin in 1884, where it was adopted for an electric lighting system. Their ear ly devices used an open iron core, which was later abandoned in favour of a more efficient circular core with a closed magnetic path. William Stanley, an engine er for Westinghouse, who built the first practical device in 1885 after George W estinghouse bought Gaulard and Gibbs' patents. The core was made from interlocki ng E-shaped iron plates. This design was first used commercially in 1886. Hungar ian engineers Ott Blthy, Miksa Dri and Kroly Zipernowsky at the Ganz company in Buda pest in 1885, who created the efficient "ZBD" model based on the design by Gaula rd and Gibbs. Nikola Tesla in 1891 invented the Tesla coil, which is a high-volt age, air-core, dual-tuned resonant transformer for generating very high voltages at high frequency. Types of transformers 1. Power transformers (Step-up and Ste p-down ) Transformers in and out MANSOOR Page 9

2. Instrument Transformers (Current and voltage) 3. HVDC Converter Transformers 4. Reactors (Series and Shunt ) 5. Isolation Transformers 6. Variable auto-trans formers 7. Signal transformers Power Transformers are used for stepping up and d own of generation and in distribution of power in a network, these are generally fully loaded transformers. Instrument Transformers are used for measurement, an d protection of HV electrical networks from faults HVDC converter Transformers a re used as an impedance load and isolation from the DC system, these are general ly at a similar voltage level 400 / 500 KV AC for where the 500 KV AC system is fed to the AC to DC converter system Reactors are used for compensation of react ive power in the network, two types of reactors used are 1) Series and 2) Shunt these are similar in principle, operation and construction as transformers. Isol ation Transformers are used to isolate two circuits physically for safety and se curity. Variable auto-transformers are used when a variable voltage (hence curre nt) is required especially for testing and calibration. Signal transformers are used in electronic circuits for electrically connecting different regions are ci rcuits and physical isolation. 1.3 Transformer ratings When a transformer is to be used in a circuit, more than just the turns ratio mu st be considered. The voltage, current, and power-handling capabilities of the p rimary and secondary windings must also be considered. The maximum voltage that can safely be applied to any winding is determined by the type and thickness of the insulation used. When a better (and thicker) insulation is used between the windings, a higher maximum voltage can be applied to the windings. The maximum c urrent that can be carried by a transformer winding is determined by the diamete r of the wire used for the winding. If current is excessive in a winding, a high er than ordinary amount of power will be dissipated by the winding in the form o f heat. This heat may be sufficiently high to cause the insulation around the wi re to break down. If this happens, the transformer may be permanently damaged. T he power-handling capacity of a transformer is dependent upon its ability to dis sipate heat. If the heat can safely be removed, the power-handling capacity of t he transformer can be increased. This is sometimes accomplished by immersing the transformer in oil, or by the use of cooling fins. The powerhandling capacity o f a transformer is measured in either the volt-ampere unit or the watt unit. If the frequency applied to a transformer is increased, the inductive reactance of the windings is increased, causing a greater ac voltage drop across the windings and a lesser voltage drop across the load. However, an increase in the frequenc y applied to a transformer should not damage it. But, if the frequency applied t o the transformer is decreased, the reactance of the windings is decreased and t he current through the transformer winding is increased. If the decrease in freq uency is enough, the resulting increase in current will damage the transformer. For this reason a transformer may be used at frequencies above its normal operat ing frequency, but not below that frequency. Apparent Power Equation or KVA rati ng of a Single phase transformer KVA = Vp * Ip where Vp is phase rms voltage in KV and Ip is rms current in Amps. Transformers in and out MANSOOR Page 10

Apparent Power Equation or KVA rating of a three phase transformer KVA = 3 * Vp * Ip where Vp is line to line rms voltage in KV and Ip is rms line current in Amp s. Construction A transformer usually has: Two or more insulated windings, to ca rry current A core, in which the mutual magnetic field couples the windings. In transformers designed to operate at low frequencies, the windings are usually fo rmed around an iron or steel core. This helps to confine the magnetic field with in the transformer and increase its efficiency, although the presence of the cor e causes energy losses. Transformers made to operate at high frequencies may use other lower loss materials, or may use an air core. Core Construction Power transformers are further classified by the exact arrangement of the core a nd windings as "shell type", "core type" and also by the number of "limbs" that carry the flux (3, 4 or 5 for a 3-phase transformer). Core type shape is mostly used in three-phase distribution transformers. The window height Ha depends on t he coil height and the core area Ar depends on the rated power S n. Fig 1.3 There are five main groups of magnetically soft alloys classified primar ily by the chief constituents of the metal. low-carbon steel silicon steel nicke l-iron cobalt-nickel-iron cobalt-iron Steel cores Transformers often have silico n steel cores to channel the magnetic field. This keeps the field more concentra ted around the wires, so that the transformer is more compact. The core of a pow er Transformers in and out MANSOOR Page 11

transformer must be designed so that it does not reach magnetic saturation. Care fully designed gaps are sometimes placed in the magnetic path to help prevent sa turation. Practical transformer cores are always made of many stamped pieces of thin steel. The high resistance between layers reduces eddy currents in the core s that waste power by heating the core. These are common in power and audio circ uits. A typical laminated core is made from E-shaped and I-shaped pieces, leadin g to the name "EI transformer". One problem with a steel core is that it may ret ain a static magnetic field when power is removed. When power is then reapplied, the residual field may cause the core to temporarily saturate. This can be a si gnificant problem in transformers of more than a few hundred watts output, since the higher inrush current can cause mains fuses to blow unless current-limiting circuitry is added. More seriously, inrush currents can physically deform and d amage the primary windings of large power transformers. Solid cores In higher frequency circuits such as switch-mode power supplies, pow dered iron cores are sometimes used. These materials combine a high magnetic per meability with a high material resistivity. At even higher frequencies (radio fr equencies typically) other types of core made of nonconductive magnetic material s, such as various ceramic materials called ferrites are common. Some transforme rs in radiofrequency circuits have adjustable cores which allow tuning of the co upling circuit. Air cores High-frequency transformers also use air cores. These eliminate the loss due to hysteresis in the core material. Such transformers mai ntain high coupling efficiency (low stray field loss) by overlapping the primary and secondary windings. Toroidal cores Toroidal transformers are built around a ring-shaped core, which is made from a long strip of silicon steel wound into a coil. This construction ensures that all the grain boundaries are pointing in t he optimum direction, making the transformer more efficient by reducing the core 's reluctance, and eliminates the air gaps inherent in the construction of an EI core. The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are wound concentrically to cover the entire surface of the cor e. This minimises the length of wire needed, and also provides screening to prev ent the core's magnetic field from generating electromagnetic interference. Toro idal cores for use at frequencies up to a few tens of kilohertz is made of ferri te material to reduce losses. Such transformers are used in switch-mode power su pplies. Windings Power transformers are wound with wire, copper or aluminum rect angular conductors, or strip conductors for very heavy currents. Very large powe r transformers will also have multiple strands in the winding, to reduce skin ef fect (The skin effect is the tendency of an alternating electric current to dist ribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core). Windings on both primary and s econdary of a power transformer may have taps to allow adjustment of the voltage ratio; taps may be connected to automatic on-load tapchanger switchgear for vol tage regulation of distribution circuits. Transformers in and out MANSOOR Page 12

1.4 Understand the terminology E-I lamination A flat transformer steel lamination composed of pairs of E-shaped and I shaped pieces. The middle projection or tongue of the E is placed through the center of a coil of wire, and the I placed at the end like this" EI" so the iron forms a complete magnetic path through the center and around the outside o f the coil. Scrapless lamination An E-I lamination with proportions such that tw o E's and two I's are stamped from a rectangle of iron with no waste left over. This is the least expensive shape for transformer iron, and is the standard for the industry for non-special purpose transformers. The proportions are special, obviously. The I's are stamped from the open areas of two end-facing E's. The mi ddle part, or tongue, of each E is twice as wide as the two outer legs, and the empty area stamped out of the E (which forms the I) is half as long as the E is high from top to bottom. As you can see, since the proportions are pre-determine d, you can specify any one dimension and all the rest are determined. E-I lamina tions are usually named by the tongue width: EI100 has a tongue that is 1.00 inc hes wide. EI150 is 1.5" wide, etc. Primary inductance If you connect only the pr imary wires of a transformer, and measure the inductance, no energy leaves throu gh any secondary windings, so the thing looks like (and is!) just an inductor. T he amount of inductance you measure is the primary inductance. The primary induc tance is a consequence of the iron and air in the magnetic field path, and is no n-linear - you would measure somewhat different values under different condition s. Secondary inductance Likewise, what you measure if you connect a measurement instrument only to the secondaries. Leakage inductance Leakage inductance is ind uctance that results from the parts of the primary's magnetic field that does no t link the secondary. This is an inductance from which the secondary can never d raw energy, and represents a loss of effectiveness in the transformer. If you sh ort the secondary winding and then measure the "primary" inductance, you will me asure the leakage inductance, which appears to be in series with the primary win ding. Core loss The iron in the core is itself conductive, and the magnetic fiel d in it induces currents. These currents cause the loss of energy, and this come s out as heat. The core loss represents a price you have to pay to use a transfo rmer. Core loss is strongly related to frequency, increasing linearly as the fre quency goes up. Eddy current Eddy currents are the currents induced in conductors in a magnetic field - such as the iron core. The inside of a conductor looks like a shorted tr ansformer turn to the magnetic field, so the currents can be large, and can caus e substantial heating, as in the core losses. Transformers in and out MANSOOR Page 13

Copper loss Copper is not a perfect conductor. Current moving through copper cau ses the copper to heat up as it moves through the resistance of the wire. Windin g window This is the area of a core available for winding wires into. Margins Sp ace left at the end of a coil former where no copper windings are placed. This k eeps the copper wire from going out to the very edges of the coil former, and im proves the voltage isolation between layers and windings. Window fill The amount of the winding window that is filled up with copper wires, insulation, etc. Usu ally expressed as a percent of the winding window area. Interlayer insulation Af ter winding a neat layer of wire on a coil, you put a thin layer of insulating p aper, plastic film, etc. over it. This is interlayer insulation. It helps keep t he insulation of the wires from breaking down from the stress of the voltage dif ference between layers, and mechanically helps form a neat, solid coil. B Magnet ic field intensity, or "flux density"; sometimes measured in flux lines, Gauss o r kiloGauss, or Teslas depending on the measurement system you use. Most transfo rmer iron saturates around 14 to 20 kGauss. Ceramic materials saturate at around 3-4kGauss. H Coercive force. This is what "forces" the magnetic field into bein g. It's usually measured in AmpereTurns per unit of magnetic circuit length, oft en ampere-turns per meter. B-H curve Pretty simply, the graph of B versus the ca usative H. When there is a large slope of B versus H, the permeability of the ma terial is high. Saturation At saturation, the permeability falls off, as more H cannot cause higher B. Insulation class Transformer insulation is rated for cert ain amounts of temperature rise. Materials which withstand temperatures under 10 5C are Class A. Class B materials withstand higher termperatures, and other lett ers even higher temperatures. Class A insulation is the most common for output t ransformers, as no great temperature rise (by power transformer standards at lea st) are encountered. This "class" is not related to the bias class of the amplif ier at all, they just happened to use the same words. Stack How much iron is put inside the coils of wire making up the windings of the transformer. The laminat ion size determines the width of the tongue, the stack height determines the hei ght, and the width times the height is the core area, which is a key determiner of the power handling capability of the transformer. All other things being equa l, more stack height means either a greater inductance for a Transformers in and out MANSOOR Page 14

given number of turns, or a fewer number of turns for the same inductance. This is one means of juggling wire sizes and window fill. Fig 1.4 Equipment associated with a power transformer in a sub-station with one incoming (HV) and four outgoing (LV) feeders (transmission lines) Where LA Light ing (Surge arrestor) CT- Current Transformer PT Voltage Transformer CB Circuit B reaker TYPE TESTS Temperature rise Short circuit Lightning Impulse Sound level E nergy Performance Switching Surge Impulse Zero Sequence Impedance ROUTINE TESTS PERFORMED ON ALL TRANSFORMERS: Ratio and Polarity Power Factor Win ding Resistance No-Load Loss and Excitation Current Load Loss and Impedance Transformers in and out MANSOOR Page 15

C.T. Current, Ratio and Polarity Standard Impulse Test (Class I I Transformers) Quality Control Impulse Test (Class I Transformers) Applied Potential Quality Co ntrol Induced Voltage Test with Corona Detection (Class I Transformers) Control Functions and Wiring Dissolved Gas Analysis Dew Point Transformers in and out MANSOOR Page 16

Chapter-2 2 2.1 MAGNETISM AND MAGNETIC FIELDS Magnetism: quantities, units and relationships Magnetic quantities in the SI Table 2.1 Quantity name coercivity effective area effective permeability induced voltage inductance factor intensity of magnetizat ion magnetic flux magnetic mass susceptibility magnetic polarization magnetizati on permeability relative permeability remnance Quantity symbol Hc Ae e e Al I J M B Quantity name o e fa to effe tive length flux linkage indu tan e initial pe me ability magneti field st ength magneti flux density magneti moment magneti s us eptibility magnetomotive fo e pe meability of va uum elu tan e Quantity symbol l/A le L i H B m Fm 0 Rm An Examp e Toroid Core Figure 2.1 torroid ore As a on rete examp e for the a u ations throughout th is page we onsider the 're ommended' toroid, or ring ore, Manufa turers use to roids to derive materia hara teristi s be ause there is no gap, even a residua one. Su h tests are done using fu y wound ores rather than just the two turn s here; but, providing the permeabi ity is high, then the error wi be sma . Transformers in and out MANSOOR Page 17

Let's take a worked examp e to find the indu tan e for the winding shown with ju st two turns (N=2). l/A = le / Ae = 27.610-3 / 19.410-6 = 1420 m-1 = 0

= 1.25710-6 2490 = 3.1310-3 Hm-1

Rm = (l/A) / = 1420 / 3.1310-3 = 4.55105 A-t Wb-1 Al = 109 / Rm = 109 / 4.55105 = 22 00 nH pe tu n2 L = Al N2 = 2200 10-9 22 = 8.8 H Co e a to :Co e a to in the I Table 2.3 Quantity name Quantity symbol Unit name Unit symbols o e fa to o geomet i o e onstant l/A pe met e m-1

The idea of o e fa to is, apa t f om adding to the ja gon :-( , to en apsulate in one figu e the ont ibution to o e elu tan e made by the size and shape of the o e. It is usually quoted in the data sheet but it is al ulated as l/A = l e / Ae m-1 o fo ou example to oid we find -

l/A = 27.610-3 / 19.410-6 = 1420 m-1 Co e fa to s a e often spe ified in millimet e s-1. You should then multiply by 1000 befo e using them in the fo mula fo elu tan e. Effe tive A ea T ansfo me s in and out MAN OOR Page 18

Tab e 2.2 Parameter Effe tive magneti path ength Effe tive permeabi ity Indu tan e fa tor saturation f ux density Symbo ue 27.610-3 m 19.410-6 m2 2490 2200 nH 360 mT

ore area Re ative e Ae r A Bsat Va

igu e 2.2 Effe tive a ea The 'effe tive a ea' of a o e ep esents the oss se tional a ea of one of its limbs. Usually this o esponds losely to the physi al dimensions of the o e but be ause flux may not be dist ibuted ompletely eve nly the manufa tu e will spe ify a value fo Ae whi h efle ts this. The need f o the o e a ea a ises when you want to elate the flux density in the o e (li mited by the mate ial type) to the total flux it a ies Ae = / B In the example to oid the a ea ould be dete mined app oximately as the p odu t of the o e he ight and the diffe en e between the majo and mino adii Ae = 6.3 ((12.7 - 6.3) / 2) = 20.2 mm2 Howeve , be ause the flux on ent ates whe e the path length is sho te it is bette to use the value stated by the manufa tu e - 19.4 mm2. o the simple to oidal shape Ae is al ulated as Ae = hln2(R2/R1) / (1/R1-1/R2) m2 This assumes squa e edges to the to oid; eal ones a e often ounded. The e is a slight twist to the question of a ea: the manufa tu e 's value fo Ae will giv e give the o e t esults when used to ompute the o e elu tan e but it may n ot be pe fe t fo omputing the satu ation flux (whi h depends upon the na owes t pa t of the o e o Amin). In a well designed o e Amin won't be ve y diffe en t f om Ae, but keep it in mind. Note :Effe tive a ea is usually quoted in millim et es squa ed. Many fo mulae in data books impli itly assume that a nume i al va lue in mm2 be used. Othe books, and these notes, assume met es squa ed. Effe ti ve Length Effe tive Length in the I Table 2.4 Quantity name Quantity symbol Uni t name Unit symbols effe tive length le met e m T ansfo me s in and out MAN OOR Page 19

The 'effe tive length' of a o e is a measu e of the distan e whi h flux lines t avel in making a omplete i uit of it. Usually this o esponds losely to th e physi al dimensions of the o e but be ause flux has a tenden y to on ent ate on the inside o ne s of the path the manufa tu e will spe ify a value fo le whi h efle ts this. In the to oid example the path length ould be dete mined a pp oximately as le = (12.7 + 6.3) / 2 = 29.8 mm However, because the flux concen trates where the ath length is shorter it is better to use the value stated by the manufacturer - 27.6 mm. For a sim le toroidal sha e le is calculated as le = 2 ln(R2 / R1)/ (1 / R1 - 1 / R2) Another common core ty e, the EE, is shown in F ig: is shown in Fig: 2.3 Figure 2.3 Flux aths The (c) line re resents the shortest ath which a flux lin e could take to go round the core. The (a) line is the longest. Shown in (b) is a ath whose length is that of the short ath lus four sectors whose radius is sufficient to take the ath mid-way down the limbs. le = 2(3.8 + 1.2) + ((2.63 - 1.2) / 2) = 12.25 mm This is all a bit a roximate; but bear in mind that since manufacturing tolerances on ermeability are often 2 5% there isn't much oint in being more exact. Table 2.5 Quantity name magnetomo tive force Quantity symbol Fm, or Unit name ampere Unit symbol A Note: Effective lengt is usually quoted in millimeters. Many formulae in data books implicitly assume t at a numerical value in mm be used. Ot er books, and t ese notes, assu me metres. Table 2.6 Quantity Magnetomotive force Electromotive force Transformers in and out MANSOOR Comparison wit wit t e Electric units Unit Formula amperes volts Fm = H le V = E (Electric field strengt ) l (distance) Page 20

MMF can be t oug t of as t e magnetic equivalent of electromotive force. You can calculate it as Fm = I N ampere turns T e units of MMF are often stated as ampe re turns (A-t) because of t is. In t e example toroid coreFm = 0.25 2 = 0.5 ampe re turns Differentiate magnetomotive force wit magnetic field strengt (magneti zing force). As an analogy t ink of t e plates of a capacitor, wit a certain el ectromotive force (EMF) between t em. How ig t e electric field strengt is wi ll depend on t e distance between t e plates. Similarly, t e magnetic field stre ngt in a transformer core depends not just on t e MMF but also on t e distance t at t e flux must travel round it. A magnetic field represents stored energy an d Fm = 2 W /

igu e 2.3 Magneti field The st ength, o intensity, of this field su ounding a st aight wi e is given by H = I / (2 r) -------Transformers in and out MANSOOR Page 21

Wheneve u ent flows it is always a ompanied by a magneti field. ientists talk of the field as being due to 'moving ele t i ha ges' - a easonable des iption of ele t ons flowing along a wi e.

magneti

field st ength H ampe e pe met e A m-1

whe e W is the ene gy in joules. You an also th ough pa t of a magneti i uit whose elu Law The e is a lea analogy he e with an ele R. Magneti ield t engthMagneti ield t name Quantity symbol Unit name Unit symbols

elate tan e t i ength

mmf to the total flux going you know. m = Rm Rowland's i uit and Ohm's Law, V = I in the I Table 2.7 Quantity

where r, the distance from the wire, is small in com arison with the length of t he wire. The situation for short wires is described by the Biot-Savart equation. By the way, don't confuse the s eed of the charges (such as electrons) with the s eed of a signal travelling down the wire they are in. Think of the signal as being the boundary between those electrons that have started to move and those t hat have yet to get going. The boundary might move close to the s eed of light ( 3x108 m s-1) whilst the electrons themselves drift (on average) something near t o 0.1 mm s-1. You may object that magnetic fields are also roduced by ermanent magnets (like com ass needles, door catches and fridge note holders) where no c urrent flow is evident. It turns out that even here it is electrons moving in or bit around nuclei or s inning on their own axis which are res onsible for the ma gnetic field. Com arison with with the Electric units Quantity Unit Formula H= M agnetic field strength am eres er metre Fm/le Electric field strength volts er metre = /d Magn tic fi ld str ngth is analogous to l ctric fi ld str ngth. Wh r an l ctr ic fi ld is s t up b tw n two plat s s parat d by a distanc , d, and having an l ctromotiv forc , , b tw n th m th l ctric fi ld is giv n by = / d V m1 H = Fm / l In th xampl th fi ld str ngth is th n - H = 0.5 / 27.610-3 = 18 .1 A m-1 Th analogy with l ctric fi ld str ngth is math matical and not physic al. An l ctric fi ld has a cl arly d fin d physical m aning: simply th forc x rt d on a 't st charg ' divid d by th amount of charg . Magn tic fi ld str ng th cannot b m asur d in th sam way b caus th r is no 'magn tic monopol ' q uival nt to a t st charg . Do not confus magn tic fi ld str ngth with flux d ns ity, B. This is clos ly r lat d to fi ld str ngth but d p nds also on th mat ri al within th fi ld. Th strict d finition of H is H = B / 0 - M This formula app li s g n rally, v n if th mat rials within th fi ld hav non-uniform p rm abi lity or a p rman nt magn tic mom nt. It is rar ly us d in coil d sign b caus it is usually possibl to simplify th calculation by assuming that within th fi ld th p rm ability can b r gard d as uniform. With that assumption w say inst ad that H=B/ Flux also m rg s from a p rman nt magn t v n wh n th r ar no wi r s about to impos a fi ld. Similarly, magn tic fi ld str ngth is Transform rs in and out MANSOOR Pag 22

A fi ld str ngth of about 2000 A m-1 is about th limit for cor s mad from iron powd r. Magn tic Flux Magn tic Flux in th SI Tabl 2.8 Quantity nam magn tic flux Quantity symbol Unit name webe Unit symbol Wb Base units kg m2 s-2 A-1

= V T / N Wb How mu h simple an the maths get? Be ause of this elationship fl ux is sometimes spe ified as volt se onds. Compa ison with with the Ele t i uni ts Quantity Unit o mula Magneti flux volt se ond =VT Ele t i ha ge amp se ond (= oulomb) Q = I T

Although as shown above flux o esponds in physi al te ms most losely to ele t i ha ge, you may find it easiest to envisage flux flowing ound a o e in the way that u ent flows ound a i uit. When a given voltage is applied a oss a omponent with a known esistan e then a spe ifi u ent will flow. imila ly , appli ation of a given magnetomotive fo e a oss a fe omagneti omponent wi th a known elu tan e esults in a spe ifi amount of magneti flux = m / Rm Th e e's a lea analogy he e with Ohm's Law. You an also al ulate flux as = I L / N lux an also be de ived by knowing both the magneti flux density and the a ea ove whi h it applies: = Ae B A magneti field ep esents ene gy sto ed within t he spa e o upied by the field. o = 2W/ m T ansfo me s in and out MAN OOR

Page 23

This is one fo m of a aday's law. If a then this boils down to -

onstant voltage is applied fo

a time T

We talk of magnetism in te ms of lines of tin fluxus, means 'flow' the English wo d a measu e of the numbe of these lines al ulate flux f om the time integ al of webe s

fo e o flow o flux. Although the La is olde and un elated. lux, then, is the total amount of magnetism. You an the voltage V on a winding = (1/N)V.dt

whe e W is the field ene gy in joules. O , equivalently, = (2W/ Rm)

Compa ison with with the Ele t i units Quantity Unit o mula 2 Magneti flux de nsity webe s pe met e B = /A ea Ele t i flux density oulombs pe met e2 D = C /A ea lux density is simply the total flux divided by the oss se tional a ea of the pa t th ough whi h it flows B = / Ae teslas Thus 1 webe pe squa e met e = 1 tesla. lux density is elated to field st ength via the B=H o fo the examp le o e B = 3.1310-3 18.1 = 0.0567 teslas suggests that the 'B field' is simply a n effe t of whi h the 'H field' is the ause. Can we visualize any qualitative d istin tion between them? Ce tainly f om the point of view of p a ti al oil desi gn the e is a ely a need to go beyond equation TMD. Howeve , the p esen e of ma gnetized mate ials modifies fo mula B = 0 (M + H) If the B field patte n a ound a ba magnet is ompa ed with the H field then the lines of B fo m ontinuous loo ps without beginning o end whe eas the lines of H may eithe o iginate o te mi nate at the poles of the magnet. A mathemati al statement of this gene al ule i s div B = 0 You ould a gue that B indi ates bette the st ength of a magneti f ield than does the 'magneti field st ength' H! This is one eason why mode n au tho s tend not to use these names and sti k instead with 'B field' and 'H field' . The definition of B is in te ms of its ability to p odu e a fo e on a wi e, length LB = / ( I L sin) Ampere's For e Lawwhere is the ang e between the wire and the fie d dire tion. So it seems that H des ribes the way magnetism is gene rated by moving e e tri harge (whi h is what a urrent is), whi e B is to do w ith the abi ity to be dete ted by moving harges. Transformers in and out MANSOOR Page 24 permeabi ity

Magneti lux Density Table 2.9 Quantity name Magneti mbol B Unit name tesla Unit symbol T

flux density, Quantity sy

In the end, both B and H are just abstra tions whi h the maths an use to mode magneti effe ts. Looking for more so id exp anations isn't easy. A fee for typ i a magnitudes of B he ps. One metre away in air from a ong straight wire arr ying one ampere B is exa t y 200 nanotes as. The earth's fie d has a va ue of ro ugh y 60 mi rotes as (but varies from p a e to p a e). A argish permanant magne t wi give 1 T, iron saturates at about 1.6 T and a super ondu ting e e tromag net might a hieve 15 T. Tab e 2.10 Quantity name Quantity symbo Unit name Unit symbo Base units f ux inkage weber-turn Wb-t kg m2 s-2 A-1

Figure 2.4 F ux Linkages In onger air- ore oi s the situation is ike y to be nearer to that shown in Fig.TFK: Here we see that the f ux density de reases tow ards the ends of the oi as some f ux takes a 'short ut' bypassing the outer t urns. Let's assume that the urrent into the oi is 5 amperes and that ea h f u x ine represents 7 mWb. The entra three turns a ' ink' four ines of f ux: 28 mWb. The two outer turns ink just two ines of f ux: 14 mWb. We an a u at e the tota 'f ux inkage' for the oi as: = 328 + 214 = 112 mWb-t L = / I = 112/5 = 22.4 mH The usefu ness of this resu t is that it enab es us to a u ate the tota se f indu tan e of the oi , L: In genera , where an idea oi is assumed, you see expressions invo ving N o Nd/dt . o g eate a u a y you substitute or d/dt. Tab e 2.11 Transformers in and out MANSOOR Page 25

In an idea indu tor the f ux generated he other other turns. Rea oi s ome a dimensions of the winding are sma permeabi ity ore guides the f ux right

by one of its turns wou d en ir e a t ose to this idea when the ross se tion ompared with its diameter, or if a high the way round.

Quantity name Quantity symbo Unit name Unit symbo Indu tan e L henry H kg m2 s-2 A-2

Comparison with with the E e tri units Quantity Unit Formu a Indu tan e webers per amp L = /I Capa itan e oulombs pe volt C = Q/V Any length of wi e has indu tan e. Indu tan e is a measu e of a oil's ability to sto e ene gy in the fo m o f a magneti field. It is defined as the ate of hange of flux with u ent L=Nd/ dI If the o e mate ial's pe meability is onside ed onstant then the elation between flux and u ent is linea and so: L=N/I By ubstitution of Equation TMM a nd Rowland's Law L = N2 / Rm You an elate indu tan e di e tly to the ene gy e p esented by the su ounding magneti field L = 2 W / I2 Whe e W is the field en e gy in joules. In p a ti e, whe e a high pe meability o e is used, indu tan e is usually dete mined f om the Al value spe ified by the manufa tu e fo the o e L = 10-9 Al N2 Indu tan e fo the to oid example is then: L = 2200 10-9 22 = 8.8 H If the e is no fe omagneti o e so is 1.0 (the oil is 'ai o ed') then a va iety of fo mulae a e available to estimate the indu tan e. The o e t one to use depends upon Whethe the oil has mo e than one laye of tu ns. The o of oil length to oil diamete . The shape of the oss se tion of a multi-lay e winding. Whethe the oil is wound on a i ula , polygonal o e tangula fo me . Whethe the oil is open ended, o bent ound into a to oid. Whethe the oss se tion of the wi e is ound o e tangula , tubula o solid. The pe meabi lity of the wi e. Page 26 T ansfo me s in and out MAN OOR

Base units

The f equen y of ope ation. The phase of the moon, di e tion of the wind et .. i ndu tan e fa to Al Nanohen y nH kg m2 s-2 A-2 Table 2.12 Quantity name Quantity symbol Unit name Unit symbol Base units Al = L 109 / N2 Al is usually alled the indu tan e fa to , defined L = 2200 10-9 22 = 8800 nH = 8.8 H The o e manufa tu e may di e tly spe ify an Al value, but f equently you must de ive it via the elu tan e, Rm. The advantag e of this is that only one set of data need be p ovided to ove a ange of o e s having identi al dimensions but fab i ated using mate ials having diffe ent pe meabilities. Al = 109 / Rm o, fo ou example to oid o e Al = 109 / 4.55105 = 2200 The indu tan e fa to may sometimes be exp essed as "millihen ies pe 1000 tu ns". This is synonymous with nanohen ies pe tu n and takes the same nume i a l value. If you have no data on the o e at all then wind ten tu ns of wi e onto it and measu e the indu tan e (in hen ys) using an indu tan e mete . The Al val ue will be 107 times this eading. Al values a e, like pe meability, a non-linea fun tion of flux. The quoted values a e usually measu ed at low (