POWER-SYSTEM COMPONENTS
`
`10-3
`
`301
`BOADA Protocols, 2. bs ieee Re wR .
`Master Stations... 2206 eee BSR 305
`SCADA Communications,
`.
`. 2... 2 ee 309
`Network Distribution SCADA.
`. 2... 324
`
`TRANSFORMERS
`
`By CARL M. PANDZA, RAMSSIS S. GIRGIS, AND KELLY A. SHAW
`
`Transformer Theory
`
`]. Elementarytheorygiven in Pars. 1 to 10 is developed from the viewpoint of a 3-phase
`three-leg concentnic-cylindneal two-winding transformer, with the primary low-voltage wind-
`ing next to the core and the secondaryhigh-voltage winding outside the primary winding. This
`corresponds to a generator-step-up transformer of moderate kVA. Most of the informationis
`also applicable to single-phase transformers with windings on twolegs, 3-phase transformers
`with five-leg cores, transformers with the primary winding outside the secondary winding,
`three-winding transformers, substation transformers,etc.
`2. Sinusoidal voltage is induced in windings by sinusoidalvariation of flux,
`
`E=4,44 X 1078a,B/N
`
`(10-1)
`
`where a, = square inches cross section of core, B= lines per square inch peak flux density,
`E=nnsvolts, f= frequency in hertz, and N = numberof turns in winding.
`The induced voltage in the primary (excited) winding approximately balances the applied
`voltage. The induced voltage in the secondary (loaded) winding approximately supplies the
`terminal voltage for the load.
`Voltage ratio is the ratio of numberof turns (“‘turn ratio’) in the respective windings. The
`rated open-circuit (no-load) terminal voltages are proportional to the turns in the windings,but
`under load the primary voltage usually must be somewhathigher than the rated value if rated
`secondary voltage is to be maintained, because of regulationeffects.
`3. Characteristics on Open Cirenit. The core loss (no-load loss) ofa powertransformer may
`be obtained from an empirical design curve ofwatts per pound ofcore steel (Fig. 10-1). Such
`curves are established by plotting data obtained from transformers ofsimilar construction. The
`basic loss level is determined by the grade ofcore steel used andis further influenced by the
`number and type of joints employed in construction of the core. Figure 10-1 applies for
`9-mil-thick, M-3 grade steel in a single-phase core with 45° mitered joints. Loss for the same
`erade ofsteel in a three-phase core would usually be 5 to 10% higher.
`Exciting current for a power transformer may be established from a similar empirical curve
`of exciting voltamperes per poundofcore steel as given in Fig. 10-2. The steel grade and core
`construction are the same as for Fig. 10-1. The exciting current charactenstic is influenced
`primarily by the number,type, and quality ofthe core joints, and only secondarily by the grade
`ofsteel. Because ofthe more complexjoints in the 3-phase core,the exciting voltampereswill be
`approximately 50% higher than for the single-phase core.
`
`4. Exciting current ofa transformer contains many harmonic components becauseof the
`varying, permeability of the steel. For most purposesit is satisfactory to neglect the
`harmo cs and assumeasinusoidal exciting current of the sameeffective value. This current
`
`yberegardedas composedofa core-loss component in phase with the induced voltage (90°
`
`flux
`damagnetizing componentin phase with the flux, as shownin Fig. 10-3.
`
`esit is necessary to consider the harmonicsof exciting current to avoid inductive
`
`communication circuits. The harmonic content ofthe exciting current in-
`
`luxdensityisincreased.Performance can bepredicted by comparison with
`using similar core steel and similar construction.
`
`
`
`LIBERTY EXHIBIT 1024, Page 1
`
`LIBERTY EXHIBIT 1024, Page 1
`
`

`

`MOTORS AND DRIVES
`
`20-21
`
`\
`
`nt volis per hertz, i.¢., voltage proportional to frequency and speed. The converter
`sristics are shown in Fig. 20-19b and 19¢, The + V, values are 1.35 times theline-line
`the ac side of each converter. For a given motor speed, frequency, and voltage, the
`on
`ee
`:
`;
`:
`‘
`eaeofthe rectifieris set at a,to yield the required de voltage V, for the link. Thefiring
`: ofthe inverteris set at ay, in the inverting quadrantof the converterso that the link voltage
`\matchesthe internal ac voltage generated by the motorat the given speed. Powerflows from
`| ectiferal V7.2, into the inverter and the motor. Theinverterfiring signals are synchronized
`the motor voltage. For decelerating the motor, the rectifier and inverter functions are re-
`enedbyshifting the firing angles, Power flows from the motorinto the de link and to the supply
`line.
`
`gibliography
`34, References for Synchronous Motors
`ritgerald, A. E., Kingsley, C., Jr.,and Kusko,A.; Electric Machinery, 3d ed.,; New York, McGraw-Hill Book
`Company, 1971.
`gama, Mulukutla S.; Syichronous Machines; New York, Gordon & Breach, 1979.
`Concordia, C.; Spachronous Machines; New York, Wiley, 1951.
`Gay, MG. Alternating Current Machines; New York, Wiley, 1976.
`vEMA Std. MS1—Motors and Generators.
`IEE Sid, 115—1965 Test Proceduresfor Synchronous Machines.
`FEE Std. 421—1972 Criteria and Definition for Excitation Systems for Synchronous Machines.
`Bost, B. K.; Adjustable Speed AC Drives; IEEE Press, 1980.
`Kosento, M., and Piotrovsky, L.; Electric Machines, vol. 2; Moscow, MIR Publications, 1974.
`Miller, T. J.; Brushless Permanent-Magnet and Reluctance Motor Drives, Oxford University Press, 1989.
`
`INDUCTION MACHINES
`
`Theory of the Polyphase Inductor Motor’
`
`35. Principle ofOperation. An induction motoris simply an electric transformer whose
`magneticcircuit is separated by an air gap into two relatively movable portions, one carrying the
`primary and the other the secondary winding, Alternating current supplied to the primary
`winding from an electric power system induces an opposing current in the secondary winding,
`when the latter is short-circuited or closed through an external impedance. Relative motion
`between the primary and secondary structures is produced bythe electromagnetic forces corre-
`sponding to the power thus transferred across the air gap by induction. The essential feature
`which distinguishes the induction machine from other types of electric motors is that the
`secondary currents are created solely by induction, asin a transformer,instead ofbeing supplicd
`byade exciter or other external power source, as in synchronous and dc machines.
`
`Induction motors are classified as squirrel-cage motors and wound-rotor motors. The sec-
`dary windings
`on therotorsof squirrel-cage motors are assembled from conductor bars
`i
`d
`ringsorare
`castinplace from aconductive alloy. The secondary windings
`
`rs
`wound with discrete conductors with the same numberofpoles as
`
`uitedbybrushes bearing onthe slip rings, or they can be
`t
`ertersfor starting and speed control.
`
`The nommal
`structure of an induction motor consists of a
`
`m
`inslots on itsouter periphery and an encircling
`
`10k
`itch apart, The superposition ofthe
`
`uced bythe 3-phase windings produces a
`
`
`ines;NewYork, John Wiley & Sons, Inc., 1951.
`
`= n
`
`are
`
`LIBERTY EXHIBIT 1024, Page 2
`
`LIBERTY EXHIBIT 1024, Page 2
`
`

`

`20-22
`
`STANDARD HANDBOOK FOR ELECTRICAL ENGINEERS
`
`sinusoidally distributed magnetic field revolving in synchronism with the Powersupply,
`quency,thetimeoftravelofthefieldcrestfromonephasewindingtothenextbeingfredaE
`timeinterval between the reaching oftheir crest values by the corresponding phase
`Thedirection ofrotation is fixed by the timesequence ofthecurrentsinsuccessiveeeebl
`and so many be reversed by reversing the connections ofone phase ofa 2- or 3-phasemojM
`
`e Phase C
`Phase B
`
`PrimaryanereWAA ofhaseA
`
`FIG, 20-20 Section of squirrel-cage induction motor,
`3-phase, 4-pole, %-pitch stator winding.
`
`Figure 20-20 shows the cross section of a typical polyphase induction motor, having inthis
`case a 3-phase 4-pole primary winding with 36 statorand 28rotorslots. The primary windingis
`composed of36 identical coils, each spanning 8 teeth, one less than the 9 teeth in one pole pitch.
`The windingis therefore said to have %pitch. As there are three primary slotsperpoleperphase,
`phase A comprises four equally spaced “‘phase belts,” each consisting ofthree consecutive coils
`connected in series. Owing to theshort pitch, the top and bottom coil sides ofeachphaseoverlap
`the next phase on either side, The rotor, or secondary, winding consists merely of28 identical
`copper or cast-aluminum bars solidly comnected to conducting end rings on each end, thus
`fe
`
`vinrel-capestructure. Bothrotorandstatorcoresare usuallybuiltonsilicon-stee!
`
`
`, or field distribution, produced bya
`
`n stator and rotoris assumed to be
`calculate the resultantfieldproduced
`
`the field of each single coil into its
`expressed by the followingequation:
`
`
`
`(20-8)
`
`LIBERTY EXHIBIT 1024, Page 3
`
`LIBERTY EXHIBIT 1024, Page 3
`
`

`

`MOTORS AND DRIVES
`
`20-85
`
`an RAS Power Electronics — Solid-State Motor Control: Reston, Virginia, Reston Publishing Com-
`Pear
`pany. 1980.
`enchi. T. 3 Theory ofSCR Circuits and Applications to Motor Control; Tokyo, Tokyo Electncal Engs-
`
`_rngCollegePress. 1969,
`weBK Adjustable Speed AC Drive Systems; New York, [EEE Press, 1980.
`sitsJM. D.: Thyristor Control ofAC Motors; Nw York, Pergamon, 1973.
`one R.: Induction Machines for Speed Purposes; New York, Chemical Publishing Company.
`ass.
`wat, §. A. and Boldea, 1. Linear Motion electric Machines; New York, Wiley, 1976.
`patoujadofl. M.; The Theory ef Linear Induction Machines; Oxford, England, Clarendon Press, ! 9580.
`
`AC DRIVES
`
`153. General Theory of AC Drives. There are three basic types of ac machines—
`snehronous machines, wound-rotor induction machines, and squirrel-cage induction ma-
`chines (see Table 20-20). Each ofthese machinesis normally applied to a fixed-speed applica-
`tion. The speed of each is determined by the internal mechanical andelectrical configuration
`(refer to Par. 1S4 and 155 for a detailed discussion). It can be displayed as
`
`Specetrpm)
`
`120 X frequency (Hz)
`No.of poles
`
`Except for special cases, the number of poles in a machine is fixed and the incomingline
`frequencyis normally fixed. Therefore, except for slip in induction machines,a given ac motor
`operated on a given electrical network will operate at a single fixed speed.
`Ifthe line frequency supplying the motor can be adjusted, then the speed of the motor can
`also be adjusted. That is the basis for adjustable-speed drives for ac motors.
`154, Application and Economics ofSpeed Control. Aspreviously noted, ac motors provide
`the motive powerfora widearrayofindustrial applications. Most ofthese involve a centrifugal
`wpe of load, e.g., fans, blowers, compressors, or pumps. The configuration of these devicesis
`such that the torque required to turn them is proportional to the square of the speed. And the
`power required to turn them is proportional to the cube of the speed. The relationships
`
`Torque “ rpm?
`
`Power « rpm?
`
`is what makes adjustable-speed drives (ASDs) economically attractive.
`Most of these devices are part of a process which requires some degree of flow or pressure
`control. This is normally performed via mechanical throttling of the flow, e.g., inlet or outlet
`dampers, guide vanes, valves, or bypass systems. The netresult of any ofthese methodsis the
`consumption of excess energy required to overcome the pressure drop or bypass flow each
`creates.
`However, efficient and precise control ofthe flow or pressure in a system can be obtained by
`directly controlling the speed ofthe device. This direct-speed control, coupled with the speed/
`powerandspeed/torque relationshipsshown above,results in an exceptionally efficient method
`ofcontrolling the process. Several programs are commercially available to calculate energy
`Savingsandpaybacks basedon energy rates, operating profiles, internal rates of return,etc.
`155. Power Semiconductor Devices.
`In orderto supply an adjustable frequency to an ac
`
`‘Motor, theincomin,
`nstant-frequency voltage or current mustfirst be rectifiedtoa de current
`Orvoltage.Thisde voltageorcurrentis then invertedto an adjustable frequency output. Thisis
`accomplishedby powersemi-conductor devices.
`_ Thesede
`allowcurrenttoflow in only one direction. They act as electronic switches.
`Various
`types can befired on and off at certain times in the cycle. This selected firing allows
`Sontroloftheresultant voltage orcurrent.
`
`___
`Ht
`
`
`
`LIBERTY EXHIBIT 1024, Page 4
`
`LIBERTY EXHIBIT 1024, Page 4
`
`

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`LIBERTY EXHIBIT 1024, Page 5
`
`LIBERTY EXHIBIT 1024, Page 5
`
`
`

`

`MOTORS AND DRIVES
`
`20-89
`
`Supply network
`
`isolation transformer
`
`Rectifier Section
`
`i DeLinkReactor
`
`[aw]
`iol
`
`Common Turn-Off Circuit
`
`—
`
`Inverter Section
`
`Output Filter
`
`Induction Motor
`
`FIG. 20-76 LCI drive with induction motor.
`
`PWM/Induction Motor Drives. With the advent of high-power GTO thyristors. pulse-
`width modulated (PWM) frequency converters for powers up to 10,000 hp are now available.
`These can be supplied as either voltage-source (Fig. 20-77) or current-source configurations.
`Foreither configuration,the ability to rurn offthe device via a gate pulse eliminates a numberof
`components in the powercircuit,
`The voltage source drive in particular has a numberof benefits. The uncontrolled diode
`Tectifier section results in a high line-side power factor (near unity) throughout the speed range.
`The distortion seen by the electrical network is also reduced since diodes always have an
`effective firing angle of zero. The PWM voltage-source output of the inverter produces a
`near-sinusoidal current in the motor. High dynamic performance can also be realized. Full
`torque can be maintained and controlled throughout the speed range —even at zero speed.
`Auniqueapplication of voltage-source PWM drives is their use on coordinated sectional
`drivesystems. Because thevoltage in the dc link is maintained at a constant value, several
`
`fer
`sections can be connected to the samerectifier/dc link section. This can result in
`
`‘Savings in money andin space.
`
`very aed? Drives. A muchdifferentsolution is a slip recovery, or cascade,
`
`
`
`
`
`motor. Wound-rotor or slip-ring motors can be speed-controlled by
`stor
`to the rotor circuit via the slip rings. Since the slip (and hence the
`
`toris directly proportional to thelosses in the rotor, increasing or
`
`a
`could vary the speed overa limited range. Historically, the
`ed viaaliquid rheostatforstepless control, or a grid resistor for several steps
`
`
`
` -
`
`LIBERTY EXHIBIT 1024, Page 6
`
`LIBERTY EXHIBIT 1024, Page 6
`
`

`

`20-30
`
`STANDARD HANDBOOK FOR ELECTRICAL ENGINEERS
`
`Supply network
`
`Input transformer
`
`Rectifier Section
`
`DC Link
`
`Inverter Section
`
`[2 Induction Motor
`
`FIG. 20-77 Voltage-source PWM inverter drive.
`
`in resistance. This method was also com-
`monly used for starting of high inertia loads.
`The motor’s starting torque and current char-
`acteristics could be adjusted during starting.
`Once it reaches rated speed,theslip rings are
`short-circuited and the motor functions as a
`squirrel-cage induction motor.
`The cascade drive controls the speed in a
`similar fashion. However, as its name implies,
`rather than dissipating the energy across ex-
`ternal resistors, it recovers the slip energy and
`retumsit to the electrical network. Thisis re-
`alized by converting the low-frequency rotor
`current into line-frequency current.It is then
`transformed to the supply voltage via a feed-
`back transformer. Starting is normally ac-
`complished via conventional means with a
`liquid or grid resistor.
`The cascade drive is an excellentsolution
`when the speed range is relatively narrow—
`normally 50 to 70% to 100%. Because the
`converter handles only the s/ip power, it is
`much smaller than other types of frequency
`converters. As an example, if the desired
`speed range is 70 to 100%, the converter must
`be sized to handle only 30% of the rated
`power. This results in a very economical solu-
`tion.
`
`Supply Network Slip-Ring Motor
`
`Rectifier
`
`DC Link
`
`Starting Resistor
`and Switch gear
`
`LIBERTY EXHIBIT 1024, Page 7
`
`LIBERTY EXHIBIT 1024, Page 7
`
`