ELECTRICAL MACHINES

WARSAW UNIVERSITY OF TECHNOLOGYFACULTY OF ELECTRICAL ENGINEERINGELECTRICAL MACHINESELECTROMECHANICAL ENERGY CONVERTERSAND TRANSFORMERSLectured for IVth semester students byWiesław PARTYKA, Ph.D., M.Sc. El. Eng.Institute of Electrical MachinesElectrical Machines DivisionBuilding beneath Chimney, room #19 (BpK19)w.partyka@ime.pw.edu.plREFERENCES - RECOMMENDED BOOKS:1. Fitzgerald A., Kingsley C., Umans S.: Electric machinery. McGraw-Hill2. Say M.G.: Alternating current machines. Direct current machines.Pitman Publishing3. Nasar S., Unnewehr L.: Electromechanics and Electric Machines.John Wiley&Sons4. Latek W.: Zarys maszyn elektrycznych. WNT, W-wa5. Bajorek Z.: Maszyny elektryczne. WNT, W-wa6. Kamiński G., Przyborowski W., Kosk J.: Laboratorium maszynelektrycznych. Oficyna Wyd. PW.

G-2ELECTRICAL MACHINE DEFINITIONElectrical machine is a converter of energy (or power converter)which converts:electrical energy (power) into mechanical one,ormechanical energy (power) into electrical one,orelectrical energy (power) into electrical - but usually ofdifferent parameters,with the help of (by means of) magnetic field. Energy conversion inelectrical machines is or is not accompanied with mechanical motion.[A margin forcomments andstudent’s own notes]Machine converters:.PinT - torque (moment) inN mΩ - angular speed ofthe shaft in rad/sPoutELECTRICALMOTORF;vT;ΩINPUT - ELECTRICAL POWEROUTPUT - MECHANICAL POWERP UI (DC circuit)P TΩ (rotational motion)P UIcosϕ (AC 1-phase)P Fv (linear motion)P 3UIcosϕ (AC 3-phase, line or phase-to-phase values)P 3UphIphcosϕ (AC 3-phase, phase LECTRICALOUTPUT.PinTRANSFORMER,or T (OFDIFFERENTPARAMETERS)IMPORTANT NOTICE: OPERATION OF ELECTRICAL MACHINEIS REVERSIBLE. MODE OF OPERATION DEPENDS ONLY UPONTHE FORM OF POWER SUPPLIED TO AND ABSORBED FROMTHE MACHINE.P - power in W (watts)F - force in linearmotion in Nv - speed (linear)in m/sPin - input powerPout - output power

G-3BASIC PRINCIPLES OF ENERGY CONVERSIONIN ELECTRICAL MACHINEELECTROMAGNETIC INDUCTIONAssume the coil having N turns. Each turn is linked with themagnetic flux Φ. The total flux linked with the coil isΨ NΦand is called coil’s flux linkage.According to Faraday-Lenz law when the change of Ψ is takingplace the electromotive force (emf) is induced in the coil:e dΨdΦ NdtdtChange of flux linkage may occur in two ways (separately orsimultaneously): flux is constant, the coil moves through it; in electricalmachines it is usually so arranged, that the straight parts ofthe coil turns move at speed v at right angles to the directionof the flux; coil is stationary with respect to the flux, the flux is varying inmagnitude.In general Φ f(x,t), ande NdΦ Φ dx Φ N N er ep tdt x dtMotional (rotational) emf in a single conductor of length l cuttingacross a magnetic field of uniform flux density B at speed v atright angle to the direction of the flux ise er BlvPulsational emf (transformer emf) in a coil of N turns, induceddue to the flux linked to the coil varying in time sinusoidallyhas the valueΦ Φmsinωt Φmsin2πfte ep NdΦ 2πfNΦ m cosωt Em cosωtdtIts root-mean-square (rms) valueE Em 4 ,44 fNΦ m2

G-4ELECTRODYNAMIC INTERACTION OF CURRENT ANDMAGNETIC FIELDWhen a current I flowing along the elementary conductor dL isunder influence of magnetic field of density B, an elementarymechanical force is developed on it, according to Lorentzrelation:dF I dL BThe highest value of the force is achieved when the conductor(and current I) is perpendicular to the magnetic field B. In sucha case, for the conductor of total length L, the total force actingat the conductor (current) isF BILand is perpendicular to both current and field.Tendency to alignthe magnetic fieldlines (alignment)DETERMINATION OF EMF AND DYNAMIC FORCEDIRECTIONSThe method of three fingers of the right hand.AMPER'S RULE FOR MAGNETIC CIRCUITH - magnetic fieldstrength in A/m.NI Θ - magnetomotiveforce (mmf) in A(or in A-t)µ µrµo - absolutepermeability in H/m. H dL NI ΘLor for finite number of the closed magnetic circuit parts ofuniform cross-section and assignable length and permeabilityµo 4π 10-7 H/m absolute permeabilityof vacuum, air ornonmagnetic materialµr - relative permeability(in per unit -p.u.) H x Lx NIxand henceNI H x Lx (xBxµxLx ) (xΦL ) Φ R µxAx µ x xxwhere Ax is a cross-section area of the x-th part of magneticcircuitRµ L- reluctanceA µ(magnetic resistance)in H-1

G-5ELECTROMAGNETIC CIRCUIT EXAMPLER – winding resistanceN – number of turnsΦ - the main flux (A; l; µ)Φl – leakage flux flowingmainly outside themagnetic circuit (Al; ll; µo)Assume i ImsinωtΦ Φmsinωt(or i 2Isinωt)N ilΦ Rµf var (saturation effect)RµfA µΦ l Φ lm sin ωt Φ l N iRµlRµl ll constAl µoIm – amplitude ofsinusoidallyvarying currentI – root-meansquare (rms)value of current iemf induced due to Φef NN2 LfRµfNIdΦN2 NΦ mωcosωt N m ωcosωt ωI mcosωtRµfdtRµf inductance of the winding corresponding tothe main flux path parametersamplitude of efEfm Xf Imrms value of efEf Xf I2Nω L f ω X f so called magnetizing reactanceRµfemf induced due to ΦldΦ lN2NI m NΦ lmωcosωt Nωcosωt ωI mcosωtel NdtRµlRµlN2 LlRµl inductance of the winding corresponding tothe leakage flux path parametersamplitude of elElm Xl Imrms value of elEl Xl IN2ω Llω X l so called leakage reactanceRµlXf Xl X(total) reactance ofthe coilEquivalent circuit with rms valuesof U, I described at complex planePhasor diagramVoltage balance equationU U R E l E f R I jX l I jX f Iϕ - phase angle

G-6DESIGN AND CONSTRUCTIONAL FEATURESOF A ROTATING MACHINE1 - windings of stator androtor embedded inslots2 - slots and teeth3 - magnetic cores ofstator and rotor(made of laminations)4 – frame, housing5 – air gap6 - bearings7 - shaftCORE LOSS(power loss in magnetic core)Hysteresis loss - due to the cycling of the material through itshysteresis loopSpecific hysteresis loss (per mass unit of magnetic material)ph k h fBm2[W/kg]

G-7Eddy-current loss - due to the induction of emfs and currents(eddy currents) circulating within the magnetic material.Eddy-current specific losspe 1k e d 2 f 2 Bm2 k e' f 2 Bm2ρρ - resistivity of magnetic[W/kg]materiald - thickness oflaminationTotal core loss intransformersrotating machinesh.r.s. - hot-rolled steel(4-5% silicon content)c.r.o.s - cold-rolled grainoriented steelDirectional properties of cold-rolled grain-oriented steelMagnetic properties inthe rolling direction arefar superior to those onany other axis.Power loss andmagnetising current inthe rolling direction areeach taken as unity.

G-8COPPER (I2R) LOSSWhen current I (rms value or DC) flows in a conductor (winding)of resistance R, the I2R loss appears.Copper & aluminium - most common conducting metals usedfor electrical machine windings. P PCu I2RTotal lossR ρl - length of conductor(winding)lρ - resistivity (Ω.m)S Cu2Specific I R loss (per volume unit of conducting material (or perunit cube of conducting material)J – current density(A/m2) p J ρ2The resistance depends on temperatureRϑ R20 (1 α ϑ )SCu – cross-sectionarea of theconductorϑ - temperature ϑ (ϑ 20) ϑ - temperature riseα - resistance-Conducting materials sity[µΩ.m]Resist temper.coefficient[1/K]Copper0.01720.003938 900Aluminium0.0450.003932 700Metal[kg/m3]MECHANICAL LOSS PmPower loss due to: bearing friction windage (fan - ventilator action, friction of rotatingparts against coolant, f.e. air) brush frictionR20 – resistancedetermined(measured) at 20oC

G-9EFFICIENCY OF ENERGY CONVERSIONEfficiency of power conversion is usually the most importantparameter of electrical machine.Pout η efficiencyPinPin - Pout Σ Ptotal power loss P PFe PCu Pmη PoutP P incan be also expressed in %Pout PPinTEMPERATURE RISE OF THE MACHINESimplifying assumptions: machine is an ideal homogeneous body, machine is internally heated by total power loss Σ P, machine is surface (externally) cooled (f.e. by means ofexternal fan):ϑoΣ PϑαThe energy balance equation for heated machine when running P d t M c d ϑ A α h (ϑ ϑ o )and its solution for temperature rise (above the ambienttemperature) ϑ ϑ - ϑot M c PTh ϑ ϑ max 1 e ϑ max Th A αhA αh The energy balance equation for cooling down (machine at rest)0 M c d ϑ A α c (ϑ ϑ o )and tTcM cA αcwhere ϑi is initial temperature rise (at the beginning of cooling) ϑ ϑ i eTc ϑo - ambient temperature(coolant temp.)ϑ - machine temperatureα - heat transfercoefficient [W/(m2.K)]M - mass of the machinec - specific heat of themachine body[J/(kg.K)]A - area of machinesurface at which theheat exchange occurs(cooling surface)αh - heat transfer coeff.of running machineTh - heating timeconstantαc - heat transfer coeff. ofresting machine(while cooling atrest)Tc - cooling time constant(at rest)

G - 10When we don’t regard a machine as a homogeneous body, thetemperature rises of the winding, core & frame can be different:What maximum temperature (or temperature rise) can be allowed forany machine part?Too high temperature (overheating) can damage the material or canshorten the material life expectancy (material life time).Insulating materials are most sensitive to temperature. Therefore,almost all usable materials are subject to temperature limitations.They are classified in accordance with limits of operatingtemperature:Insulation classoMax temperature CAEBFH105120130155180or, when we assume the ambient temperature ϑo 40oC and takeinto consideration the average temperature rise (for example thetemperature rise of the entire winding determined by means of itsresistance increase), we can describe the maximum temperature rise:Insulation classAEBFHMax temp. rise, K607580105125IEC and European Standard 60034-1 Edition 11: “Rotatingelectrical machines – Part 1: Rating and performance” providesthree degrees of thermal classification:Thermal classification130 155 180Max temp. rise, K80105125Thermal life expectancyTemperature of windingmeasured by means ofresistance measurementmethodA, E, B, F, H – previouslyused abbreviations ofmachines’ insulationclasses (still inapplication in machinesof older manufacturing)Most actual system ofthermal classificationFor large machines the life expectancy is about 30 years, providingthe maximum temperature of insulating material used in the machineis not exceeded. Increased temperature above the permissible valuecauses the quicker degradation of insulating material.Machine life expectancy (time to failure) is halved for each 8oCtemperature rise above that maximum permissible value(continuously).8oC ruleMontsinger’s rule

G - 11DUTY TYPES OF THE MACHINEThere are various applications of the machines. Standardmotors & transformers are rated in terms of continuousoperation. But there are also other possible types of operation duty types:N - operation underrated condition ofloadR - machine at restandde-energisedD - starting timeF - braking timeV - operation atno-load butrotatingCyclic duration factorsS3: N/(N R)S4: (D N)/(D N R)S5:S1 - continuous running dutyS2 - short-time dutyS3 - intermittent periodic dutyS4 - intermittent periodic duty with startingS5 - intermittent periodic duty with electric brakingS6 – continuous-operation periodic duty .Maximum temperature rise must not exceed the appropriatepermissible value for the given insulation class of the machine.Insulation class (thermal classification) of the machine is alwaysgiven at the machine nominal plate.The rated (nominal) power of the machine is referred to(corresponds to) the chosen duty type which should also begiven at the machine nominal plate by means of: duty typesymbol (S1 S10), corresponding cyclic duration factor andmoments of inertia of machine and of the load.(D N F)/(D N F R)S6: N/(N V)(usually expressed in%: 15, 25, 40 or60%)Cycle duration - 10 minS2: N 10, 30, 60 or90 min

FACULTY OF ELECTRICAL ENGINEERING ELECTRICAL MACHINES ELECTROMECHANICAL ENERGY CONVERTERS AND TRANSFORMERS Lectured for IVth semester students by Wiesław PARTYKA, Ph.D., M.Sc. El. Eng. Institute of Electrical Machines Electrical Machines Division Building beneath Chimney, room #19 (BpK19)