控制电缆烧损事故之分析改善与预防对策ppt课件

1、 Organized byTask Force on Harmonics Modeling & SimulationAdapted and Presented by Paulo F Ribeiro AMSCMay 28-29, 2021Contributors: S. Tsai, Y. Liu, and G. W. ChangIntroductionNonlinear magnetic core sourcesArc furnace3-phase line commuted convertersStatic var compensatorCycloconverterThe purpos

2、e of harmonic studies is to quantify the distortion in voltage and/or current waveforms at various locations in a power system.One important step in harmonic studies is to characterize and to model harmonic-generating sources. Causes of power system harmonics Nonlinear voltage-current characteristic

3、s Non-sinusoidal winding distributionPeriodic or aperiodic switching devicesCombinations of aboveIn the following, we will present the harmonics for each devices in the following sequence:Harmonic characteristicsHarmonic models and assumptionsDiscussion of each modelIntroductionNonlinear magnetic co

4、re sourcesArc furnace3-phase line commuted convertersStatic var compensatorCycloconverterHarmonics characteristicsHarmonics model for transformersHarmonics model for rotating machinesCauses of harmonics generationSaturation effectsOver-excitationtemporary over-voltage caused by reactive power unbala

5、nce unbalanced transformer loadasymmetric saturation caused by low frequency magnetizing currenttransformer energizationSymmetric core saturation generates odd harmonics Asymmetric core saturation generates both odd and even harmonics The overall amount of harmonics generated depends onthe saturatio

6、n level of the magnetic corethe structure and configuration of the transformerHarmonic models for a transformer:equivalent circuit modeldifferential equation modelduality-based modelGIC (geomagnetically induced currents) saturation model In time domain, a single phase transformer can be represented

7、by an equivalent circuit referring all impedances to one side of the transformerThe core saturation is modeled using a piecewise linear approximation of saturationThis model is increasingly available in time domain circuit simulation packages. IpR pL pL sR sIexL mImR m+-V m+-V inV out+-IsThe differe

8、ntial equations describe the relationships between winding voltageswinding currentswinding resistancewinding turnsmagneto-motive forcesmutual fluxesleakage fluxesreluctancesSaturation, hysteresis, and eddy current effects can be well modeled. The models are suitable for transient studies. They may a

9、lso be used to simulate the harmonic generation behavior of power transformers. NNNNNNNNNNNNNNNiiidtdLLLLLLLLLiiiRRRRRRRRRvvv212122221112112121222211121121 Duality-based models are necessary to represent multi-legged transformersIts parameters may be derived from experiment data and a nonlinear indu

10、ctance may be used to model the core saturationDuality-based models are suitable for simulation of power system low-frequency transients. They can also be used to study the harmonic generation behaviorsMagnetic circuitElectric circuitMagnetomotive Force (FMM) Ni Electromotive Force (FEM) E Flux Curr

11、ent I Reluctance Resistance R Permeance Conductance Flux density Current density Magnetizing force H Potential difference V /1R/1AB/AIJ/Geomagnetically induced currents GIC bias can cause heavy half cycle saturationthe flux paths in and between core, tank and air gaps should be accountedA detailed m

12、odel based on 3D finite element calculation may be necessary.Simplified equivalent magnetic circuit model of a single-phase shell-type transformer is shown.An iterative program can be used to solve the circuitry so that nonlinearity of the circuitry components is considered.FACDCRc1Ra1Ra4Ra4Rt4Rc3Rc

13、2Rc2Ra3Rt3Harmonic models for synchronous machineHarmonic models for Induction machineHarmonics origins:Non-sinusoidal flux distributionThe resulting voltage harmonics are odd and usually minimized in the machines design stage and can be negligible. Frequency conversion processCaused under unbalance

14、d conditions SaturationSaturation occurs in the stator and rotor core, and in the stator and rotor teeth. In large generator, this can be neglected.Harmonic modelsunder balanced condition, a single-phase inductance is sufficientunder unbalanced conditions, a impedance matrix is necessaryFor balanced

15、 (single phase) harmonic analysis, a synchronous machine was often represented by a single approximation of inductance h: harmonic order : direct sub-transient inductance : quadrature sub-transient inductanceA more complex model a: 0.5-1.5 (accounting for skin effect and eddy current losses) Rneg an

16、d Xneg are the negative sequence resistance and reactance at fundamental frequency 2/qdhLLhLdLqLnegnegahjhXRhZThe balanced three-phase coupled matrix model can be used for unbalanced network analysisZs=(Zo+2Zneg)/3Zm=(ZoZneg)/3 Zo and Zneg are zero and negative sequence impedance at hth harmonic ord

17、erIf the synchronous machine stator is not precisely balanced, the self and/or mutual impedance will be unequal.smmmsmmmshZZZZZZZZZZHarmonics can be generated fromNon-sinusoidal stator winding distributionCan be minimized during the design stageTransientsHarmonics are induced during cold-start or lo

18、ad changingThe above-mentioned phenomenon can generally be neglectedThe primary contribution of induction motors is to act as impedances to harmonic excitationThe motor can be modeled asimpedance for balanced systems, ora three-phase coupled matrix for unbalanced systemsBalanced ConditionGeneralized

19、 Double Cage ModelEquivalent T ModelUnbalanced ConditionRsjXsRcjXmjXrR1(s)jX1R2(s)jX2StatorExcitation branchAt the h-th harmonic order, the equivalent circuit can be obtained by multiplying h with each of the reactance. mutual reactance of the 2 rotor cages 2 rotor cages s is the full load slip at f

20、undamental frequency, and h is the harmonic order- is taken for positive sequence models+ is taken for negative sequence models. RsjhXsRcjhXmjhXrRrshhshsh1The balanced three-phase coupled matrix model can be used for unbalanced network analysisZs=(Zo+2Zpos)/3 Zm=(ZoZpos)/3 Zo and Zpos are zero and p

21、ositive sequence impedance at hth harmonic orderZ0 can be determined fromRs0jXs0Rm020.5Rr0(-2+3s)jXm02jXr02Rm020.5Rr0(4-3s)jXm02jXr02smmmsmmmshZZZZZZZZZZIntroductionNonlinear magnetic core sourcesArc furnace3-phase line commuted convertersStatic var compensatorCycloconverterTypes:AC furnaceDC furnac

22、eDC arc furnace are mostly determined by its AC/DC converter and the characteristic is more predictable, here we only focus on AC arc furnaces The nature of the steel melting process is uncontrollable, current harmonics generated by arc furnaces are unpredictable and random.Current chopping and igni

23、ting in each half cycle of the supply voltage, arc furnaces generate a wide range of harmonic frequencies (a)(b)Nonlinear resistance modelCurrent source modelVoltage source modelNonlinear time varying voltage source modelNonlinear time varying resistance modelsFrequency domain modelsPower balance mo

24、del(a)simplified toR1 is a positive resistorR2 is a negative resistorAC clamper is a current-controlled switchIt is a primitive model and does not consider the time-varying characteristic of arc furnaces. modeled asTypically, an EAF is modeled as a current source for harmonic studies. The source cur

25、rent can be represented by its Fourier seriesan and bn can be selected as a function ofmeasurement probability distributionsproportion of the reactive power fluctuations to the active power fluctuations. This model can be used to size filter components and evaluate the voltage distortions resulting

26、from the harmonic current injected into the system. 10cossinnnnnLtnbtnatiThe voltage source model for arc furnaces is a Thevenin equivalent circuit.The equivalent impedance is the furnace load impedance (including the electrodes)The voltage source is modeled in different ways:form it by major harmon

27、ic components that are known empiricallyaccount for stochastic characteristics of the arc furnace and model the voltage source as square waves with modulated amplitude. A new value for the voltage amplitude is generated after every zero-crossings of the arc current when the arc reignitesThis model i

28、s actually a voltage source modelThe arc voltage is defined as a function of the arc lengthVao :arc voltage corresponding to the reference arc length lo, k(t): arc length time variationsThe time variation of the arc length is modeled with deterministic or stochastic laws.Deterministic: Stochastic: 0

29、0laoVtklaV tDlltlosin12 tRltloDuring normal operation, the arc resistance can be modeled to follow an approximate Gaussian distribution is the variance which is determined by short-term perceptibility flicker index PstAnother time varying resistance model:R1: arc furnace positive resistance and R2 n

30、egative resistanceP: short-term power consumed by the arc furnaceVig and Vex are arc ignition and extinction voltages RAND22cosRAND1ln2 RRarc222221RVRVPVRexigigr is the arc radiusexponent n is selected according to the arc cooling environment, n=0, 1, or 2recommended values for exponent m are 0, 1 a

31、nd 2K1, K2 and K3 are constants 22321irKdtdrrKrKmnIntroductionNonlinear magnetic core sourcesArc furnace3-phase line commuted convertersStatic var compensatorCycloconverterLine-commutated converter is mostly usual operated as a six-pulse converter or configured in parallel arrangements for high-puls

32、e operations Typical applications of converters can be found in AC motor drive, DC motor drive and HVDC linkUnder balanced condition with constant output current and assuming zero firing angle and no commutation overlap, phase a current is h = 1, 5, 7, 11, 13, .Characteristic harmonics generated by

33、converters of any pulse number are in the order of n = 1, 2, and p is the pulse number of the converter For non-zero firing angle and non-zero commutation overlap, rms value of each characteristic harmonic current can be determined by F(,) is an overlap function )cos(cos/),(6hFIIdhhhathhIti)sin()/2(

34、)(111 pnhHarmonic models can be categorized asfrequency-domain based modelscurrent source modeltransfer function modelNorton-equivalent circuit modelharmonic-domain modelthree-pulse model time-domain based modelsmodels by differential equations state-space modelThe most commonly used model for conve

35、rter is to treat it as known sources of harmonic currents with or without phase angle information Magnitudes of current harmonics injected into a bus are determined from the typical measured spectrum and rated load current for the harmonic source (Irated)Harmonic phase angles need to be included whe

36、n multiple sources are considered simultaneously for taking the harmonic cancellation effect into account. h, and a conventional load flow solution is needed for providing the fundamental frequency phase angle, 1spsphratedhIIII1/)(11spsphhhThe simplified schematic circuit can be used to describe the

37、 transfer function model of a converterG: the ideal transfer function without considering firing angle variation and commutation overlapG,dc and G,ac, relate the dc and ac sides of the converterTransfer functions can include the deviation terms of the firing angle and commutation overlapThe effects

38、of converter input voltage distortion or unbalance and harmonic contents in the output dc current can be modeled as wellcbaVGVdcdc, ,a,b,ciGidcac , ,The nonlinear relationship between converter input currents and its terminal voltages isI & V are harmonic vectorsIf the harmonic contents are smal

39、l, one may linearize the dynamic relations about the base operating point and obtain: I = YJV + INYJ is the Norton admittance matrix representing the linearization. It also represents an approximation of the converter response to variations in its terminal voltage harmonics or unbalance IN = Ib - YJ

40、Vb (Norton equivalent)(VIfUnder normal operation, the overall state of the converter is specified by the angles of the state transitionThese angles are the switching instants corresponding to the 6 firing angles and the 6 ends of commutation angles The converter response to an applied terminal volta

41、ge is characterized via convolutions in the harmonic domainThe overall dc voltageVk,p: 12 voltage samplesp: square pulse sampling functionsH: the highest harmonic order under considerationThe converter input currents are obtained in the same manner using the same sampling functions. HhHnnphpkpppkdVV

42、V121,121,IntroductionNonlinear magnetic core sourcesArc furnace3-phase line commuted convertersStatic var compensatorCycloconverterHarmonic currents are generated for any conduction intervals within the two firing anglesWith the ideal supply voltage, the generated rms harmonic currents h = 3, 5, 7,

43、, is the conduction angle, and LR is the inductance of the reactor ) 1(sin)cos()sin(cos4)(21hhhhhLVIRhThree single-phase TCRs are usually in delta connection, the triplen currents circulate within the delta circuit and do not enter the power system that supplies the TCRs.When the single-phase TCR is

44、 supplied by a non-sinusoidal input voltagethe current through the compensator is proved to be the discontinuous current tttthhLhVtihhh and 0 , 0 ),cos()cos()(1hhhsthVtv)sin()(Harmonic models for TCR can be categorized asfrequency-domain based modelscurrent source modeltransfer function modelNorton-equivalent circuit modeltime-domain based modelsmodels by differential equations state-space modelhhhhthIti)sin()(tttthhLhVtihhh and 0 , 0 ),cos()cos()(1by discrete Fourier analysisNorton